{"paper":{"title":"A Modification of LLR","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Thomas Morrell","submitted_at":"2013-04-08T19:00:01Z","abstract_excerpt":"The Lucas-Lehmer (LL) primality test for Mersenne numbers is the fastest known primality test. In 1969, Hans Riesel published a modification of LL to test numbers of the form $N = h \\cdot 2^n - 1$, where $h < 2^n$ is an odd integer and $n \\ge 2$ \\cite{Riesel}. This test is now known as the Lucas-Lehmer-Riesel (LLR) primality test. In Algorithm \\ref{PrimalityAlgorithm}, we present a modification of LLR which works for any odd integer $N$. A probabilistic version of our algorithm runs in expected time $\\tilde{O}(\\log^3 N)$, and a deterministic version in expected $\\tilde{O}(\\log^4 N)$. We conclu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2314","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}