Bounded gaps between primes

• 成果类型: Article
• 署名作者: Zhang, Yitang
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.179.3.7
• 发表日期: 2014
• 页码: 1121-1174
• 关键词: arithmetic progressions; large moduli; numbers

摘要

It is proved that lim inf(n ->infinity)(p(n+1)-p(n)) < 7 x 10(7), where p(n) is the n-th prime. Our method is a refinement of the recent work of Goldston, PintzandY1ld1rm 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.