Large gaps between consecutive prime numbers

doi:10.4007/annals.2016.183.3.4

Large gaps between consecutive prime numbers

2016-05-01

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DOI：10.4007/annals.2016.183.3.4

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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.

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INVERSE THEOREM

Large gaps between consecutive prime numbers

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