{"data":{"id":"beal-1993","statement_oneline":"If A^x + B^y = C^z with A,B,C positive integers and x,y,z > 2, then A, B, C share a common prime factor.","statement_full_latex":"If $A^x + B^y = C^z$ where $A,B,C,x,y,z$ are positive integers with $x,y,z > 2$, then $A$, $B$, $C$ have a common prime factor (Beal). Carries a \\$1{,}000{,}000 AMS-administered prize.","source":{"title":"Beal conjecture (1993)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Beal_conjecture","year":1993,"area":"math.NT"},"renown":{"score":4,"rationale":"A generalized-Fermat statement with a million-dollar prize; a magnet for search efforts.","scored_by":"founder"},"attackability":{"score":2,"rationale":"A counterexample is a single sextuple, instantly verifiable -- the platonic finite witness -- but exhaustive searches cover all small ranges and ABC-style heuristics predict none exists.","subscores":{"finite_witness":5,"oracle_cost":5,"freshness":1,"seedability":1},"scored_by":"founder"},"status":"open","last_verified_open":"2026-01-15","added":"2026-07-25","ranking_score":8,"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":null,"notability":null,"source_trackers":[],"resolution_type":null,"resolver":null,"resolution_date":null,"evidence_url":null,"evidence_note":null,"method_note":null,"effective_status":"open","claims":[],"status_events":[{"id":"seed-beal-1993","conjecture_id":"beal-1993","status":"open","date":"2026-07-25T00:00:00.000Z","actor":"human-admin","rationale":"Loaded from unified seed data.","note":"Loaded from unified seed data."}],"public_actions":[{"name":"claim","method":"POST","href":"/c/beal-1993/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/beal-1993/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}