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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: .... Homepage.. 196 AND OTHER LYCHREL NUMBERS.. My Blackboard.. Current News.. Archive 2006.. Archive 2005.. Archive 2004.. Archive 2003.. Archive 2002.. Archive 2001.. Other Lychrels.. Lychrel Records.. Identified Seeds.. Finding New Lychrels.. Software.. Standalone Software.. Networked Software.. Screenshots.. Trivia.. The Ratio.. Alphabetic Palindromes.. Trivial Insights.. Get It In Perspective.. Where Were You.. ETC.. Files to Download.. Quest History.. Mistakes and False Starts.. Credit to Others.. My Wish List.. Links.. Contact.. Random Quote.. Site Links.. FAQ.. Terms and Definitions.. Milestones.. File Verification.. Data Set Information.. Math Solutions.. Other People's Notes.. Please Help.. Welcome to.. p196.. org!.. This site is about a set of numbers that do not form a palindrome through the process of reversing and adding their digits.. These numbers have become known as "Lychrel Numbers".. For example.. , let's begin with the number 7,326.. If we reverse its digits and add it to the original number, we get 13,563.. Like so:.. 7326 + 6237 = 13563.. Since this new number is not a palindrome, we can continue the reverse and add process and it may become one:.. 13563 + 36531 = 50094.. 50094 + 49005 = 99099 ---- A Palindrome.. Most of the time only a few iterations (less than 10) are needed before the number becomes a palindrome.. In the case of Lychrel Numbers, it is believed that they will never become palindromes, no matter how many iterations are performed on the number.. This page started as my experience with the first of those magical numbers.. But has since grown to include enough information, about other numbers, that I couldn't really call it "Nothing but 196" any longer.. I  ...   good page to read.. gives a history of major milestones in the 196 quest.. Some of the lower Lychrel numbers have been tested out hundreds of millions of digits without becoming palindromes.. Obviously, a standard calculator isn't of any value.. The programs listed on the.. Software Comparisons.. page represent hundreds of hours of work by the authors and were all written specifically for this quest.. none of it is "off the shelf" software.. :-) These.. would all be easily classified as world records by groups such as Guiness Book, if we were interested enough to submit them.. Mostly we only do this for fun.. Although there is a lot of information on these pages that deal with mathematical ideas and thoughts, this is not a math site.. The vast majority of these pages are written so that with minimal thought, the concepts and ideas should be clear to everyone.. Some of the papers listed on the.. page are a bit more challenging.. But even those should be understandable if you give them a bit of thought.. I hope everyone finds something enjoyable in this site.. A lot of people have spent.. a lot.. of time contributing to it.. We are proud of what we have created.. Thanks for visiting!.. Wade.. By The Way.. If you like peppers, I'd like you to try.. Regal Peppers.. I'm actively involved with them.. As hot as it gets, if you want it that hot.. If not, we have something milder.. It rocks!.. org en Español.. org in Italiano.. org in Deutsch.. org em Português.. org हिठदॠमॠà¤.. org en Françaisa.. 2010.. All Rights Reserved..

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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: Iterations Completed.. Digit Count.. 1,000,000,000.. 413,930,770.. 12/27/11.. I have been seriously remiss in delaying the announcment of 1 billion iterations of the 196 problem.. Romain Dolbeau sent me the following file header:.. the "Sun Oct 2 16:20:43 UTC 2011 : 413930770 ; 1000000000 -> 3932472453326071578739224".. !!.. A billion iterations!!! It's been a long time on this road, and when I started out all this craziness so long ago, none of us even imagined we'd ever get so far.. WOW.. Congratulations to Romain!!.. I have almost completely thrown in the towel on the project.. Romain has made such huge advances in the ability to calculate the iterations, that I was never going to be able to keep anything productive going on while I was always just chasing him at a tiny fraction of the speed.. So I have wandered off the topic, and even with huge news such as this, I just couldn't ever seem to "find the time" to update the site.. (Which really just means I have finally run out of interest in the project.. ) It took a number of things happening right here around December where I had to make some updates and get some additional news out.. Romain has rolled out a page here:.. http://www.. caps-entreprise.. com/private/dolbeau/p196/p196.. html.. to access the source for his app and any notes he may feel like adding.. With any luck, it'll stay up a while.. I'll try to mirror it locally, but you know how that goes over the years.. Matt Stenson has been as busy as ever running that old Lychrel Seeds search.. Matt has dedicated a lot of years to the search to determine how many Lychrel seeds there are and now, he has answered the question for all 18 digit numbers as well.. Have a look at the.. Lychrel Seeds.. page to marvel in Matt's glory and let him know what an amazing effort he has completed.. Like me, Matt has kind of decided that he's not going to carry the search out for Lychrel seeds any further than he has.. And who can blame him? He's spent at least 6 years letting that program run.. Even compared to John Walker's original.. "Three Years of Comupting".. , Matt has gone above and beyond.. Thanks for all you've done Matt! Hope you've enjoyed it as much as I have!.. I would like to introduce Jake Harry.. Jake forgot to tell me where he's from, but he has devised a new method of generating a palindrome from a number, that is similar to the reverse and add process, yet is a different process.. I have copied Jake's instructions to a new page.. that can be located here.. It is an interesting new look at a problem some of us have probably grown stale with.. He is using it as a method to generate palindromes that even solves 196 and the other Lychrel Seeds.. It's good to see some fresh eyes looking at the problem and coming up with new ideas.. Thanks for the comments Jake and the interesting paper!.. Back in October, Matthew Cowen-Green in the United States sent me a Java application that tests for convergence between two lychrel threads.. Matthew took it upon himself to write the app after reading it on my.. Wish List.. It took me forever to get around to playing with it, but I finally did and it seems to work quite well.. I have put a copy.. HERE.. , if you want to play around with it.. 9/25/11.. I'd like to introduce Romain Dolbeau of France.. Romain has created another amazing parallel processing app and is lucky enough to have access to an incredibly fast network of machines.. Let me put that in perspective when I say and incredible network of machines.. As mentioned below, I have been re-running the data sets for verification.. Back in Oct 2010, I started at the 210 mark and this week, I got over 280.. So 70 million digits in about a year.. Romain started for the first time, from 0 in August of 2011 and by utilizing only free time on the system, has completed everything up to 375 millions digits!! Where I am taking a little over 4 days to do a dataset right now, Romain's system is doing it in a little.. UNDER.. 2 hours! He sent me verification data for various points as he continued beyond 234, which is what is posted here online, and 300  ...   completed the verification of all data sets up to 240 million digits.. 1/13/11.. It is difficult to rebuild the site in a foreign language in which I'm reasonably comfortable like Spanish.. Simply verifying the links and trying to maintain the formatting is a huge task.. But then I started and completed German, and that was a little more difficult.. The difference being, that I don't recognize even 1/2 of one percent of the words.. Nor can I relate to the syntax of the sentances, so I have very little idea if I am breaking the sentances correctly.. Now, I've discovered just how blind you can be and what it must feel like to be completely illiterate at all, by trying to translate the site into.. Hindi.. ! Now, I can't even recognize the letters of the page, and have to rely 100% on Google to do an accurate translation and not mess up my meaning.. It is probably a completely lost cause, but if it gets even one more student to see the site, and appreciate the beauty of the problem, than it is worth it.. And if you are reading this in any of the languages that I have tried to translate to, and you want to take on the task of truely localizing the pages for your language, I would be happy for your help.. (And credit you on the pages of course!).. 1/12/11.. Continuing what I started a couple days ago, I have completed translating the site into.. German.. as well.. If you're reading the site in one of the languages other than English, and you notice something that is just completely messed up, please let me know and I'll do my best to fix it.. Thanks.. 01/09/11.. For no reason other than I thought it would be fun to do, I've been translating the site into languages other than English.. Well, actually Google Translate has been doing all of the heavy work, but the program murders HTML code, so it's been time consuming to get all the links, paragraphs, and other tags corrected to the new pages and get everything looking right again.. Google does a reasonable job I think of getting the vast majority of the translation correct.. If you are reading this in a language other than English, and it just doesn't make any sense, then I apologize.. But I think the software does a good enough job, that most of the important points should come across.. I started with.. Spanish.. and.. Italian.. and I hope to get around to other languages as I can.. In addition, I have continued verifiying the milestone files as described below.. I am currently working on the 240 data set.. It's a slow process, just like it was the first time around.. 11/06/10.. If you've been to the site before, you'll recognize a major transformation since the last time you were here.. For days I have been altering the layout and look of the site.. Trying new things and just generally playing around.. I'll continue to repair broken links, and make edits that needed to be made years ago.. I find myself with a renewed interest in the topic, and the site in general.. We'll see if it goes anywhere new.. If you find a broken link, if you want to let me know about it, it'll help me get it corrected.. If you don't want to take the time to let me know about it, I understand, and will get to it eventually as I find it.. 10/25/10.. I have made a number of updates to the site in general to correct links that have broken over the years of inactivity.. I have been running Pierre Andre Laurent's application on a new machine recently, and may continue to do so, to increase the quest to new levels.. At the moment, I am backing up a bit, and verifying some of the files that I had previously.. I never reran anything beyond 210 million, so I started there again a few weeks ago, and have been checking the milestones against the verification page, and my files.. I figure since finishing this group, will mean I have run the entire quest twice over the years, but with different machines and different applications than the first go around, the files have a far greater reliability.. I'll probably keep you posted.. If you're looking for older news, try the archives from the "MY BLACKBOARD" pulldown menu..

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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: NEWS ARCHIVE FROM 2006.. 11/06/06.. I've redone the 300 dataset, and updated the info above just for posterity.. 11/2/06.. WOW!! Where have I been?!?!? Lost in other worlds and busy.. I'm not even going to say that I'm back in any normal sense of the word, but I have finally gotten around to updating the.. page to the point that I stopped at back on May 1, 2006.. When I reached 300 million digits, I was just getting ready to move to North Florida.. So I turned the machine off, to pack it up.. Then I moved, and it just never seemed to get put back together.. The summer is always busy with activities, and this one was no exception.. Then it's kids back in school and whatever, and now, well.. I still don't have the time to work this site, but I did want to at least put out a message that it's on long-term hold.. So if you're new to the site, I still thank you for coming by, and hope that your not disappointed that I have stopped the quest.. If you're one of my old friends, I apologize to you all for being absent for so long.. I do have the site on a new server, and a new email address on the.. Contact Me.. page.. With any luck, these changes will last quite a while.. I do currently have Vaughn's app re-running the 299 dataset, since I seem to have deleted the 300.. Bummer! At a minimum, I want to be able to fill in the table above accurately for iterations and calculations.. MAYBE.. I'll let it keep running, maybe not.. Regardless, I've enjoyed this quest immensely, and all the friends I've made and people I've met.. I just became mildly bored with it, and when that collided with all the other events.. Well.. You understand.. THANKS TO ALL OF YOU FOR YOUR SUPPORT!!!!!!!!!!!!!!!!!!!!!!.. 2/3/06.. For better or worse, I have made changes to the way my "Table of Contents" is displayed.. I never liked the fact that if someone linked to a subpage, or if a subpage showed up in a search engine, when the user clicked on the link, it brought them over here, and kicked them all the way to the intro page.. I figured if they wanted to see something on the.. page, they should get the Milestones page! At the time, that I made the switch to using Javascript to display the T.. O.. C.. , it was because I was frequently adding entire sections to the site, and had to keep updating ALL the pages when I added a new section.. Well, I've only added a single new section in quite a while, so I've gone back to a set of hard links on each page.. I'm sure someone knows a better way, than what I've done, and I'm willing to listen to suggestions if there are any.. (I know Jason had an idea a number of years ago for me, but I never implemented it at the time, and now I can't find the email.. :-( I should have listened better then.. ).. If anyone really HATES it, let me know, and I may change it back.. 1/27/06.. Changes and updates all over the place.. Most of them minor.. Matt and Pierre have both sent me their latest results and I have updated the.. page and the appropriate subpages.. I've made some minor corrections and updates to the.. I've broken out a separate page for testing of "Network Capable" 196 apps.. Right now, it is available.. here.. , and can be clicked on from the.. I'm not sure I like it linked that way, but it is what it is for now.. I've updated the.. page itself with the latest times from Pierre and Vaughn.. Vaughn has moved smoothly into number 1 slot on that page.. I haven't asked him if it's stable enough yet to be used as working app, so right now, I'm staying with what I've been using, even at the risk of losing some time.. Of course, with Pierre's app hanging out there in space, losing a few hours or days just doesn't seem relevant any longer!! :-).. I was happy to add Afghanistan and Monaco to the.. page, for a new total of 114 visiting countries.. 1/26/06.. I have crossed 100 Quadrillion digit pairs added!!!.. Pierre has released v1.. 01 to me, and I have been testing it in various configurations.. It is indeed faster still.. Turns out that in this case, the more CPU's I add to the mix, the better the results.. (Not that I had any doubt about that, but it is nice to verify that the load is being spread across other CPU's and not getting bogged down with network traffic!!) I have been mixing and matching P4's and P3's and wireless and Cat5, trying to come up with the best overall configuration.. My notes are scattered and random, but I will try to get some data up this weekend.. One thing that came across in e-mail this week among the group, is that Pierre managed to process the Lychrel 10577 out to.. 73 million digits in only 2 1/2 DAYS.. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.. WOW!!! We have no word yet on how many processors were involved, or  ...   of 300 and we have agreed on a limit of 315 for the 19 digit set.. Both Jason and Vaughn have since moved on to the 19 digit numbers.. The difference is that Jason expects around 5.. 5 years to complete the set, and Vaughn's new distributed app is expected to finish in only around 9 1/2 months!.. Then, on November 30th, Jason announced he had discovered a new record for longest delayed 119 digit palindrome at 261 iterations.. If I have the dates and info correct, Vaughn actually found a 259 iteration record before Jason found this one, but they were independently running over the dataset in a different method, so Vaughn found one and jason found a different one within a short period of time.. Check out Jason's.. World Records.. web page for details.. On December 7th, 2005, I got a note from Kevin Bowman of the United States.. He wrote about about his thoughts and adventures here:.. Scherzi.. I'm really happy he wrote, since it introduced me to the following piece of electronic test equipment:.. The Palindrometer.. !! I've just got to get one!! Just in case that the linked original dies in the future, I have shamelessly copied the photo to my own site, and you can get it.. My thanks to Kevin for the article.. Jason made a very persuasive argument about crediting the people that worked on the 196 problem BEFORE John Walker's 1 million digits.. As a result, I've added some information on their accomplishments to the.. Credited People.. pages.. Right now, all of that information comes directly from Jason's page, with his permission.. If I find more references, I'll add them as well.. My thanks to Jason!!.. And I think finally for today.. I would like to introduce Pierre-Andre Laurent.. Pierre has written the first app that I have ever seen that will run the 196 quest across a network!! The one item that has been longest on my.. has finally been offered to me.. Pierre and I have been talking most of the month of December, and I have been testing one version or another all month long.. Some of them ran across the network but didn't output a file I could verify.. Others output a file, but wouldn't run across my network.. Still others did both, but wouldn't load my ISF files for deep testing.. Earlier today, Pierre sent me a version that does all three!! This was the minimum functionality that I would accept for an announcement.. How does it stack up??? I should wait a month to report my results, so that everyone can fume with anticipation, but I can't do that to you guys.. But I first need to say that Pierre has an entire list of "to do" items before he's satisfied with it enough for "real world use".. The app I have is very much a work in progress.. Soooo????? How does it perform right now?? In a word: Amazing.. Consider the improvements to any of the apps over the last couple years have only been measured in a few seconds in deep testing.. The fastest I have been able to get this app to perform is a full.. 3 minutes and 49 seconds.. faster in the deep test than Eric Goldstein's app!!! So you'll know I didn't mistype it, I'll repeat it: 3:49 faster than Eric's app.. As a stand alone app, Pierre has managed to get a time of 1:09 Shallow and 15:25 Deep (Compared to the record 1:00 and 13:55.. ) However, the more occurrences of the app I add to the system, the faster it seems to go.. Taking advantage of the P4's Hyper-threading ability, I can get a host and two clients running on one machine and 2 additional clients running on a second machine talking to each other through my 100 mbs router.. This gives me a total deep time of 10:27.. When I add my 2.. 53 GHz laptop, and run 2 clients on it as well, the time for the deep test drops to 10:06.. At this point, I'm out of fast, easy machines to hook up.. I've got others around the house, but for tonight, I'm just not going to go through the headache.. (But I'm sure I will tomorrow.. :-) ).. Pierre has offered me ownership of the app and I asked him to release it in the same manner Ben and others have with their apps under a GPL license.. I'm sure he will when he's complete with it, and I'm hoping he'll send a copy to Ben Despres for inclusion on.. Ben's Site.. That way, everyone can poke around in the guts of the thing, and maybe make even more improvements.. I've put a sort of screen shot for the monitoring program.. Here.. It is showing the 6 clients running during the best test of the night.. (Don't forget, that a 7th copy is running as the host.. This really is the biggest news in my end of the quest in quite a number of years.. I really hope everyone agrees with me that Pierre has done an amazing job, and deserves a huge congratulations!!.. And for the record, I'm still using Eric Goldstein's app, right now, until there is a bit more polish on this new distributed app..

