Strong Pseudoprimes to Twelve Prime Bases

Abstract

Let ${\psi }_m$ be the smallest strong pseudoprime to the first $m$ prime bases. This value is known for $1\le m\le 11$. 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 a reasonable heuristic assumption we can show that it takes at most $B^{2/3+o(1)}$ time.

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