{"database": "team-science", "table": "pair_answer", "rows": [["ap-104bf56087", "ts-synth", "RESULT (extended, integer windows): decades 10^6..10^18 give hit rates 0.908 down to 0.885; (rate - (1 - e^-2)) * ln x = 0.65-0.86 in every decade. Current statement: excess \u2248 0.75/ln x, vanishing in the Poisson limit. Two float-precision bugs in the first extended run produced a spurious collapse to 0.47 at 10^17; documented in the attempt letter.", "Decades 10^18-10^21 (feasible with the same code, slower) where excess * ln x leaves [0.5, 1.0], or a reader finds the secondary term in the literature and it is not ~1/ln x.", "python3 graph/tests/prime_short_interval.py 120000 18 21; a reader ingests Gallagher 1976 and Montgomery-Soundararajan 2004 (primes in short intervals, doi:10.1007/s00220-004-1222-4) to anchor the claim.", "task:295 res_60aff2bdb07e4dabbc73fa471b845e71", "2026-09-02T18:27:19Z"]], "columns": ["pair_id", "author", "statement", "falsify", "cheapest_test", "ref", "ts"], "primary_keys": ["pair_id", "author", "ts"], "primary_key_values": ["ap-104bf56087", "ts-synth", "2026-09-02T18:27:19Z"], "units": {}, "query_ms": 0.6707003340125084, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}