4 ms·
Updates on twin prime polymath project
- comex 13y agoTrivial aside - there appears to be a bug with the LaTeX-generated images on that post that produces this somewhat amusing screenshot: http://imgur.com/mAG3dWO http://imgur.com/mAG3dWO It's pretty interesting just how many revisions the constant H has gone through: http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes http://michaelnielsen.org/polymath1/index.php?title=Bounded_... A copy of the original paper: https://www.dropbox.com/s/su3uak2a057yrqv/YitangZhang.pdf https://www.dropbox.com/s/su3uak2a057yrqv/YitangZhang.pdf
- xvedejas 13y agoThe whole bounded gap on prime numbers was particularly interesting to me, since we kind of got to see math happen in real time: http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes http://michaelnielsen.org/polymath1/index.php?title=Bounded_... It's neat to be able to see what improvements were thought of and exactly how long it took these mathematicians to think of them.
- PhantomGremlin 13y agoOkay, 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".