A prime number is an integer greater than 1 that is divisible onlyby 1 and itself. Mathematicians have been studying primes and theirproperties for over twenty-three centuries. One of the very first resultsconcerning these numbers was presumably proved by Euclid of Alexan-dria, sometime before 300 B.C. In Book IX of his legendary Elements
(see [2]) we find Proposition 20, which states: