Ruzsa’s genus-one problem

witness #2295

N
2,900
|A|
36
exponent log |A| / log N
0.4495
status
current record for this modulus
submitted by
Yongxi (Aaron) Lin
submitted at
2026-08-10 05:45:10 UTC

Elements (36)

740, 791, 957, 1017, 1177, 1210, 1222, 1240, 1252, 1760, 1772, 1835, 1870, 1876, 1885, 1891, 1945, 1951, 1960, 1966, 2117, 2162, 2337, 2340, 2352, 2400, 2412, 2415, 2427, 2450, 2471, 2480, 2501, 2525, 2712, 2757

Commentary

Tail/arc compression with threshold sweep. Starting from the size-35 N/4-tail record, a neutral 2↔2 exchange {957,2147}->{1017,2162} escaped the shallow local maximum. An exact 2→3 search then found {2192,2727}->{957,1177,2757}, giving size 36. The final witness still satisfies a>N/4 (minimum 740>725).

last edited by Yongxi (Aaron) Lin at 2026-08-10 05:45:10 UTC · history

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