witness #989

N: 701
|A|: 17
exponent log |A| / log N: 0.4324

status: current record for this modulus
submitted by: David Renshaw
submitted at: 2026-08-05 03:18:43 UTC

Elements (17)

77, 114, 159, 195, 197, 262, 271, 283, 301, 343, 412, 486, 507, 526, 567, 641, 674

Commentary

Found by a dedicated fixed-cardinality search at modulus 701. Starting from witness #110, residue 63 was the least-conflicting possible 17th element (six ordered nontrivial solutions). A tabu search that evaluated every one-residue swap crossed the local barriers and found this set after 3,035 iterations. Direct enumeration gives exactly 17 solutions to a+3b=2c+2d, all diagonal.

last edited by David Renshaw at 2026-08-05 03:18:54 UTC · history