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feat(ErdosProblems/888): record 2026 order-of-growth solution#4380

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feat(ErdosProblems/888): record 2026 order-of-growth solution#4380
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Sanexxxx777:erdos-888-order-of-growth

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@Sanexxxx777

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erdosproblems.com/888 now marks the problem SOLVED: the order of growth of the extremal set is $\Theta(n \log\log n / \log n)$ — the semiprimes (noted by Cambie and Weisenberg) give the sharp lower bound, and a matching upper bound $f(n) \ll n \log\log n/\log n$ was proved by GPT-5.5 Pro (prompted by Chojecki). This records both sharp bounds as research solved variants and updates the module docstring.

The main theorem erdos_888 asks for the exact value of Nat.findGreatest, which is only known up to constants, so it stays research open — happy to adjust if the maintainers prefer a different treatment.

Closes #4099

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github-actions Bot commented Jul 2, 2026

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👋 This is an automated welcome message. 🤖
Thanks for the contributions!

A few friendly reminders while the review gets started:

  • Please take a look at the style guidelines,
    especially the conventions for references, categories, AMS tags, and answer(sorry).
  • You can manage some PR labels by leaving a comment with +label-name or -label-name; for example, +awaiting-author or -awaiting-author.
  • This repository is mainly for formalised statements. Proofs longer than about 25-50 lines are usually out of scope; longer proofs are welcome to be included/linked via the formal_proof mechanism.

Thanks again for helping improve Formal Conjectures.

@github-actions github-actions Bot added the erdos-problems Erdős Problems label Jul 2, 2026
@danielchin

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Looks like I may have beaten you to the punch, this is a duplicate of #4376

@Sanexxxx777

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You're right — #4376 covers this and more (the status change matches the site's SOLVED marker, plus the category-count fix in FC100OpenSet1). Closing in favour of yours. Thanks for pointing it out!

@Sanexxxx777 Sanexxxx777 closed this Jul 3, 2026
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Erdős Problem 888: status mismatch (repo=open, erdosproblems.com=solved)

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