witness #1010

N: 25,375
|A|: 100
exponent log |A| / log N: 0.4541

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-06 21:29:35 UTC

Elements (100)

4930, 4931, 4935, 4936, 4958, 4960, 4963, 4965, 5016, 5021, 8700, 8701, 8705, 8706, 8728, 8730, 8733, 8735, 8786, 8791, 8845, 8846, 8850, 8851, 8873, 8875, 8878, 8880, 8931, 8936, 10730, 10731, 10735, 10736, 10758, 10760, 10763, 10765, 10816, 10821, 13920, 13921, 13925, 13926, 13948, 13950, 13953, 13955, 14006, 14011, 15225, 15226, 15230, 15231, 15253, 15255, 15258, 15260, 15311, 15316, 18270, 18271, 18275, 18276, 18298, 18300, 18303, 18305, 18356, 18361, 20155, 20156, 20160, 20161, 20183, 20185, 20188, 20190, 20241, 20246, 20880, 20881, 20885, 20886, 20908, 20910, 20913, 20915, 20966, 20971, 23345, 23346, 23350, 23351, 23373, 23375, 23378, 23380, 23431, 23436

Commentary

Product/lift construction: {a + 145·b : a ∈ A, b ∈ B} where A is the size-10 record for N=145 (witness 19) and B is the size-10 record for N=175 (witness 72), both due to Bhavik Mehta. Since the coefficients of a + 3b − 2c − 2d sum to zero, reducing any solution mod 145 forces the A-components to form a solution mod 145 (hence all equal), after which the relation 145·(b₁+3b₂−2b₃−2b₄) ≡ 0 mod 25375 forces the B-components to form a solution mod 175 (hence all equal). So solution-freeness lifts and sizes multiply: 10·10 = 100 elements mod 25375 = 145·175. Constructed and verified by Claude.

last edited by David Renshaw at 2026-08-06 21:29:35 UTC · history