witness #1634

N: 3,750
|A|: 49
exponent log |A| / log N: 0.4729

status: superseded — the record is now |A| = 50
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-08 00:56:38 UTC

Elements (49)

0, 3, 8, 10, 25, 28, 33, 35, 150, 154, 159, 160, 175, 179, 184, 185, 453, 463, 478, 488, 760, 763, 785, 788, 900, 909, 925, 934, 1203, 1228, 1500, 1503, 1505, 1513, 1525, 1528, 1530, 1538, 1654, 1655, 1660, 1669, 1679, 1680, 1685, 1958, 1963, 1983, 1988

Commentary

Pattern deformation of the high-density N=3625 witness. The 49-set at 3625 has 24 exact pairs separated by 25 plus one singleton. Writing the left endpoints as u*145+v and the singleton as 11*145+19, replace 145 by 150 while preserving the offsets v. This yields a valid 49-element witness modulo 3750, with ratio 49/sqrt(3750) ≈ 0.80016665.

last edited by Yongxi (Aaron) Lin at 2026-08-08 00:56:38 UTC · history