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arXiv · 1806.08697

Fast tabulation of challenge pseudoprimes

Andrew Shallue·Jonathan Webster
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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.

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Andrew Shallue, Jonathan Webster. 2018-06-22. Fast tabulation of challenge pseudoprimes. https://doi.org/10.2140/obs.2019.2.411

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