{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OE5OYFVCUWRSGFDVYFD2OEAKQ3","short_pith_number":"pith:OE5OYFVC","schema_version":"1.0","canonical_sha256":"713aec16a2a5a3231475c147a7100a86cf9f9ac7f00e57b000ba5b62a92ad515","source":{"kind":"arxiv","id":"1808.03846","version":1},"attestation_state":"computed","paper":{"title":"Elliptic Fermat numbers and elliptic divisibility sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandra Walsh, Seoyoung Kim","submitted_at":"2018-08-11T18:14:39Z","abstract_excerpt":"For a pair $(E,P)$ of an elliptic curve $E/\\mathbb{Q}$ and a nontorsion point $P\\in E(\\mathbb{Q})$, the sequence of \\emph{elliptic Fermat numbers} is defined by taking quotients of terms in the corresponding elliptic divisibility sequence $(D_{n})_{n\\in\\mathbb{N}}$ with index powers of two, i.e. $D_{1}$, $D_{2}/D_{1}$, $D_{4}/D_{2}$, etc. Elliptic Fermat numbers share many properties with the classical Fermat numbers, $F_{k}=2^{2^k}+1$. In the present paper, we show that for magnified elliptic Fermat sequences, only finitely many terms are prime. We also define \\emph{generalized elliptic Ferma"},"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":"1808.03846","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-11T18:14:39Z","cross_cats_sorted":[],"title_canon_sha256":"8bb1889d56ec939f6ecb59d86635f7184a06f66144f7dda80222171c8b2cb473","abstract_canon_sha256":"ba24f70849cc1a6613be2c8c046f27c1cb28ac20162034a1e1a045c20ac05058"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:19.558352Z","signature_b64":"bYPI0vz7d+//cNkCJW0U4wKsSejtvHSzRmi1C3nFSwzoMf8P6azrNRoGPWnjxfaFuzIWufiH24GikfCYJD2UDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"713aec16a2a5a3231475c147a7100a86cf9f9ac7f00e57b000ba5b62a92ad515","last_reissued_at":"2026-05-18T00:08:19.557803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:19.557803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic Fermat numbers and elliptic divisibility sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandra Walsh, Seoyoung Kim","submitted_at":"2018-08-11T18:14:39Z","abstract_excerpt":"For a pair $(E,P)$ of an elliptic curve $E/\\mathbb{Q}$ and a nontorsion point $P\\in E(\\mathbb{Q})$, the sequence of \\emph{elliptic Fermat numbers} is defined by taking quotients of terms in the corresponding elliptic divisibility sequence $(D_{n})_{n\\in\\mathbb{N}}$ with index powers of two, i.e. $D_{1}$, $D_{2}/D_{1}$, $D_{4}/D_{2}$, etc. Elliptic Fermat numbers share many properties with the classical Fermat numbers, $F_{k}=2^{2^k}+1$. In the present paper, we show that for magnified elliptic Fermat sequences, only finitely many terms are prime. We also define \\emph{generalized elliptic Ferma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03846","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":"1808.03846","created_at":"2026-05-18T00:08:19.557885+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.03846v1","created_at":"2026-05-18T00:08:19.557885+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03846","created_at":"2026-05-18T00:08:19.557885+00:00"},{"alias_kind":"pith_short_12","alias_value":"OE5OYFVCUWRS","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OE5OYFVCUWRSGFDV","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OE5OYFVC","created_at":"2026-05-18T12:32:43.782077+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/OE5OYFVCUWRSGFDVYFD2OEAKQ3","json":"https://pith.science/pith/OE5OYFVCUWRSGFDVYFD2OEAKQ3.json","graph_json":"https://pith.science/api/pith-number/OE5OYFVCUWRSGFDVYFD2OEAKQ3/graph.json","events_json":"https://pith.science/api/pith-number/OE5OYFVCUWRSGFDVYFD2OEAKQ3/events.json","paper":"https://pith.science/paper/OE5OYFVC"},"agent_actions":{"view_html":"https://pith.science/pith/OE5OYFVCUWRSGFDVYFD2OEAKQ3","download_json":"https://pith.science/pith/OE5OYFVCUWRSGFDVYFD2OEAKQ3.json","view_paper":"https://pith.science/paper/OE5OYFVC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.03846&json=true","fetch_graph":"https://pith.science/api/pith-number/OE5OYFVCUWRSGFDVYFD2OEAKQ3/graph.json","fetch_events":"https://pith.science/api/pith-number/OE5OYFVCUWRSGFDVYFD2OEAKQ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OE5OYFVCUWRSGFDVYFD2OEAKQ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OE5OYFVCUWRSGFDVYFD2OEAKQ3/action/storage_attestation","attest_author":"https://pith.science/pith/OE5OYFVCUWRSGFDVYFD2OEAKQ3/action/author_attestation","sign_citation":"https://pith.science/pith/OE5OYFVCUWRSGFDVYFD2OEAKQ3/action/citation_signature","submit_replication":"https://pith.science/pith/OE5OYFVCUWRSGFDVYFD2OEAKQ3/action/replication_record"}},"created_at":"2026-05-18T00:08:19.557885+00:00","updated_at":"2026-05-18T00:08:19.557885+00:00"}