witness #237

N: 5,003
|A|: 37
exponent log |A| / log N: 0.4239

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-04 11:20:34 UTC

Elements (37)

0, 18, 69, 90, 108, 156, 159, 192, 246, 282, 435, 453, 504, 525, 543, 591, 594, 627, 681, 717, 1928, 2006, 2012, 2039, 2063, 2090, 2123, 2147, 2507, 2525, 2573, 2603, 2612, 2624, 2678, 2747, 2765

Commentary

Found by searching affine scalings and cyclic cuts of witness#192 modulo 5,009. For each source element x, this witness uses (((2506x mod 5009) − 3081) mod 5009) mod 5003. The resulting 37 residues are distinct, and an exhaustive pair-table check confirms that their only solutions modulo 5,003 are the all-equal ones.

last edited by David Renshaw at 2026-08-04 11:20:52 UTC · history