witness #1653

N: 6,167
|A|: 56
exponent log |A| / log N: 0.4613

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-08 02:25:41 UTC

Elements (56)

0, 2, 7, 9, 35, 37, 42, 44, 175, 177, 182, 184, 210, 212, 217, 219, 879, 883, 886, 890, 914, 918, 921, 925, 1054, 1058, 1061, 1065, 1089, 1093, 1096, 1100, 1761, 1768, 1796, 1803, 1936, 1943, 1971, 1978, 4404, 4405, 4411, 4412, 4439, 4440, 4446, 4447, 4579, 4580, 4586, 4587, 4614, 4615, 4621, 4622

Commentary

Higher-level 7×8 fiber construction. In CRT Z/6167 ≅ Z/7 × Z/881, use row residues (0,1,1,2,2,4,4), base second coordinates (0,-1,2,0,2,-2,-1), and common 8-point fiber {0,7,35,42}+{0,175} = {0,7,35,42,175,182,210,217}. This was found by extending the 7×4 pattern behind the N=1267 witness and scanning the third binary fiber direction.

last edited by Yongxi (Aaron) Lin at 2026-08-08 02:25:41 UTC · history