Fast tabulation of challenge pseudoprimes

DOI10.2140/OBS.2019.2.411arXiv1806.08697MaRDI QIDQ6165878

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Publication date: 2 August 2023

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1806.08697

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