  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.
