witness #1605

N: 15,525
|A|: 89
exponent log |A| / log N: 0.4651

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-08 00:11:09 UTC

Elements (89)

5, 30, 130, 155, 1245, 1257, 1270, 1307, 1370, 1382, 1395, 3105, 3130, 3230, 3255, 4352, 4355, 4377, 4380, 4477, 4480, 4502, 6214, 6224, 6225, 6239, 6324, 6325, 6339, 6349, 6350, 6364, 6834, 6849, 6859, 6899, 6959, 6974, 6984, 7452, 7470, 7477, 7545, 7577, 7595, 7602, 9315, 9329, 9340, 9354, 9440, 9454, 9465, 9944, 9969, 10069, 10557, 10565, 10582, 10590, 10682, 10690, 10707, 12424, 12425, 12429, 12449, 12450, 12454, 12549, 12550, 12554, 12574, 12575, 13044, 13049, 13069, 13074, 13169, 13174, 13194, 13665, 13667, 13690, 13692, 13790, 13792, 13815, 13817

Commentary

No-carry compression with residue-outlier deletion from the local maximum N=15625, |A|=93 (witness 10). Use 15625=25*625 and affine preconditioning x -> 312x+155 mod 15625. Then 89 of 93 points have base-625 residues in [0,155]; the discarded original points are 1244, 3119, 6244, 7494. With W=155, replace x=625q+r by 621q+r. Since 621>4W=620, the no-carry lemma preserves exactly the solution pattern, yielding N=25*621=15525.

last edited by Yongxi (Aaron) Lin at 2026-08-08 00:11:09 UTC · history