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Mathematics of Computation

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Strong pseudoprimes to twelve prime bases


Authors: Jonathan Sorenson and Jonathan Webster
Journal: Math. Comp.
MSC (2010): Primary 11Y11, 11Y16; Secondary 11A41, 68W40, 68W10
Published electronically: June 2, 2016
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Abstract: Let $ \psi _m$ be the smallest strong pseudoprime to the first $ m$ prime bases. This value is known for $ 1 \leq m \leq 11$. We extend this by finding $ \psi _{12}$ and $ \psi _{13}$. We also present an algorithm to find all integers $ n\le B$ that are strong pseudoprimes to the first $ m$ prime bases; with reasonable heuristic assumptions we can show that it takes at most $ B^{2/3+o(1)}$ time.


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Additional Information

Jonathan Sorenson
Affiliation: Department of Computer Science and Software Engineering, Butler University, Indianapolis, Indiana 46208
Email: sorenson@butler.edu

Jonathan Webster
Affiliation: Department of Mathematics and Actuarial Science, Butler University, Indianapolis, Indiana 46208
Email: jewebste@butler.edu

DOI: https://doi.org/10.1090/mcom/3134
Received by editor(s): September 2, 2015
Published electronically: June 2, 2016
Additional Notes: This work was supported in part by a grant from the Holcomb Awards Committee.
Article copyright: © Copyright 2016 American Mathematical Society