Rabin-Miller primality test: composite numbers which pass it

Abstract

The Rabin-Miller primality test is a probabilistic test which can be found in several algebraic computing systems (such as Pari, Maple, ScratchPad) because it is very easy to implement and, with a reasonable amount of computing, indicates whether a number is composite or "probably prime" with a very low probability of error. In this paper, we compute composite numbers which are strong pseudoprimes to several chosen bases. Because these bases are those used by the ScratchPad implementation of the test, we obtain, by a method which differs from a recent one by Jaeschke, composite numbers which are found to be "probably prime" by this test.