spb/prime-mystery-engine
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1<!--2README.md — Prime Mystery Engine3Author: Simon-Pierre Boucher — contact@spboucher.ai4-->56# 🔬 Prime Mystery Engine78**A verification-first computational laboratory for prime gap statistics.**9101112131415161718192021An autonomous research pipeline that studies gaps between consecutive primes under a strict22epistemic protocol: **no claim without a certificate**. Every statement is labelled23`PROVEN` / `CERTIFIED` / `VERIFIED UP TO X` / `CONJECTURED` / `REFUTED`, every scan is24deterministic and bit-reproducible across machines, and every headline object ships with a25standalone re-verification script.2627---2829## 🏆 Headline results3031| Result | Status |32|---|---|33| **Race conjecture refuted** — "N(2,x) > N(4,x) for x ≥ 10⁶" is false: first tie at end-prime **80 966 861**, first strict overtake at **80 966 933**; the lead changes forever up to 10¹³ | `REFUTED` (minimal counterexample) |34| **Certified prime desert** — gap of exactly **260** after the 25-digit prime `1116336781708038449369693` (merit 4.70), built from a hybrid covering system mod primes ≤ 59 | `CERTIFIED` |35| **Scaling law for consecutive-gap correlation** — ρ(x)·ln x = c + d/ln x with **c = −0.4835 ± 0.002**, d = −1.777; out-of-sample predictions confirmed at 10¹² (−0.549 ± 0.005 → −0.54756) **and** 10¹³ (−0.5432 ± 0.004 → −0.54264) | `CONJECTURED`, 2/2 hits |36| **Lag-2 law** — ρ₂(x)·ln x → c₂ ≈ −0.278, prediction confirmed at 10¹³ (−0.2545 ± 0.004 → −0.25247) | `CONJECTURED`, 1/1 hit |37| **First-order Hardy–Littlewood triple model rejected** — right sign and drift form, but only ~32 % of the observed magnitude | `MODEL REJECTED` |38| **All published tables reproduced** — 53/53 maximal gaps below 10¹³ (OEIS A005250/A002386), twin counts, π(10ᵏ), CSG maxima | `VERIFIED` |3940**Predictions on record (falsifiable):** ρ·ln x(10¹⁴) = −0.5387 ± 0.004 · ρ·ln x(10¹⁵) = −0.5350 ± 0.004 · ρ₂·ln x(10¹⁴) = −0.2553 ± 0.0044142---4344## ⚡ Verify the headline claims yourself (stock Python 3)4546```bash47# the certified 260-gap desert (independent Miller–Rabin implementation)48python3 certs/verify_desert.py4950# the race-conjecture refutation (stdlib-only sieve, ~30 s)51python3 certs/verify_c2_refutation.py5253# the core-primitives validation gate (37 checks, needs numpy)54python3 src/test_core.py55```5657## 🗂 Repository layout5859```60src/ core primitives, scans, distributed worker/merger, Metal GPU sieve, models61certs/ certificates + standalone verifiers (the "trust nothing" layer)62data/ raw checkpoint JSONs for every campaign (deterministic, re-mergeable)63paper/ LaTeX manuscript (main.tex → main.pdf, 13 pp., full math detail)64journal.md complete research journal: every cycle, decision, failure65conjectures.md the conjecture ledger with epistemic statuses66records.md state of the art (what would count as new; thresholds to beat)67report_cycle{1..4}.md per-cycle syntheses68```6970## 🖥 Compute7172| Campaign | Range | Fleet | Wall time |73|---|---|---|---|74| Cycle 1 | 4×10⁹ | 1 laptop core | 15 s |75| Cycle 2 | 4×10¹⁰ | laptop + M3 Ultra (1 core each) | ~2 min |76| Cycle 3 | 10¹² | 12 Apple-silicon nodes, 162 CPU cores | ~5 min |77| Cycle 4 | 10¹³ | 3 nodes: 58 CPU cores + **3 GPUs (custom Metal kernel)** | ~50 min |7879The distributed design uses *mergeable* streaming statistics (exact integers < 2⁵³ in80float64 → **zero rounding**, bit-identical across machines) with checkpoint-aligned chunking81and a junction buffer, so a 10 000-chunk merge equals the single-machine scan exactly.82The Metal sieve kernel was accepted only after producing byte-identical prime sets to the83CPU sieve; it processed 11.7 % of cycle 4.8485## 📄 Paper8687Full write-up with all equations, proofs of the infrastructure lemmas, robustness checks and88threats-to-validity: [`paper/main.tex`](paper/main.tex) → [`paper/main.pdf`](paper/main.pdf).8990## 👤 Author9192**Simon-Pierre Boucher** · [contact@spboucher.ai](mailto:contact@spboucher.ai)93