Frobenius Pseudoprimes
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 creations of stronger tests; another is to aid in proving results about large classes of pseudoprimes.
Cite
@article{arxiv.1903.06820,
title = {Frobenius Pseudoprimes},
author = {Jon Grantham},
journal= {arXiv preprint arXiv:1903.06820},
year = {2019}
}