Small gaps between primes
成果类型：
Article
署名作者：
Maynard, James
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2015.181.1.7
发表日期：
2015
页码：
383-413
关键词：
摘要：
We introduce a refinement of the GPY sieve method for studying prime k-tuples and small gaps between primes. This refinement avoids previous limitations of the method and allows us to show that for each k, the prime k-tuples conjecture holds for a positive proportion of admissible k-tuples. In particular, lim inf(n)(p(n)+(m) - p(n)) < infinity for every integer m. We also show that lim inf(p(n)+(l) - pn) <= 600 and, if we assume the Elliott-Halberstam conjecture, that lim inf(n) (p(n)+(1) - p(n)) <= 12 and lim inf(n) (p(n)+(2) - p(n)) <= 600.