Ruzsa’s genus-one problem

witness #243298

N
41,735
|A|
158
exponent log |A| / log N
0.475848
status
current record for this modulus
submitted by
Natanael Wildner Fraga
submitted at
2026-10-24 18:39:43 UTC

Elements (158)

0, 2946, 2948, 2963, 2965, 3031, 3033, 3050, 3920, 3954, 4005, 4039, 4421, 4472, 4506, 4938, 5023, 6403, 6437, 6488, 6963, 6980, 7368, 7372, 7385, 7389, 7453, 7457, 7470, 7474, 8338, 8347, 8355, 8364, 8423, 8440, 9848, 9933, 11293, 12266, 12267, 12300, 12351, 12352, 12385, 12768, 12780, 12785, 12853, 12865, 12870, 13261, 13312, 13346, 14733, 14750, 14818, 14835, 15228, 15242, 15245, 15313, 15327, 15330, 16719, 16779, 16796, 16804, 19657, 20631, 20647, 20648, 20716, 20732, 20733, 21598, 21615, 21625, 21683, 21700, 21710, 23069, 23086, 23154, 23171, 23558, 23572, 23592, 23643, 23677, 25032, 25058, 25066, 25117, 25126, 25151, 26508, 26525, 26593, 26610, 27989, 28040, 28072, 28074, 28089, 28960, 28977, 29045, 29062, 29457, 29479, 29508, 29542, 29564, 29945, 29955, 29972, 29979, 30030, 30040, 30057, 30064, 31427, 31450, 31512, 31535, 32004, 32396, 32426, 32430, 32460, 32481, 32511, 32515, 33490, 34855, 34889, 34940, 34974, 36353, 36436, 36438, 37804, 37821, 37889, 37906, 39763, 39797, 39848, 39882, 40252, 40266, 40283, 40337, 40743, 40756, 40828, 40841

Commentary

Constructed offline from published witnesses using exact 3-4 swap. 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 18:39:44 UTC · history

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