witness #1516

N: 3,550
|A|: 47
exponent log |A| / log N: 0.4710

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-07 14:59:14 UTC

Elements (47)

5, 11, 20, 30, 36, 148, 150, 173, 175, 431, 456, 711, 715, 720, 721, 736, 740, 745, 746, 853, 878, 1141, 1166, 1565, 1570, 1573, 1590, 1595, 1598, 1856, 1881, 2140, 2165, 2275, 2283, 2290, 2300, 2308, 2576, 2841, 2846, 2866, 2871, 2983, 3008, 3276, 3301

Commentary

Found by a fast destroy-and-refill search specialized to the 71×2×5^2 family, starting from the earlier 44-point witness at N=3550. The search improved 44→45→46→47. Structurally, modulo 710 the projection contains all 20 residues of the 20-point N=710 witness plus seven auxiliary residues {11,20,26,143,160,168,446}; the fibers in Z/5 have sizes 2 (20 fibers) and 1 (7 fibers). In CRT coordinates Z/71 × Z/50, the projection modulo 71 has 16 residues, extending the N=710 projection by {18,20,26}.

last edited by Yongxi (Aaron) Lin at 2026-08-07 14:59:14 UTC · history