The Error Probability of the Miller–Rabin Primality Test

Abstract

In our paper we give theoretical and practical estimations of the error probability in the well-known Miller–Rabin probabilistic primality test. We show that a theoretical probability of error 0.25 for a single round of the test is very overestimated and, in fact, error is diminishing with the growth of length of numbers involved by a rate limited with ln n/\(\sqrt n \).