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Erdős Problem #451

Number theory · posed by 1979 · partial

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Statement

Let nkn_k be the least integer greater than 2k2k for which ∏i=1k(nk−i)\prod_{i=1}^k (n_k - i) has no prime factor in (k,2k)(k, 2k). How rapidly must nkn_k grow?

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    GPT-5.5 Pro

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    the conjectured superpolynomial growth is established; the sharper order remains open

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