Lots and Lots of Perrin-Type Primality Tests and Their Pseudo-Primes

By Robert Dougherty-Bliss and Doron Zeilberger

.pdf    .tex   

First Written: July 15, 2023; Previous version (with five additional DB-Z pseudoprimes): Aug. 2, 2023.

Appeared in INTEGERS, v. 23 (2023), #A95.

This version: Oct. 13, 2023 (adding the DB-Kauers even better powerful primality test)

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, proving the mere existence of infinitely many of them.

C programs

See Robert D-B's github site

Maple packages

Sample Input and Output for Perrin.txt

Sample Input and Output for PerrinVV.txt

Articles of Doron Zeilberger

Doron Zeilberger's Home Page

Robert Dougherty-Bliss 's Home Page