Evaluation of the Effectiveness of the Frobenius Primality Test

Publication date: 19 July 2018

Abstract: The Frobenius primality test is based on the properties of the Frobenius automorphism of the quadratic extension of the residue field. Although it is probabilistic, we show that is "very rarely wrong". To date there are no counterexamples to this method and there are reasons to believe that they do not exist at all. In this paper, we suggest a version of the Frobenius test and prove that it does not fail for numbers less than

2^{64}

. We also show that a "Frobenius pseudoprime" will necessarily have a prime divisor greater than 3000.

Has companion code repository: https://github.com/khash2a/FrobeniusPython

Mathematics Subject Classification ID

Primality (11Y11)

This page was built for publication: Evaluation of the Effectiveness of the Frobenius Primality Test

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6304389)