Displaying similar documents to “A note on primes between consecutive powers”

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.

Landau’s problems on primes

János Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

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At the 1912 Cambridge International Congress Landau listed four basic problems about primes. These problems were characterised in his speech as “unattackable at the present state of science”. The problems were the following : Are there infinitely many primes of the form n 2 + 1 ? ...