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

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)?

• A general comment: The Polymath project has essentially ended, and they're just focusing on getting their papers to print. I don't expect much progress beyond 246 from that group (at least until some other discovery catalyzes them to further action). – Charles May 1 '14 at 23:13

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 "$246$").