#### Vol. 2, 2019

 Recent Volumes 2: ANTS XIII 1: ANTS X
 The Open Book Series About the Series Ethics Statement Other MSP Publications
Fast tabulation of challenge pseudoprimes

### Andrew Shallue and Jonathan Webster

Vol. 2 (2019), No. 1, 411–423
##### Abstract

We provide a new algorithm for tabulating composite numbers which are pseudoprimes to both a Fermat test and a Lucas test. Our algorithm is optimized for parameter choices that minimize the occurrence of pseudoprimes, and for pseudoprimes with a fixed number of prime factors. Using this, we have confirmed that there are no PSW-challenge pseudoprimes with two or three prime factors up to ${2}^{80}$. In the case where one is tabulating challenge pseudoprimes with a fixed number of prime factors, we prove our algorithm gives an unconditional asymptotic improvement over previous methods.

pseudoprimes
##### Mathematical Subject Classification 2010
Primary: 11Y11, 11Y16
Secondary: 11A41, 68W40