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arXiv · 2503.17330

Counting Frobenius Pseudoprimes

Andrew Fiori·Hiva Gheisari
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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 $n$ 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.

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Andrew Fiori, Hiva Gheisari. 2025-03-21. Counting Frobenius Pseudoprimes. https://arxiv.org/abs/2503.17330

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