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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: NEWS ARCHIVE FROM 2005.. 11/23/05.. There really is no need to explain my long dormancy on this site.. I'm lazy, I've been busy, Florida springs and summers are meant for being outdoors, but really, I think it mostly boils down to the fact that nothing really new has happened.. There have of course been events going on, but as far as radical new ideas or programs, it's all just been maintaining an even keel.. Some of the notable events since April.. Back on 11/6/05, Eric Goldstein passed 200 million digits for the Lychrel number 879!! Great job Eric!!! His status has been updated on the.. Felipe Barone has been forced to close the 196 forum.. He has been recently plagued by hack attempts and member requests from spammers.. Anyway, it never really took off like we expected it to, and he just doesn't have the time for the maintenance on it.. Thanks for all your efforts Felipe!.. Jason Doucette has finished his longest delayed quest search of all 18 digit numbers.. As soon as I get permission from Jason, you will be able to see the results on his own.. web page, or here on the.. The reason for the delay is that Vaughn Suite also has calculated the same data and since Jason has not published his, and I have not shared it with Vaughn, they are in essence verifying the accuracy of Vaughn's app through a blind test.. The paper by Chris Pazsint, that I mentioned in the last update has been posted on the.. Chris really did a great job with this, and I thank him for his effort!.. On 11/19/05, Pierre-André LAURENT from "France, working in Ireland" wrote to let me know that my.. is wrong where I answer the question:.. Does this have any use?.. with the response:.. Absolutely none.. If you have a use, let us know.. Otherwise, it doesn't really have any application.. He makes his argument that it has validity with the 2 emails that I have condensed and put.. Thanks Pierre! It's nice to think that someday, someone will look at our work and put it to a practical application.. Ironically, the NEXT DAY (!!) I got an email from Jim Branson of the United States also discussing the reason for continuing our research into palindromes, 196 and Lychrel numbers in general.. There was some information in the email that I didn't fully understand, and I have written him to ask for clarification, but he closed his note with a paragraph that I really enjoyed for some reason.. maybe you will enjoy it as well:.. One knows that dividing any number by seven, imparts a repeating nature to the result.. I think we need to think about a lot of data as patterns and not only as quantities.. If this seems to smack of "intelligent design" then one should consider the basic nature of "observation" that separates quantum mechanics from Einstein's world.. It seems to me that we ourselves curve the very nature of the material world by what we think centuries from now.. Is that God? I don't really think so.. Invoking the nature of God seems to end intelligent thought and folks walk away from serious analysis.. And finally, Me??? What I have accomplished in the last 7 months?? Not much.. But my computer is still plugging away, and all of the.. entries have been updated.. And just for goofy fun.. Even though I haven't added any new.. visiting countries.. in the last few months, the Real Tracker reports that I've had 40,890 unique visitors to the site since I started the monitoring on August 4, 2002.. Kinda cool.. 4/28/05.. Chris Pazsint dropped me the following bit of information concerning the new class of palindromes:.. I did come up with a name for numbers like 111, 131, 171, 191 etc I called them "Prime Palindromes".. They are not hard to find it has to do with the odd number of digits and the center digit being odd.. I have not quite worked out the finer details on the subject.. I think XYX where Y is odd will turn out to not be the result of an add reverse.. Simple reason behind it is odd+odd = even and even + even = even.. The center number in an odd digit length number will always be added to itself.. Makes perfectly good sense to me.. Dan (no last name) wrote to vote for the name "Pazsint Palindromes" since they were discovered as a result of Chris' work.. I'm O.. K.. with that.. So far, those are the only two contributions I've had.. Send me more!.. Pazsint Palindromes is an interesting sounding phrase, but it's a mouthful to say, isn't it?!?! :-).. I know.. I'm probably making a mountain out of a molehill.. But I really like the idea of naming this group of numbers, so one way or another, I'm going to.. I get final say on this site, right? :-) :-) :-).. Syria has been added to the.. list.. 4/25/05.. I've made a new discovery in.. MY.. world of knowledge!! Now, one of you can tell me that you've already thought of it, done it, or proven it or disprove me in this particular case.. Chris Pazsint of the United States wrote me a short while ago, and asked if I had ever figured out which thread the number 17509097067 comes from as mentioned on my.. He said he was going to take on the challenge of figuring out how to "Un Reverse and Add" a number.. I told him I had not worked on it, and as far as I knew, neither had any one else.. Earlier today, I got a really elegant paper describing the process to "Un Reverse and Add" a number from Chris.. It seemed a bit confusing to me at first, but I have spent almost the entire evening sitting here on my couch and working problems over and over again on my laptop, using his process.. And even I have figured it out, and have managed to find what the possible Kin Numbers are for the thread that leads to the given number.. It really is remarkable to me in it's simplicity of operation.. I've asked Chris for permission to post it, so when I hear back from him, I'll get it here somewhere.. I'm sure some of you might find it a no brainer and nothing to get excited about, but it opened up a new area for me to play around with and occupy an otherwise unproductive Monday evening.. ANYWAY.. While trying to make sure I understood the process, I was trying solve numbers that I knew what the answers SHOULD be so I knew if I had it right or not.. For example, I solved the Kins leading up to 7,436 which is the third iteration of 196 and I solved the Kins leading to 52,515 which is the 5th iteration of 196.. Stuff like that.. Then at random, I tried the palindrome 123767321.. After trying and trying and worrying that I had a mistake somewhere, it occurred to me that the palindrome 123767321 CANNOT be created through the Reverse and Add process!!.. As far as I can remember, this is the first time that I have ever considered whether all palindromes can be made through the RaA process.. We have spent so many countless hours thinking about trying to get non palindromes to become palindromes, that I don't think it ever occurred to me to wonder if a palindrome HAD to come from the RaA process.. This was a "breakthrough" in some part of my mind.. Naturally, the next thought I had down this path was "What is the smallest palindrome that can't be made through the Reverse and Add process?".. So some quick mental work, a double check with Chris' algorithm and I can't solve 111 from anything.. (This is where you can disprove me!!).. But that in turn brought up another thought.. One that we could actually waste EVEN MORE computer cycles on.. How many palindromes are there that don't come from other numbers in the RaA process?? And which ones are they?? There are 10 that solve, before the first one comes up, (11, 22, 33, 44, 55, 66, 77, 88, 99, 101) and I found one at random, so I would expect there to be quite a few.. I mean 131 is just two steps away.. But maybe not and I just got lucky with the 123767321 number.. I am really excited that we have identified an entirely new  ...   in size.. If I use WinZip v8 on the file, I get a new size of 110,817 KB.. Very nice.. However, if I use Eric's app instead of WinZip, the file shrinks to only 70,113 KB!! Remarkable.. In complete fairness, I'm not sure if the method was Eric's alone, or if it was based on input from Matt, Ben and Vaughn.. I know all of them have been talking, I just don't remember how it actually came about.. I applaud them all, and apologize if I have the credit wrong!!.. Matt also wrote a small app that strips header information from all my files, and will save me hours and hours of time, when I do my site updates.. Thanks Matt!!.. Other than that.. I've been watching the email quietly, and keeping in the background while these master artists paint there worlds.. I can't wait to see what they come up with next!!.. 1/27/05.. I have modified the.. page quite heavily.. Breaking it up into smaller more easily managed sections.. I think it's nicer.. One modification I have made is that I have decided to not list the "Date Reported" for each of the verification sub-pages.. It proved to be cumbersome for me, to get straight, and I didn't see where it added that much value.. Instead, I changed the column to be the credited person with that milestone.. I'm sure no one will mind the change, but if for some reason, you feel I should add that column back into place, let me know, and I'll consider it.. The "Date Result Reported" is still listed on the overall "Leaderboard" as the most recent data that I know of.. 1/23/05.. You can see I've archived everything prior to 1/1/05, so if there is something old that you're looking for, head over to the.. Vaughn has started running some of the other lychrel numbers on various machines he has access to.. He says in his email to me:.. I would like to announce that I have started processing 9999, 99999, 999999, 9999999, 99999999, and have taken all to 2 million digits or above as following.. Please note that all seem to follow different paths since the first 2 million digit number of each is different.. I intend to take them all to 20 million digits in the first instance, and thereafter one by one to 100 million digits.. I intend to use a 2.. 66GHz machine with a 533MHz memory bus, so it will be severely memory bound.. I have added his information to the.. Lychrel Records.. Vaughn also provided the verification data for each file, similar to what I have done for 196 on the.. File Verification.. I thought it was a great idea, so I have asked Matt and Eric to send me the data for their files as well.. I asked them to only send me the data for every 25 million digits.. So for now, I have broken the Lychrel Records page into two sections.. Identified Lychrel Seeds.. page shows how many digit sets have been searched and the number of known lychrel numbers found so far.. page has changed to only show the non 196 seed numbers that are being tested using a similar "brute force" method to what I'm doing.. Wandering the web earlier today, I stumbled across a 196 implementation that I found quite funny.. Apparently, there is a programming language with the really funny name of BRAINFUCK that can be read about in the following.. Wikipedia entry.. Well, Mats Linander took the time to write a 196 program in this oddly titled language! With all the commenting removed, it looks like this:.. ].. ++++++++++[->++++++++++>+++++++++++>+++.. >+.. >.. ++++++.. --.. >++.. -.. +++++.. ++[--.. >.. [-].. +>>->.. ,----------[-->++++++[-.. +>+.. +>>>>>,----------].. >>>>>>>[.. >[>>>>>].. >>]>>[>>>>>].. >>+>>[>>>>>].. >[-.. >>>>[-]>>>>>].. >>>>>>[.. >>>>>].. [->+>+.. +>-.. [-.. ]>>[-.. >].. >>>>>[>>>>>].. [.. >>>>>>>>[.. >>>>>>>]++++++++[-.. >>].. >+++.. >+++++[-.. ++++++++[-.. >>>>>>[>>>>>]+[.. >>>>[.. >-.. +.. ]>[>>-.. [>>+.. >>-.. >]>[->[-].. >>+>[-.. >>>>>>].. >>>>[>>>>>].. [>[->+>+>+.. >]++++++++[->++++++.. >[->+>+>+.. +++++++++.. ---------.. ++++++++++[->++++++++>+++++++++++>++++++.. ++++.. >--.. ---.. +++++.. >--.. >>+[>>>++++++++.. >>]++++++++++.. I.. THINK.. I only removed the comments.. I may have deleted some data as well, so if your interested in reading Mats' original writeup, you can see it at.. http://esoteric.. sange.. fi/brainfuck/bf-source/prog/196-commented.. b.. And if the link stops working for whatever reason, there is a local copy.. I just found it interesting, so I made note of here.. Maybe Ben will add a copy of it to his site! :-O.. 1/18/05.. My apologies to Vaughn!! Yesterday, I said:.. He's very busy lately with the first birthday for his son coming this month, but.. Well, he wrote and let me know that his.. DAUGHTER.. will be happy to celebrate her birthday on 1/25/05.. I goofed.. I hope she's not reading this!! :-).. Matt sent updates for his searches with 1997 and 10877.. He's passed the 106 and 42 million digit mark respectively.. It was nice, because I haven't had an update for 10877 since 9/16/03!! Of course, it's now all updated on the.. 1/17/05.. Man, It's been a while since I updated this site, and many of you have written to let me know!! Sorry.. We all know how it is.. You get doing something else, and the newer task becomes more interesting than the one that you have been doing for a while.. Maintaining this site, and "studying" this problem is something I've done for quite a while now, and it just gets "boring" sometimes, when compared to other things I could be doing.. As a result, this site suffers.. Not that it matters to anyone, but just to give you an idea of what has been absorbing my time: I took a trip to England for the entire Christmas - New Years holiday period.. That was a great time.. I learned to SCUBA dive back in October, with my girlfriend and we've been trying to do that as much as possible.. (Even going so far as to dive the English Channel on 12/27/04!! It was MUCH, MUCH colder than the Florida water that we've been used to!!! :-) ) I modified my milling machine to operate as a CNC machine.. And that project alone has kept me in the workshop almost every evening for the last 2 months.. I made my first drawings with the machine only recently on 1/14/05, by using a pencil instead of an end mill in the cutter.. So it's working, and now it's a matter of cleaning up all my parts and circuits.. It turned out to be a MUCH bigger task than I had originally planned!! Anyway.. That's what I've been doing.. The downside, is that now, it's taken me most of an afternoon to update this site!!.. NOW.. The simple stuff: Cuba, Ecuador, Kuwait, Sri Lanka, Venezuela and Yemen have all been added to the visiting countries list, bringing the total to 106 countries.. Eric passed 160 million digits for 879, way back on 11/25.. I would speculate that he has passed 170 by now, but I haven't confirmed it with him.. On December 15, Jason Doucette completed the longest delayed palindrome search for all 17 digit numbers.. The output information from his program is over on the.. Congratulations to Jason for pushing that quest to the limits he has!! His page is.. Here.. Eric sent me a new version of his app back on 11/6/04, but due to my goofing around, I just got to testing it today.. It's interesting.. On Eric's machine, the last three updates he's done (v253, v254 and v255) have all shown speed increases for him, but when I run them on my machine, they are all slower than v252.. 1 that I have been using since Oct of 03.. They are faster compared to each other (ie v255 is faster than v254 which is faster than v253), but the v255 is still not as fast as v252.. 1 on my machine.. There must be an explanation for it, but one of you programmer type people will have to figure it out.. It's beyond me.. Vaughn Suite has been busy as well.. On 12/30/04, he sent me his latest jump into the pool.. His latest app did indeed run faster for me than the last one he sent.. He has cut 1 minute and 18 seconds from his previous best deep test time!! The new results are posted on the.. Great job to Vaughn!!! He's very busy lately with the first birthday for his son coming this month, but I expect he'll keep squeezing every last cycle out of my CPU.. And finally, I wish everyone a safe and happy 2005!!!..

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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: NEWS ARCHIVE FROM 2004.. 10/7/04.. Couple new things since the last update.. Florida has been pounded by 2 hurricanes since the 9/9 post.. Ivan missed me completely, and did it's damage to the extreme northwest of Florida.. Jeanne however, followed an almost identical path to the Frances storm early last month.. The houses, and businesses that were damaged by Frances that had not been repaired, were finished off by Jeanne.. Again, I lost power for a week, but no damage or injuries.. Whenever I would get upset about the heat, I would stop and think of the people who had lost everything.. It's a big, fat mess of rubble all over south-central Florida.. I hope they recover as quickly as possible.. Other stuff:.. You'll notice that my girlfriend has a new license plate for her car.. :-) Crazy huh?!?.. Eric has passed 150 million digits for 879 and Matt has passed 70 million digits for 1,997.. They are updated on the.. My run time spreadsheet has been updated again, so if you feel the need to see all the milestones, you can look at it.. I've uploaded a new copy of the log file output by Eric's app.. If you need to see it, it is.. Guatemala, Nigeria are the two newest countries to visit the site, bringing the total to 99 countries! The.. list shows them all.. I would like to say a big HUGE hello to all of Ms.. Bursey's students in Roanoke Virginia!! Ms.. Bursey wrote me the following wonderful email which I received today:.. Hi Wade,.. I teach 8 to 10 year olds at a small private school in Roanoke, Virginia.. Our children loop, so I have many of the same children for math this year that were in my class last year.. I love teaching them about palindromes and every now and then I get a group that particularly loves working with them.. Today they asked me to check your site to see what progress you have made.. It is difficult for children this age to comprehend just how much a million is, so although they don't completely understand the magnitude of your work, they are in awe of what you are doing.. I just wanted you to know that you are inspiring young boys and girls.. Who knows maybe one of them will eventually carry on the quest.. Betsy Bursey.. Roanoke, Virginia.. If the thought of young children being interested an math problems like this doesn't make you feel good about the school system, what would?!?!.. 9/12/04.. After 1,125 days of run time, on 9/11/04 at 10:26am, I logged the 500,000,000th iteration!!!!!!!!!!.. That milestone is an answer that is 206,967,875 digits long.. 9/9/04.. Well, all is safe here.. I lost power on 9/3 at 10 minutes to 11 in the morning, soon after the last update here.. I didn't get it back on until 9/8 at around 6:30pm.. As you can imagine, it was a LLLOOONNNGGG 5 1/2 days in the Florida summer with no power.. I ran a 3,000 watt inverter off the car's alternator off and on to try to keep some small fans running, but I could only do that when it wasn't raining, which wasn't very often.. The other trouble was that the input current from the alternator is so low, that even though the inverter was rated to 3kW, I could only get around 200 watts as an output.. This morning, I managed to get a generator from the store, so next time, I'll be in better shape.. (They sold 300 generators this morning in less than an hour.. I got one of the last 6!!).. Everyone is safe, and there was no damage to speak of to the house.. That was all I really cared about!!.. NOW, Hurricane Ivan is closing in on Florida, and I might get to do it all over again THIS WEEKEND!!! It'll make three hurricanes in less than 5 weeks.. Boy, I could do without THAT!!.. I'm at 499,201,457 iterations right now, so I'm hoping to cross 1/2 billion by the time the power goes out again! I'll update as I can.. 9/3/04.. I'm looking forward to possibly, later this week, passing 1/2 a BILLION iterations!!! I'm closing in rapidly on a.. MAJOR.. milestone!! The reason I say possibly, is that we here in Central Florida of the United States, we are going to have Hurricane Frances make landfall later this evening.. I'm not worried about life or property, but I'll miss the milestone for possibly a week, when the power goes out.. Three weeks ago today, Hurricane Charlie, hit the West coast of Florida, (landfall about 200 miles from where I am at.. ) and I lost power here, for about 46 hours.. Frances is supposed to hit land around 80 miles South of here.. So We'll get far more wind, since it won't get broken up by the land like it did last time.. They are predicting loss of power to some neighborhoods for up to two weeks!!.. My family and I should be safe.. We have a good plan for the storm in general, We have a backup plan if things get too bad, and we have a third backup plan, if things get catastrophic!! I'll even try to force myself to post an "all clear" when I get power back on.. welcome to Algeria, Bangladesh, Belarus, Belize, Benin, Bolivia, Kenya and Venezuela who are all new to the visitor's page since my last update.. Eric Goldstein has passed 145 million digits for 879, back on: 2004-08-05 at iteration: 350271548.. Congratulations to him!!.. 7/4/04.. Barbados and Morocco are new to the visitors list, bringing the total number of visiting countries to 89.. I need to thank Andreas Zetterlund from Sweden.. he was kind enough to point out that I made a mistake in my conversions of sq/kilometers to sq/miles.. He writes:.. One square mile does not equal 1.. 609 square kilometers, it's 2.. 59  ...   number of additions that that computer has actually made up to the current (or projected) milestone.. It was simple, and easy to measure, so I went with it.. Eric Goldstein says that his app has actually done less than that number, due to optimization.. (I don't remember exactly what he said, but I know he took the time to email me once, and point this out.. ) The end result, is that I know that the "Total Calculations" counter is not exactly accurate, but I also know that it's a fairly reasonable approximation of the amount of work it has taken the processor to get to this point.. Besides, how else could it be measured, considering the different number of applications use?? So my "continuous days" counter is working on the same principle.. Incidentally, I crossed the 40 quadrillionth calculation mark sometime during the 182 dataset!!.. And finally, the world's most populous nation has joined the ranks of visitors to p196.. org.. I welcome the 2 visitors from China!!.. 5/9/04.. I just happened to notice, that today is my 1,000th consecutive day of running the 196 problem.. I started 14,000,001 on 8/13/01.. 5/4/04.. Hmmm.. I guess it shows you how closely I've been paying attention, when I passed 30,000 visitors to the site, and didn't even notice it!! O well.. Back on 4/28, Matt sent me a note with the following:.. I just thought I'd let you know where Ben and I are up to with the Seed search.. We have successfully collected E15 and are presently post processing the results to remove Kin numbers.. E15 has proven larger than I would have imagined.. By the end of the data collection phase I had 67 fast P4 computers connected as clients.. 22 of them were running 24/7 and the rest were running 12 hours a day.. We ended up with over 42 000 results files and some 30 gig of data.. The post processing will take at least 4 months and maybe as long as 8 months depending on how much it speeds up with the ever reducing number of Kins.. WOW!!!.. Great job to Matt and Ben!!.. I wanted to see how all the files compared to each other for processing time.. The following chart is quite a bit misleading, since there are so many variables for each milestone.. In some cases, the hardware changed, in others, it was the app used to process the file, that made the big differences.. The spikes up, are where I was testing something, and it slowed down the processing.. Remember, that I stop all processing, to do the comparison tests when someone sends a new app.. In most cases, the spike up, is followed by a drop in time right afterwards.. These are interesting to see, and the rise that follows afterward, as the program slows again as the files get larger.. I could go back and note all the points when I changed apps, but that is beyond what I was doing here.. Regardless, it's still kind of a neat image.. 4/17/04.. Eric has passed 130,000,000 digits.. 3/17/04.. Egypt, Ethiopia, Macedonia, Pakistan, and Puerto Rico are all new countries on my visitor's page.. Eric has passed 125,000,000: 2004-03-17 17:02:55 Notification: iteration 301955457, digit 125000000.. 2/27/04.. 8:38am - There are 165,576,658 digits at iteration 400,000,000.. :-).. Closing in on 30,000 visitors to the p196.. org domain.. I have added 5 new countries to the Visitor's page.. They are Guadeloupe, Iran, Nepal, Niue, and Tonga.. I had never heard of Guadeloupe or Niue before.. A quick check of the.. CIA World Fact Book.. shows that Guadeloupe is a small island in the Caribbean Sea which has been a French territory since 1635, and has a land area of 1,706 sq/km (About 659 sq/miles) and a population of a bit more than 440,000 people.. Niue on the other hand, has a land area of only 260 sq/km (about 100 sq/miles) and a population of 2,145 people.. It is one of the Cook islands, and is in the South pacific, about 2,400 km (1,491 miles) Northeast of New Zealand.. Just think.. This site has been seen by about 1/3 of 1% of an entire country!!.. :-O.. 2/14/04.. Been a while since an update, but that's the way it has been for the last 1/2 a year.. :-( There just always seems to be something I need to do, other than update this site!! At least I keep an eye on things on the processing!!.. On January 22, 2004, Eric Goldstein passed the 115 million digit mark for 879.. 1/3/04.. I hope everyone had a WONDERFUL holiday period and a happy and safe New Year.. I wish everyone the best of luck health and fortune in the year 2004!!!.. I've crossed 350,000,000 iterations.. I've also crossed 150,000,000 digits.. Still going.. On December 29, 2003, Eric Goldstein has passed the 110 million digit mark for 879.. Everyone is welcome to come look at a message board set up by Felipe Barone, at.. barone.. pro.. br/196board/index.. php.. Felipe has had the board up for a few months or so now, and a few of us have been passing info back and forth on it.. As a group, we decided to open most of it up for public viewing.. There are some sections that are still "Members Only", and if I understand it correctly, non-members are not allowed to post messages to the board.. This was done strictly to keep the garbage off the board.. I get enough email asking for help with people's homework, that we don't want that type of info on the board.. Everyone is welcome to read, and if you have something to add, you can email me or one of the other members.. We will contact Felipe and ask him to give you full access to the board.. There are some great ideas there, including a horror story about me, a propane torch, and a poisonous.. Coral Snake..

