Welcome to p196.org!
Every story starts somewhere, and this one started one day while randomly following hyperlinks off of some long forgotten page...
I first read about palindromes in 1998 from John Walker's incredibly intriguing web site: FOURMILAB. As I wandered around his pages a bit, I stumbled upon his excellent description of palindromes, and how one in particular grabbed his attention. His interest turned into a quest for a one million digit number titled: Three Years of Computing.
The following is quoted from Mr. Walker's site:
Pick a number. Reverse its digits and add the resulting number to the original number. If the result isn't a palindrome, repeat the process. Do all numbers in base 10 eventually become palindromes through this process? Nobody knows.
For example, start with 87. Applying this process, we obtain:
87 + 78 = 165
165 + 561 = 726
726 + 627 = 1353
1353 + 3531 = 4884, a palindrome
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.
Whether all numbers eventually become palindromic under this process is unproved, but all numbers less than 10,000 have been tested. Every one becomes a palindrome in a relatively small number of steps (of the 900 3-digit numbers, 90 are palindromes to start with and 735 of the remainder take less than 5 reversals and additions to yield a palindrome). Except, that is, for 196. This number had been carried through 50,000 reversals and additions by P. C. Leyland, yielding a number of more than 26,000 digits without producing a palindrome. Later, P. Anderton continued the process up to 70,928 digits without encountering a palindrome.
NOTE: The statement above about 196 being the only number below 10,000 not to form a palindrome is wrong! I seem to be getting a lot of email on this, and as you can see by reading some of the other pages of this site, there are many other numbers below 10,000 which do not form palindromes.
NOTE: I made mention on 1/02/02 that Vincent Prosper of France corrected me and others, that the notion of not have any carries in the number is not accurate. He pointed out the number 29, which leads to a palindrome of 121. Understand that Mr. Walker made a mistake in his description, although I did not know this at the time.
The story is well known by anyone who has spent any time searching for information on palindromes. What is also well known is that In 1995, Tim Irvin and Larry Simkins carried the reversals and additions another million digits, in About Two Months of Computing.
I used my VERY LIMITED programming knowledge, and attempted to compile Mr. Walker's code, to continue the quest, but failed sadly. It really was a miserable effort!!
But, after reading these pages, I was hooked. I started searching for other pages, to see what had been done with the work. I have no claim at all to be a math wizard, and don't even understand WHY these numbers work like this, but I read all the web information that I can find on palindromes, and in particular, the 196 "problem", which, surprisingly, isn't much. Of the pages that DO exist, some of them are very informative and well done.
I found an excellent site from a gentleman in England named Ian Peters. His page takes a slightly different angle on palindromes, in his Search For The Biggest Numeric Palindrome.
I contacted Mr. Peters to ask if he was working on 196, and if he had a program that I could run on an extra computer that I had in my spare room. It turned out that Mr. Peters was running Linux, and since I had absolutely no knowledge of Linux at the time, it wouldn't have done me any good for him to send me his application. Instead, he directed me to Jason Doucette in Canada.
Mr. Doucette's web site's page on palindromes, held the record for published World Records for the 196 quest as well as the Most Delayed Palindromic Number. I was really impressed by the level he had taken the 196 puzzle to, and by his work on most delayed palindrome. His is a site well worth the time to visit. I got in touch with Mr. Doucette in the spring of 2000, and asked him if he had an application I could run.
Now, don't get me wrong. I had made dozens of attempts to write a C++ application that could do the math of reversing, and adding 196, but I am forced to admit that I am doomed to never being a software writer. It eludes me from here to tomorrow. I must beg from other generous souls. I accept it. But I digress....
Mr. Doucette had recently lost access to the "spare" computer he had been using, and quickly returned my email, forwarding me a copy of both his applications. He told me that he had begun thinking about stopping all work on the 196 quest, since every new digit added to the number made it slightly less likely that a palindrome would be found. He was focusing on the longest delayed palindrome, and I agreed to run the 196 application to take the file he had of 12 1/2 MILLION digits to 13 Million.
I loaded up his application, started the machine turning, and went to bed.
Jason had hard coded his application to automatically stop after each million digits, so he could maintain a solid record of his progress. Some while later, when my machine finished at 13 million, he reset the file for 14 million, and we began again.
In November 2000, right before I was going on vacation for Christmas, the computer that I had his application running on, finished up, and spit out a text file that contained a 14 million digit number which was still not palindromic. It seemed there was no end in sight.
