<i>However, I made an error back in 2000: my program ruled out all cases where A and B had a common factor, but actually, as long as C does not also share the factor, it is a valid counterexample.</i><p>Is there a proof for Norvig's less stringent "misinterpretation" that only A and B must share a prime factor? Or is it also unproved? What about C and just one of the others? Is it clear that all these cases are true or false together?
Aside from playing, what is the use of this? To be sure, there's nothing <i>wrong</i> with playing, but I think that intellectual honesty would demand that Norvig acknowledge that this (running a straightforward Python program) is not how the conjecture will eventually be resolved, even if it is false.<p>I suppose somebody has to check the small possibilities, but true numerical search uses algorithms that are either incredibly optimised or run on huge time scales in order to check truly huge numbers. See, for example, the discussion of the Collatz conjecture at <a href="http://sweet.ua.pt/tos/3x+1.html" rel="nofollow">http://sweet.ua.pt/tos/3x+1.html</a> , where experimental verification is currently up to 2^(60) \approx 10^(18).