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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: NEWS ARCHIVE FROM 2003.. 11/24/03.. Back on November 11, Eric Goldstein passed 100 million digits with the number 879!!!.. 11/6/03.. I have been slow with the updates for these pages.. But I've been slow with them in the past, and I'm sure there will be times in the future that I am slow with them.. It's just life.. Berend Jan van der Zwaag of the Netherlands has brought to my attention that the palindromes and the quantities listed on the.. Dataset Info.. page is probably wrong.. His testing showed different results than mine.. I went back, and my initial tests show that he is correct.. I seem to have made an error in my LabView app that was looking for those numbers.. I'm TRYING to find the problem and get it corrected.. I don't think there is anyone who is using those numbers for anything, but I bring it up, just in case.. Felipe Barone of Brazil has mentioned that there are references and ideas that we seem to have missed, located at.. cs.. arizona.. edu/icon/analyst/ia.. htm.. He cites articles 30 through 35, 37, 39, 40, 43, 45 through 51, and 57.. It appears that.. Icon.. is a programming language, and the articles are geared specifically toward this language, but they are still worth a quick read.. Even though they are aimed at applications written in Icon, it is well worth the time to read the articles, since they provide an array of ideas for math solutions and other thoughts about the questions on Lychrel numbers.. It's also nice to see that the digit distribution they show in paper 31, is similar to the pairings I talked about back around October 2002.. 10/19/03.. I have spent most of the day reading, and re-reading all of the pages that make up this site.. With the exception of the Blackboard Archive, I have gone through and made an attempt to modify and reword all of the other pages to match the terms defined on the new Definitions page.. I'm SURE I missed some.. If you notice something on another page that conflicts with what is there, trust the Definitions page first, and contact me to make the change.. THANKS!!.. Thanks to Jason for all of his "advanced features" web page help!!.. 10/18/03.. LOTS and lots of changes here.. Mostly the frame for navigating.. I THINK it is working correctly.. If you have any problems, please report them to me!!! I've tested with Opera and IE, and they seem to be O.. , but, I'm never confident till it's been worked over a while.. :-) If anyone is linking to any page other than www.. p196.. org, I'd ask you to change it.. That way, everyone comes in through the front door.. I've noticed that the site seems to be just fine in Opera if entered from the index.. html page, but if I just come in from a subpage, Opera hangs.. IE seems to work fine, but not Opera.. I guess it's JavaScript just ain't up to snuff.. Eric G.. has managed to cut 2:31 from his deep time!! He said;.. I coded a neat trick to handle carries even better.. ".. now I use only MMX!.. His new times put him back in front of Vaughn, and can be seen over on the Software Comparisons page.. Matt sent me a new app to test, but it lost time compared to his last one.. I'm waiting to hear from him.. I've added a "Files, Files, Files" page.. There probably isn't anything there that most people want, but I've got lots of odds and ends gathered in one spot.. Some of the bigger files aren't actually there, but if you want them, let me know, and I'll send them to you directly.. I expect this page to grow larger as I get things organized from this "move".. I've got a space holder set up for a "Definitions" page, but there are still a lot of them that need to get ironed out, so for right now, it is blank.. I'll get them up as I feel confident that there is no debate going on over a particular word.. 10/12/03.. Matt has moved ahead of Chris Lomont for his newest app.. He shaved over a minute off his shallow time, and almost 12 minutes off his deep test.. Great Job Matt!!.. Felipe Barone of Brazil has written an application testing the "Order of Magnitude" of palindromes, as I asked for on my.. He sent it to me this evening, and I currently have it running from 1 - 10 digits.. I'm not sure how long it will take to complete that many digits, but we'll find out.. I have it running to 125 iterations for each number that does not form a palindrome.. Jason Doucette's recommendation of 3 times the.. current world record.. seems more appropriate for what he's doing, but since he has shown that all numbers with 10 digits or less solve in 109 iterations or less, I figured 125 was a nice round number.. (Unless I'm misunderstanding Jason's page!!).. Anyway.. I got a couple of other interesting emails from Felipe today.. One of his quotes:.. that lead me to an observation that i think you missed in your trivial insights: There are infinitely many Twin Palindromes! Or in other words: there are infinitely many numbers P such that P and P + 2 are palindromes! Just like its conjectured that there are infinitely many twin primes! isn't this exciting!!!.. I observed that from the order analyzer results and as i stop to think ITS SOMEWHAT OBVIOUS: 99 and 101, 999 and 1001, and so on.. I don't have a proof for this conjecture, yet.. but its empirically true.. Some other examples might be 689, 691 and 1495, 1497.. Although 691 is obviously a kin number of 196, and the other three are Kin numbers of something else.. (It's late, I need to go to bed, and I can't think right now.. Figure it out for yourself.. :-) ) But it does some an interesting "pattern" as you scroll through the list of numbers.. I say again that I really like the fact that almost every time someone new comes to my pages and writes me, they make a statement or point out an observation that no one has ever pointed out before.. Is the above note useful in proving Lychrel numbers will not solve? Probably not.. But is it interesting in itself? My answer is yes!!.. Then, in a follow up email to me, he sends me this:.. Thought that was interesting? check this one:.. conjecture 2: there are infinitely many twin Lychrel numbers.. to name some:.. 2944 and 2946.. 3583 and 3585.. 61731 and 61733.. 79869 and 79871.. And also I observed some "freaks" along the way that are in the form L, L+1,L+2, L+3 all being Lychrels!!! for example: 99486, 99487, 99488, 99489.. and some in the form L, L+1, L3 and L, L+2, L+3.. Very cool!! Right off the bat, I was inclined to call these "Barone Lychrels".. Since he was the first to point them out.. Everyone that has written me has been more than generous with giving credit to anyone who makes a discovery, and I think everyone would have agreed with me here too.. This seems like a good discovery.. It has a definite formula and result.. Like (2^n)-1 is called a "Mersenne Prime".. However, when I mentioned this to Felipe, he asked me in no uncertain terms to abandon my idea of crediting him like this! In fact he said:.. PLEASE DON'T DO THIS TO ME!!!!!! LOL! Not at all, thanks a lot, but no.. O.. , I won't refer to them as Barone Lychrels, but I think he should get the credit as their discoverer.. I will agree with his definitions though:.. Lets use L to denote Lychrel numbers.. Twins:.. L and L+2 are both Lychrel, they are twins.. There are infinitely many twins.. Consecutives:.. L and L+1 are both Lychrel, they are consecutives.. There are infinitely many consecutives.. Sequence:.. L, L+1, L+2,.. , Ln are Lychrel, they form a sequence of nTh degree.. So 99486, 99487, 99488, 99489 would be a sequence of 4th degree.. I can't wait to get a better look at his data or to see what else Felipe comes up with!! My great thanks to Felipe!!.. 10/4/03.. 300,000,000 iterations complete!.. 10/2/03.. I'VE DONE IT!!!.. I've managed to make a functioning 196 app!!!!!.. I was waiting for some car repairs today, and with my laptop, I started poking around in LabView, with the specific goal of writing a functioning app.. 7 or 8 hours later, I have one running!! It's.. SLOW AS A DOG!!.. But I really had no intention of trying to get anything other than a functioning app.. I even know of a couple improvements that I could make, that.. might.. make it faster, but I have no intention of even trying to implement them.. At least, not as of right now.. I expect that it will be.. far.. slower than even John Walker's app, but again, that was not my goal.. (I expect it will be at least 3 hours for the shallow test!!).. I will get the time of the shallow test on my Comparisons page, when it finishes.. There are a lot of.. bolds.. , !!!!!'s, and CAPITALS in this entry, but it's only because I'm so excited at completing something I have tried so many times before, and failed at each time.. Update:.. It's far worse than I feared!! I have succeed in setting the record for the slowest 196 app ever written!! Yeah for me!! With a time of 4:16:52 I have only completed 1,725 Iterations, @ 716 digits!! Keep in mind, that I didn't purposely do anything to slow it down.. I didn't put 30 second delays in or anything.. :-) My arrays and digit handling must be miserably inefficient, but I am actually still happy about the whole thing.. 9/30/03.. Vaughn's application has moved even farther down the timer.. He is at 15:44 currently, and at the rate he is going, I expect he will shave at least another 15 seconds shaved off by the end of the week!!.. I am still currently using Eric Goldstein's app though.. I have said before that I am hesitant to use a command line app, and for right now, Vaughn has not had the time to get his core routine wrapped in a Windows cloak.. I'm sure it will come in time.. There were a.. LOT.. of notes passing back and forth between Eric Sellers, Eric Goldstein, Vaughn Suite, Matt Stenson and Ben Despres over the weekend.. They were all good enough to CC me on their answers.. Even though I don't have the slightest idea of the function of the following lines:.. pshufw mm0, memory, 27.. movq mm1, mm0.. psllw mm0, 8.. psrlw mm1, 8.. por mm0, mm1.. I was still nice to read all the traffic.. :-) They shared their thoughts on the core algorithms, and the best ways to get even more speed out of all the apps.. I thought long about posting the data on a new page, but on one hand, I don't know if all the authors would approve, since they didn't know they would be writing "for the public", and on another hand, it would have been a mess, since there were so many replies to replies, with more replies following those!! I would have spent the next DAY, just trying to format it all out!! If someone really wants to see any of the data, email me, and I'll ask the appropriate people if I can forward their messages.. There was also a bit of traffic, discussing the changing of the benchmarking tests, yet again.. Vaughn's point is that the shallow test, is mostly redundant, since memory speed becomes so important for the higher iterations.. He is of the opinion that the shallow test ought to be done, using only the number of digits that will fit into the CPU's cache.. That might give a clearer picture of the raw core algorithm's performance.. Then a deeper one, to test overall app response.. I admit, I was hesitant to test all of the apps over again, but I did.. There were indeed performance gains for the apps that suffer from older memory usage schemes.. For example, Istvan's app now has a time of 11:31 for the 603,567 iterations tested.. But it took over 9 minutes, to get the next 200,000 iterations!! Overall, I'm glad I followed Vaughn's advice.. Check out all the updates on the.. While your there, you might notice that Matt has improved his app by almost 300%!! Actually, the story from Matt is that.. Ben.. improved Matt's app by almost 300%.. He writes:.. Ben deserves all the credit for writing the new non-MMX flip and add assembler routine that I am currently using.. All I did was work with Ben to figure out how to interface with it from Fortran.. For this new test, his old time was 13:14.. He has now cut that down to 4:31.. Not as fast as Vaughn or Eric.. But I think he's running them down.. If so, it'll be the first time that there have ever been 3 people in the heat of the race.. I'm hoping he gets down there with them, even though it'll surly mean more frequent testing for me!! :-).. Eric Goldstein has passed 90 million, working with 879.. And finally for tonight.. I've added three more countries to the.. Bringing the total to 74, they are Jamaica, Kazakhstan, and Mauritius.. 9/29/03.. I've been in Virginia for a few days, to celebrate my son's birthday with him, and I have a TON of things in my inbox, that I have to sort out.. I'll get to it in the next day or so.. Back on the 21st, Matt Stenson was kind enough to compile John Walker's code for me.. I wanted it, simply for a comparison test.. 0 - 1,000,000 iterations gives a time of 1 hr, 51 min, 45 secs.. My thanks to Matt!!.. 9/25/03.. A new deep time of 16:06 puts Vaughn ahead of Eric for the moment on the Comparisons page.. With a couple "minor revisions" as Vaughn put it, he has shaved 10 seconds off his app, and is about 3 seconds ahead of Eric.. CONGRATULATIONS Vaughn!! This is the first time in.. a long time.. that Eric Goldstein has not held the top spot!!.. I have been getting regular improvements from Vaughn every couple days for the last few weeks.. I am going to be away till Sunday night, (9/28/03) for my son's birthday, but I can't wait to get back, to see new apps in my inbox!!.. 9/23/03.. Check out the.. Screen shots.. of all the apps from the.. 9/20/03.. A LOT of changes, to a lot of pages tonight.. I've made another configuration change to my computer.. I have added a second 512Mb module of DDR400 (PC3200) RAM to the machine, and gotten some major performance increases from all of the applications tested.. It seems that DDR memory is only really effective if you have.. PAIRS.. of identical DIMMs.. Since I have always used a single DIMM in the past, I never seemed to get the performance out of it.. I really suspect that this was the single largest cause of the differences in expected times from Eric's tests and mine.. Now my times are right in line with his expectations for the last revision.. I have also changed the CPU from a Pentium IV 2.. 8GHz with a 533MHz Front Side Bus, to a Pentium IV 2.. 8GHz with a 800MHz Front Side Bus.. That too gave some speed increases from all the apps.. (Of course, TODAY, I read about Intel's 64 but chips coming down the line, and the expected price reductions coming also, and I'll have to retest all of these apps again in a few months!!! :-) ).. Since Eric Goldstein and Vaughn Suite have both managed to create applications that were so close to each other in performance, it was getting difficult to judge the speed of the apps against each other.. I mean how do you determine which app is faster than the other, when they each give 32 seconds for a shallow test, and 3:31 for a deep test?!? As a result, I have changed my comparison tests, to "enhance" any differences between the next generation of applications.. The new times and testing criteria have been updated on the.. Currently, Eric is ahead of Vaughn, but only by 12 seconds.. (This is at 50,000 iterations at 20,000,000 digits!!) It's like the Tour De France.. You can race for over 2,000 miles, and STILL have the outcome be decided by only seconds or minutes!! Exciting huh?.. Another.. VERY.. interesting function of the RAM swap and deeper testing, is that Ben Despres has moved back in front of Eric Sellers for speed, even though his app has not been updated since 6/18/2002!!! I guess Ben's app was REALLY helped out by the DDR ram in the higher iterations!!.. The new marks, give a better idea of what is going on, so I am glad I spent the entire evening retesting all of the apps.. I hope everyone agrees.. I also got thinking this weekend, that if anyone would like to take the time to compile John Walker's original code, and send me an EXE, I would very much like to "benchmark" it!! No improvements, just a functioning EXE.. I think it would be a wonderful addition to that page.. The original code can be found on John Walker's original.. page, or on Ben Despres'.. Lychrel Numbers.. Vaughn wrote me a email that can be found on the.. It concerns the probability of a given number becoming a palindrome on it's next iteration.. It works hand in hand with some of the information Jason Kruppa provided back in October of last year.. I've also added some notes I wrote a number of months ago, but never finished.. Maybe there is something of interest to someone.. 9/15/03.. 25,000 visitors to www.. 9/11/03.. As it stands RIGHT NOW.. Vaughn Suite of Trinidad is probably in the lead with his 196 app.. I say probably, since the times are so damn close, and can vary from a single test to the next.. In reality, the two apps are so close to each other, that I for one don't feel comfortable calling one ahead of the other.. Also understand, that this is changing RAPIDLY! Eric's work recently has made advances, and Vaughn has kept up with him step for step.. Added into the mix and confusion, is the fact that I have changed my processor, and BIOS configurations, recently, and there is a lot of things to keep up with!!.. In fact, I really need to test ALL the apps again, to get them all onto the same baselines.. I'm fighting a really good cold right now, so I probably won't do it this week, but I will sooner or later.. Eric has sent me an update:.. 2003-09-08 12:26:41 Notification: iteration 205328334, digit 85000000.. I thought it might be a good idea to give the credit to Eric and Matt for the status of their searches for palindromes on some of the other Lychrel numbers.. As a result, I have started listing their results on the.. I will update it as they send me info.. 9/4/03.. I've been testing, retesting, and retesting apps over and over again for the last day.. I've actually made very little progress on the actual search in the last week, since all these computer problems lead to system changes, and now app testing.. To help ID the problems with memory, Matt has asked me to test Eric's app with various combinations of the 2.. 8 and 1.. 9 chips, with each of the 266 and 400MHz memory.. I'm working those tests out.. Meanwhile, Vaughn Suite has sent me his latest app, and has bumped himself into 2nd place on the Comparisons page.. His shallow time, matches Eric's right now, at 0:34, and his deep test time is only 7 seconds off the mark at 3:55.. (His old times were 0:41 and 6:43) So now, I have ANOTHER page update to make!!!.. O Well.. I'll make the changes, happily.. That's what this is all about after all!! :-).. 9/3/03.. A few days ago, I fried my 2.. 4GHz chip somehow or another.. I contacted Intel for warranty work and they had accepted it back for "repair or replacement", but before I shipped it, I was looking over the receipt again, and noticed that I had chosen the "in-store replacement" option that CompUSA (www.. compusa.. com) offers when I bought the 2.. 4 chip.. (My girlfriend insisted, and now I'm glad she did!!!) It allows you, for 2 years, to bring the part back into the store to get it replaced, instead of sending it back to the manufacturer.. It turns out that it's their policy that they will hand you the same part, or apply the PURCHASE price towards an upgrade!! Well, since I bought that chip at around $325.. 00, they credited me with $325.. 00.. (even though the current price is around $279.. A P4-2.. 8GHz in store is $335.. 11, so I paid the $10 difference, picked up the new warranty (of course!! :-) ) and now have an upgrade to 2.. 8GHz for $10.. 00!!!.. I also picked up a new ASUS P4P800 motherboard.. It supports the PC3200 400MHz RAM, and an 800MHz FSB.. Of course, I'm still running the 2.. 8 at 533, since that's what I have, but now it'll be easier to upgrade in the future.. The long and short of it all, is that my.. page is all out  ...   