{"paper":{"title":"Sierpinski's Hypothesis H1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Matt Visser (Victoria University of Wellington)","submitted_at":"2025-12-27T00:01:58Z","abstract_excerpt":"Sierpinski's Hypothesis H1, formulated in 1958, is the conjecture that (provided $n\\geq 2$), when the first $n^2$ counting numbers, $1, 2,3,\\dots n^2$, are arranged in a square, then each row contains at least one prime. This conjecture is particularly interesting in that it subsumes and is stronger than both the Oppermann and Legrendre conjectures. Herein I shall verify Sierpinski's Hypothesis H1 for (at least) the first $n \\leq \\hbox{10 070 368 414} \\approx 10 \\hbox{ billion}$ of these Sierpinski matrices. I shall also demonstrate some partial but more general results. For example: Even for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.22413","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.22413/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}