Twin Primes and a Primality Test by Indivisibility

Details Twin Primes and a Primality Test by Indivisibility Twin Primes and a Primality Test by Indivisibility

2002-11-03

arxiv.org/abs/math/0211034v3

Mathematics

Number Theory

There are no changes in this version, except for added journal information: to be published in the July 2011 issue of the Math

Scientific paper

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.

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