Mathematics > Number Theory
[Submitted on 19 Jul 2018 (v1), last revised 13 Nov 2020 (this version, v2)]
Title:Evaluation of the Effectiveness of the Frobenius Primality Test
View PDFAbstract: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.
Submission history
From: Sergei Khashin [view email][v1] Thu, 19 Jul 2018 06:09:04 UTC (13 KB)
[v2] Fri, 13 Nov 2020 03:07:12 UTC (15 KB)
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