{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OP53OQORYADWIT3HZDUXO5PCTE","short_pith_number":"pith:OP53OQOR","schema_version":"1.0","canonical_sha256":"73fbb741d1c007644f67c8e97775e2992d05d63cb3767138545523ab7408db15","source":{"kind":"arxiv","id":"1408.4505","version":2},"attestation_state":"computed","paper":{"title":"Large gaps between consecutive prime numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ben Green, Kevin Ford, Sergei Konyagin, Terence Tao","submitted_at":"2014-08-20T01:41:55Z","abstract_excerpt":"Let $G(X)$ denote the size of the largest gap between consecutive primes below $X$. Answering a question of Erdos, we show that $$G(X) \\geq f(X) \\frac{\\log X \\log \\log X \\log \\log \\log \\log X}{(\\log \\log \\log X)^2},$$ where $f(X)$ is a function tending to infinity with $X$. Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the existence and distribution of long arithmetic progressions consisting entirely of primes."},"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":"1408.4505","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-20T01:41:55Z","cross_cats_sorted":[],"title_canon_sha256":"4b96318c31f64093b2de6d369c3f6cd256896a061214b4b2bc1108661861b4c4","abstract_canon_sha256":"6f9c0ed9188e3b7a958c8c51e38bfc6a6167aea831cae52515b5181696faf38b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:03.586928Z","signature_b64":"1q1XwIA1yjz3Z7FFzsKMg2jKHMG/93bpJLCCigWN4DWt0oNpKk9wZodDjDTM9t6iH5/iqYqTr2gRYhwEhkRZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73fbb741d1c007644f67c8e97775e2992d05d63cb3767138545523ab7408db15","last_reissued_at":"2026-05-18T01:11:03.586564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:03.586564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large gaps between consecutive prime numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ben Green, Kevin Ford, Sergei Konyagin, Terence Tao","submitted_at":"2014-08-20T01:41:55Z","abstract_excerpt":"Let $G(X)$ denote the size of the largest gap between consecutive primes below $X$. Answering a question of Erdos, we show that $$G(X) \\geq f(X) \\frac{\\log X \\log \\log X \\log \\log \\log \\log X}{(\\log \\log \\log X)^2},$$ where $f(X)$ is a function tending to infinity with $X$. Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the existence and distribution of long arithmetic progressions consisting entirely of primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4505","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":""},"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":"1408.4505","created_at":"2026-05-18T01:11:03.586623+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.4505v2","created_at":"2026-05-18T01:11:03.586623+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4505","created_at":"2026-05-18T01:11:03.586623+00:00"},{"alias_kind":"pith_short_12","alias_value":"OP53OQORYADW","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OP53OQORYADWIT3H","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OP53OQOR","created_at":"2026-05-18T12:28:41.024544+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/OP53OQORYADWIT3HZDUXO5PCTE","json":"https://pith.science/pith/OP53OQORYADWIT3HZDUXO5PCTE.json","graph_json":"https://pith.science/api/pith-number/OP53OQORYADWIT3HZDUXO5PCTE/graph.json","events_json":"https://pith.science/api/pith-number/OP53OQORYADWIT3HZDUXO5PCTE/events.json","paper":"https://pith.science/paper/OP53OQOR"},"agent_actions":{"view_html":"https://pith.science/pith/OP53OQORYADWIT3HZDUXO5PCTE","download_json":"https://pith.science/pith/OP53OQORYADWIT3HZDUXO5PCTE.json","view_paper":"https://pith.science/paper/OP53OQOR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.4505&json=true","fetch_graph":"https://pith.science/api/pith-number/OP53OQORYADWIT3HZDUXO5PCTE/graph.json","fetch_events":"https://pith.science/api/pith-number/OP53OQORYADWIT3HZDUXO5PCTE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OP53OQORYADWIT3HZDUXO5PCTE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OP53OQORYADWIT3HZDUXO5PCTE/action/storage_attestation","attest_author":"https://pith.science/pith/OP53OQORYADWIT3HZDUXO5PCTE/action/author_attestation","sign_citation":"https://pith.science/pith/OP53OQORYADWIT3HZDUXO5PCTE/action/citation_signature","submit_replication":"https://pith.science/pith/OP53OQORYADWIT3HZDUXO5PCTE/action/replication_record"}},"created_at":"2026-05-18T01:11:03.586623+00:00","updated_at":"2026-05-18T01:11:03.586623+00:00"}