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 $1 \leq m \leq 11$. 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 a reasonable heuristic assumption we can show that it takes at most $B^{2/3+o(1)}$ time.
 Publication:

arXiv eprints
 Pub Date:
 September 2015
 arXiv:
 arXiv:1509.00864
 Bibcode:
 2015arXiv150900864S
 Keywords:

 Mathematics  Number Theory;
 Computer Science  Data Structures and Algorithms;
 Computer Science  Mathematical Software;
 Primary 11Y16;
 11Y16;
 Secondary 11A41;
 68W40;
 68W10
 EPrint:
 doi:10.1090/mcom/3134