Large gaps between consecutive prime numbers

• 成果类型: Article
• 署名作者: Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.183.3.4
• 发表日期: 2016
• 页码: 935-974
• 关键词: inverse theorem

摘要

Let G(X) denote the size of the largest gap between consecutive primes below X. Answering a question of Erdos, we show that G(X) >= f(X) log X log log X log log log log X/(log log log X)(2) where f(X) is a function tending to infinity with X. Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the existence and distribution of long arithmetic progressions consisting entirely of primes.