Which is currently the best result on bounded gaps between primes?

Question

In his paper "Bounded gaps between primes", Yitang Zhang proves that there are infinitely many pairs of prime numbers which differ by less than $70,000,000$. Which is currently the best improvement on this result? Also, where can I find a list of all the results that have been obtained as regards Zhang's theorem (I guess we have to check the Polymath Project)?

Answer 1

I don't follow the precise status. But I think you can do worse than keeping an eye on the blog of Terence tao http://terrytao.wordpress.com/ and his posts on the Polymath 8b project.

Answer 2

This is the page which keeps the current best bounds, with a timeline of the bounds being linked to.

http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes

I don't know where you can find a comprehensive list of all the results obtained from it but the papers by Pintz and Maynard are the big ones.

Answer 3

Here is the current Polymath page, which puts the bound at $246$. If additional unproven hypotheses are assumed, the gap falls to $6$ or $12$. This is also cited by Wikipedia (search the page for "$246$").