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 e-prints
- Pub Date:
- September 2015
- DOI:
- 10.48550/arXiv.1509.00864
- 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
- E-Print:
- doi:10.1090/mcom/3134