Ruzsa’s genus-one problem

witness #242606

N
41,065
|A|
128
exponent log |A| / log N
0.456751
status
superseded — the record is now |A| = 129
submitted by
Natanael Wildner Fraga
submitted at
2026-10-24 18:19:29 UTC

Elements (128)

0, 1, 14, 15, 35, 36, 49, 50, 205, 207, 214, 219, 240, 242, 249, 254, 408, 422, 443, 457, 1019, 1023, 1026, 1030, 1054, 1058, 1061, 1065, 1442, 1443, 1477, 1478, 1642, 1647, 1677, 1682, 1850, 1885, 2447, 2451, 2458, 2461, 2482, 2486, 2493, 2496, 2856, 2857, 2863, 2864, 2891, 2892, 2898, 2899, 3061, 3063, 3068, 3084, 3096, 3098, 3103, 3264, 3271, 3299, 3306, 5317, 5352, 7140, 7141, 7154, 7155, 7175, 7176, 7189, 7190, 7345, 7347, 7354, 7359, 7380, 7382, 7389, 7394, 7548, 7562, 7583, 7597, 8159, 8163, 8166, 8170, 8194, 8198, 8201, 8205, 8582, 8583, 8617, 8618, 8782, 8787, 8817, 8822, 8990, 9025, 9587, 9591, 9598, 9601, 9622, 9626, 9633, 9636, 9996, 9997, 10003, 10004, 10031, 10032, 10038, 10039, 10201, 10203, 10208, 10224, 10236, 10238, 10243

Commentary

Constructed offline from published witnesses using integer-transfer. Independently verified by exact full pair multiplicities: sum_v r1(v)*r2(v) = |A|. Every solution of a+3b=2c+2d is trivial.

last edited by Natanael Wildner Fraga at 2026-10-24 18:19:29 UTC · history

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