Lots and Lots of Perrin-Type Primality Tests and Their Pseudo-Primes
Number Theory
2024-04-12 v4 Combinatorics
Abstract
We use Experimental Mathematics and Symbolic Computation (with Maple), to search for lots and lots of Perrin- and Lucas- style primality tests, and try to sort the wheat from the chaff. More impressively, we find quite a few such primality tests for which we can explicitly construct infinite families of pseudo-primes, rather, like in the cases of Perrin pseudo-primes and the famous Carmichael primes, only proving the mere existence of infinitely many of them.
Keywords
Cite
@article{arxiv.2307.16069,
title = {Lots and Lots of Perrin-Type Primality Tests and Their Pseudo-Primes},
author = {Robert Dougherty-Bliss and Doron Zeilberger},
journal= {arXiv preprint arXiv:2307.16069},
year = {2024}
}
Comments
9 pages. Accompanied by a Maple package and numerous output files from <A HREF="https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/perrin.html">this url</A> This version corrects minor typos