On the number of witnesses in the miller-rabin primality test

Abstract

In this paper, we investigate the popular Miller-Rabin primality test and study its effectiveness. The ability of the test to determine prime integers is based on the difference of the number of primality witnesses for composite and prime integers. Let W(n) denote the set of all primality witnesses for odd n. By Rabin's theorem, if n is prime, then each positive integer a