witness #1007

N: 24,025
|A|: 100
exponent log |A| / log N: 0.4566

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-06 19:00:46 UTC

Elements (100)

0, 8, 20, 28, 39, 59, 62, 66, 82, 86, 1240, 1248, 1260, 1268, 1279, 1299, 1302, 1306, 1322, 1326, 3100, 3108, 3120, 3128, 3139, 3159, 3162, 3166, 3182, 3186, 4340, 4348, 4360, 4368, 4379, 4399, 4402, 4406, 4422, 4426, 6045, 6053, 6065, 6073, 6084, 6104, 6107, 6111, 6127, 6131, 9145, 9153, 9165, 9173, 9184, 9204, 9207, 9211, 9227, 9231, 9610, 9618, 9630, 9638, 9649, 9669, 9672, 9676, 9692, 9696, 10230, 10238, 10250, 10258, 10269, 10289, 10292, 10296, 10312, 10316, 12710, 12718, 12730, 12738, 12749, 12769, 12772, 12776, 12792, 12796, 13330, 13338, 13350, 13358, 13369, 13389, 13392, 13396, 13412, 13416

Commentary

Square lift of the N=155 record: B = {a + 155·b : a, b in A} with A = Bhavik Mehta's size-10 witness for 155 (score 0.8032). Since the coefficients of a + 3b − 2c − 2d sum to zero, any solution mod 155² reduces to a solution among the low digits mod 155 (forcing them equal, with contribution vanishing exactly as integers) and then to a solution among the high digits mod 155 (forcing them equal as well). Size 100 at N = 24025, score 100/155 ≈ 0.645 — the square of the base score. Companion to the analogous 145² = 21025 lift (witness 1003). Verified locally by exhaustive pair-count convolution (exactly 100 solutions, all trivial).

last edited by David Renshaw at 2026-08-06 19:00:46 UTC · history