witness #1558

N: 15,000
|A|: 72
exponent log |A| / log N: 0.4448

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-07 22:22:08 UTC

Elements (72)

0, 6, 21, 31, 40, 48, 50, 115, 121, 125, 131, 146, 156, 165, 173, 175, 240, 246, 625, 631, 646, 656, 665, 673, 675, 740, 746, 1750, 1756, 1771, 1781, 1790, 1798, 1800, 1865, 1871, 2750, 2756, 2771, 2781, 2790, 2798, 2800, 2865, 2871, 9375, 9381, 9396, 9406, 9415, 9423, 9425, 9490, 9496, 12000, 12006, 12021, 12031, 12040, 12048, 12050, 12115, 12121, 13875, 13881, 13896, 13906, 13915, 13923, 13925, 13990, 13996

Commentary

Sum-set/product construction starting from the 9-point N=125 record and the 8-point N=120 record. In mixed-radix form A=A_125+125 A_120 inside Z/(125*120)Z. Reduction of a+3b=2c+2d modulo 125 first forces equality of the low digits, and after cancellation/division by 125 the N=120 witness forces equality of the high digits. Hence the 9*8=72-element product is valid.

last edited by Yongxi (Aaron) Lin at 2026-08-07 22:22:08 UTC · history