On intervals (kn,(k+1)n) containing a prime for all n>1
Number Theory
2012-12-24 v3
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.
Cite
@article{arxiv.1212.2785,
title = {On intervals (kn,(k+1)n) containing a prime for all n>1},
author = {Vladimir Shevelev and Charles R. Greathouse and Peter J. C. Moses},
journal= {arXiv preprint arXiv:1212.2785},
year = {2012}
}
Comments
12 pages