Twin Primes and a Primality Test by Indivisibility
Number Theory
2009-12-04 v3
Abstract
In Wilson's Theorem the primality of a number hinges on a congruence. We present a similar test where the primality of a number m hinges, instead, on the indivisibility of 4(m-5)! by m. One implication of this theorem is a necessary and sufficient condition for two numbers to be twin primes, a result reminiscent of Clement's theorem but involving indivisibility. MSC: 11A41 and 11A51.
Cite
@article{arxiv.math/0211034,
title = {Twin Primes and a Primality Test by Indivisibility},
author = {M. Chaves},
journal= {arXiv preprint arXiv:math/0211034},
year = {2009}
}
Comments
There are no changes in this version, except for added journal information: to be published in the July 2011 issue of the Math. Gaz. (4 pages, LATEX, amsfonts)