me, he added this feature.. The other new update, is that he has now added a Mod-9 test to his app.. It will test the number on startup, and also at each save point.. This should help me avoid the problems I was having before, with running a bad number.. From now on, if the number isn't good, it just flat out won't process it.. I really hope all future apps from ANYONE, includes this function!!.. On the.. page, there is reference to a post by Vinny Romano, that I had serious doubts about.. Well, Vinny was good enough to write me, and set some of the facts straight!!.. With respect to http://home.. cfl.. rr.. com/p196/false_starts.. html, I agree that my claim of having gone to 24 million digits was not correct.. I would say I probably simply forgot a decimal point and actually only achieved 2.. or maybe it was only 1 million digits and 2.. 4 million reversals.. I don't know.. If I recall, the program I wrote was much more efficient than the one that was used by John Walker, Tim Irvin and Larry Simkins for their 2 million achievement.. Furthermore, I too was running my program on a 'supercomputer' at the University of Maryland, not a P90.. I've been away from this problem for years now.. I just happened to be surfing and I came across your page.. -Vinny.. I was really happy to hear from Vinny!! In my OPINION, if he had simply been boasting in the post from 1995, and didn't do the work, he surely wouldn't have written to me now, to correct it.. He would have ignored it altogether, and we would have never known.. The very fact that he was reading this site, tells me that he was at least still thinking about the 196 search, and was looking around the net.. Vinny, THANKS for setting the record straight!!! I'm sure you deserve some credit for your work, so if you can firm up some of the data or dates, or anything, I'll try to get you into the correct "chronological history".. I crossed 75,000,000 digits yesterday, 2/19/03.. 2/10/03.. 175,000,000 iterations produces a 72,433,237 digit number!!.. Eric Goldstein commented that the 9's in yesterday's post, actually could be considered 1's instead.. From his note:.. I think that the 9's should be 1's too.. e.. g.. 9 minus 0 equals 9, but 9 plus 1 equals 0.. So the difference between 9 and 0 is actually 1.. See what I mean?.. More generally speaking: if the absolute difference (a) is greater than 5, then a = 10 - a.. This will result in differences that are always less than or equal to 5.. I have to say I agree with this thought.. As a result of this idea, I rearranged the Boolean tests I was doing in LabView, and re-calculated the file from yesterday.. Now, the.. 100,000 digits.. of iteration 2,417,447, ONLY contains 0's and 1's.. I'm going to redo the other files I have, and see how some of the other iterations behave.. 2/9/03.. Everything has been going smoothly the last few days.. That's good!! :-).. I got another notification from Eric Goldstein:.. 2003-02-08 16:57:23 Notification: iteration 84542533, digit 35000000.. It's good to have one of the other numbers being followed out.. I keep hoping to get an email from him, saying that his XX million iteration matches one of the ones on my.. page!! :-) It would sure stir up some of my thoughts about 196 being "magical" all over again, if the 2nd Lychrel number joined up with the same thread!!.. I was following up a bit with the thought that I had on 1/23/03, about some of the iterations, being a palindrome for quite a few digits, then breaking apart.. Eric Goldstein mentioned, that it was interesting to notice that in a good many of the iterations, the absolute difference between digits was often 1 or even 0.. Obviously, if all the differences were a 0, the number would be a palindrome.. Iteration 2,417,447 actually goes 15 digits, before it breaks down.. I know 15 digits out of a million is pretty weak, but it was still interesting to see.. The file.. shows the first and last 20 digits of the iterations between 2,415,837 and 2,420,837, along with the absolute difference between the digits.. Most of the iterations that have a lot of 1's and 0's, actually have more of 1's and 0's than any other number.. They seem to be very close to forming a palindrome.. For example, 100 places of iteration 2,415,884 looks like this:.. 0000000011001100110110000001101111000000001011111000000000000110011077770110110111111191000011100900.. Carried out even further, the same general clusters of 1's/0's and rare odd numbers follows.. In fact, if you look at.. of iteration 2,417,447, there are ONLY 0's, 1's and 9's.. In some other cases, there are other numbers like a 6 here and an 8 there, but they are "rare".. Then I manually reformatted the file, (the 2417447 file) and ran it through Ben's file checker program.. Of course it failed all of the checks, but I was curious if there was a visual pattern in the 1's, 0's and 9's.. As far as I can tell, there is not.. I looked at it in dozens of different pixel modes, including the programs "auto-mode".. Nothing but the typical "static pattern".. Although it does look a bit different from what I'm used to seeing, since there are only 3 pixel colors!!! :-).. Is this useful?? Is it in anyway helpful?? I don't know.. Neither did Eric or even Ben.. I throw it out here, so that someone with other ideas, can think about it, and maybe give me an idea of how it might help solve any of the million questions that make up this site.. 2/6/03.. I have had a hell of a time keeping things straight this week!!! I've had a few errors happen this week, and they have all been my fault! :-( But I feel like I'm over the "shock" of the Columbia explosion, and decided today would be a good day to get this site back into shape.. I finished the 71 million data set early yesterday morning, but I had mistyped the save directory in Eric's ini file, and it didn't capture it.. I'm running it again from 70,996,903, which happens to be the save point just before the "error".. In fact, by the time I have this page updated, it will probably have finished, and there is no reason to even post this, but.. I never did exactly figure out what was going wrong last week.. I have simply been checking the files a couple times a day.. I haven't come up with another "bad" file yet, but I was really starting to think there was something wrong with Eric's app!! For some reason, I didn't think it wanted to get that 70 file complete! Turns out, that everything seems to be fine, Eric's app it rolling along smoothly, and if I would put in the correct data into the ini file, all would be well! :-).. I was smart enough to save the file from this afternoon, before I re-ran the 71 section.. That way, in about 20 minutes, when 71 is complete and safe, I can go right back to 71,389,992 from above.. Eric Goldstein forwarded a line from his log for 879:.. 2003-01-29 02:18:01 Notification: iteration 72466349, digit 30000000.. 2/1/03.. It's been a very long day for those of us who live right here, (within 15 miles) near the Kennedy Space Center.. Most of you know that until Feb of 2002, I was working at KSC.. I have a lot of friends at the Center, and I am thinking of all of them.. I am an AVID space supporter.. I watch the launches to see the most complex machine ever made by man, and marvel at the miracle of it's success.. I saw Challenger explode in 1986.. Now, there is Columbia.. I have watched EVERY Space Shuttle launch since the first launch of Columbia in 1981, if I was living in Florida.. (I actually missed a few while I was in the navy, but not that many.. ) Since I worked at KSC, probably 1/4 of the launches I've ever seen, I was at the 3 mile limit for access.. (Where the VIP's get to sit.. :-) ) This was the first launch that I was ever in the area for, that I missed!! I didn't even know about it on launch day.. I have seen most of the landings.. I had no intention of going anywhere to watch this one, but I would have been able to see it from my back yard.. It's a sad day.. This.. was about two years ago.. I finally got a valid 70,000,000 file.. I have done the 70 data set 4 times!!! The one, posted below as an error.. Then as I was working it again, I ended up with two DIFFERENT invalid files.. I don't know what in the world is going on!! I am watching the files VERY closely as of late.. Currently, it is O.. , I keep expecting to find another problem.. With all the activity today, I don't feel like posting the milestone and data.. I'll it all up in a day or two.. 1/26/03.. Yesterday morning, the 13 digit Lychrel numbers finished.. There were 4,451,740 new numbers added to the list, bringing the total to 5,238,380.. I don't think I'm going to do the 14's right now.. Maybe in a few days or a week, but for right now, I want to use that machine to play with some of the datasets.. 1/23/03.. I have to admit.. right at the moment, I don't have the slightest idea of.. how.. Ben made the following image, but it sure looks nice!! :-).. His comments that came with the image are this:.. I've started looking at the fractal nature of reversal-and-addition, which I briefly mentioned once before, but have started looking into seriously.. I've made one good preliminary image of the attractor, which I've attached.. It represents the mapping of the palindromeness, in the 4d Kins-space (the 1e8 range in base-10), unwrapped into 2d.. I've tried different 2d mappings to get better clustering of palindrome-reaching points, but it has proven exceptionally difficult.. You will probably notice that each section appears to neatly subdivide into two areas, recursively.. This has so far proven an illusion, and attempts to clarify the image based on that binary nature give something that looks very much the same, amazingly enough.. You may also notice (if you've seen these structures) that the parts of the image bear a strong resemblance to the Sierpinsky carpet and triangle.. This doesn't really surprise me, but it does give me hope that a proof may yet exist for whether or not Lychrels really exist.. -Ben.. Maybe someone will see something interesting in there.. I leave that for others right now.. As an example of a totally free afternoon, I was reading all of the papers on the new.. page, for about the 100th time.. (I'm trying to really understand what is going on on this site!! :-) ) Anyway, the paper:.. Self-Similar Reverse-Sum Sequences.. written by Kevin Brown, got me thinking about my own files, and whether they have this recurring pattern anywhere.. I didn't find a recurring pattern in the 175 iterations, from 1,000,000 to 1,000,065, (well, I did, but it was all in my imagination, or stretching the fact so far, that no one else would have agreed!! :-) ) but I did find a few lines, that I hadn't expected to see!! There are quite a few iterations which begin to form palindromes, but fail after 5 or 6 digits.. One of the example lines, (Iteration 2,415,848) actually makes it to 10 digits, before the palindrome breaks down.. I had a lot of free time this afternoon!! I doubt that this is any significant finding.. But it was fun.. I was surprised, maybe someone else will be.. The result file is.. if you want to take a look.. 1/22/03.. It appears there is good news for the future of the word "Lychrel".. Some clarification that I got from Vincent Prosper is that "Kin Numbers" are only the ones that relate to each other, and do not form a palindrome, not the class of numbers overall.. It actually works out very well for my purposes!! I had made the following comment on the.. page:.. I've had people tell me that numbers like 295 and 394 should be called Lychrel numbers.. I have never agreed, and am happy that Ben's application does not include them.. If anyone else wants to name the "extra" numbers, I'll be happy to try to use the name.. Otherwise, maybe I'll come up with something.. Now, it turns out, that someone already HAD named the "extra" numbers.. So I am going to update that page.. And from now on, I will make it a point to try and differentiate between Kin Numbers and Lychrel Numbers.. Of course, I'm still listening to arguments from anyone who wants to offer a different opinion!!.. Vincent was also kind enough to send me a copy of his 2001, joint paper with Sebastien Veigneau, in PDF format.. You can look at it on the.. Ben's Lychrel app has an expected 6 days left to complete the 13 digit numbers.. There are a little over 4.. 9 million Lychrel numbers currently in the 240 megabyte list.. 1/21/03.. I think what happened, was that at some time, as I was backing up an.. ACTIVE.. file from between 67 and 68 million, and it got messed up.. The newest 68 million file did not match the one that I had, that had been reported as bad by Ben Depsres' checker application.. Luckily, the new one does pass Ben's app!! :-).. So.. I've lost about 2 weeks of progress.. No big deal.. Again, it could have been worse.. It could have been 2 months!! Eric Goldstein's app is so fast, that I expect to have it all recovered in about 9 days.. I guess I need to get back into the habit of checking EVERY milestone, instead of just random ones!!.. 1/19/03.. I got an email from Vincent Prosper of France today, in which he had a lot of things for me to think about, change, and update.. One of the items he talked about was this:.. In the process of computing numbers that can't lead to a palindrome, a lot of operations are irrelevant.. When you compute 196+691, you also compute 295+592, 394+493, and more generally 2 x [ (7/2)9(7/2) ], where 7/2 should be considered as a (pseudo-)digit.. That is to say, 196, 295, 394,.. all belong to the 'class' of the pseudo-palindrome 7/2 9 7/2 (where 7=1+6, 2+5, 3+4).. We characterized these 'kins numbers' without any trouble in our article for any basis.. I saw on your web pages that you call them 'Lychrel numbers' for the decimal basis.. Please update your ethymology/history: they were called 'kins numbers' by a Japanese mathematician K.. Yamashita (see http://www.. jams.. or.. jp/mj/45-1.. html for references) in 1997, and we, together with Sébastien Veigneau, gave the right math definitions in 1998 - published in 2001.. I asked him for a bit of clarification.. If in fact Koji Yamashita (or Vincent and Sebastien) described "Kin Numbers" as including 295, 394, 887 etc, then I am reinforcing the idea that a Lychrel number is only the ROOT number such as 196, 879 or 1997!! On the other hand, if they called 196 and 879 "Kin Numbers" but not 295 and 887, then I have to admit that I am VERY disappointed, by the loss of the name Lychrel Numbers!!!! So I until I'm corrected.. Kin Numbers are the list numbers overall, and Lychrel Numbers are the root numbers of any thread, like I've always claimed.. He also pointed out that:.. The result given by Jason Kruppa - 10 Oct 2002 - in your web page.. , was also mentioned in our article (last page, Appendix B 'Lucky numbers').. Their article can be found.. I had read their paper, but since it had been so long ago, I did not recognize Jason's comments as a duplicate of Vincent and Sebastien's work.. I still thank Jason Kruppa for his contribution, but I think the "discovery work credit" should go to Vincent and Sebastien.. Also, the PROBABILITY page has been removed altogether, and replaced with one titled.. it is an attempt to gather information for a "logical" conclusion to this quest, instead of the "brute force" method I am currently using.. Maybe there is something of interest to you math oriented people.. On another note, my girlfriend found a story which made us both smile.. Luigi Morelli had let me know in the past that it was in the works.. It's nice to see it on the web.. I assume that it is only meant to be a very short story.. The original Italian version is at:.. http://online.. infomedia.. it/riviste/dev/103/articolo04/articolo.. For those of us, who don't speak Italian, a rough translation can be gotten from Google,.. It's coherent enough to make me smile.. If anyone can provide a cleaner translation, I'd love to have a copy.. I emailed Luigi to tell him that I'd seen it.. Maybe he'll provide a translation.. It was nice.. And from now on, I am going to have my girlfriend start calling me a "lofty mind of the planet"!!! :-).. 1/17/03.. Something has gone wrong.. The data files since 67 million all fail to pass Ben's app.. I've tried quite a few different things to identify whether the problem is in my files, Ben's app, or Eric's app.. So far, everything points to a corrupt file.. For right now, I'm running 67 to 68 again, and going to look at the results.. I am leaving all the milestone info on the site for right now, but I have to assume that everything after 67 will turn out to be wrong, and will be replaced.. Wish me luck.. 1/14/03.. A few random updates tonight.. I have found a drawback to using Eric Goldstein's application.. The problem is that since it is running so fast, it is completing milestones, faster than I can (o sometimes even feel like) update the pages, and keep this site current.. :-) (That's a joke.. :-)).. Seriously, his app is turning out a new million digits in about 80 hours.. It's great.. I am beginning to think I need to reformat some of the pages now though.. Having all the dataset information, for example, on the same page seems to be getting cumbersome.. Maybe it's just me, I don't know.. As noted below, Eric Goldstein has stopped following me on the 196 quest.. He is currently running the 879 thread.. He sent me the following line from his log file:.. 2003-01-13 09:56:51 Notification: iteration 48,304,915, digits 20,000,000.. As he keeps me posted, I'll post them here.. It would be really great for 1 of the two searches to find a palindrome.. It would create a really huge question mark on this entire project!!.. As far as the Lychrel search.. Currently Ben Despres' app is working on the 13 digit numbers.. It is finding an average of 2.. 9 new numbers every second.. As of 1:10am GMT, 1/15/03, there are 3,516,077 Lychrel numbers in my list.. The program expects to finish the 13 digit set in another 1,278,456 seconds.. (Almost 15 days.. ) The thought of 1.. 3 million seconds is kind of funny.. That's the way Ben's app displays expected time remaining.. I like looking at it that way.. I guess that's it.. More as it happens.. 1/7/03.. Ben Despres has sent me a copy of his Lychrel Search program.. It is now running on my 1.. 9 GHz machine.. He has made some pretty impressive advances in search speed.. If I remember correctly, during the summer, it took him around four days to calculate all the numbers from 0 to 8 digits.. Today, I managed to do 0 to 11 digits in just over 2 1/2 hours!! Very Cool!!.. I have made some massive updates to the.. My intent is to let that app run full time on the 1.. Ben estimates that my 640 Meg of RAM and 40 G-byte hard drive, should last till about the middle of 1e14.. (~19,153,856 discovered Lychrel numbers.. ) Then I'll have to upgrade, or someone will have to figure out a better way to search.. 1/4/03.. I got the following note from Eric Goldstein:.. Well, I stopped my 196 search (quite a decision, actually) and started 879 at Jan 3rd 2003, 11:40 pm GMT +01:00 from iteration 24153360.. Now I can only hope to find a palindrome before you do!.. Eric.. His thoughts being that since he had finally gotten his app to run as fast under Win XP as on WinME, and since he and I were both using the same app now, and finally that my machine was faster than his, that he would run on number, instead of "running a losing race".. I imagine that, that was a hard decision for him to make.. I have thought a few times, whether I should continue or not.. I've always said yes.. :-) I sent him my existing 10 million digit number to give him a head start, and he's on his way.. 1/01/03.. I hope that everyone had a safe and happy New Years!!.. I am not a very religious person.. Very little in fact.. But I got an interesting email yesterday from Dennis Nelson in the USA.. He writes as follows:.. Genesis 1:1 in Hebrew has 7 words and 28 letters with the Hebrew sum of 2701.. Now 7x28 = 196.. To me this number is easy to understand.. Maybe he's on to something..

