{"paper":{"title":"Explicit primality criteria for $h\\cdot2^n\\pm1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dandan Huang, Yingpu Deng","submitted_at":"2013-06-19T08:50:05Z","abstract_excerpt":"We describe an explicit generalized Lucasian test to determine the primality of numbers $h\\cdot2^n\\pm1$ when $h\\nequiv0\\pmod{17}$. This test is by means of fixed seeds which depend only on $h$. In particular when $h=16^m-1$ with $m$ odd, our paper gives a primality test with some fixed seeds depending only on $h$. Comparing the results of W. Bosma(1993) and P. Berrizbeitia and T. G. Berry(2004), our result adds new values of $h$ along with this line. Octic and bioctic reciprocity are used to deduce our result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4456","kind":"arxiv","version":2},"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"}