Large gaps between consecutive prime numbers containing perfect powers

Kevin Ford; D. R. Heath-Brown; Sergei Konyagin

doi:10.1007/978-3-319-22240-0_5

Large gaps between consecutive prime numbers containing perfect powers

Kevin Ford
, D. R. Heath-Brown
, Sergei Konyagin

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

For any positive integer k, we show that infinitely often, perfect kth powers appear inside very long gaps between consecutive prime numbers, that is, gaps of size (formula) where p is the smaller of the two primes.

Original language	English (US)
Title of host publication	Analytic Number Theory
Subtitle of host publication	In Honor of Helmut Maier's 60th Birthday
Publisher	Springer
Pages	83-92
Number of pages	10
ISBN (Electronic)	9783319222400
ISBN (Print)	9783319222394
DOIs	https://doi.org/10.1007/978-3-319-22240-0_5
State	Published - Jan 1 2015

ASJC Scopus subject areas

General Mathematics
General Computer Science

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10.1007/978-3-319-22240-0_5

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author = "Kevin Ford and Heath-Brown, \{D. R.\} and Sergei Konyagin",

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Large gaps between consecutive prime numbers containing perfect powers

Abstract

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