witness #235

N: 49,999
|A|: 120
score |A|/√N: 0.5367
exponent log |A| / log N: 0.4425

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-04 03:25:40

Elements (120)

0, 4, 61, 89, 192, 200, 248, 322, 334, 350, 362, 375, 399, 403, 404, 432, 571, 599, 619, 677, 693, 742, 770, 774, 934, 962, 970, 1048, 1092, 1104, 1855, 1859, 1916, 1944, 2047, 2055, 2103, 2177, 2189, 2205, 2217, 2230, 2254, 2258, 2259, 2287, 2426, 2454, 2474, 2532, 2548, 2597, 2625, 2629, 2789, 2817, 2825, 2903, 2947, 2959, 9275, 9279, 9336, 9364, 9467, 9475, 9523, 9597, 9609, 9625, 9637, 9650, 9674, 9678, 9679, 9707, 9846, 9874, 9894, 9952, 9968, 10017, 10045, 10049, 10209, 10237, 10245, 10323, 10367, 10379, 11130, 11134, 11191, 11219, 11322, 11330, 11378, 11452, 11464, 11480, 11492, 11505, 11529, 11533, 11534, 11562, 11701, 11729, 11749, 11807, 11823, 11872, 11900, 11904, 12064, 12092, 12100, 12178, 12222, 12234

Commentary

This is the mixed-radix product A = X + 1855Y, where X is witness#148 modulo 1,855 and Y = {0, 1, 5, 6} is witness#26 modulo 31. An integer relation first reduces modulo 1,855, forcing its four X-digits to be equal; after they cancel, the relation in Y forces its four Y-digits to be equal. Thus the product is solution-free over the integers. Every element lies in [0, 12,234], so |a + 3b − 2c − 2d| ≤ 48,936 < 49,999; consequently it is also solution-free modulo 49,999. Its size is 30 · 4 = 120.

last edited by David Renshaw at 2026-08-04 03:26:05 · history