# Bounded gaps between primes

Annals of Mathematics

Pages 1121-1174 from Volume 179 (2014), Issue 3 by Yitang Zhang

### Abstract

It is proved that

lim infn→∞(pn+1−pn)<7×107,

where pn is the n-th prime.

Our method is a refinement of the recent work of Goldston, Pintz and Yıldırım 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, but it is adequate for our purpose.

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