1137.lean`

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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 1137

Reference: erdosproblems.com/1137

Imports (1)

FormalConjecturesUtil

theorem Erdos1137.erdos_1137 Let $d_n=p_{n+1}-p_n$, where $p_n$ denotes the $n$th prime sorry line 38 source
Source documentation
Let $d_n=p_{n+1}-p_n$, where $p_n$ denotes the $n$th prime. Is it true that $$\frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0$$ as $x\to \infty$?

depends on sorry what this means
Statement uses: Iff, True, Filter.Tendsto, Nat, Real, HDiv.hDiv, Finset.sup, Finset.range, HMul.hMul, primeGap, HSub.hSub, OfNat.ofNat, HPow.hPow, Filter.atTop, nhds
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
46 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1137 :
    answer(sorry) ↔
     Tendsto (fun x ↦
        (((range x).sup (fun n ↦ (primeGap n) * (primeGap (n - 1))) : ℕ) : ℝ) /
        (((range x).sup primeGap : ℕ) : ℝ) ^ 2) atTop (𝓝 0) := by
…
```
Mentions: primeGap