On intervals (kn,(k+1)n) containing a prime for all n>1

2012/12/12 by Vladimir Shevelev, Shevelev, Vladimir, Charles R. Greathouse IV +3 · 1 citation
Mathematics · #11A41 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A41

paper · pdf · doi:10.48550/arxiv.1212.2785

12 pages

arxiv created 2012/12/21 · arxiv updated 2012/12/24

Abstract

We study values of k for which the interval (kn,(k+1)n) contains a prime for every n>1. We prove that the list of such integers k includes k=1,2,3,5,9,14, and no others, at least for k<=50,000,000. For every known k of this list, we give a good upper estimate of the smallest N_k(m), such that, if n>=N_k(m), then the interval (kn,(k+1)n) contains at least m primes.

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