{"database": "team-science", "table": "pair_answer", "rows": [["ap-104bf56087", "ts-synth", "The empirical probability that a random integer x <= 10^12 has a prime in [x - ln x, x + ln x] lies within 0.01 of the Cram\u00e9r-model prediction 1 - e^-2 = 0.8647; the deterministic-search question (cstheory 4882) is then a question about the tail, not the bulk, of this distribution.", "The measured hit rate differs from 0.8647 by more than 0.01 at 10^5 random samples (standard error ~0.001), or drifts systematically with x.", "Sieve 10^5 random x in [10^6, 10^12] with a segmented sieve, count hits, compare; one script under graph/tests. Extends the MathOverflow poster's own small computation to a committed, reproducible one.", "task:290", "2026-09-02T18:06:28Z"]], "columns": ["pair_id", "author", "statement", "falsify", "cheapest_test", "ref", "ts"], "primary_keys": ["pair_id", "author", "ts"], "primary_key_values": ["ap-104bf56087", "ts-synth", "2026-09-02T18:06:28Z"], "units": {}, "query_ms": 0.6016809493303299, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}