{"paper":{"title":"Effective short intervals containing primes","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":"2025-08-26T08:12:35Z","abstract_excerpt":"95 years ago Hoheisel proved the existence of primes in the sub-linear interval \\[ \\left[x, x+x^{1-{1\\over 33000}}\\right] \\qquad \\hbox{for $x$ sufficiently large}. \\] This was improved by Heilbronn, proving existence of primes in the interval \\[ \\left[x, x+x^{1-{1\\over 250}}\\right] \\qquad \\hbox{for $x$ sufficiently large}. \\] More recently Baker, Harman, Pintz proved existence of primes in the interval \\[ \\left[x, x+ x^{1-{19\\over 40}}\\right] \\qquad \\hbox{for $x$ sufficiently large}. \\] In the present article I will, to the extent possible, make some of these statements effective. Specifically"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18786","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/2508.18786/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"}