Counting Frobenius Pseudoprimes
Number Theory
2025-03-24 v1
Abstract
We generalize the work of Erdos-Pomerance and Fiori-Shallue on counting Frobenius pseudoprimes from the cases of degree one and two respectively to arbitrary degree. More specifically we provide formulas for counting the number of false witnesses for a number with respect to Grantham's Frobenius primality test. We also provide conditional assymptotic lower bounds on the average number of Frobenius pseudoprimes and assymptotic upper bounds on the same.
Keywords
Cite
@article{arxiv.2503.17330,
title = {Counting Frobenius Pseudoprimes},
author = {Andrew Fiori and Hiva Gheisari},
journal= {arXiv preprint arXiv:2503.17330},
year = {2025}
}