**Author:** Yitang Zhang

**DOI:** https://doi.org/10.4007/annals.2014.179.3.7

**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 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.