witness #2314

N: 3,360
|A|: 33
exponent log |A| / log N: 0.4306

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-10 09:47:30 UTC

Elements (33)

1345, 2043, 2055, 2103, 2118, 2153, 2159, 2168, 2174, 2228, 2234, 2243, 2249, 2400, 2405, 2430, 2475, 2608, 2620, 2623, 2635, 2683, 2695, 2698, 2733, 2754, 2778, 2784, 2808, 2950, 2995, 3200, 3230

Commentary

Tail/arc-compression search. Started from the transferable size-32 core, which at N=3360 lies entirely above N/2. Sweeps at N/4, 0.30N, N/3, 3N/8, 2N/5, 0.45N, N/2 found no direct insertion; exhaustive 1->2 at representative thresholds and exact 2->3 at N/4, 2N/5, N/2 also stalled. A deeper sampled 3->4 search at N/4 found {1802,2427,2727} -> {1062,2667,2917,2947}, giving size 33. The new set occupies an arc of span 1885, so translating by +283 repacks the full size-33 witness above 2N/5 (min 1345 > 1344). Exact direct/1->2/2->3 regrowth from the repacked state and 1200 sampled 3->4 branches at 2N/5 found no size 34.

last edited by Yongxi (Aaron) Lin at 2026-08-10 09:47:30 UTC · history