witness #1689

N: 42,630
|A|: 130
exponent log |A| / log N: 0.4566

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-08 04:08:20 UTC

Elements (130)

0, 1, 5, 6, 28, 30, 33, 35, 86, 91, 725, 726, 730, 731, 753, 755, 758, 760, 811, 816, 1015, 1016, 1020, 1021, 1043, 1045, 1048, 1050, 1101, 1106, 18560, 18561, 18565, 18566, 18588, 18590, 18593, 18595, 18646, 18651, 19575, 19576, 19580, 19581, 19603, 19605, 19608, 19610, 19661, 19666, 24215, 24216, 24220, 24221, 24243, 24245, 24248, 24250, 24301, 24306, 24360, 24361, 24365, 24366, 24388, 24390, 24393, 24395, 24446, 24451, 25230, 25231, 25235, 25236, 25258, 25260, 25263, 25265, 25316, 25321, 25375, 25376, 25380, 25381, 25403, 25405, 25408, 25410, 25461, 25466, 30305, 30306, 30310, 30311, 30333, 30335, 30338, 30340, 30391, 30396, 30740, 30741, 30745, 30746, 30768, 30770, 30773, 30775, 30826, 30831, 31320, 31321, 31325, 31326, 31348, 31350, 31353, 31355, 31406, 31411, 31755, 31756, 31760, 31761, 31783, 31785, 31788, 31790, 31841, 31846

Commentary

Sum-set/product construction from the size-13 witness for N=294 and the size-10 record witness for r=145: A = A_145 + 145 A_294. This is valid because reduction mod 145 forces all first coordinates equal, then division by 145 leaves the witness relation mod 294.

last edited by Yongxi (Aaron) Lin at 2026-08-08 04:08:21 UTC · history