#!/usr/bin/env python3 """ scan_quartet.py - Repair / discover the (K, delta) that completes a valid Martini Quartet for a TRUSTED twin midpoint MT. The twin midpoint MT is trusted (MT-1, MT+1 already prime). This tool finds which K (for a fixed delta) or which even delta (for a fixed K) makes the Martini pair MP +/- delta/2 prime, where MP = MT * K. Useful when a published K or delta is suspected to be a typo: pin the field you trust, scan the other. Screening uses gmpy2 BPSW (fast, near-certain). Confirm any hit with PFGW / verify_quartet.py before publishing. Modes: --scan-k fix --delta, search K in a window around --k --scan-delta fix --k, search even delta in a window around --delta --typo-only restrict search to single-edit typos of the pinned-as- suspect field (transpose / delete / substitute / insert) Usage: py scan_quartet.py --mt-file mt1051.txt --k 3545 --delta 297914 --scan-k --k-window 12000 py scan_quartet.py --mt-file mt1051.txt --k 3545 --delta 297914 --scan-delta --delta-window 200000 py scan_quartet.py --mt-file mt1051.txt --k 3545 --delta 297914 --typo-only """ import argparse import sys import time try: import gmpy2 from gmpy2 import mpz, is_prime except ImportError: sys.exit("gmpy2 not found. Install with: pip install gmpy2 --break-system-packages") def load_mt(args): if args.mt_file: raw = open(args.mt_file).read() elif args.mt: raw = args.mt else: sys.exit("Provide MT via --mt or --mt-file.") cleaned = "".join(c for c in raw if c.isdigit()) if not cleaned: sys.exit("No digits found in MT input.") return mpz(cleaned) def martini_ok(MT, K, D): """True if MP +/- D/2 are both prime, where MP = MT*K.""" if D % 2: return False MP = MT * mpz(K) h = mpz(D) // 2 return is_prime(MP - h) and is_prime(MP + h) def typo_variants(value): """All single-edit variants of an integer's decimal string: adjacent transpositions, deletions, substitutions, insertions.""" s = str(value) out = set() for i in range(len(s) - 1): # transpose adjacent l = list(s); l[i], l[i + 1] = l[i + 1], l[i]; out.add(int("".join(l))) for i in range(len(s)): # delete one if len(s) > 1: out.add(int(s[:i] + s[i + 1:])) for i in range(len(s)): # substitute one for d in "0123456789": if d != s[i]: out.add(int(s[:i] + d + s[i + 1:])) for i in range(len(s) + 1): # insert one for d in "0123456789": out.add(int(s[:i] + d + s[i:])) out.discard(int(s)) return sorted(v for v in out if v > 0) def report_hit(K, D, K0, D0): print("\n" + "=" * 56) print(" VALID QUARTET FOUND") print("=" * 56) print(f" K = {K} (published: {K0})") print(f" delta = {D} (published: {D0})") if K != K0: print(f" -> correction is in K: {K0} -> {K}") if D != D0: print(f" -> correction is in delta: {D0} -> {D}") print("\n Confirm before publishing:") print(f" py verify_quartet.py --mt-file --k {K} --delta {D}") def main(): ap = argparse.ArgumentParser(description="Find the (K, delta) that completes a Martini quartet for a trusted MT.") g = ap.add_mutually_exclusive_group() g.add_argument("--mt", help="MT as decimal string") g.add_argument("--mt-file", help="file containing MT") ap.add_argument("--k", required=True, type=int, help="published / starting K") ap.add_argument("--delta", required=True, type=int, help="published / starting delta") ap.add_argument("--scan-k", action="store_true", help="fix delta, scan K") ap.add_argument("--scan-delta", action="store_true", help="fix K, scan delta") ap.add_argument("--typo-only", action="store_true", help="only test single-edit typos of the suspect field(s)") ap.add_argument("--k-window", type=int, default=10000, help="+/- range for K scan (default 10000)") ap.add_argument("--delta-window", type=int, default=200000, help="+/- range for delta scan (default 200000)") ap.add_argument("--all", action="store_true", help="list all hits instead of stopping at first") args = ap.parse_args() MT = load_mt(args) K0, D0 = args.k, args.delta print(f"MT: {MT.num_digits()} digits") if not (is_prime(MT - 1) and is_prime(MT + 1)): print("WARNING: MT-1 / MT+1 are NOT both prime -- MT itself may be wrong.") else: print("MT twin pair (MT-1, MT+1): both PRP [trusted]") hits = [] # ---- typo-only mode: cheap, try single edits of each field first ---- if args.typo_only or (not args.scan_k and not args.scan_delta): print("\nSingle-edit scan: delta variants (K fixed) ...") t = time.time() for D in typo_variants(D0): if martini_ok(MT, K0, D): hits.append((K0, D)) if not args.all: break print(f" done [{time.time()-t:.1f}s]") if not (hits and not args.all): print("Single-edit scan: K variants (delta fixed) ...") t = time.time() for K in typo_variants(K0): if martini_ok(MT, K, D0): hits.append((K, D0)) if not args.all: break print(f" done [{time.time()-t:.1f}s]") # ---- windowed K scan ---- if args.scan_k and not (hits and not args.all): lo, hi = max(1, K0 - args.k_window), K0 + args.k_window print(f"\nScanning K in [{lo}, {hi}] at delta={D0} ...") t = time.time() # search outward from K0 so the closest hit comes first order = sorted(range(lo, hi + 1), key=lambda k: abs(k - K0)) for K in order: if martini_ok(MT, K, D0): hits.append((K, D0)) if not args.all: break print(f" done [{time.time()-t:.1f}s]") # ---- windowed delta scan ---- if args.scan_delta and not (hits and not args.all): D0e = D0 if D0 % 2 == 0 else D0 + 1 lo, hi = max(2, D0e - args.delta_window), D0e + args.delta_window print(f"\nScanning even delta in [{lo}, {hi}] at K={K0} ...") t = time.time() MP = MT * mpz(K0) order = sorted(range(lo, hi + 1, 2), key=lambda d: abs(d - D0e)) for D in order: h = mpz(D) // 2 if is_prime(MP - h) and is_prime(MP + h): hits.append((K0, D)) if not args.all: break print(f" done [{time.time()-t:.1f}s]") if not hits: print("\nNo valid quartet found in the searched space.") print("Try a wider --k-window / --delta-window, or check MT itself.") sys.exit(1) if args.all: print(f"\nAll hits ({len(hits)}):") for K, D in hits: print(f" K={K}, delta={D}") else: K, D = hits[0] report_hit(K, D, K0, D0) if __name__ == "__main__": main()