Papers › Evaluation of the Effectiveness of the Frobenius Primality Test

Evaluation of the Effectiveness of the Frobenius Primality Test

19 Jul 2018arXiv:1807.07249links table onlyarchive 2025-07-28

Sergei Khashin

The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.

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

PaperPDFCode

Code

khash2a/FrobeniusPython mentioned on GitHub report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections