witness #1654

N: 30,667
|A|: 112
exponent log |A| / log N: 0.4567

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-08 02:27:51 UTC

Elements (112)

0, 2, 7, 9, 35, 37, 42, 44, 175, 177, 182, 184, 210, 212, 217, 219, 875, 877, 882, 884, 910, 912, 917, 919, 1050, 1052, 1057, 1059, 1085, 1087, 1092, 1094, 4379, 4383, 4386, 4390, 4414, 4418, 4421, 4425, 4554, 4558, 4561, 4565, 4589, 4593, 4596, 4600, 5254, 5258, 5261, 5265, 5289, 5293, 5296, 5300, 5429, 5433, 5436, 5440, 5464, 5468, 5471, 5475, 8761, 8768, 8796, 8803, 8936, 8943, 8971, 8978, 9636, 9643, 9671, 9678, 9811, 9818, 9846, 9853, 21904, 21905, 21911, 21912, 21939, 21940, 21946, 21947, 22079, 22080, 22086, 22087, 22114, 22115, 22121, 22122, 22779, 22780, 22786, 22787, 22814, 22815, 22821, 22822, 22954, 22955, 22961, 22962, 22989, 22990, 22996, 22997

Commentary

Higher-level 7×16 fiber construction. In CRT Z/30667 ≅ Z/7 × Z/4381, use row residues (0,1,1,2,2,4,4), base second coordinates (0,-1,2,0,2,-2,-1), and the common 16-point fiber obtained by four binary directions 7, 35, 175, 875: F={0,7}+{0,35}+{0,175}+{0,875}. This extends the 7×4 and 7×8 hierarchy; scanning the next 5-adic-style direction gives the first modulus for this fixed skeleton at q=4381.

last edited by Yongxi (Aaron) Lin at 2026-08-08 02:27:51 UTC · history