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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: NEWS ARCHIVE FROM 2002.. 12/30/02.. I had asked Eric Goldstein for the address to his own site, and he provided me with.. this.. It is a commercial site that has nothing to do with the 196 or Lychrel search, but the software he has given me is a.. perfect.. example of the type of work his company can provide.. I give him the highest compliments for his work.. After all.. He wrote the fastest 196 app I have ever used so far!! He has listened to all of my requests and implemented them quickly.. Maybe his company can do something for you.. Hey it's my site.. If I want to promote a business, I have that option.. :-) Besides, after all the Eric has done for me, linking to his company is trivial!!.. 12/29/02.. I hope everyone is having a wonderful holiday season!!.. My girlfriend took me to the computer store for Christmas!! I have replaced the 1.. 9GHz chip with a 2.. 4GHz.. I also replaced the motherboard, so I could take advantage of the speed increase offered by the DDR SDRAM.. It runs at 266MHz instead of the 133MHz, of the PC133 I was using.. Very nice!!.. Eric Goldstein seems to have finally figured out why his app was running slower on a Windows XP machine, compared to any other OS.. As a result, he sent me his latest version, I have tested it, and it is indeed the fastest 196 application to date!! Congratulations Eric!! Since I coincidently completed the 66 million set today, Eric Goldstein's app is the one that is running now, heading for 67 million and beyond.. Software Comparison.. The new numbers show the tests with the 2.. 4GHz chip.. Again, I hope everyone is having a great holiday season, and I hope New Year's is all that you hope for.. 12/13/02.. I have finally gone too far with this 196 thing.. 12/7/02.. 18:45 Eastern Standard Time USA - 150,000,000 Iterations!!!.. 11/26/02.. I've been very bad about updating the numbers on this page.. But I.. am.. still processing, even though I'm not spending any time on updating this site.. I've been on the computer very little lately.. I'll try to do better!!.. 11/2/02.. A number of things have kept me from updating any of the pages recently.. Some of them silly, some of them bad judgment, some of them "disastrous".. If anyone is looking for a new game for their PS2, I highly recommend "Kingdom Hearts" from Square Soft.. It's the same people that put out Final Fantasy, and I think it is the game that has given me the most fun from the entire PS2 lineup.. For more hours than my girlfriend could tolerate, I loved it, and now that I have finished playing it, I can get back to the rest of my life!! :-).. Too make very, very a long story short, I formatted my drive and lost all of the email that I have received since my monthly backup on 10/1/02!!! I have all my 196 data.. except.. recent email.. I backup the 196 data at least weekly, and I made sure it was all valid, before the format.. But not the 196 email.. As a result, I would like ANYONE who has emailed me recently to mail me again.. Really, all I NEED is an empty email, so I can recover your address, but if there is anything you still have a copy of I would like you to just fwd it to me again.. Thanks!!.. Oh.. Did I mention that I wiped out the file that I had, that contained all of my passwords across the web, including this site?!?!? Note to self: Multiple, complex passwords are a good thing, only when stored.. on a separate disk.. I was trying to get my.. Mame.. cabinet networked to my main machine using a wireless network.. It seemed to be setup on the Mame cabinet, and it seemed to be setup on the main machine, but I couldn't get them to talk to each other.. I had spent.. days.. trying to get it functioning, and in a moment of extremely poor judgment, I formatted my hard drives, in an effort to start from scratch, to get it working again.. I loaded everything back up, and even that didn't work!! So I lost all of the email for nothing!!.. Turns out, that it all can down to my own firewall!! In an effort to protect my machine, I had set the firewall to not allow any machine to connect to my main.. It wasn't!! I wish someone would have included some comments about firewalls in any of the dozens and dozens of FAQ's and troubleshooters that I have read!!! It just wasn't something I ever thought about!! :-(.. I started the attempt to get the two machines talking in SEPTEMBER!!! Here it is November, and I just got it all up yesterday!! :-(.. So anyway.. I think I'm all back up.. I haven't missed any 196 processing time in the last couple weeks, since the machine was working, but I didn't reload my backups until today, for fear of messing something up in my madness.. None of these pages got updated.. Should be back to normal now.. 10/17/02.. 125,000,000 iterations - 51,737,154 digits.. 10/11/02.. Interesting.. Eric Goldstein wrote me today, with the following.. I just tested my program on a 2.. 0 GHz P4 on Win XP.. I got the same symptoms you got!!.. A fast shallow test, 1:06, and a slow deep test.. The deep test ran in about 16 minutes, but it didn't run solely all the time.. My conclusion is that there is something about Win XP that slows the app down.. Since Eric S' app doesn't show these symptoms it must be possible to solve my problem by modifying the code.. I only have to figure out what, where and how.. I'll keep you informed.. There might be something in this, that we'll all like to know!!!.. 10/10/02.. I have been spending a lot of time, playing with Ben's newest checker application.. ISF Tool.. It has all kinds of "neat" things going on inside, like statistics of the number being read, a greyscale visual image of the number, a Discrete Fourier Transformation of the number, etc.. is the image of the 1 million digit dataset in a 998x632 pixel image.. I know it looks like static, and to be frank, I'm kind of happy about that! Like I said on the Blackboard entry for 10/3/02 "I am relieved, not to find a face staring back at me or something like that!!!" :-).. Ben's app shows that the files are pretty darn close to being pseudo-random numbers.. Regardless, I have been resizing and opening different files and closing and trying everything I could make the app do, to find some sort of pattern, not.. IN.. the file, but.. BETWEEN.. the files.. I'm sure that there is no repetition in any given file, but now, I'm wondering if there is any "commonality" or "repeating pattern" when comparing one file to another.. (I think I just came up with a new entry for my.. !!).. Like I said, one of the things that Ben's app shows is "statistical" info about a file.. is a good example from the 1 million data set.. As I understand it, the vertical bars are relative to each other, not absolute values.. That is O.. , because that is really what I would rather see.. The interesting thing is that if you look at all the data sets, you begin to see a "repetition" of the images.. For example, if you look at the.. 4.. ,.. 19.. 20.. 33.. 36.. 39.. or.. 48.. images, they all are remarkably similar in their distributions.. The 0's and 9's peak well above the rest, and the numbers graduate into a nice valley shape.. I see other distinct "repetitive patterns" in other datasets.. (And although none of them look as "pleasing" as the 7 above.. They are distinct.. I ran the sequence of 55 consecutive iterations starting from 1 million digits.. Then I converted them all to their "statistical image".. So far I haven't found anything that I can put my finger on.. (For example, they are not spaced evenly apart.. ) But the "patterns" are still there.. I haven't "classified" them, but I would say that there are 6 patterns that exist.. (That 1 million file from above is another of them.. ) It is difficult, because I don't know of anyway to.. REALLY.. compare them, other than loading them all into Paint Shop Pro, and rapidly scrolling them like a slide show.. (But that LOOKS impressive!!).. So here is my theory and question to anyone who wants to answer it.. Any random (pseudo-random) file with enough digits will fall into one of those 6 general patterns.. Is that true?.. OR.. am I on to something and need to be spending even more time looking into this?!?.. 10/10/02 50,000,000 digits!!!!!!!!!!.. Jason Kruppa from the United States sent me the following.. I found it interesting.. It is almost exactly what I was thinking about when I wrote the note on my.. I have corrected a couple of typing errors in the note, but I am.. positive.. that I have not changed any of Jason's meaning!!.. I remember reading someone's thoughts either on your site or on a Slashdot post that was talking about how a number and it's reverse, when added together, must not have any carries if it is to come out to be a palindrome.. I thought that seemed reasonable, and didn't bother to pursue that thought.. But yesterday I was looking on your pages and someone pointed out the simple fact that 29 + 92 generates carries, yet still comes out to a palindrome, 121.. That got me wondering what the patterns would turn out to be, so I wrote a little program to look for numbers that generated palindromes and had carries when performing a reverse-add.. On first run I kicked out all the numbers that would lead to a palindrome that was the result of a carry, but that was not the useful data.. The useful data was when I did a single reverse-add on a number, checked for palindromicity (is that a word?) and checked to see if it generated a carry.. That gave me the output from the attached.. file.. Looking at that, you see that numbers have to be of the form:.. "a1 b1 b2.. c2 c1 d1".. or.. 0.. Where A1 and D1 total 11 (pairs of (2,9), (3,8),.. ) and Bx and Cx have to be pairs totaling 11 or (0,0).. Using this information, it is possible to calculate the percent chance of picking at random an x digit number and having it be a single iteration palindrome that had carries.. I created a small excel2k spreadsheet.. (See Below).. that shows this.. As you can see, as the numbers get larger there is indeed a smaller and smaller chance of getting a number that's going to lead to a single iteration palindrome.. I suspect that your overall chance of an x digit number becoming a palindrome on the next iteration is the sum of this percentage and the percentage chance that the number will have no carries.. Anyway, I hope this is useful to you, or of some use in one way or another.. If you'd like to discuss with me, let me know.. Jason Kruppa.. Here is Jason's Excel data:.. Number of Digits.. Number of Single.. Iteration Palindromes.. With Carry.. Percentage of Numbers.. that are Single Iteration.. Palindromes With Carry.. 2.. 3.. 5.. 6.. 7.. 8.. 9.. 10.. 11.. 12.. 13.. 14.. 15.. 16.. 17.. 18.. 21.. 72.. 648.. 5832.. 52488.. 472392.. 4251528.. 38263752.. 344373768.. 3099363912.. 0.. 088888889.. 008888889.. 008.. 0008.. 00072.. 000072.. 0000648.. 00000648.. 000005832.. 832E-07.. 2488E-07.. 2488E-08.. 72392E-08.. 72392E-09.. 25153E-09.. 25153E-10.. 82638E-10.. 82638E-11.. 44374E-11.. 44374E-12.. His first column was simply the number of digits.. His formula for the second column looked like this: "=8*(9^FLOOR((A2-1)/ 2,1))", with "A2" being the cell for number of digits.. And his third column formula looked like this: "=B2/(POWER(10, A2-1) * 9)", with "B2" also being the appropriate cell.. I think this is very interesting, specially since it does something that I had already wondered about.. Maybe someone else wants to comment??.. 10/9/02.. Three quadrillion calculations.. 10/4/02.. I made a mistake in yesterdays note about Eric Goldstein's machine.. Here are the correct specs for differences, as I know them.. (If they're wrong again, Eric can let me know, and I'll correct them again.. My Machine.. Eric's Machine.. CPU:.. OS:.. RAM:.. P4 - 1.. 9GHz.. Win XP pro.. 256m.. 7GHz.. Win 2k pro.. 512m.. Gives us the following test results:.. Coder.. Eric G's Machine.. Shallow Test.. Eric S.. Deep Test.. Very Deep Test.. 1:09.. 1:37.. 15:14.. 9:39.. 16:07.. 9:40.. 1:16.. 1:47.. 9:29.. 10:22.. Unknown.. I think this is accurate.. I have tested, tested and retested both apps on my machine.. My times are.. CONSISTENTLY.. within 1 second of each other.. I'm sure Eric G.. 's are also.. Now, that I look at it all in one place, it strikes me as even more confusing.. Again, I ask.. Anyone have any idea of.. WHY.. ?!?.. 10/3/02.. Ben Despres has written a program to do two of the things I had asked for my.. He has written a checker app that runs under Windows, and at the same time, shows a greyscale image of the number being tested.. VERY COOL!!.. If anyone wants it, it can be downloaded from his site:.. LOCAL MIRROR OF BEN'S SITE.. He is adding the ability to save the image, and scroll to see the rest of the image, so he'll probably have those up in a few days, but the first version that he has sent me, is very fun to play with.. As I expected, the datasets that I have run through his app, look like static.. Really, I am relieved, not to find a face staring back at me or something like that!!!.. Jason Doucette has finished all 15 digit numbers for his Longest Delayed palindrome quest.. You can see them on my.. I should have had these up a couple days ago, but.. Thanks Jason.. Looks like his Longest Delayed Palindrome is still 201 iterations.. At least until 196 solves out!! :-).. Eric Goldstein sent me his app a week or two ago, and I was testing it for him.. An interesting thing is occurring.. Maybe someone can point something out to us.. On his P III - 1.. 7GHz machine, with his app, he is getting times faster than Eric Sellers.. (Two minutes faster in deep testing, if I remember correctly.. ) On my P4 - 1.. 9GHz machine, he is slower then Eric S, by almost 6 minutes for the same test.. (20,000 iterations from 10 million.. ) And about 6 minutes slower for the 5,000 iterations ending at 96,650,213 (which is 40,000,000 and up.. The two differences that we have thought of between the two machines are that he is running Win 2000, while I am running Win XP pro.. And that I have a P4 and he is running a P3.. Beyond that.. I also noticed a new 196 comment on the kiro5hin.. org site.. The post.. from Aug 9, 2002, claims to have taken 196 out to 250 million iterations.. From the language of his post, I take it that he did this in one day!! I don't see anyway to contact him/her to try to verify that incredible statement.. I'm skeptical.. 10/01/02.. No "news" to speak of.. 9/27/02.. Eric Goldstein is around 18.. 5 million.. His program is getting faster and faster.. Eric Sellers still has the fastest program that.. I.. have tested.. Now, it's working on 48 million.. 9/22/02.. There is a new name on the.. page!! Eric Sellers' app was the fastest at the time I started the 46 million set, so I ran it.. I had to make a decision during the 45 million set, how I was going to credit different software writers for a data set and when I would use a new app.. I decided that whichever program I was running for a given set, would be the one to finish that set, regardless of whether I had received a faster one while it was in work.. Then, when I started the next set, I would look at all of the programs, select the fastest, and use that one to completion.. It seems like a good strategy to me.. It seemed the most fair, and no one could argue with me over something like "My app did 55% and his did only 45%, so why didn't I get the credit?" I am.. that I would have never heard something like that from the current 1/2 dozen writers that I have apps for, but in the future.. It seemed like a good idea to set a "standard".. As a result, Ben's app finished the 45 and Eric's began and finished 46.. Now, Eric's is still the fastest one I have, so it will be the one I use to get to 47,000,000.. I interesting thing happened to me a week or two ago.. Eric and I were "debugging" his app, and it wasn't giving the correct answer on some iterations, but was totally correct on others.. we were kind of confused for a day or so.. What really bugged ME though, was the fact that for a given iteration, I had two different numbers, and BOTH of them passed Ben's checker program.. This brought to focus, that I didn't understand how the program functioned.. Eric and Ben both explained it to me, and now I think I have a much better idea of what is going on, but it drove home one of Ben's statements, that he had made earlier, but I had forgotten, or maybe just ignored :-(.. "This relates to what I mentioned to you about how the checker can prove *incorrectness* but not *correctness*.. Passing just means it has the right MOD-9 value.. Or, to think of it probabilistically, only ten distinct MOD-9 values exist (0 through 8).. A completely random file therefore has about an 11% chance of "passing" the test.. So I learned something new.. As it turns out, Eric's program.. was.. giving us the correct number for the odd iterations, it was just reversed.. So, it SHOULD have passed Ben's checker.. Eric has since "fixed the bug" and now, every time it saves a file, it puts the number in correct order.. On to 47 million digits.. 9/12/02.. Eric Sellers sent me his latest app.. He too has managed to improve his time.. You can see them on the.. page, as always.. Also, an entry for Udo Zallmann.. His app was slow, but I think most of it was due to the fact that I think he was writing to the disk EVERY iteration.. :-( Check them out.. One of the things I LOVED about Eric's program, is that it saves a file with an "ISF" extension.. It is his tribute to "Istvan Standard Formatting".. I will use it as my default extension from now on.. In case anyone is wondering, Eric Goldstein of the Netherlands is currently around 12.. 8 million digits in his 196 search.. 9/11/02.. Chris Lomont (His page.. ) has done it again! This time pulling 2 min 20 sec off of the deep testing and 24 seconds off the shallow testing.. Currently, he has the fastest app that I have ever tested.. His times are: 0 - 413,280 iterations in 1:01, and 24,159,531 - 24,179,531 in 10:27.. Amazing!! Hopefully, he will decide to send Ben a copy of his source code, so that the world can marvel at it.. Of course, I'm sure everyone would like to see Eric's code also.. To see such a radical speed increase WITHOUT MMX!!.. Ben?? Eric?? Time to kill a few more brain cells, and set the next mark to beat! :-).. I have also added a new page.. is a list of programs that I would write if I had the ability to do so.. Since I don't, it is a list on this site.. My hope is that someone will want a project other than a 196 app, and maybe will write one of these.. 9/10/02.. One of the things that I find interesting, that really has NOTHING to do with this site, is the fact that I average 1 visitor every day, because of the.. Not for the fact that people are looking for alphabetic palindromes.. No.. I get one visitor a day because people are looking for love letters, and the title of that page is "Letters Need Love Too.. Consider today's visitor, who typed.. my love letters.. and Google ranked me 7th of 1,950,000 hits!! Or yesterday's which was a Yahoo search for.. love letters example.. , which ranked my page 3rd of 816,000 returns.. I mean the other queries found on the Extreme Tracker link at the bottom of this page make sense in one way or another, but LOVE LETTERS?!?!? For this site?!?!? Even though.. Google.. is my default browser home page, and it provides remarkable results, it still seems like more work needs to be done in the search engine arena.. Of course, maybe one of those people looking to plagiarize love letters to send to their soul mate, might the one who has the background to solve the 196 question once and for all, so who am I to question my visitors???.. But I still find it interesting.. Sorry about this update.. It was a lllooonnnggg day at work.. 9/9/02.. It looks like, I will have to adjust my "shallow iteration" testing again.. 413,280 iterations is going to be getting harder and harder to compare, if the future keeps pace of last couple days!!!.. Chris Lomont has managed to pull another 18 seconds off his shallow run and 1 minute 58 seconds off of his deep iterations.. The app I have right now, stands at 1:25 and 12:48 respectively.. So at the moment, he is the fastest in the shallow iterations, and still second in the deeper iterations.. (I've updated the.. page yet again.. He and I were confused by the fact that his tests on his P3, 1GHz machine showed a doubling of the speed between the two latest apps, but my machine (p4 1.. 9GHz) only showed about a 15% increase.. The mystery seems to be solved by the following comment from a note of his today:.. I just realized on your system it will perform at 1/2 speed due to my threads :) I have a dual processor.. I will make the code only use one thread, and that should give you a good speed increase.. When I run it at school on a single processor it uses only 1/2 CPU time.. So that should double.. TWICE.. as fast, as what he has already sent?!?!.. I am anxiously waiting.. 9/8/02.. Holding steady at 107,407,247 iterations.. I deleted my 44 mill number, and am forced to run 43-44 a second time to get it back! I'm sure you understand I was MAD!!! When I "recreate" 44, I will continue from the above mark, and be back on track.. A.. interesting day.. I have not only tested a new application from Eric Sellers of Canada, but also a new one from Chris Lomont from the US, who is completing his PHD in math.. Chris' application was very interesting, from the point that it had a lot of "other" functions in it, other than simply a 196 search.. It was also VERY fast!!.. Eric Sellers of Canada.. compact and fast, That is the best way to describe it.. It looks like there may be a new king of the hill.. All of the numbers:.. Test.. Chris.. 0 - 413,280 Iterations.. 24,159,531 - 24,179,531 Iterations.. 1:33.. 15:23.. 1:58.. 11:35.. 1:43.. 14:46.. So Ben was still quicker in the low end, but as the numbers got large, Eric and Chris began moving away.. Eric credits this to the fact that he is using 1/2 the memory as Ben's application.. Chris didn't give any indication of what he had done.. With my limited knowledge, and the way that people have explained it to me, during these tests, what amazes me, is that Eric did not use any MMX functions for his speed increase!!! I haven't seen his code, and I doubt it would mean anything to me, even if I did, but I'm hoping that he will send a copy of it to Ben.. I have a feeling that he has discovered some amazing new flip and add routine, that if it were combined with MMX functions.. You see where I'm going.. Eric still has to finish the "eye candy" end of things.. Saving at specific iterations and digits, beginning from different numbers, etc.. But I doubt those functions would hurt the performance.. (Would they??) (and if they did.. Eric, LEAVE THEM OUT!!).. I believe Chris's app is complete.. Although there are still some questions I have asked him, that I'm waiting to hear back on.. When everyone gets back to me, I'll test everything again.. But one way or another, there might be a new name on the.. page for 45 million.. I think everyone is with me, when I say "Great Job" to Eric and Chris!!.. 