witness #1006

N: 46,655
|A|: 140
exponent log |A| / log N: 0.4597

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-06 19:00:37 UTC

Elements (140)

12, 23, 50, 66, 103, 124, 135, 136, 162, 178, 184, 248, 292, 296, 2420, 2431, 2458, 2474, 2511, 2532, 2543, 2544, 2570, 2586, 2592, 2656, 2700, 2704, 6032, 6043, 6070, 6086, 6123, 6144, 6155, 6156, 6182, 6198, 6204, 6268, 6312, 6316, 8440, 8451, 8478, 8494, 8531, 8552, 8563, 8564, 8590, 8606, 8612, 8676, 8720, 8724, 11751, 11762, 11789, 11805, 11842, 11863, 11874, 11875, 11901, 11917, 11923, 11987, 12031, 12035, 17771, 17782, 17809, 17825, 17862, 17883, 17894, 17895, 17921, 17937, 17943, 18007, 18051, 18055, 18674, 18685, 18712, 18728, 18765, 18786, 18797, 18798, 18824, 18840, 18846, 18910, 18954, 18958, 19878, 19889, 19916, 19932, 19969, 19990, 20001, 20002, 20028, 20044, 20050, 20114, 20158, 20162, 24694, 24705, 24732, 24748, 24785, 24806, 24817, 24818, 24844, 24860, 24866, 24930, 24974, 24978, 25898, 25909, 25936, 25952, 25989, 26010, 26021, 26022, 26048, 26064, 26070, 26134, 26178, 26182

Commentary

Digit lift for 46655 = 301·155: B = {a + 301·b : a in A1, b in A2} with A1 = Bhavik Mehta's size-14 witness for 301 (score 0.8069) and A2 = his size-10 witness for 155 (score 0.8032). Validity: because the coefficients of a + 3b − 2c − 2d sum to zero, any solution reduces mod 301 to a solution among the low parts, forcing them equal and making their contribution vanish exactly; the carry is then a solution mod 155 among the high parts, forcing those equal too. Size 140, score 140/√46655 ≈ 0.648, the product of the factor scores. Verified locally by exhaustive pair-count convolution (exactly 140 solutions, all trivial).

last edited by David Renshaw at 2026-08-06 19:00:37 UTC · history