{"data":{"event":{"id":"41eb33e9-5810-4e82-8da8-000988968f06","slug":"gpt6-astra-bounded-prime-gaps","title":"GPT-6 Astra improves short and large prime-gap bounds","short_summary":"On 3 September 2026 OpenAI released GPT-6 Astra with two analytic number-theory results: a proof that infinitely many consecutive primes differ by at most 186, and an improvement to a large-gap bound that had been stuck for more than 80 years.","full_description":"OpenAI’s GPT-6 Astra launch materials present two prime-gap theorems as realized mathematical work by the named release, not as benchmark scores. The short-gap paper proves lim inf (p_{n+1} − p_n) ≤ 186 by establishing DHL[40,2] for an admissible 40-tuple of diameter 186, combining Polymath8a and Stadlmann equidistribution estimates with a larger Selberg-sieve support. Stadlmann independently had 240. A Lean 4 development (openai/PrimeGaps186) formalizes the main theorems conditionally on explicit exponential-sum and numerical-integral axioms, with a Python-FLINT certificate for the numerics. The large-gap result is described in the same announcement as improving a term unchanged for more than 80 years, with posted proofs. These are bounded improvements in analytic number theory, not Millennium Prize problems. Credit stays with Astra because OpenAI attributed the proofs to that named release.\n\nUpdate (2026-09-09): GPT-6 Astra: The next generation in intelligence for work. Meet GPT-6 Astra, OpenAI’s most capable model for business, with advanced reasoning, computer use, and stronger writing and design judgment.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-09-03T00:00:00.000Z","discovery_date":"2026-09-03T00:00:00.000Z","first_published_date":"2026-09-03T00:00:00.000Z","last_reviewed_date":"2026-09-09T00:00:00.000Z","geographic_scope":"International","affected_population":"Analytic number theory research community","base_impact_tier":2,"base_score":"3.00","attribution_multiplier":"0.8500","evidence_multiplier":"0.5000","realization_multiplier":"0.5500","durability_multiplier":"0.7500","current_event_score":"0.525900","confidence_level":"medium","score_explanation":"Improved classical prime-gap bounds are notable mathematics (tier 2), not a Millennium problem. OpenAI attributes the short-gap proof to GPT-6 Astra (0.85). Evidence is a developer launch plus posted papers and a conditional Lean repo (0.40). Realization is a demonstrated theorem with incomplete Lean axioms (0.55). The bound itself is durable if the analysis holds. Follow-up ingest: independent source raised evidence; added a follow-up source.","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-09-03T00:00:00.000Z","created_at":"2026-09-13T21:33:49.339Z","updated_at":"2026-09-17T03:01:01.948Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.1"},"contributions":[{"id":"e5158ade-e905-46aa-b46a-930fd29aff2c","event_id":"41eb33e9-5810-4e82-8da8-000988968f06","model_id":"0f0d18fc-d3f1-4551-9eaf-a13f1f93b1a5","role_description":"Named 3 September 2026 release credited with the short-gap theorem and the large-gap improvement.","attribution_multiplier":"0.8500","credit_share":"1.0000","contribution_score":"0.525900","attribution_rationale":"The short-gap paper states the proof is due to GPT-6 Astra; the launch post presents both gap results as Astra 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primes","excerpt":null,"content_hash":null,"source_reliability_class":"low","is_primary_source":true,"is_independent":false,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"c62c9de2-e072-4563-b99d-347ac8a62d66","event_id":"41eb33e9-5810-4e82-8da8-000988968f06","url":"https://openai.com/index/gpt-6-astra/","canonical_url":"https://openai.com/index/gpt-6-astra/","source_type":"developer_announcement","publisher":"OpenAI","author":null,"publication_date":"2026-09-03T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"GPT-6 Astra: A new generation of intelligence","excerpt":null,"content_hash":null,"source_reliability_class":"low","is_primary_source":true,"is_independent":false,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"b7b22f16-ee98-4bc2-b447-b1e0e888fced","event_id":"41eb33e9-5810-4e82-8da8-000988968f06","url":"https://github.com/openai/PrimeGaps186","canonical_url":"https://github.com/openai/PrimeGaps186","source_type":"other","publisher":"OpenAI","author":null,"publication_date":"2026-09-03T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"PrimeGaps186 Lean formalization and numerical certificate","excerpt":null,"content_hash":null,"source_reliability_class":"low","is_primary_source":false,"is_independent":false,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"6b91c136-7393-4e7e-8dd3-53ba0b912d89","event_id":"41eb33e9-5810-4e82-8da8-000988968f06","url":"https://openai.com/index/gpt-6-astra-next-generation-work","canonical_url":"https://openai.com/index/gpt-6-astra-next-generation-work","source_type":"developer_announcement","publisher":"OpenAI News","author":null,"publication_date":"2026-09-09T00:00:00.000Z","retrieved_at":"2026-09-17T03:01:01.934Z","title":"GPT-6 Astra: The next generation in intelligence for work","excerpt":"Meet GPT-6 Astra, OpenAI’s most capable model for business, with advanced reasoning, computer use, and stronger writing and design judgment.","content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-17T03:01:01.934Z"}],"claims":[{"id":"20a6852d-142b-4965-b1d1-ee6200cef626","event_id":"41eb33e9-5810-4e82-8da8-000988968f06","claim_text":"The posted argument establishes lim inf of consecutive prime gaps ≤ 186 via DHL[40,2] on a diameter-186 admissible 40-tuple.","claim_type":"outcome","claim_status":"supported","confidence_score":null,"created_at":"2026-09-13T21:33:49.339Z","updated_at":"2026-09-13T21:33:49.339Z"},{"id":"1cbfe064-7934-45b9-ac4d-e7dcd631cfa6","event_id":"41eb33e9-5810-4e82-8da8-000988968f06","claim_text":"The Lean formalization is unconditional and replaces human review of the exponential-sum 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