

Updates on twin prime polymath project  - nature24
http://terrytao.wordpress.com/2013/08/17/polymath8-writing-the-paper/

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xvedejas
The 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_...](http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes)

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.

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comex
Trivial 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_...](http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes)

A copy of the original paper:

[https://www.dropbox.com/s/su3uak2a057yrqv/YitangZhang.pdf](https://www.dropbox.com/s/su3uak2a057yrqv/YitangZhang.pdf)

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PhantomGremlin
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
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
Tao 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
I 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
Nevermind, I saw "we prove that there are infinitely often primes differing by
16 or less" but missed the caveat "assuming the Elliott-Halberstam
conjecture".

