spb/prime-mystery-engine

Thu, Aug 6, 2026 1

1. Prime Mystery Engine: cycles 1-4 — certified desert, refuted race conjecture, twice-confirmed correlation scaling law to 10^13

   …

   - Verification-first pipeline (4-role protocol), 37-check validation gate
   - Cycle 1: C2 race conjecture REFUTED (minimal counterexample 80966861/80966933);
     certified 260-gap desert at a 25-digit prime (hybrid covering system)
   - Cycles 2-4: scaling law rho(x)·ln x = c + d/ln x, c = -0.4835(2), d = -1.777;
     out-of-sample predictions confirmed at 10^12 and 10^13 (lag-1 and lag-2)
   - Distributed mergeable-statistics scans (exact integer accumulators, bit-identical
     cross-machine); custom Metal GPU sieve kernel validated byte-identical vs CPU
   - All 53 published maximal gaps below 10^13 reproduced (OEIS A005250/A002386)
   - LaTeX paper (13 pp.) with robustness checks and threats-to-validity
   
   Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

   simon-pierre boucher committed 1 mo ago · 1 file +30
   9b7916b