Displaying similar documents to “Primes of the form [cP].”

Primes in tuples IV: Density of small gaps between consecutive primes

Daniel Alan Goldston, János Pintz, Cem Yalçın Yıldırım (2013)

Acta Arithmetica

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We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η is given explicitly, providing a new quantitative way, in addition to that of the first paper in this series, of measuring the effect of the knowledge on the level of distribution of primes.

Gaps between primes in Beatty sequences

Roger C. Baker, Liangyi Zhao (2016)

Acta Arithmetica

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We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).