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Okay, for those who glanced at the article and (like me) couldn't immediately understand what the "breakthrough" was about, here is a simple explanation ripped
by PhantomGremlin 13y ago
Okay, for those who glanced at the article and (like me) couldn't immediately understand what the "breakthrough" was about, here is a simple explanation ripped off from replys there:
What these brilliant mathematicians are trying to do is solve a 3000 year-old problem which is to prove that no matter how high up in the numbers you look you will always find some twin primes. Primes are whole numbers that are exactly divisible only by themselves and one; an example is “13.” Twin primes are primes separated by 2 as in 11 and 13, or 17 and 19.
- gre 13y agoZhang 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".