Abstract

Abstract. The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word “pseudoprime ” in them. Examples include pseudoprimes, Euler pseudoprimes, strong pseudoprimes, Lucas pseudoprimes, strong Lucas pseudoprimes, extra strong Lucas pseudoprimes and Perrin pseudoprimes. Though these tests represent a wealth of ideas, they exist as a hodge-podge of definitions rather than as examples of a more general theory. It is the goal of this paper to present a way of viewing many of these tests as special cases of a general principle, as well as to re-formulate them in the context of finite fields. One aim of the reformulation is to enable the creation of stronger tests; another is to aid in proving results about large classes of pseudoprimes. 1.

Citations

61	There are infinitely many Carmichael numbers - Alford, Granville, et al. - 1994
13	Strong primality tests that are not sufficient - Adams, Shanks - 1982
3	On the difficulty of finding reliable witnesses, Algorithmic Number Theory - Alford, Granville, et al. - 1994
2	Characterizing pseudoprimes for third-order linear recurrence sequences - Adams - 1987