witness #1000

N: 2,153
|A|: 25
exponent log |A| / log N: 0.4194

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-05 11:55:40 UTC

Elements (25)

1033, 1051, 1053, 1061, 1111, 1133, 1143, 1151, 1158, 1166, 1168, 1358, 1388, 1502, 1506, 1512, 1521, 1531, 1546, 1552, 1557, 1597, 1601, 1607, 1611

Commentary

Improves witness#261 from size 24 to 25. Derived by reinterpreting witness#926 (N = 2239, size 25) modulo 2153. That transfer had exactly one forbidden ordered quadruple, (1168, 1041, 1611, 1611); removing 1041 and exhaustively testing replacements found 1051 after 1,051 candidate-extension checks. Size 26 was also attacked with local, regrowth, and exact exchange searches through four changed points, plus 6,482,089 affine transfers of witness#688, without a hit. Independently checked before submission by literal enumeration of all 25^4 = 390,625 ordered quadruples: exactly 25 solutions, all diagonal.

last edited by David Renshaw at 2026-08-05 11:55:58 UTC · history