{"paper":{"title":"On consecutive primitive elements in a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Stephen D. Cohen, Tim Trudgian, Tom\\'as Oliveira e Silva","submitted_at":"2014-10-22T23:34:05Z","abstract_excerpt":"For $q$ an odd prime power with $q>169$ we prove that there are always three consecutive primitive elements in the finite field $\\mathbb{F}_{q}$. Indeed, there are precisely eleven values of $q \\leq 169$ for which this is false. For $4\\leq n \\leq 8$ we present conjectures on the size of $q_{0}(n)$ such that $q>q_{0}(n)$ guarantees the existence of $n$ consecutive primitive elements in $\\mathbb{F}_{q}$, provided that $\\mathbb{F}_{q}$ has characteristic at least~$n$. Finally, we improve the upper bound on $q_{0}(n)$ for all $n\\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6210","kind":"arxiv","version":1},"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"}