witness #123497

N: 44,370
|A|: 170
exponent log |A| / log N: 0.479967

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-09-03 20:08:01 UTC

Elements (170)

2092, 2099, 2177, 2184, 2635, 2636, 2652, 2653, 2720, 2721, 2737, 2738, 3149, 3151, 3166, 3168, 3234, 3236, 3251, 3253, 5223, 5227, 5257, 5261, 5308, 5312, 5342, 5346, 5745, 5751, 5779, 5830, 5836, 5864, 6805, 6822, 6890, 6907, 9922, 9925, 10007, 10010, 13572, 13580, 13657, 13665, 14114, 14118, 14131, 14135, 14199, 14203, 14216, 14220, 14636, 14653, 14721, 14738, 15674, 15708, 15759, 15793, 17237, 17322, 19840, 19847, 19874, 19881, 19925, 19932, 19959, 19966, 20366, 20367, 20451, 20452, 20880, 20882, 20965, 20967, 23499, 23533, 23584, 23618, 24536, 24565, 24582, 24621, 24650, 24667, 27670, 27673, 27704, 27707, 27755, 27758, 27789, 27792, 28731, 28738, 28748, 28755, 28816, 28823, 28833, 28840, 31320, 31328, 31354, 31362, 31405, 31413, 31439, 31447, 31845, 31849, 31930, 31934, 32367, 32390, 32407, 32452, 32475, 32492, 34985, 35019, 35070, 35104, 36561, 36564, 36578, 36581, 36646, 36649, 36663, 36666, 38114, 38115, 38148, 38149, 38199, 38200, 38233, 38234, 38628, 38630, 38662, 38664, 38713, 38715, 38747, 38749, 40211, 40219, 40228, 40236, 40296, 40304, 40313, 40321, 42284, 42296, 42318, 42369, 42381, 42403, 43876, 43893, 43961, 43978

Commentary

Structured witness: A = B ⊕ 85·E with E=[0, 1], B a nested parabola set in Z/85 × Z built from the chain [17, 5] (outermost first): y = Σ_i w_i·y_i(u_i) where y_i is a compact representative of λ_i·u_i² mod p_i and w_i = p_1⋯p_{i-1}, placed in Z/44370 = Z/(85·522) by CRT. Mixed-radix encoding keeps the y-span at Σ w_i·s_i + g·max E; M below the span-rule bound 4·span+1 is obtained by checking wrap-around solutions exactly and greedily dropping a hitting set (0 dropped). Generalizes witness#44533 / witness#54659; same method at every modulus g·M in this range.

last edited by David Renshaw at 2026-09-03 20:08:01 UTC · history