{"paper":{"title":"Primes in the intervals between primes squared","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kolbj{\\o}rn Tunstr{\\o}m","submitted_at":"2014-08-02T21:22:22Z","abstract_excerpt":"The set of short intervals between consecutive primes squared has the pleasant---but seemingly unexploited---property that each interval $s_k:=\\{p_k^2, \\dots,p_{k+1}^2-1\\}$ is fully sieved by the $k$ first primes. Here we take advantage of this essential characteristic and present evidence for the conjecture that $\\pi_k \\sim |s_k|/ \\log p_{k+1}^2$, where $\\pi_k$ is the number of primes in $s_k$; or even stricter, that $y=x^{1/2}$ is both necessary and sufficient for the prime number theorem to be valid in intervals of length $y$. In addition, we propose and substantiate that the prime counting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0420","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"}