Large gaps between consecutive prime numbers

Kevin Ford, Ben Green, Sergei Konyagin, Terence Tao

Research output: Contribution to journalArticlepeer-review


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 in finity 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 exis- tence and distribution of long arithmetic progressions consisting entirely of primes.

Original languageEnglish (US)
Pages (from-to)935-974
Number of pages40
JournalAnnals of Mathematics
Issue number3
StatePublished - May 1 2016

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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