Bounded gaps between primes

Abstract

It is proved that
$\liminf_{n\to \infty}\, (p_{n+1} - p_n) < 7 \times 10^7,$
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.

Authors

Yitang Zhang

Department of Mathematics and Statistics
University of New Hampshire
Durham, NH 03824