Large gaps between primes

Abstract

We show that there exist pairs of consecutive primes less than $x$ whose difference is larger than \[ t(1+o(1))(\log{x})(\log\log{x})(\log\log\log\log{x})(\log\log\log{x})^{-2}\] for any fixed $t$. This answers a well-known question of Erdős.

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Authors

James Maynard

Magdalen College, Oxford, England