By now, all of my web searching had led to the same few sites over and over again, and as far as I could tell, Jason Doucette had the largest published result for calculations of 196 on the planet. Mr. Doucette's brain had done all of the work, my computers had helped him with some of the work, and I was just happy to be able to be a part any of it. My sincerest gratitude goes to Mr. Jason Doucette for his efforts!!!
When the computer finished the 14,000,000 digits, I emailed Jason, and asked him to again reset the application, to continue to 15 million. Here, my absence from this quest begins...
Mr. Doucette was in the middle of attempting to develop an internet game company Sawtooth Distortion , and it appears that he has been fairly successful, judging by the demos that he, his brother and friends have released on the site. But I have never heard from him again. I have made several attempts to get in touch with him, but have never received any reply. Then, recently, I see that the Sawtooth Distortion website announces that the game is "TEMPORARILY ON HOLD". I don't know what this means, but my thoughts go out to Mr. Doucette, and I sincerely hope that nothing serious has happened to him or his family.
NOTE: Jason is alive and well, as can be seen by his many comments throughout the rest of the site. I leave the above intact for the fact that it shows I was forced to stop the quest for a time.
After repeatedly trying to get in touch with Mr. Doucette, I went back to trying to find a source on the web to download a program and running it. I was hesitant to attempt to reverse engineer Mr. Doucette's software. I have a pretty good idea of the effort that he must have put into the application, based on my hours of failure, and didn't feel right about modding his program without his permission. I seriously doubt that I could have done it, even if I made the attempt. But I didn't. I made several more attempts at writing my own application. Then, one afternoon, I revisited Mr. Doucette's World Records page, and saw a reference to Mr. Istvan Bozsik's web site in Hungary.
Mr. Bozsik, like most other people following the 196 quest, had read about John Walker's three year quest and Tim Irvin's follow on work. He carried on the work independently of Mr. Peters or Mr. Doucette. (I believe the two of them have worked together fairly closely.) On his site The Palindrome 196 Problem , he discusses his progress to get to 6 million digits, where he decided to stop.
I fired off a request to Mr. Bozsik, and he was more than generous, by sending me a copy of his application. He was even more generous, by writing a small conversion program, that allowed me to use the text file that I had from Jason Doucette's program, by reformatting the text, so it could be read by his application. This was almost more than I could have hoped for. This allowed me the obvious advantage of being able to continue from 14,000,000, instead of starting all over and spending another year to get back to the same place.
On August 1, 2001, after 7 months of idleness, I had the chance to follow the quest again.
Mr. Bozsik explains on his web site, that he had already verified his application, by comparing it to the one million digit number on John Walker's site, and the two million digit number, provided by Tim Irvin. He knew that the application's math was correct. That was good news. In order to not waste any time, I went a step farther, and after backing up my 14 million digit number in about 6 locations, I generated a new number with Mr. Doucette's application. I ran it for about 5 minutes, and stopped it at random. I now had a new number that was 73,845 digits long. Then, I set Mr. Bozsik's program to stop at the same iteration that had been reported by Jason's program. A couple of minutes later, I was more than happy to see that it had also generated a number that was 73,845 digits long. This was great news. It meant that there was a pretty good chance everything was going to play nice together. I made the format changes to the two files, by removing the header information, and deleting all of the other formatting in the files. Then, with a bit of anticipation (or maybe it was hesitation. :-) ), I did a file compare on the two files, to search for any differences.
THEY WERE IDENTICAL!!
Now, I had to give them both a lot of credit. I had just proven that both of the programmers knew exactly what they were doing, since both applications, came up with exactly the same result, after a specific number of iterations, using different applications.
A NOTE I GOT FROM JASON: "My program was created in Turbo Pascal 7.0, but the inner loop which does 99.9% of the program's work, was hand coded and hand optimized in assembly language (ASM). So my program was written in Pascal and ASM, just as Istvan's program was written in Delphi (which is actually Pascal) and ASM. So I guess we both made ours in Pascal and ASM! :)"
As a last verification, I let Mr. Bozsik's application run to 14,000,000, on a second machine, simply to make another, final check against an independent source. When I compared the 14,000,008 digit number that I got from Jason's app, with the one from Istvan, They were identical. That was great news!
As can be seen on the Milestones page, I have been non-stop processing ever since. Thousands and thousands of hours of processing. Hundreds of millions of iterations. It goes on and on.
I have gone on to use faster and faster applications which have been written by different people. You can read more about the different apps on the Software Comparisons page, and about my progress in general on the My Blackboard and Blackboard Archive pages.
How long will I continue The Quest? I'm sure that I will continue, for as long as I have access to a computer, or until the question is solved that it will or will not form a palindrome by some other means. Besides.... It's kind of fun.