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Welcome to p196.org!

There have been other people that have traveled down this road before. Some of them have apparently made a mistake somewhere along the line, or exaggerated their work all together.

I don't intend to insult those people, or especially to bring attention to them for having made an error somewhere along the way. I simply intend to point out, that with text files of millions of digits long, you need to be EXTREMELY careful about your work, or what you claim. I have checked, rechecked, and re-re-checked my numbers in anyway I could. I've run the same applications on different machines, I've run to the same numbers with different applications to compare the results, and I've taken number values that I have found on the web, and compared against them. I've stopped at random iterations, and digit lengths to do this. I'm as confident in my findings, as I can reasonably be. All I'm trying to do is solve this quest. I seriously doubt I will, but I hope that my work is accurate enough for someone else to duplicate through an independent method, if in fact 196 ever does become palindromic!!

For the first note on this page, I would like to point out, that even I had a major problem with my files. If you read through the Blackboard Archive, you will notice that I had moved to around 34 million, when I discovered that everything I had done since 29,000,001 was wrong. I will not go into it all again on this page, since you can read about it on the Archive, but I had to redo a month's worth of work. No one is perfect. We just have to try to be super careful!!

Istvan Bozsik points out on his site, that there was a posting to rec.puzzles archive where someone solved 196 to 3,924,257 digits, after running 9,480,000 iterations. All current applications show this to be false. When any correct application is run to 9,480,000 iterations, the resulting number is 3,924,578 digits long. The rec.puzzles answer is 321 digits short of the correct answer. Istvan believes that the poster simply interpolated some other work of a lesser value, and was wrong. For my part, after testing different people's software, I would tend to agree with Istvan, not the poster.

There is a page on the web here that claims the same iteration and digit count as the posting above. It is worded exactly the same as the link above, but broken out onto it's own separate page. I'm sure that this is a mirror of the rec.puzzles.archive.

There is yet another site here that claims the same figures. They too claim that "If you start with 196, after 9,480,000 iterations you get a 3,924,257-digit non-palindromic number.". This quote at the bottom of the page is worded differently, so at least the user didn't cut and paste the posting from rec.puzzles.archive. At least they typed it by themselves!! I have thought about contacting vomit13@hotmail.com and correcting them, but I haven't yet. Call me lazy.

There is a posting on Maple User Group Answers that makes me really doubt the poster's credibility. I have to take this entire post with a smile of doubt.

The question posted to the group was basically this: Does 89 ever become a palindrome? Do all integers have palindromes? How does one estimate the number of iterations or size of the answer?

On September 22, 1995 Vinny Romano posts:

It'll take about 4 more iterations....

Has anyone ever seen this before? Do all integers have palindromes?

I have. Actually, this problem appeared in an old Scientific American.

It has been conjectured that all numbers have palindromes, but the number 196 is the only one less than 10000 that has not yet produced a palindrome. Personally, I have ran my program (non-Maple) which finds palindromes (It'll do 98 in less than a second) on 196 for over a week--non-stop. The resulting non-palindromic number was some 24odd million digits long!!!

UPDATE: I had some serious doubts about the accuracy of the post above, but on 2/20/03, I received the following from Mr. Romano:

With respect to http://home.cfl.rr.com/p196/false.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 2.4 million...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.

So to set the record straight... I believe Vinny's email with the changes. I am going to leave the above post intact, because there are copies of it on the web, and I don't want someone to point it out to me later, and say I missed something. Probably the above post is more valid on the Mistakes and False Starts page, not as an example of bad processing, but as an example of "a bad press release"!! :-)

My thanks to Vinny Romano for the correction!!

I have seen many references to other people calculating 196 to "several thousand" or "several million" iterations or digits, but they gave no hard numbers to compare to, so I can only assume that they are quoting other sources, and have not done the work themselves.