Displaying similar documents to “The Romanoff theorem revisited”

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.

On pairs of equations in unlike powers of primes and powers of 2

Liqun Hu, Li Yang (2017)

Open Mathematics

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In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.

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).