{"paper":{"title":"The strange story of an almost unknown prime number counter: The Rafael Barrett formula","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Rafael Barrett created a prime-counting formula in 1903 that stayed unknown until its 1935 publication.","cross_cats":[],"primary_cat":"math.HO","authors_text":"Eduardo Mizraji","submitted_at":"2025-09-12T22:58:48Z","abstract_excerpt":"In this brief article, we present the formula created by Rafael Barrett in 1903 in a note to Henri Poincar\\'e, which remained unknown for decades. Discovered in the 1930s by a Uruguayan mathematician, this formula was published and analyzed in a journal published in Montevideo in 1935. In this study, we present Barrett's formula and analyze a challenge it could pose."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Barrett's formula created in 1903 is a prime number counter that remained unknown for decades and poses a challenge worth analyzing after its 1935 publication.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The historical facts about the formula's creation, discovery in the 1930s, and 1935 publication are accurate, and the formula is correctly presented without transcription errors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Presents Rafael Barrett's 1903 prime number counting formula and examines a challenge it could pose after its 1935 publication.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Rafael Barrett created a prime-counting formula in 1903 that stayed unknown until its 1935 publication.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ac0790ed36d039d0d8b3580fe25d70acbd20992b37f912db00e6a3dfd651dab9"},"source":{"id":"2509.19324","kind":"arxiv","version":7},"verdict":{"id":"24939843-af2d-44cf-b931-3e4b4c4c624a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T17:36:36.357596Z","strongest_claim":"Barrett's formula created in 1903 is a prime number counter that remained unknown for decades and poses a challenge worth analyzing after its 1935 publication.","one_line_summary":"Presents Rafael Barrett's 1903 prime number counting formula and examines a challenge it could pose after its 1935 publication.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The historical facts about the formula's creation, discovery in the 1930s, and 1935 publication are accurate, and the formula is correctly presented without transcription errors.","pith_extraction_headline":"Rafael Barrett created a prime-counting formula in 1903 that stayed unknown until its 1935 publication."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.19324/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"}