4 ms·
Fermat's Unfinished Business
- philjackson 15y agoWhen Andrew Wiles's wife finally thought it was over...
- ctdonath 15y agoGreat time to raise something I've long wondered about: N[0] = 2 N[i] = 2^N[i-1] - 1 Does _that_ generate only primes?
- deleted 15y ago[deleted]
- ctdonath 15y agoM(p) = 2^p - 1 M does not produce primes for most values of p. The subset I noted, for what few values we can generate, seems to. Just wondering if anyone had worked on that particular subset.
- tzs 15y agoThat's not yet known. It's not even known if that sequence contains infinitely many primes or not.
- ionfish 15y agoAnother sense in which it's not over is the question of what the weakest system is which will prove FLT. Various people have suggested that it should be provable in PA. Colin McLarty has been working on this and has managed to reduce the requirements substantially. There's a preprint available of a paper to be published in the Bulletin of Symbolic Logic, although he may have progressed further since writing that. http://www.cwru.edu/artsci/phil/Proving_FLT.pdf http://www.cwru.edu/artsci/phil/Proving_FLT.pdf
- fragsworth 15y agoConjecture: For each set of numbers 2^2^n+1, 2^2^2^n+1, 2^2^2^2^n+1, etc., none of these sets contains exclusively prime numbers.