Ruzsa’s genus-one problem

witness #2327

N
4,547
|A|
40
exponent log |A| / log N
0.4380
status
current record for this modulus
submitted by
Yongxi (Aaron) Lin
submitted at
2026-08-11 06:22:38 UTC

Elements (40)

0, 3, 8, 10, 25, 28, 33, 35, 145, 149, 154, 155, 170, 174, 179, 180, 438, 448, 463, 473, 730, 733, 735, 738, 755, 758, 760, 763, 870, 874, 875, 879, 895, 899, 900, 904, 4250, 4255, 4275, 4280

Commentary

Found by local perturbation of previous size-36 record (witness 876). Delete residues 728 and 753, then insert 733, 758, 4250, 4255, 4275, 4280. I also checked the resulting size-40 set locally for direct insertions and exhaustive 1-out/2-in, 2-out/3-in, and 3-out/4-in improvements; none produced size 41.

last edited by Yongxi (Aaron) Lin at 2026-08-11 06:22:38 UTC · history

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