{"paper":{"title":"Vinogradov's three primes theorem with almost twin primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kaisa Matom\\\"aki, Xuancheng Shao","submitted_at":"2015-12-10T11:08:16Z","abstract_excerpt":"In this paper we prove two results concerning Vinogradov's three primes theorem with primes that can be called almost twin primes. First, for any $m$, every sufficiently large odd integer $N$ can be written as a sum of three primes $p_1, p_2$ and $p_3$ such that, for each $i \\in \\{1,2,3\\}$, the interval $[p_i, p_i + H]$ contains at least $m$ primes, for some $H = H(m)$. Second, every sufficiently large integer $N \\equiv 3 \\pmod{6}$ can be written as a sum of three primes $p_1, p_2$ and $p_3$ such that, for each $i \\in \\{1,2,3\\}$, $p_i + 2$ has at most two prime factors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03213","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"}