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.
|Journal||Journal of Integer Sequences|
|State||Published - 1 Jan 2013|
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics