Number theory
$4,994 bountynobody has started
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
contrib new erdos-680-parts-iiCommand line, then a pull request on GitHub.
Nothing has been published against this problem yet.
A first lemma is worth as much as a last one: whoever closes the problem shares the pool with everyone who got them there.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«680»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos680.erdos_680.parts.ii" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ ∀ ε > 0, ∃ C > 0, ¬∀ᶠ (n : ℕ) in Filter.atTop, ∃ k, k ≠ 0 ∧ ↑(n + k).minFac > Real.exp ((1 + ε) * √↑k) + COriginal conjecture source: FormalConjectures/ErdosProblems/680.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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