witness #2313

N: 3,345
|A|: 32
exponent log |A| / log N: 0.4271

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-10 09:44:42 UTC

Elements (32)

1760, 1772, 1802, 1820, 1835, 1870, 1876, 1885, 1891, 1945, 1951, 1960, 1966, 2117, 2122, 2147, 2192, 2325, 2337, 2340, 2352, 2400, 2412, 2415, 2427, 2450, 2471, 2495, 2501, 2525, 2712, 2727

Commentary

Tail/arc-compression search. Transferred the compact 32-element upper-tail core from nearby successful moduli. At N=3345 the whole set lies above N/2 (min=1760 > 1672.5). Swept thresholds N/4, N/3, 2N/5, N/2 and nearby 0.30, 3/8, 0.45; no direct insertion. Exhaustive 1->2 and 2->3 searches at representative thresholds found no growth, and sampled 3->4 searches reached refill pools up to 11 without a compatible 4-refill. Submitted the verified size-32 hard-tail core.

last edited by Yongxi (Aaron) Lin at 2026-08-10 09:44:42 UTC · history