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

Vladimir Shevelev, Charles R. Greathouse, Peter J.C. Moses

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3 Scopus citations


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 1, 2, 3, 5, 9, 14 and no others, at least for k ≤ 100, 000, 000. Moreover, for every known k in this list, we give a good upper bound for the smallest Nk(m), such that if n ≥ Nk(m), then the interval (kn, (k + 1)n) contains at least m primes.

Original languageEnglish
JournalJournal of Integer Sequences
Issue number7
StatePublished - 1 Jan 2013

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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