{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/evaluation-of-the-effectiveness-of-the","title":"Evaluation of the Effectiveness of the Frobenius Primality Test","arxiv_id":"1807.07249","date":"2018-07-19","proceeding":null,"authors":["Sergei Khashin"],"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.","url_abs":"http://arxiv.org/abs/1807.07249v2","url_pdf":"http://arxiv.org/pdf/1807.07249v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"evaluation-of-the-effectiveness-of-the","repo_url":"https://github.com/khash2a/FrobeniusPython","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}