witness #236

N: 49,999
|A|: 121
exponent log |A| / log N: 0.4432

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-04 11:15:53 UTC

Elements (121)

64, 77, 114, 119, 266, 292, 330, 352, 411, 432, 533, 609, 651, 652, 677, 698, 737, 817, 834, 847, 884, 889, 994, 1003, 1037, 1083, 1100, 1113, 1925, 1951, 1989, 2002, 2039, 2044, 2073, 2191, 2217, 2255, 2277, 2336, 2357, 2458, 2534, 2576, 2577, 2602, 2623, 2662, 2742, 2759, 2772, 2809, 2814, 2919, 2928, 2962, 3008, 3025, 3038, 9625, 9651, 9689, 9702, 9739, 9744, 9773, 9891, 9917, 9955, 9977, 10036, 10057, 10158, 10234, 10276, 10277, 10302, 10323, 10362, 10442, 10459, 10472, 10509, 10514, 10619, 10628, 10662, 10708, 10725, 10738, 11550, 11576, 11614, 11627, 11664, 11669, 11698, 11816, 11842, 11880, 11902, 11961, 11982, 12083, 12159, 12201, 12202, 12227, 12248, 12287, 12367, 12384, 12397, 12434, 12439, 12544, 12553, 12587, 12633, 12650, 12663

Commentary

Start with the 124-element mixed-radix product A₀ = X + 1925Y, where X is witness#150 modulo 1,925 and Y = {0, 1, 5, 6} is witness#26 modulo 31. This product is solution-free over the integers, but its range slightly exceeds 49,999/4, creating wraparound solutions modulo 49,999. An exhaustive pair-table calculation finds exactly 10 distinct offending supports. Their minimum hitting sets have size three; deleting {0, 26, 148} removes them all and leaves this 121-element witness.

last edited by David Renshaw at 2026-08-04 11:16:08 UTC · history