9/6/02.. A 44,444,444 digit number occurs at iteration 107,382,665, and the first 25 digits are on the.. 9/3/02.. At a suggestion from G.. S.. Chong, I have retested the applications that have been sent to me, and redone the way I will report the results.. Instead of testing for a specific.. TIME.. length, G.. suggested that it would be more accurate to measure the time to get to a specific.. ITERATION.. So from now on, I will time the apps from iterations 0 - 413,280 and from 24,159,531 to 24,179,531.. The 413,280 is a TOTALLY arbitrary iteration which happens to correspond to 171,104 digits.. This will give me a very quick look at what to expect.. The 24,159,531 iteration corresponds to 10 million digits, and 24,179,531 is simply 20,000 iterations above.. That should give me a better idea of one program compared to another, when the numbers are starting to get pretty large.. If someone can think of better numbers to use, explain to me why I should change, and I probably will.. I've made the changes to the.. I'll try to get the rest of the info up soon!!.. The other thing I noticed, that has little or no relevance to anything, is that the precision of.. is getting more and more refined.. It seems to be consistent to 4 decimal places now.. This is I think what everyone expected, and not surprising, but it is something I noticed.. Specifics are probably best seen.. 8/29/02.. Doug Hoyte has sent me a 196 program and I have forwarded it and it's source code to Ben.. My testing tonight showed that it turned out 835,072 iterations and 346,012 digits in a 30 minute run from 0.. Of course, looking at the.. page, it's easy to see that in 15 minutes, Istvan's program was far faster, and Ben's at 1,032,282 iterations and 427,640 digits is in no danger yet of being replaced.. A huge thanks to Doug for his effort, anyway.. Maybe he'll take it as a challenge.. UPDATE: 9/6/02.. As seen on the.. page, Doug's version 2 was considerably faster, and is currently in the Number 2 ranking, being faster than Istvan's.. Great job Doug!!.. 8/27/02.. I had some free time this evening, and was scrolling through the.. Lychrel Numbers between 0-1,000,000,000.. I noticed, that between 100,000,000 and 200,000,000, the last digit of each Lychrel number seemed to be considerably more 4's and 6's than anything else.. So I started looking a bit closer.. Between 0 and 100,000,000 the numbers look fairly scattered about.. Nothing that really stood out at me.. Then there is a majority of 4's and 6's from 100,000,000 to 200,000,000.. Then, every Lychrel number between 200,000,000 and 1,000,000,000 ends in a 9.. This led me to wonder what the most common last digit really was.. I opened LabView, spent about a 1/2 hour testing around, until I was sure it was working correctly, then let it go on the Lychrel list 1e9.. I expected that 7, 8, and 9 would be the easy winners.. With 9 having far higher occurrences than anything else.. But as with so many things during this quest, I was surprised.. I watched the counters closely, and even though they are moving quicker than you can SEE, you can get a "feel" for what is going on.. The things that struck me, were that there were only about 475 4's below 100,000,000.. Most of the other counters were in the 2,000 to 3,000 range.. (I don't know the specifics.. like I said.. this was mostly "feeling" what was going on, although the numbers are fairly close.. ) 0 and 1 were in the 1,000 range.. Then as I crossed 100,000,000, the six counter started racing, and the 4 counter started following.. just about everything else moved, but.. very.. little.. By 200,000,000, the number of 4's and 6's had almost tripled.. Then, crossing above 200,000,000 nothing moved again that I saw, except 9's.. The final numbers look like this:.. Ending Digit.. # of Occurrences.. 1.. 1,527.. 2,211.. 2,548.. 3,000.. 1,129.. 3,133.. 5,343.. 3,913.. 3,946.. 4,964.. Nothing is as lopsided as I expected.. There were only around 2,800 9's at 200,000,000.. The rest of them were made up all in a row, at the end of the file.. And in fact there are less 4's than any other number, and more 6's than any other number.. I'm curious.. In the end, there is probably no value to what I did this evening, but I killed some time, and maybe it makes sense to someone.. Or maybe there is something there after all, we just haven't seen it yet.. I can't wait to get a look at the 1e10 list.. 8/25/02.. I have made minor changes to almost every page on the site.. There has been a wonderful influx of ideas and information coming to me from many people since the Slashdot article.. A lot of the changes are very minor, but people seemed to want/need them to clarify certain points.. I hope I got everyone's inputs correct!!.. Beth Cooper and Chun Yi asked to see the spreadsheet that I mentioned somewhere on the site, that I use to track the status of my progress.. I don't know if anyone else is interested, and I don't even know what value it could be to someone, but.. here it is.. in a zipped Excel file.. Maybe there is value to people like Eric Goldstein, who is verifying all of my work, by running 196 also.. (Currently, he is around 10 million.. ) I don't intend to update it except maybe rarely, but it is current as of this afternoon.. It is there if someone wants it.. If nothing else, it shows a really nice "timeline" of how I have moved forward!!.. 8/21/02.. I am a chowder head again, and it took Mr Eric Sellers to point it out to me.. Eric noted that the numbers I had on my.. Software Comparisons page.. , didn't quite match up with the results on.. The Ratio page.. It seems that I transposed Istvan's iterations with Ben's digit length, resulting in a ratio of around 1.. 7 and 1.. 8 for each application.. On top of that, when I ran it again, to verify the iterations and digit length, they weren't even correct for Ben's app!!! I must have been sleeping when I did that!! I have corrected it now, and feel completely and properly chastised for my error.. Many thanks to Eric for noticing that!!!!.. It really is nice to have so many fresh eyes looking at the site.. 8/20/02.. I seem to have survived the Slashdot effect.. Looks like the visitors are tapering off fairly quickly at this point.. For Sunday, Monday and today, there were around 13,000 visitors to the site.. Those of you who came back for a second time, I'm glad you did.. Those of you who will never read this sentence, because you thought there was no point in this, well.. think.. I replied to all of the email that I got.. If you sent me a message, and didn't get a response, write me again, please.. I will write you back.. I haven't heard if Ben or Jason or anyone else got anything interesting from the links off my page, but I'm sure I will in the next few days.. There were quite a few very interesting emails that I got though.. I'm really not sure how to put out some of the ideas and thoughts that I received.. Maybe the best place will be to add them to the.. Yeah, I think that will work for now.. If anyone sees their note on that page, and wants it removed, let me know, and I will remove it.. immediately.. It almost seems like a small thing after the excitement of the last few days, but iteration 101,476,346 contains a 42 million digit number.. I know there is more that I wanted to mention, but it escapes me for the time being.. 8/18/02.. org has been listed on Slashdot!.. I've put a very quick FAQ.. I'll add to it as I get time.. or as I see more of the same questions being posted.. Reading through the posts, there are a lot of people that want to know what the point of this all is.. Well, what's the point to figuring pi to the millionth decimal? What's the point of a lot of things? Math theory seems to rarely have a point in the beginning, but sooner or later, someone might find a use for any given problem.. Someone posted that maybe there would be uses for something like this in encryption, because of the huge numbers that have been generated.. I don't know.. This is something that strikes me and a few others as interesting, and we're following it, by giving time to it.. There isn't really a point, except that no one else has done what I and the other people listed on these pages are doing.. If you need anything other than that, sorry.. There were a few posts about people wanting a more "theoretical approach" instead of the "brute force" method that we are using.. I can only speak for myself, but I am NOT a math wizard.. I state that over and over again in these pages.. If I thought I could find a solution theoretically, I would have already done that.. As far as anyone listed on these pages knows, there is no proof ever yet developed that answers the question of whether 196 does or does not form a palindrome.. We're doing only the testing we can think of.. and implement.. for this problem.. We welcome.. anyone.. who has the knowledge or interest to help us.. DennisZeMenace said we should make a fractal image of the number.. Interesting thought.. Those of you who found the pages interesting, welcome.. I'd like to hear from you.. Those of you who can add any valuable thoughts or ideas to anything I and the others have done, I would like to hear from you.. Those of you who think the entire thing is a waste of time, I thank you for stopping by anyway, I'm sorry you didn't enjoy yourself.. The incredible exposure that Slashdot has given on this tiny corner of trivial math, is welcome to us all.. And at a minimum, my visiting country list has doubled in size in the last 3 hours!!!.. Thanks,.. Ben had posted to the article the following as part of a post:.. Additionally, most Slashdot readers run Linux.. Although I plan to write a Linux client, at the moment my optimized reverse-and-add routine only builds under Windows (mostly because I hate AT&T syntax assembler, I actually prefer coding for Linux otherwise).. So, if anyone wants to volunteer to convert a 250+ line in-line assembler function (with MMX) from Intel format to AT&T, drop me a line (you would of course get full credit for your contribution).. That was followed by a post from bp33 that said:.. > Additionally, most Slashdot readers run Linux.. Really? I don't want an OS flame war but wonder how you knew this.. I would like to comment that in my tracking, I was surprised to see the following:.. Of the visitors that have hit the site today, Windows Users were 70.. 61% of the traffic, Unix (Linux) users were 21.. 46%, Mac users were 6.. 61% and other covered the remaining 1.. 3%.. For all the blow and hype on Slashdot of Linux and how everyone seems to bash MS all the time, looks like most of them are Windows users! (I'll never read Slashdot with the same slant again!!.. 8/16/02.. 10:12am EST: It took around 2,069,427,300,000,000 calculations and who can guess how many hours, to reach 100,000,000 iterations, resulting in a number 41,388,546 digits long.. But now it's been reached and still no palindrome forming from adding and reversing 196.. What a major milestone!!.. Again, I've moved old news to the.. (If that wasn't obvious!! :-) ).. 8/13/02.. 2 quadrillion calculations passed yesterday.. All that  ...   someone asked for them.. I've never thought about it.. I've never been asked for them.. I do know that I'd be kind of disappointed for someone to use my own files as a starting point and beat me to 100,000,000 iterations while I was still working on the search.. If I decided to quit the search, I'd give them away without ever even hesitating.. Just as Jason and Istvan did to me.. Regardless.. I'm excited to see what Ben and Jason come up with!! I'll post more as I know it.. 5/20/02.. I have written an application in LabView to search for Lychrel Numbers.. inefficient, but it has begun the search.. I figure that if someone writes a program for me, I'll end up dropping the one I built and using theirs, but there is no telling how long it will be until someone has enough free time to write a search program.. So I decided to at least get something written that could start.. I used the methods described on the.. Lychrel Challenge.. LabView is very poor at handling large numbers.. On top of that, my "coding" is almost as poor as if I'd tried to write it in a different language.. But like I said.. It's something.. I'll post them as I find them.. 5/15/02.. There are three iterations that contain a 34,000,000 digit number.. The first one is 82,146,096.. Who has time to write a program?!? Even if you do not have time to run it, does anyone have time to write a program to discover Lychrel Numbers? I know and have stated many times on these pages that I can not do it.. So, I am kind of throwing this out as a challenge to all of you reading these pages.. If someone will write the program, I will find a machine to run it on.. Or, if you write the program and can run it, and want to send me the numbers, I will post them.. You will get all of the credit as the discoverer (or as the code writer).. As far as I can tell, the first 1,895 have been discovered.. Ian Peters has a reference to them on his web page.. I have sent him a note asking for a list of them, but have not heard back yet.. I would have to give him credit as discoverer, but number 1,896 is still waiting to be found!!! Write a program, send me the numbers, get your name in history.. More info can be found on the newest page to this site.. The Lychrel Code Challenge.. 5/13/02.. I tend to think about this 196 problem quite a bit.. Recently, I have been thinking about all of the seed numbers that I know exist, and why they do not form palindromes.. In the middle of my twisting and turning these numbers around in my mind, I realized that I have never seen a name for these numbers.. I mean there is a name for a number that is the same forward and backward.. It's obviously "palindrome".. There is a name for the types of numbers that are only evenly divisible by themselves and 1, they are "prime numbers".. There are the words Integer, Fraction, Odd, Even, Factors, Mersenne Prime, and a whole lot more, that "Name" a class of numbers.. But I've never seen one for the class of numbers that do not form palindromes.. Not even on Patrick De Geest's.. wonderful site.. can I find a name.. (Although I will admit that there is so much info on his site, that I sometimes get lost, and may have just missed it!!).. But assuming that I am the first person to think that these numbers need a name, I get to choose what I think the name should be, Right? So, until someone tells me that I am not the first person to name this set of non-palindrome forming numbers, I am going to call them.. LYCHREL.. numbers.. (la-shrel).. Update your websites and spread the news.. All together, we can add a new word to our languages and have a name for a very amazing set of numbers!!.. 5/11/02.. I was thinking about probability and randomness the other day, and it made me start thinking about if the datasets could be called random numbers.. I know that they are not actually random, because there was a distinct path to get to them, that could easily be duplicated by anyone, and they would get the same result as I did.. But for a practical test, could they be USED as a very large set of random numbers?.. Again, I fired up the LabView program, tried to figure out a test for randomness.. The first thing I did, was build a program to count the occurrences of each digit.. I assumed that in a random set of numbers, the digits 0-9 would each show up 10% of the time.. This is what I wanted to test for.. The results look like this for the 1 million dataset:.. 0 - 105,335.. 1 - 97,694.. 2 - 98,116.. 3 - 96,807.. 4 - 100,954.. 5 - 101,360.. 6 - 95,821.. 7 - 98,976.. 8 - 98,693.. 9 - 106,244.. Total - 1,000,000.. Each digit shows up pretty much 10% of the time, (A perfect 10% would be 100,000 times each.. ) This test took about 15 hours to run, so I doubt that I'll run it on a larger dataset.. I don't really think I want to spend 495 hours running the 33 million set!!.. I'm still thinking of other tests that I could apply to show if the number is a practical random number.. Not that I have any need for a 33,000,000 digit random number, but if I ever did, it would be nice to know that I have one that I can use already on my computer.. 5/10/02.. I've finished all of the searches for odd digit palindromes within the datasets.. Back to crunching on 196.. 5/7/02.. 5:19:48pm Eastern Time, USA.. Someone from the domain "Shaw Communications" in Canada was the 500th visitor to the p196.. 5/6/02.. If anyone has been paying attention to the counter above, you will have noticed that it has stopped progressing.. I have.. TEMPORARILY.. stopped the 196 calculations.. I mentioned last time, that I built a program to find odd digit palindromes within the datasets.. This is what I've been spending the CPU power on for the last few days.. LabView really tries to grab 100% of the processor when it's running.. It's not very friendly at multi tasking with another application.. Especially one as intense as Istvan's program!!! :-) As a result, both programs were killing each other for CPU cycles.. The results were pretty poor.. Both programs suffered terribly.. So I've turned off the 196 program, while I complete the search for odd digit palindromes within the datasets.. It's taking about 9 hours to complete a dataset search.. There are only about 11 more to do.. A couple more days.. Once the.. page has been filled in with all the missing numbers, I'll turn LabView back off and get the 196 program running again.. Go look at the data page.. There are some interesting results on there that maybe someone can explain.. I've never seen anyone comment on the results I found, so I can only assume that I have found something "new" that no one has thought of before.. Comments?.. While looking for other large number sets to compare, I found this page:.. Mathews: The Archive of Recreational Mathematics.. by Walter Schneider.. I had done a Google search for "+million +digits" -pi" and after bouncing around a few minutes, found his page.. Most of his information is a bit over my head, but it was really nice to see a lot of familiar names and links to web pages there.. He even has mine listed as 30 million digits, so his page is updated regularly, or at least recently.. (last updated 02.. 05.. 2002 to be exact) Mr.. Schneider, It's good to meet you.. 5/2/02.. As you can see, I've archived the past notes onto an.. Archive.. I just felt that this page was getting too long.. I keep adding to the top, and the page gets longer and longer.. So I moved it.. That's one of the joys about owning the page.. I can move things around to fit what I think is a better layout.. I've given a lot of thought to the layout of the site lately.. It's growing quite large, and I keep thinking of things that I would like to put here, but it's also getting to be a bit cumbersome to manage.. Every milestone has 4 or 5 pages that need to be updated or at least checked to still be accurate.. Some of the info seems to go together, but I don't know what the simplest method is to display it all.. I really want to keep the simple style, and fast page loads.. Don't be surprised if everything moves around as I try to sort it all out.. I'm also.. open to suggestions if anyone has any.. Anything you'd like to see, something that is stupid that should go away, a particular page, my colors? Anything that would make the page better for everyone, and maybe easier for me, I'd like to hear about it.. My machine has been "hanging up" for 30 or 40 seconds, every time I access the site.. It sits and won't let me do anything at all, then it all begins working again.. I'm trying to figure out why.. The only thing I can think of, is the Real Tracker banner below.. If anyone else is having a problem with the pages loading,.. LET ME KNOW.. !!! As much as I like looking at where people come from, I will remove the banner if it's slowing things down!!!.. I have taken the time to build a LabView program to figure out the largest palindromes in the datasets that have an odd number of digits.. I'll get the results of the searches on the.. page as I get them.. Some of the results are pretty interesting.. It appears that in general, there are larger odd digit palindromes in a given string of numbers than there are even digit palindromes.. It also appears from my files that there are far.. more.. odd digit palindromes than even digit ones.. For example, in the 7 million data set, there are 1,532 even digit palindromes with 6 or more digits, but there are 4,645 odd digit palindromes with 7 or more digits.. I'm seeing results like this in every data set.. Another example is the 33 million dataset, which has 4,110 even palindromes with 6 or more digits compared to 11,020 odd numbers with 7 or more digits.. Does this tell us anything about palindromes (or probability of numbers) in general? I'll think about it, and if I think of something, or someone writes me, I'll post it.. 4/30/02.. Iterations 80,535,060 / 80,535,061 / 80,535,062 / 80,535,063 and 80,535,064 all produce a 33,333,333 digit number.. 4/26/02.. There are two iterations that contain a 33 million digit number.. The first one is 79,728,684.. 4/17/02.. There is a 32,192,735 digit number at the 77,777,777th iteration.. 4/14/02.. Iterations 77,311,782, 77,311,783 and 77,311,784 all contain a 32 million digit number.. 4/12/02.. There hasn't been any "news", so I haven't written for a while.. Just updates to the numbers.. And to the.. visitors.. page, as I see new countries.. I did get a note from Istvan Baktai.. He also lives in Mezokovesd Hungary and happens to know Istvan Bozsik.. Istvan, it was good to get your note and kind words.. Thank you.. I figure about 2 more days to 32 million digits and maybe 4 till 77,777,777 iterations.. 4/3/02.. 4:01am Eastern Time, USA.. 75,000,000 iterations.. (31,042,350 digits).. 4/2/02.. The 74,897,447th and 74,897,448th iterations both are a 31,000,000 digit number.. 