To complete the story started as a rumour report in ‘Primes gotta stick together‘ and confirmed in ‘Primes really do stick together‘, here we report that *Annals of Mathematics* has posted the PDF of ‘Bounded gaps between primes‘ by Yitang Zhang on its ‘to appear in forthcoming issues’ page. After the seminar on 13th May, Zhang apparently submitted a revised manuscript on 16 May, which was accepted 21 May 2013. So if you’ve been itching for details, here’s your chance (assuming you have access to a subscription to *Annals*).

Here’s the abstract:

It is proved that \[ \liminf_{n\to \infty}\, (p_{n+1} – p_n) < 7 \times 10^7 \text{,}\] where $p_n$ is the $n$-th prime.

Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the small gaps between consecutive primes. A major ingredient of the proof is a stronger version of the Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime divisors only (see Theorem 2), but it is adequate for our purpose.

**The paper: ***Bounded gaps between primes* by Yitang Zhang, in *Annals of Mathematics*.