{"paper":{"title":"Counting primes by sums of frequencies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alejandro Miralles, Dami\\`a Torres","submitted_at":"2016-07-19T11:03:23Z","abstract_excerpt":"We introduce the sequence $(a_n) \\subset (0,1]$ and prove that the asymptotic behaviour of $\\sum_{k=1}^n a_k$ is the same than $\\pi(n)$, the prime-counting function. We also obtain that $\\pi(n) \\sim n a_n$ and we estimate $\\frac{1}{a_n}-\\frac{n}{\\pi(n)}$ showing that $\\lim_{n \\rightarrow \\infty} \\frac{1}{a_n}-\\frac{n}{\\pi(n)}$ is convergent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05517","kind":"arxiv","version":4},"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"}