3/30/02.. I got a note from Nathan Moinvaziri a couple days ago.. (He didn't mention where he was writing from.. ) He sent me another 196 application to test.. He believed that his program would be faster than anything I've got.. I tested it out, and was sorry to write him back that it was in fact slower than Istvan's program.. (Which is the only one I tested against.. I don't know what Istvan actually did to make his program so efficient, but I still have to say that it is the fastest palindrome program that I've seen yet.. Most of the others that I've tested have been considerably slower.. Congratulations Istvan.. You made a good one.. This all brings up an interesting question that I thought about while I was running Nathan's program, and is the reason that I haven't (and probably won't) run David Gillies Linux program.. At this point, does it really matter who's program I run? In my mind, with only 2.. 5330 iterations per second being turned out by the processor (Pentium IV 1.. 9 GHz) it seems to me that even some of the most poorly written code (like what I might write) would "keep up" with the best.. The difference is apparent when the machine is just starting from 0, and is doing 2,600 iterations per second.. Then, the efficient code would have to be better.. But when the machine is spending the vast majority of it's time, just adding the string, again I ask.. Does it matter at this point?!?.. I think no.. I'm not saying that I don't want to continue getting people's applications.. I like looking at the different approaches people take, to get to the same result.. And secretly, I like the suspense, of testing, to find out if "this one" is going to become the new "king"!! But until someone writes a faster program.. writes a "conversion" applet, to read Istvan's 30.. 7 Million file, I'll just continue like I am.. I've also added two new pages to the site.. One to try to put things into perspective of how large the data sets have become, and another, announcing the countries that have visited the site, based on the Real Tracker data.. The are listed below, or you can just click.. Here for Visitors.. Here for Perspective.. 3/22/02.. I've crossed 30,000,000.. There are four iterations that have a 30 million digit number.. They are 72,483,743 through 72,483,746.. 3/19/02.. I decided that I wanted to use a faster server, and since the geocities ftp always gave me trouble, I decided to move to this one.. While I was doing that, I decided that I would break down, and register a domain name for the site.. In a tribute to Istvan's application, which has kept me going, I chose P196.. ORG.. txt is the file name that his app uses.. It's the most current file in the 196 quest.. I back up the saves and copies, but there is only one file named p196.. txt.. That way, I always know to be VERY careful, and not erase it.. That would suck!! :-).. Then I added the tracker thing at the bottom of each page.. It has some pretty neat statistic information.. Just for my curiosity.. I got a note from David Gillies in Costa Rica.. He wrote a 196 Linux app after reading these pages.. He claims that it should be 14% faster, based on the testing he's done.. I have a Linux drive on my machine, that I can boot into.. In the next couple days, I'm going to try to find some time to shut down WinXP, boot into Linux, and run his app for a couple hours.. I told him that I really couldn't run it with any seriousness, but I'd like to try it out.. My girlfriend would probably have a very hard time working in Linux, and since she and I share this machine, I have to leave it running in XP.. I'll get some "results" up on the.. page when I have them.. He also gave me permission to post the source code, if anyone wants to see it.. I'll have to figure out where it would fit in, or maybe I'll have to write a special page for his application.. Getting Mr.. Gillies application made me think that I now have quite a few variations of a 196 program.. I have John Walker's original, one from Jason Doucette, 4 different versions from Jack Ryan, 3 from Istvan, and now 2 from David Gillies.. Maybe I need to start a "196 APPLICATION MUSEUM".. I hope no one minds updating their bookmarks.. (If anyone has any!!! :-O ) The geocities page is not going to be updated any more.. 3/10/02.. There are 2 iterations that contain a 29 Million digit number.. The first one is 70,067,270.. 3/8/02.. 8:26am Eastern Time, USA.. Iteration.. Calculations Performed.. 69,513,622.. 28,771,338.. 999,999,957,083,118.. 69,513,623.. 28,771,339.. 1,000,000,006,225,600.. More than 1 quadrillion calculations!!!!.. 3/7/02.. Quite a few notes and comments tonight.. I got an email from Juergen Dankert in Germany.. He was the one below that called me a "Computer Freak".. He returned from a vacation, to find my message in his inbox.. He replied with the following:.. The official German dictionary ("the Duden") writes under the keyword "freak":.. >"Somebody who feels enthusiastic about something very much.. ".. >In this meaning it matches well anyway?.. >However, I like to be ready write another expression for you to my web page ("Palindrome specialist", "196s guru",.. ?).. >Best of luck four you, dear "Computer Freak".. >.. >Your Juergen Dankert.. Now, this made me laugh!! I would never call myself a "Palindrome Specialist!!! I guess one of the problems with languages, that I have never thought of before, is the fact that not everything translates exactly, from one language to another.. It seems simple to me, that every word in one language would have an equivalent word in another.. My limitation is that I am an American.. I did not grow up learning anything other than English.. Those of you from around the world that speak more than one language, have my admiration!! You are good people for taking the time to learn English.. (How else could you read this site? :-) ) On top of that, I really do enjoy reading email from people around the world and knowing that it is not their primary language.. Istvan, your English is VERY good.. Some of the email I have received from others, has been a "challenge" to understand, but I really enjoy it!!!.. Geocities Site Statistics tell me that there have been over 1,000 visitors to this site, and over 4,000 page views.. I never imagined that there would be that many people visiting this site!!! I don't know if anyone has learned anything other than the fact that I am a "freak" ( :-) I think I'm going to remember Juergen's comments for a long time.. :-) ) but it's nice to know that because of everyone's links, that this site is number 2 on a Google search of "palindrome +196".. And the first link, is Patrick De Geest's site, mentioning this one.. I wish I had more details about where in the world, everyone has come from.. Maybe I'll start keeping a better list of visiting countries.. Simply for my enjoyment.. I expect that sometime later tonight, I will cross 1,000,000,000,000,000 (1 quadrillion) calculations!! I've been watching it very closely, so I can try to determine a time for the crossing, but I don't have any way to "predict" when (iteration*digit)/2 will be 1 +15E.. So I'm saving frequently, and trying to keep a close eye on it.. I'd really like to be able to capture that time!!!.. Speaking of time.. Something I've been thinking about over the past month, and it ties in with the viewer stats, is a question to any of you as readers.. Are any of the pages, like this one, taking too long to load?.. I was on a T-1 line at work, and am on a cable modem here at home, so I never notice page load times.. They are VERY fast.. but, would it be better for anyone, if I "archived" most of this page? Would it better if I broke up any of the other pages? This site is for you as readers.. If it were just for me, I could just keep my notes locally on my hard drive, but I know there are people who check this site regularly, and I want it to be as easy for you as it can be!! If there is anything I can do to speed it up for you,.. let me know!!.. Another thing.. Since I am on a static IP address now, with the cable modem, and it is always on, I may move the site, and start serving it from my own machine.. That would eliminate the Geocities ads that show up.. Also, it might make it faster for those of you who are on other, fast connections.. And there might not be any reason to worry about trying to make the site faster.. If anyone has any ideas, (Jason?) I'd like to hear them.. And of course.. Any ideas for what would make a good domain name for this site?!?.. I think that's it for tonight.. 2/28/02.. There are 2 iterations that have 28,000,000 digits.. The first one is 67,648,377.. 2/24/02.. The 66,666,666th iteration is a number 27,593,723 digits long.. 2/23/02.. , I'm back up and running.. I got the parts from the store yesterday, and have the 196 application running on a P IV 1.. 9 GHz machine with 256m RAM.. It's humming!! Last week, it was averaging 1.. 5823 iterations per second.. Now, it's running at over 2.. 7998 per second.. COOL!!! We should have some rapid progress.. For a while.. 2/21/02.. I got thinking about the time palindrome below.. Last night as I was waiting for it to occur here on the Eastern coast of the US, I started thinking that what is quoted below is wrong.. There will be another Time / Date palindrome that is symmetrical.. December 21, 2112, at 9:12 PM.. Will be 21:12 21.. 12.. 2112.. So there you go.. I have brought all of my stuff home from my old work, and now, I will be running the 196 problem from home.. I ordered a Pentium IV 1.. 9 GHz board and chip.. I'm just waiting for the store to call and tell me that it's arrived.. Hopefully it'll be here in the next couple days!! I can't wait to get it working on this number!! Updates will show up as they happen.. A couple days ago, I saw a referring link to these pages that I hadn't seen before.. So I followed it back to.. this page.. Now, I can't read German, but I opened the page in a GOOGLE translation, so I could understand at least some of what they were saying.. I have to laugh at the phrase "Computer Freak", that the person used to describe me and these pages.. That doesn't seem fair.. I guess it does seem crazy to do this, but I find it interesting enough, that I can live with being called a freak.. I emailed the author of the page, but didn't hear back.. I guess I'll just keep on being a "Computer Freak".. 2/13/02.. A time Palindrome.. As the clock ticks over from 8:01PM on Wednesday, February 20th, 2002, time will (for sixty seconds only) read in perfect symmetry.. To be more precise: 20:02, 20/02, 2002.. It is an event which has only ever happened once before, and is something which will never be repeated.. The last occasion that time read in such a symmetrical pattern was long before the days of the digital watch (or the 24-hour clock): 10:01AM, on January 10, 1001.. And because the clock only goes up to 23.. 59, it is something that will never happen again.. I'm going to send this to Patrick De Geest, just for fun.. 2/11/02.. The 27 Million dataset finished last week, but I've been busy, and didn't have time to update this page.. There were 4 iterations that contained a 27,000,000 digit number.. Remember, you can see the.. pages for details.. In the next couple weeks, I am going to be changing jobs.. I intend to continue this search, but I won't have access to all the machines that I have now.. I'll have to focus on one thing at a time, using the machines I have at home, which is an AMD 333Mhz and a 133Mhz.. (Unless I can find something at the new company.. :-O ) My girlfriend wants a new machine at home, so maybe I'll break down, and buy a 1.. 8 or something like that.. But, faster or slower, processing will continue, and these pages.. SHOULD.. continue to be updated!! Wish me luck.. 1/30/02.. Still no solution for the 196.. changed digit.. testing.. It's added 10.. 2 million iterations and 4.. 1 million digits, without forming a palindrome.. I think I am going to turn it off.. I want to use the machine for some other things.. I'll save the file, and maybe continue on at another time.. But, I don't see the "added value" by continuing any farther right now.. I learned that it'll take far longer than I expected, so at least that's something.. I can only assume that the 26 million file would take FAR, FAR longer to solve than the 1 million file.. Maybe I'll change the LSB of the 1 million data set later and try it again.. The current run of 196, is supposed to finish 27 million on Feb 6.. It is down to completing 1.. 6218 iterations per second, and adding 0.. 6716 digits to the total per second.. It gets slower and slower.. I've got to find a faster machine!! :-).. 1/28/02.. testing for 196 is over 8.. 5 million iterations added, and still has not solved into a palindrome.. 1/24/02.. testing for 196 has reached 8,681,531 iterations and 3,593,280 digits.. It still has not found a palindromic solution! This surprises me.. It has gone through an additional 6,265,695 iterations and added 2,593,280 digits, since I changed the first number from a 1 to a 2.. I'm thinking that it must be because the original number started with 1 million digits, that it's gonna solve eventually, but it will take a lot longer than I thought.. Again, I think I wasn't taking into account the sheer size of the original number.. Should I keep it running? I don't know.. I think I will, until I want to use that machine for something else.. 1/21/02.. 26 Million solved on Saturday.. There are 4 iterations that have a 26,000,000 digit number.. On another note, I started testing changed save states, like I said below.. I changed the first digit of the 1 million data set for 196 from a number 1 to a number 2 and started the program.. It's now done a bit over 4.. 6 million iterations, and has added almost 2 million digits, but it has not formed a new palindrome.. I'm not surprised at this, but on the other hand, this isn't what I would have expected.. I figured it would take a while, but I don't think I expected it to take 5 million iterations!! I'm going to keep running it for another couple days, and see what happens.. 01/17/02.. I think the cause of the error last week was due to network problems.. First, I must explain that I don't actually normally run the applications from local hard drives.. I have them stored along with the data files, on a networked drive, so that I can access any of the files from any computer that I'm using.. I've noticed this week, that the network has been going down A LOT.. I have indeed had a couple of error messages this week, where the programs could not access the drive to save.. I'm going to assume that what must have happened last week, was that in the middle of saving or reading the file, that the network connection got whacked, which in turn corrupted the data file.. What I have done for right now, is located the data and program files on the independent local drives, so that this shouldn't be a problem again.. I'm gonna continue like this for a little while, until I think the network is stable again.. The responsibility for the network here where I work has coincidentally been shifted from one company to another, within the last two weeks, and I think they are doing some upgrades at the same time.. I'm sure that it will stabilize out in the near future, and I can go back to doing things the "easy" way.. Istvan asked me to play around with one of the saved files, and change a digit in the file, to see how fast it would migrate to a solved solution.. Would it take a couple iterations and only a few seconds? Or would it take another 100,000 iterations and a couple days? We don't know.. I am thinking that it should only take a relatively few number of iterations, to find a solution.. The chances of stumbling upon a separate branch of numbers that has no solution, by changing one random number in the data file are even smaller than the odds of 196 solving out! And since the vast majority of numbers solve into palindromes in a very small number of iterations, I would expect that this would also solve fairly quickly.. Even though I'm guessing that it will take several hundred or thousand iterations, simply because of the number of digits.. But, I could be totally wrong!! This sounds like a very interesting idea, and I will most certainly try it out in the next couple days.. The other comment he made, was to maybe run "verification checks" on the existing data files, to ensure that they are still accurate.. If I rerun the data file for say 19-20 million on a separate machine, and the result was the same, I could believe that there were no processing errors in the answer.. My thoughts here, are that I will play around with the files first, changing a bit here or there, first, last, middle, etc.. Then, if the data shows that it will only take a small number of iterations to solve into a palindrome, then I can rerun the data for 25-26 and if it is correct, I will be able to safely assume that the ones prior to that are correct.. This sounds like a very worth while thing to do!! If nothing else, it will make it easier to prove a result, if I do these checks at certain times, should I ever see that word "SOLVED" on my screen again.. 01/15/02.. You can imagine my excitement when I looked at the program Friday afternoon, (01/11/02 after I'd made the update for this page) and saw the following printed on the screen:.. Solved.. Initial value: 196.. Iteration: 62255820.. Number of digits: 25768054.. I stood there for a second, and couldn't get a grasp on what I was seeing!! I went outside to get a cigarette, and to think for a moment.. I came back inside, and opened the file.. I still didn't believe that the file was correct.. I looked at the first dozen digits, then went to look at the last dozen, to see if they were indeed the same.. They were!! I started randomly picking out sections of the file, and searching for them in the end of the file.. If the Most Significant Digits match the Least Significant Digits, then everything should be right in the middle right?!? Everything matched up.. Five minutes after the last one, I needed another cigarette!! Imagine how excited I was!!.. While I was smoking, I thought I should hold off on the grand announcement, and verify my findings.. (I'd hate for someone else to find out I had made a mistake!!) I decided that I would use my latest backup, and would run it on all of the machines over the weekend, so that when I came into work on Monday, they would all say that it was solved, or they would say that there was an error.. I backed up the data files on three separate drives on the network, so that I wouldn't lose the answer.. Then I found the latest backup that I had.. I backup the file about every other day, so that if the program messes up, or the files get messed up, I only lose a few hours worth, not the entire million since the last save point.. It turned out that I had a file from the morning of the 10th.. So I stopped all other work that I had in progress, turned all of the machines on to 196, turned off the lights, and went home.. Well, I came into work this morning, and with an excitement that I almost couldn't control, turned on the first of the five monitors.. Something had gone wrong last week.. 196 had NOT solved out.. All of the computers had moved up to iteration number 62,255,820, and moved on.. You can see above, that the search still continues.. I was VERY disappointed!! This afternoon, still feeling let down, by the "failure", I opened the data file that had "solved" and started poking around inside it for a few minutes.. You have to remember that this is a text file of over 25,000,000 digits, so when I am looking around in there, it's pretty hard to look at the whole thing in any logical manner.. I started randomly bouncing around in the file.. Just looking for anything that stood out.. Then, right about the middle of the file, I saw it.. The other thing to think about in this text file, is that with THAT many digits, it.. LOOKS.. random.. You can scroll the screen using "page down" for 3 minutes, and just watch the numbers scroll by, and it just looks like a bunch of numbers that have no meaning.. (I've never had the patience to scroll on the line level.. :-0 ) So when you see an entire dozen screens of 00000000000000000000000, it catches your attention!! Right there in the middle of the file, is a string of zeros.. I didn't count them, but there are a bunch of them.. (I'm going to guess that it's in the hundreds of thousands range) All of the digits before the zeros, match all of the digits after the zeros.. (Except reversed of course.. ) I don't know what happened.. I've restarted again, back on the same machine, and am hoping to be able to duplicate the problem.. But I doubt it will.. I'll know tomorrow morning.. I don't know what else to do.. So I've also restarted counting up, and maybe, just maybe, the next time, the program spits out a solved message, it really will be a valid solution!!!.. 01/02/02.. I've been away from work for about 10 days, so I haven't updated the pages or numbers.. I hope that everyone had a wonderful holiday period and a most happy New Year! I've got a couple updates I need to make, so I've been bouncing around the pages for a while, correcting this and that.. Hopefully I got them all correct!.. There are four iterations that result in a 25 million digit number.. The first one is 60,398,130.. I got to this number on Dec 28th.. The total resulting calculation was 7.. 54977E+14.. I think I may add the information for calculations for all the data sets, somewhere on the site, but I don't know where it would be appropriate.. Maybe I'll create a "data" type page, similar to the Trivia page that I wrote.. I'll have to think about it.. I also made some advances on 879, 1997, and 7059.. You can still keep up with those numbers on the ".. Other Seed Numbers.. " page.. I got an email from Mr.. Vincent Prosper in France.. He and Sebastien Veigneau have papers that I've read which can be found.. here.. He pointed out a couple things in my writings that are good and bad.. He pointed out another error in John Walker's pages that I had missed.. (Again, he wrote something I didn't question, but accepted.. ) In the section where John is talking about what a palindrome is, he makes the statement:.. In order for addition of a digits-reversed number to yield a palindrome, there must be no carries in the addition and hence each pair of digits must sum to 9 or less.. I took this at face value, and have repeated the idea, based on it made sense, and if John Walker said so, it MUST be true!! :-(.. Mr.. Prosper points out the example of number 29.. Again, I have made a fairly large mistake.. What I am happy about is that all of you are correcting me one piece at a time, and the site is becoming more and more accurate.. There was some other comments that Mr.. Prosper made, that I have to think about a bit, before I fully understand them, but I'll write somewhere when I understand them.. (Or If I can't figure it out, I'll write them, and someone else can HELP me understand them!!).. Again, HAPPY NEW YEAR TO ALL!!..

