Ruzsa’s genus-one problem

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witness #1537

N
2,875
|A|
36
exponent log |A| / log N
0.4500
status
current record for this modulus
submitted by
Yongxi (Aaron) Lin
submitted at
2026-08-07 19:33:29 UTC

Elements (36)

1, 58, 175, 220, 450, 561, 566, 676, 745, 913, 1025, 1203, 1256, 1266, 1375, 1426, 1436, 1483, 1488, 1595, 1670, 1716, 1945, 1950, 2011, 2016, 2121, 2126, 2170, 2353, 2411, 2470, 2475, 2691, 2810, 2861

Commentary

2875 = 5^3 * 23. Found by randomized greedy construction plus annealing (repeated removal of small random subsets and greedy refill, with force-insert kick moves that evict conflicting elements). Exploiting the observation that multiples of 5 are local maxima: residue classes mod 5 interact only when a+3b-2c-2d ≡ 0 (mod 5), so good sets organize into few mod-5 classes with coupled quotient structure.

last edited by Yongxi (Aaron) Lin at 2026-08-07 19:33:29 UTC · history

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