Bounded gaps between primes

Abstract

It is proved that where pn 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, but it is adequate for our purpose. © 2014 Department of Mathematics, Princeton University.