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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: NEWS ARCHIVE FROM 2001.. 12/12/01.. Iteration 57,982,436 is the only one that produces a 24 million digit number.. Also, I thought it might be interesting to keep track of total calculations, as Istvan had done below, so I started tracking that in my spreadsheet.. For 24,000,000 the answer is 6.. 95789E+14 (almost 700 trillion).. 12/06/01.. I got a note in my mailbox today from John Walker.. I thought he might be interested to know what the rest of us had done, since had stopped his search, so I sent him a note yesterday, pointing out that I was keeping his search alive, and that he might be interested in looking at these pages.. He was, and says that he enjoyed reading the site.. It's kind of strange thinking that the man who "started" all of this, was reading what I've written here.. I mean everyone who has a site on the web about this, references John's pages.. I was literally taught about palindromes, by reading his pages.. Now, to think he was reading my pages! I feel flattered.. His "note of approval" will probably inspire me to keep going far beyond even where I would have quit.. (Where ever THAT might be in the future! Not soon I assure you!).. 12/03/01.. Still moving forward day after day.. Maybe today is the day? Maybe.. I've been playing around with the data files, and looking at the numbers.. The huge, mind numbingly large numbers.. I still am fascinated at the numbers that are as large as the "results" that I have.. As a result, I've been kind of "goofing off" with some of them.. Maybe you want to look at the newest page to this site.. 11/26/01.. 23,000,000 digits, and still no palindrome in sight.. 11/20/01.. I'm.. still.. happy about yesterdays discovery!!!.. I was goofing around with all of the files that I'm accumulating, and just so that everyone knows.. 196, 1997 and 879.. have not.. converged on the same number by the 9 million digit mark.. They are all still independent numbers.. I'm sure that no one has tested this theory yet, so I did.. To be frank, I was kind of hoping that they would have converged somewhere along the way, but as of 9 million, they're still independent chains.. I know that's what I expected, but I was still hoping.. Also, here's a note I got from Istvan.. (Istvan, I hope it's O.. , to copy this.. ) I just had to share it with anyone else reading these pages.. Hello Wade,.. Just for fun I wanted to know, how many digits were processed.. So starting from three (196) digits and reaching 22489774 digits is one of the legs of a right-angled triangle, the other is 54332039 unit long, the iterations.. Approximately this triangle's area gives the number of processed digits.. It's about 611 trillion digits so far, 6*10^14.. About five hundred times as much as the first milestone, the million digits.. Istvan.. What else is there to say about this.. 11/19/01.. THEY MATCH!!!!!!!!!! I just got to look at the numbers from my original data file from Jason's application, and from Istvan's new 14,000,008 digit number that had started at 0.. :-) They are the same number!! There has never really been any doubt in my mind that they would be the same number, but now, I know.. Now, it is confirmed.. Now, I am almost beside myself with happiness!!!! We have not wasted all this time.. Both applications came up with the same number on the same iteration count.. What I did, was set the auto-save to stop at 13,999,975.. That way, I could watch and see what happens.. Then, while I watched, I started the program again, and let it tick away the last couple iterations.. There is a 14,000,008 digit number at the 33,824,792 /.. 793 and.. 794th iteration.. It is the second one that I wanted.. Jason's program had spit out a data file with 33,824,793 iterations.. I looked at this iteration, and all is well!!! WHAT A RELIEF!! I would have been VERY sorry, if there had been a problem.. Now, I can dedicate that machine to running 1997 full time.. Or someone could write a program for me to search for seed numbers.. Thanks again to Jason for his original support and program, and thanks to Istvan, for allowing me to continue this search!! I hope you guys are as excited about this milestone, as I am!!.. 11/12/01.. 8:56AM - 22 Million digits takes 53,148,015 iterations!! Remember.. You saw it here first.. Along the same line, 1997 has passed 25 million iterations and 10 million digits.. 879 is almost 20 million iterations and just over 8 million digits.. 11/06/01.. In another couple days, the second machine will have finished  ...   Updates are on the ".. 10/11/01.. I had written Jason, to ask if he had his old data files, so we could find the date stamps on them, to update the MILESTONES page.. Luck was with us, and he did.. So now, I've got the most accurate completion dates on the records, that we could come up with!! No more guessing!! I'm quite pleased.. 10/10/01.. I've tried to incorporate most of the comments Jason made to me the other day.. The reason I quit messing with web pages a couple years ago, is that I realized, how much work has to be done to one, to keep it current!! Now, I'm trying to find time, to keep this one relatively accurate.. As things get explained to me, and I figure them out on my own, it's difficult to go back and rework the pages.. That's why the format of the page is so simple.. I don't want to make more work for myself than I have to.. I write all of the pages is a text editor, writing the tags by hand.. (That's why some of the links were broken.. I wasn't careful enough!!) I don't know how to do really fancy stuff, and don't want to take the time to figure it out.. So if you find something that isn't right, let me know, and I'll correct it case by case, as I can.. Most of the pages, only needed minor changes.. Some, I've deleted entire sections, because, after Jason explained some things to me, I really couldn't think of any better way to write it, so I deleted the "misinformation".. I am debating seriously about removing the software comparisons page altogether.. I don't know if it's added value to the site or not.. The last thing I want, is to give the impression that I have a favorite application by any author.. My favorite is which ever app I'm running at the moment to continue.. Originally, I put up the comparison page, so that if someone were trying to write a new program, or if Jason, Jack or Istvan were re-writing their apps, they could have some benchmarks to aim for, and maybe some feed back from someone who has tried more than one way to get to the same result.. Don't be too surprised to see the entire section missing some afternoon.. 10/08/01.. Well, the network connection of the computer was broken by some unknown party, early this morning, so I lost about 12 hours of processing on 196, as a result.. :-( The application couldn't save to the networked drive, so it halted.. Thank god for Autosave!! O well.. Better to have lost 12 hours, than the last 4 days!.. Got a long letter from Jason today.. He had lots of comments, that I'll get into the pages as I can.. Most of them were very good.. Some of them were wonderful to my own understanding of these numbers.. 10/01/01.. 19 Million digits has been reached!! It took 45,901,512 iterations.. Now, on to 20 Million.. Excel says it should be finished around the October 13th.. (If the machine can stay dedicated to the task that is.. Jack Ryan has sent me a new version of his app.. And I'm sorry to say Jack, that you went backwards.. The app ran longer than the other night, but you added less iterations.. THAT's not going to work.. 09/30/01.. Jason Doucette is alive and well!! I got a note from him this past weekend, and he had been trying to return my mail, but apparently, it was not getting through.. I don't know what was happening, but it is good to know that all is O.. with him!! He's busy at the moment, and not spending any time on the 196 search, but he thinks he knows a way to speed up the applications even more.. I can't wait till he finds time to streamline the process, and speed things up!! (Assuming that he'll let me run the app!! :-) ).. I have met another gentleman in the US, that is interested in palindromes.. His name is Jack Ryan.. He contacted me last week, after finding this site, and asked me to test his beta version for him.. It was another Windows application, but I was forced to tell him, that his app was not up to speed yet.. It lagged pretty far behind Jason or Istvan's programs.. (Remember, that I can run different applications at the same time, on separate identical machines, to compare them.. ) But it was accurate at the couple iteration and digit settings that I compared it to.. He took my testing notes and comments, and went back to the computer to try to speed things up.. I hope he succeeds!!..

    Original link path: /archive_2001.html
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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: By now, I've drilled it into your head that there are more numbers than 196 that are called Lychrel Numbers.. There are also other people as crazy, addicted, motivated, persistent and interested as I am, who wonder about these numbers, and have taken it upon themselves to follow the same "brute force" method for finding a palindrome as I have.. This page was developed to credit those other brave souls who are burning CPU cycles on other numbers.. NOTE:.. Unlike my.. 196 Milestones.. , the column "Date Result Reported" on THIS page is typically the date that I received the email announcing the milestone.. It may or may not be the actual date the the person achieved the result.. Please understand that sometimes someone will send me something, and I may not know when their file was completed, but I should always know when I got the email.. I try to use the actual file date, if I know it, but I don't typically write back to ask for that information.. If you need the specific date, contact me or the credited person, and we will try to find it out.. The links in the table open the verification data for the specific seed.. As  ...   to get verifiable results in a short manner of time.. The other data points are important to not have too large a gap between last know separation, should we ever discover that two seeds have converged onto the same thread.. The 25 million point and above is just a convenient point for me to compile data and not clutter things TOO badly!!.. What I will take.. , is whatever you send me.. In the cases where I know someone has passed a milestone, but not sent me the data yet, or that they have sent it to me, and I have lost it, the column simply reads: "Data Not Yet Reported".. As I get the data, I will fill in the holes.. Seed Under Test.. Digit Milestone.. Date Result Reported.. Credited Person.. 879.. 1,997.. 7,059.. 9,999.. 10,563.. 10,553.. 10,577.. 10,877.. 99,999.. 999,999.. 9,999,999.. 99,999,999.. 210,000,000.. 150,000,000.. 44,400,000.. 25,000,000.. 34,600,000.. 33,100,000.. 90,000,000.. 44,000,000.. 507,311,639.. 362,373,714.. 107,259,370.. 60,392,862.. 83,582,443.. 79,967,949.. 217,440,699.. 101,452,280.. 60,400,631.. 60,396,593.. 60,395,527.. 60,393,206.. December 27, 2005.. January 16, 2006.. October 13, 2003.. March 15, 2005.. October 2, 2003.. January 21, 2006.. January 18, 2005.. March 18, 2005.. March 3, 2005.. February 24, 2005.. February 19, 2005.. Eric Goldstein.. Matt Stenson.. Vaughn Suite.. Pierre Laurent..

    Original link path: /lychrel_records.html
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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: This site began as information on the number 196 only.. Since then, it has kind of grown to include other Lychrel Numbers.. Here are some of the other seeds that have been identified.. The first search that produced Lychrel Numbers was work done by.. Jason Doucette.. of Canada, and.. Ian Peters.. of England.. Although neither of them were looking specifically for Lychrel Numbers, the work that they were doing led to the discovery of these numbers in an indirect way.. I don't know if either one of them even created a list, but I do know that neither person ever published a list of the numbers they found.. Note:.. Jason has emailed me, questioning whether he should be given any credit for the above paragraph.. Part of his note read like this:.. Although I did calculate which numbers did not solve out while I was trying to find the ones that took the longest to solve out, I did not compile or save this data.. In other words - Although I did calculate specific Lychrel numbers (such as 196, 295, 887, etc), I did not calculate specific Lychrel threads (in which the copies are removed, such as 196, and NOT 295, then 887, etc) - since I did not save the data, I couldn't possibly have compiled it.. In my opinion, he was still one of the first two people that I can see who did any work that would have identified Lychrel Numbers.. A save function in his program would have compiled a list of numbers that he had "marked as infinite" (quoted from his site).. Each person can decide for themselves, (Just as I don't agree that 9,999 qualifies as a Lychrel Number, but others might disagree.. ) but I still believe my above statement is true in spirit.. End Note.. Ian Peters states on his site that there are 1,895 Lychrel Numbers between 0-9,999,999.. Jason doesn't give any reference to how many he found.. On March 29, 2002 Ben Despres of the USA sent me a list of numbers between 0 and 99,999,999.. As a result, it is difficult for me to decide who should get credit as the discoverer of the numbers between 0 and 9,999,999.. I have data that says Ian should be credited, but he has not responded to a few emails I have sent him asking for his list.. I trust that he did discover the numbers, but I have no "proof".. On the other hand, I have the lists that Ben sent.. I guess to be fair to my instincts, I am going to trust that Ian Peters discovered the first 1,895 Lychrel Numbers, and that they are the same ones Ben found.. The dates that he discovered them is unclear to me.. But in my mind, I am going to credit him with the discovery.. If anyone disagrees, let me know, and I'll reconsider.. On the other hand, I can say with fair certainty, that Ben Despres deserves the credit for the discovery of all of the Seed Numbers between 10,000,000 and 99,999,999,999.. As far as how many of them are there, the following table shows the number of discovered Seed Numbers for a given number range:.. Number Range.. Date Complete.. Discoverer.. App Coder.. Seeds Found.. 0 - 99.. (2 Digits).. 100 - 999.. (3 Digits).. 1,000 - 9,999.. (4 Digits).. 10,000 - 99,999.. (5 Digits).. 69.. 100,000 - 999,999.. (6 Digits).. 99.. 1,000,000 - 9,999,999.. (7 Digits).. 1,728.. 10,000,000 - 99,999,999.. (8 Digits).. May 29, 2002.. 1,651.. 100,000,000 - 999,999,999.. (9 Digits).. June 25, 2002.. 28,162.. 1,000,000,000 - 9,999,999,999.. (10 Digits).. January 5, 2003.. 25,780.. 10,000,000,000 - 99,999,999,999.. (11 Digits).. January 7, 2003.. 374,431.. 100,000,000,000 - 999,999,999,999.. (12 Digits).. Wade VanLandingham.. 354,715.. 1,000,000,000,000 - 9,999,999,999,999.. (13 Digits).. January 25, 2003.. 4,451,746.. 10,000,000,000,000 - 99,999,999,999,999.. (14 Digits).. March 31, 2003.. 4,455,551.. 100,000,000,000,000 - 999,999,999,999,999.. (15 Digits).. February 15, 2005.. 49,436,290.. 1,000,000,000,000,000 - 9,999,999,999,999,999.. (16 Digits).. February 2005.. 52,964,177.. 10,000,000,000,000,000 - 99,999,999,999,999,999.. (17 Digits).. July 2010.. 529,181,042.. 100,000,000,000,000,000 - 999,999,999,999,999,999.. December 2011.. 606,337,405.. I've been informed that some people feel that Ian Peters should be credited with the seeds up to and including all the 10 digit sets, based on the last section of.. Ian's Page.. I don't disagree that it certainly appears that Ian did the work before Ben, but I have NOTHING from Ian to provide enough dates or data to feel like he is being "cheated" for his work.. If Ian decides to write me and give me some dates, I'll reconsider the table above.. I just wanted to make note of it here, for clarity that I have seen  ...   always refer to the.. Definitions.. For word usage, the Definitions page will always be more up to date than any other page on the site.. SOME INTERESTING OBSERVATIONS ABOUT THE ABOVE TABLE BY BEN AND WADE>>>>>>>>>.. From: Ben To: Wade.. >> I don't know if you looked at the number of Lychrels in.. >> a given number range, but it looks like this:.. Hmm, no, I hadn't actually broken it down like that and considered it.. Comparing against the hypothesis of Lychrels having a "random" distribution, we would expect to see nine times as many for N+1 digits as for N digits (since nine times as many numbers exist in that larger range).. If anything, I would expect to see *less* than nine times as many, since at least *some* should converge with earlier series.. Yet, we seem to have somewhere around 17 times as many, slightly less than 9*2 times more per order of magnitude.. Obviously that trend cannot last, since at some point the number of Lychrels would overtake the number of integers (a fairly rigid upper limit ).. >>I don't know how many iterations you have taken these to,.. >>but it seems to me that the larger the starting number is,.. >>the longer it should take to form a palindrome.. First, I need to explain that I've used the AI technique of "iterative deepening", where I consider "number of digits" as the measure of depth.. So, because of that, I can more quickly check a set of known possible Lychrels to a greater depth (For example, the ones I sent you I ran to 500 and took two weeks, but checked to 5000 overnight).. I first check them to 11 digits (which weeds out numbers that very quickly reach a palindrome), then to 40 digits (which eliminates all but a very small number of stragglers), then to 500 digits.. Between 40 and 500, fewer than 1% dropped out as Lychrels.. Between 500 and 5000, not a single one did (and, as I mentioned for the 1E8 data, I ran those *much* further and not a single one dropped out from 500 to whatever-i-ran-them-to (100,000 digits?)).. So, this seems to imply rather strongly that the numbers I sent you, while not "proven" as Lychrels, will not fail as Lychrels for any digit length limit that we can reasonably test.. I fully expect that *some* will eventually prove non-Lychrels, but a handful at most (assuming, of course, that Lychrels exist at all.. It would certainly make us stop and think for a minute if 196 suddenly reached a palindrome, eh?.. From: Wade To: Ben.. Hey Ben.. I was thinking about this, and wanted your thoughts.. I don't know if you looked at the number of Lychrels in a given number range, but it looks like this:.. 0 - 100 = 0.. 100 - 1,000 =2.. 1,000 - 10,000 =3.. 10,000 - 100,000 =69.. 100,000 - 1,000,000 =99.. 10,000,000 - 100,000,000 =1,728.. 100,000,000 - 1,000,000,000 = 29,813.. A quick thought that I have had about the fact that there are so many more numbers for a higher range than a lower one was to wonder if they too will form out, but it will take a higher average number of iterations.. (Is this the same as Jason's work?!?).. For example, if between 0 and 10,000, it takes an average of say, 5 iterations, to form a palindrome, and between 10,000 and 1,000,000 it takes an average of 60 iterations, (I'm just making up the numbers here) wouldn't it be logical that 100,000,000 to 1,000,000,000 would take say, 1,000 iterations or even 10,000,000?.. For that matter, what *is* the average number of iterations that it takes to form a palindrome for the range 0-10,000 or 100,000,000 to 1,000,000,000? (There's ANOTHER program you can try to find time to write and I'll find a machine to run!!) :-).. I don't know how many iterations you have taken these to, but it seems to me that the larger the starting number is, the longer it should take to form a palindrome.. Either that, or as seems to be indicated on the chart and list that you provided, they will become more and more common, until eventually every number will be a Lychrel Number.. I don't know if you ever read that I changed the MSB of the 1 million data set, and ran it for 10 million iterations (ending archive entry 1/30/02), without a palindrome forming.. I either hit a Lychrel Number by accident, or because they were more frequent, or because it required a far higher number of iterations to solve.. Any opinions?..

    Original link path: /lychrel_seeds.html
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  • Title: 196 and Other Lychrel Numbers
    Descriptive info: From one of Jason's emails:.. I am very curious.. I remember I read somewhere that out of all the numbers under 5,000 or something like that, all numbers fell into one of 3 seeds (I assume one of 196, 879, or 1997 - from the numbers above in this email), and I couldn't believe it.. I would have assumed there would be 100's of them.. It was very intriguing that they all fell into 3.. It makes it seem that there is something very special with those numbers - that all others which do not become palindromes fall into one of them - if they don't, they become palindromes! It could help provide data to prove, once and for all, that 196 will never solve out!.. Personally, I would be sad to find a proof that 196 has no palindromic solution.. I have spent a lot of time on that number, and.. On the other hand, I would love to find something common to the numbers that have no palindromic solution!! That is why I decided that there needs to be a list of them somewhere.. So that people can look at them, poke them with a stick, and just generally give them a bit of thought.. Is there a commonality among them? We know that 196 is the smallest one, what is the largest one we know of? (Infinity doesn't count.. I have already decided that Infinity itself must be a palindrome.. Jason, Istvan and I have talked about these numbers.. The following are some of the notes that I compiled from the discussions, as well as the best probable approach to.. efficiently.. searching for the next larger Lychrel Number.. The first half of the work below can be credited to Jason Doucette.. Istvan is the one who explained it to me, but I believe that he was explaining what Jason had already done for efficiently searching in his Longest Delayed Palindrome work.. I tried to rewrite it simply, so that people like me could understand it, with a little thought.. I think most of the second step is Istvan's work and ideas.. (It's difficult sometimes to remember who contributed what, and ensure that they are recognized!!) I doubt that I added very much to the discussion.. It would be easy enough to begin with a list of every number between two given points.. Say, 0-1,000,000.. The first obvious step to me, would be to go through the list and delete any numbers that are already palindromes.. This will eliminate a bunch of numbers right from the start.. One of the first things we must do is find and eliminate all of the numbers that will follow  ...   the number being examined has an odd number of digits, we should multiply by ten, because of the digit in the middle:.. xxx0xxx.. xxx1xxx.. xxx9xxx.. As you can see, to calculate, for example, how many iterations are needed to check all those 7 digit numbers which differ in the digit pair sums, we should multiply these coefficients:.. 18*19^2*10= 64,980 iterations (instead of 9000000).. 18 is for the outer pair of digits, 10 is for the middle digit, 19^2 is for the two inner pairs.. You can see how much faster this search would be in the long run.. We can even construct a general formula to calculate the number of numbers to be checked:.. 18*19^((n-2) div 2)*10^(n mod 2).. n is the length of the number, and should be larger than 1.. The 10^(n mod 2) part gives 10 for odd lengths, 1 for even lengths.. The following table may help to demonstrate:.. NOTE:.. This is not complete.. It is only an example of what would have to be done to check numbers between 3 and 17 digits.. Total Digits.. Numbers to be Checked.. Ratio.. Every Nth to be Checked.. SUM:.. 900.. 9,000.. 90,000.. 900,000.. 9,000,000.. 900,000,000.. 9,000,000,000.. 90,000,000,000.. 900,000,000,000.. 9,000,000,000,000.. 90,000,000,000,000.. 900,000,000,000,000.. 9,000,000,000,000,000.. 90,000,000,000,000,000.. 99,999,999,999,999,900.. 180.. 342.. 3,420.. 6,498.. 64,980.. 123,462.. 1,234,620.. 2,345,778.. 23,457,780.. 44,569,782.. 445,697,820.. 846,825,858.. 8,468,258,580.. 16,089,691,302.. 160,896,913,020.. 186,819,193,422.. 000000%.. 800000%.. 722000%.. 137180%.. 026064%.. 004952%.. 000941%.. 000179%.. 000187%.. 26.. 138.. 728.. 3,836.. 20,193.. 106,279.. 559,364.. 535,276.. So, if we are only going search numbers between 3 and 17 digits, there are 186,819,193,422 numbers that should be checked in order to only check one consequence of each thread.. Second step: filtering out the independent Seed Numbers.. The next thing to do would be to begin the reverse/add process for each of the remaining numbers and eliminate the upstream numbers for each.. For example, if we were going to 9 digits, 887 / 7,436 / 13,783 / 52,514 / 94,039 / 187,088 / 1,067,869 / 10,755,470 / 18,211,171 / 35,322,452 / 60,744,805 / 111,589,511 / 227,574,622 / 454,050,344 and 897,100,798 would all have to be removed from the list, since they are all in the 196 thread.. At the same time, any numbers that lead to a palindrome, will be deleted.. For example, 89, 187, 968, 1837,.. 8,813,200,023,188 would all be deleted, since 89 will become a palindrome in 24 iterations.. When you are finished, anything left on your list, should be a Seed Number.. I admit that this is not the only way to search for these numbers.. It might not be the easiest to program.. It might not be anywhere near the fastest way to find these numbers.. But it is one way that seems sound..

    Original link path: /identifying_lychrels.html
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