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We relate the arithmetic of the Somos-5 sequence to the elliptic curve $E : y^{2} + xy = x^{3} + x^{2} - 2x$ and use properties of Galois representations attached to $E$ to prove the density of primes $p$ dividing some term in the Somos-5 sequence is equal to $\\frac{5087}{10752}$."},"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":"1507.05896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-21T16:24:45Z","cross_cats_sorted":[],"title_canon_sha256":"cff54eed14feb0b666c50bd932703389f2e1b3c00bfcffa1d63f8f169ceb7075","abstract_canon_sha256":"92eb251ac9c63115d8ed3ccb42dbd3d744d45359f567746d311ab9242445d3f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:35.141937Z","signature_b64":"BVV0hZId9CprenRP/hG1Sc3n9R0OIqskmC2iX5di+CzfGzgC63zfzRUSXBh9fnQKCWW4xY8rwap7gcMk4tjGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7e6de44b9fd8c132eeac41ea0f5f7652a4fcf1b171bfae8848c046c42b6bd91","last_reissued_at":"2026-05-18T00:25:35.141292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:35.141292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The density of primes dividing a term in the Somos-5 sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bryant Davis, Jeremy Rouse, Rebecca Kotsonis","submitted_at":"2015-07-21T16:24:45Z","abstract_excerpt":"The Somos-5 sequence is defined by $a_{0} = a_{1} = a_{2} = a_{3} = a_{4} = 1$ and $a_{m} = \\frac{a_{m-1} a_{m-4} + a_{m-2} a_{m-3}}{a_{m-5}}$ for $m \\geq 5$. We relate the arithmetic of the Somos-5 sequence to the elliptic curve $E : y^{2} + xy = x^{3} + x^{2} - 2x$ and use properties of Galois representations attached to $E$ to prove the density of primes $p$ dividing some term in the Somos-5 sequence is equal to $\\frac{5087}{10752}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05896","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.05896","created_at":"2026-05-18T00:25:35.141418+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.05896v1","created_at":"2026-05-18T00:25:35.141418+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05896","created_at":"2026-05-18T00:25:35.141418+00:00"},{"alias_kind":"pith_short_12","alias_value":"47TN4RFZ7WGB","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"47TN4RFZ7WGBGLXK","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"47TN4RFZ","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU","json":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU.json","graph_json":"https://pith.science/api/pith-number/47TN4RFZ7WGBGLXKYQPKB5PXMU/graph.json","events_json":"https://pith.science/api/pith-number/47TN4RFZ7WGBGLXKYQPKB5PXMU/events.json","paper":"https://pith.science/paper/47TN4RFZ"},"agent_actions":{"view_html":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU","download_json":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU.json","view_paper":"https://pith.science/paper/47TN4RFZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.05896&json=true","fetch_graph":"https://pith.science/api/pith-number/47TN4RFZ7WGBGLXKYQPKB5PXMU/graph.json","fetch_events":"https://pith.science/api/pith-number/47TN4RFZ7WGBGLXKYQPKB5PXMU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU/action/storage_attestation","attest_author":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU/action/author_attestation","sign_citation":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU/action/citation_signature","submit_replication":"https://pith.science/pith/47TN4RFZ7WGBGLXKYQPKB5PXMU/action/replication_record"}},"created_at":"2026-05-18T00:25:35.141418+00:00","updated_at":"2026-05-18T00:25:35.141418+00:00"}