Long gaps between primes

Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao

Research output: Contribution to journalArticlepeer-review


Let Pn denote the nth prime. We prove that (Formula Presented) for sufficiently large X, improving upon recent bounds of the first, second, third, and fifth authors and of the fourth author. Our main new ingredient is a generalization of a hypergraph covering theorem of Pippenger and Spencer, proven using the Rödl nibble method.

Original languageEnglish (US)
Pages (from-to)65-105
Number of pages41
JournalJournal of the American Mathematical Society
Issue number1
StatePublished - 2018

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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