Large Gaps Between Consecutive Prime Numbers Containing Perfect Powers

Kevin Ford (), D. R. Heath-Brown () and Sergei Konyagin ()
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Kevin Ford: University of Illinois at Urbana-Champaign, Department of Mathematics
D. R. Heath-Brown: Radcliffe Observatory Quarter, Mathematical Institute
Sergei Konyagin: Steklov Mathematical Institute

A chapter in Analytic Number Theory, 2015, pp 83-92 from Springer

Abstract: 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 c k log p log 2 p log 4 p ( log 3 p ) 2 , $$\displaystyle{c_{k}\frac{\log p\log _{2}p\log _{4}p} {(\log _{3}p)^{2}},}$$ where p is the smaller of the two primes.

Keywords: Consecutive Prime Numbers; Perfect Power; Prime Ideal Theorem; Record Stood; Sieve Theory (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22240-0_5

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

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