462.lean`

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L4DEL: Lean4 Domain Explanation Language

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 462

Reference: erdosproblems.com/462

Imports (1)

FormalConjecturesUtil

theorem Erdos462.erdos_462 Let $p(n)$ denote the least prime factor of $n$ sorry line 39 source
Source documentation
Let $p(n)$ denote the least prime factor of $n$. Is there a constant $C>0$ such that $$\sum_{x\leq n\leq x+C\sqrt{x}(\log x)^2}\frac{p(n)}{n}\gg 1$$ for all sufficiently large $x$?

depends on sorry what this means
Statement uses: Iff, True, Exists, Real, And, LT.lt, OfNat.ofNat, Filter.Eventually, Nat, LE.le, Finset.sum, Finset.Icc, Nat.floor, HAdd.hAdd, HMul.hMul, Real.sqrt, HPow.hPow, Real.log, HDiv.hDiv, Nat.minFac and 1 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
54 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_462 : answer(sorry) ↔
    ∃ C c : ℝ, 0 < C ∧ 0 < c ∧ ∀ᶠ x : ℕ in atTop,
      c ≤ ∑ n ∈ Finset.Icc x
        ⌊(x : ℝ) + C * Real.sqrt x * (Real.log x) ^ 2⌋₊, (n.minFac : ℝ) / n := by
…
```
Mentions: c