Even More Collatz
You know, the reason we have so much trouble trying to prove The Collatz Conjecture suggests to me that it might not be true.
Buford Lister, personal communication
How many posts can I write based on something as simple as The Collatz Conjecture? Apparently, at least one more. If you are unfamiliar with it, all you have to do is take any positive integer you want and if it is even, divide it by two. If it is odd, multiply it by three and then add one. In 1937, Lothar Collatz, a man who haunts my dreams, conjectured that any positive integer you can think of will meander its way back to one when you apply that rudimentary algorithm. It is a very simply stated problem. As I sit here today, no one knows how to prove the conjecture, and no one has found a counterexample.
People have often asked me if there is a prize for proving The Collatz Conjecture. Until recently, the answer was no; all you could hope for is mathematical immortality. I was surprised to hear that Bakuage, a Japanese web services company, has offered 120,000,000 Yen to anyone who can prove the “truth” of the conjecture. To me, that means that a counterexample will get you the prize of about 1.1 million U.S. dollars.
I know that people worldwide are committing computer power to find any elusive number that defies Collatz. Now that there is money on the table, it wouldn’t surprise me if a counterexample is found relatively soon, that is, if one exists.
There has actually been a prize on offer for solving the Collatz conjecture on the Unsolved Problems website run by Tim Roberts at http://unsolvedproblems.org/ for around 15 years or so, I think. Currently the prize is US$2,000 and a bottle of champagne, although it has fluctuated between around $1000 and $3000 for the last six years or so while I have been an active member of the associated forum. I assume that anyone finding a valid solution to the conjecture might be eligible to claim both Tim’s and Bakuage’s prizes.
Thank you for the information. The other day I heard a mathematician say that the reason we are having so much trouble proving The Collatz Conjecture true is that it is probably not true. That said, any counterexample might be so elusive as to keep my Raspberry Pi busy for decades to come. I appreciate the comment. Once I find a solution (cough, cough), I will be sure to email you before I upload the result.
Thank you again,
RTNM