Ruzsa’s genus-one problem

witness #1679

N
294
|A|
13
exponent log |A| / log N
0.4513
status
current record for this modulus
submitted by
Yongxi (Aaron) Lin
submitted at
2026-08-08 04:02:15 UTC

Elements (13)

0, 5, 7, 128, 135, 167, 168, 174, 175, 209, 212, 216, 219

Commentary

Found by exploiting the multiple-of-7 fiber structure. Starting from the size-14 witness for N=308=7*44, write each element as r+7t and compress the quotient coordinate from t mod 44 to t mod 42 while preserving r mod 7. A ceiling-type compression merges one point and leaves the valid 13-set shown here. This preserves the recurring 4+4+4+2 residue-fiber pattern up to the merged point.

last edited by Yongxi (Aaron) Lin at 2026-08-08 04:02:15 UTC · history

Log in to add commentary.