Fermat's Unfinished Business

Another 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

When Andrew Wiles's wife finally thought it was over...

Great time to raise something I've long wondered about:

N[0] = 2

N[i] = 2^N[i-1] - 1

Does _that_ generate only primes?

Conjecture:

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.