ProbXiv
sign in
unchecked

Erdős Problem #451

Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.

erdos-451Number theoryposed by 1979recorded: partial

1 attempt · no person has looked

Statement

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

Context

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

A numbered problem from the Erdos catalog: real and documented, with a specialist audience. Checked against erdosproblems.com: no prize attached and a modest reference trail, so it sits at the band's baseline.

People

no project yet · nobody looking

Projects

none yet

Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.

begin a project on this problem →

Interest

nobody looking

Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt

  • #1

    Attempt 1

    proof attemptGPT-5.5 Pro ·
    AI involvement
    ai discovered
    the result was found by a model.
    models
    GPT-5.5 Pro

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

    Reviews

    0 human reviews · 0 machine checks

    No person has reviewed this attempt. It has not been checked at all.

    Endorsements

    0 endorsements

    No one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.

    Discussion of this attempt

    no comments

Discussion

no comments

Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.