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Zhang proved that there are infinite "twin primes" separated by 80,000,000 or less. People have been lowering the bound, but it seems like this approach will no
by gre 13y ago
Zhang proved that there are infinite "twin primes" separated by 80,000,000 or less. People have been lowering the bound, but it seems like this approach will not reach the goal of 2 without another breakthrough.
- ksrm 13y agoTao mentions in the post that H=16 has already been proven [1]. [1] http://arxiv.org/abs/math/0508185 http://arxiv.org/abs/math/0508185
- apetresc 13y agoI don't think that's what he's saying. What Goldston et al. have proved is that Zhang's approach can't prove a bound any better than H=16 without major modifications, but it doesn't actually establish the H=16 bound. In principle, if the twin prime conjecture were only true for, say, H=20, that would still be consistent with both results.
- ksrm 13y agoNevermind, I saw "we prove that there are infinitely often primes differing by 16 or less" but missed the caveat "assuming the Elliott-Halberstam conjecture".