{"paper":{"title":"Leading Digits of Mersenne Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A.J. Hildebrand, Junxian Li, Matthew Faust, Yuan Zhang, Zhaodong Cai","submitted_at":"2017-12-12T18:35:37Z","abstract_excerpt":"It has long been known that sequences such as the powers of $2$ and the factorials satisfy Benford's Law; that is, leading digits in these sequences occur with frequencies given by $P(d)=\\log_{10}(1+1/d)$, $d=1,2,\\dots,9$. In this paper, we consider the leading digits of the Mersenne numbers $M_n=2^{p_n}-1$, where $p_n$ is the $n$-th prime. In light of known irregularities in the distribution of primes, one might expect that the leading digit sequence of $\\{M_n\\}$ has \\emph{worse} distribution properties than \"smooth\" sequences with similar rates of growth, such as $\\{2^{n\\log n}\\}$. Surprisin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04425","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"}