English

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.

Keywords

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)