Large gaps between consecutive prime numbers

被引：25

作者：

Ford, Kevin ^{[1
]}

Green, Ben ^{[2
]}

Konyagin, Sergei ^{[3
]}

Tao, Terence ^{[4
]}

机构：

[1] Univ Illinois, Urbana, IL USA

[2] Math Inst, 24-29 St Giles, Oxford OX1 3LB, England

[3] VA Steklov Math Inst, Moscow 117333, Russia

[4] Univ Calif Los Angeles, Los Angeles, CA USA

来源：

ANNALS OF MATHEMATICS | 2016年 / 183卷 / 03期

基金：

欧洲研究理事会; 美国国家科学基金会;

关键词：

INVERSE THEOREM;

D O I：

10.4007/annals.2016.183.3.4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：935 / 974

页数：40

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