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\\; Nicholson). \\] \\[ g_n \\leq p_n \\left( \\left(p_n {\\ln n\\over\\ln p_n}\\right)^{1/n} -1 \\right)\\qquad (n>4; \\; Farhadian). \\] While a general proof of any of these conjectures is far out of reach I shall show that all three of these conjectures are unconditionally and explicitly "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.00499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-31T22:33:31Z","cross_cats_sorted":[],"title_canon_sha256":"201b2083921bec70acc98f96aad0d3b051d189508328b6a5ebd2a3e7282528b3","abstract_canon_sha256":"ab147cb41692ea39eb5a19d86ae0b75ab1c77534a8bbc9b47f71ce82ef677416"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:54:28.299458Z","signature_b64":"N95RsZwI4g4PrcxyKIf03kHbWjG1DefFk1Az9x/Orn40azSo2+wPxXdjOWOI0c3jdDsPVMtEBieSCF+Etc53Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7323189d3fd52c93287843b8e09423feebd4f6fd569f12f59efb668c129ea761","last_reissued_at":"2026-07-05T10:54:28.298990Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:54:28.298990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap","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":"2019-03-31T22:33:31Z","abstract_excerpt":"The Firoozbakht, Nicholoson, and Farhadian conjectures can be phrased in terms of increasingly powerful conjectured bounds on the prime gaps $g_n := p_{n+1}-p_n$. \\[ g_n \\leq p_n \\left(p_n^{1/n} -1 \\right)\\qquad\\qquad\\qquad (n \\geq 1; 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