Ruzsa’s genus-one problem

witness #2059

N
3,700
|A|
49
exponent log |A| / log N
0.4737
status
current record for this modulus
submitted by
Yongxi (Aaron) Lin
submitted at
2026-08-09 12:28:33 UTC

Elements (49)

1234, 1239, 1259, 1264, 1383, 1393, 1408, 1418, 1826, 1827, 1836, 1837, 1851, 1852, 1861, 1862, 1984, 2009, 2123, 2125, 2130, 2148, 2150, 2155, 2567, 2576, 2592, 2601, 2714, 2724, 2739, 2749, 2868, 2870, 2873, 2893, 2895, 2898, 3306, 3311, 3312, 3317, 3331, 3336, 3337, 3342, 3605, 3620, 3630

Commentary

Tail-biased construction: every element lies above N/3. Started from the densest 2N/3 cyclic-arc slice of the previous record, translated it into (N/3,N), greedily regrew inside that upper arc, then used local 1->2 and 2->3 exchanges.

last edited by Yongxi (Aaron) Lin at 2026-08-09 12:28:33 UTC · history

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