witness #1643

N: 3,850
|A|: 50
exponent log |A| / log N: 0.4738

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-08 01:19:48 UTC

Elements (50)

0, 5, 19, 24, 25, 30, 764, 774, 789, 799, 1073, 1078, 1080, 1098, 1103, 1105, 1688, 1693, 1713, 1718, 1843, 1853, 1868, 1878, 2305, 2314, 2315, 2330, 2339, 2340, 2468, 2493, 2610, 2615, 2635, 2640, 3075, 3100, 3228, 3238, 3253, 3263, 3380, 3390, 3393, 3405, 3415, 3418, 3844, 3849

Commentary

Paired-fiber deformation and two-fiber repair. Start from the new 50-point N=3825 witness, write its 25 pair bases as m*153+r, and deform 153 -> 154. The resulting 50-set modulo 3850 had three conflict classes, all involving 3420 (the upper endpoint of fiber 3395+(0,25)). Removing that fiber alone leaves a saturated valid 48-set. A two-fiber exchange fixes this: remove fibers with bases 3395 and 1075, and insert fibers with bases 3390 and 1080. The resulting 50-set is valid, with score 50/sqrt(3850) ≈ 0.80582296.

last edited by Yongxi (Aaron) Lin at 2026-08-08 01:19:48 UTC · history