1203.lean`

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

3 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 1203

References:

erdosproblems.com/1203

Imports (1)

FormalConjecturesUtil

def Erdos1203.F If $\omega(n)$ counts the number of distinct prime divisors of $n$ then let $F(n)=\max_k \omega(n+k)\frac{\log\log k}{\log k}.$ line 38 source
Source documentation
If $\omega(n)$ counts the number of distinct prime divisors of $n$ then let $F(n)=\max_k \omega(n+k)\frac{\log\log k}{\log k}.$

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Real
Proof uses: iSup, HMul.hMul, ArithmeticFunction, ArithmeticFunction.cardDistinctFactors, HAdd.hAdd, HDiv.hDiv, Real.log
14 instances, coercions and auxiliary constants left out.
```
noncomputable def F (n : ℕ) : ℝ :=
…
```
theorem Erdos1203.erdos_1203 Prove that $F(n)\to \infty$ as $n\to \infty$ sorry line 45 source
Source documentation
Prove that $F(n)\to \infty$ as $n\to \infty$.

depends on sorry what this means
Statement uses: Iff, True, Filter.Tendsto, Nat, Real, Erdos1203.F, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
5 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1203 :
    answer(sorry) ↔ Tendsto F atTop atTop := by
…
```
Mentions: Erdos1203.F
theorem Erdos1203.erdos_1203.variants.lower_bound It is easy to prove that $F(n)\geq 1-o(1)$ sorry line 53 source
Source documentation
It is easy to prove that $F(n)\geq 1-o(1)$.

depends on sorry what this means
Statement uses: Real, GT.gt, OfNat.ofNat, Filter.Eventually, Nat, GE.ge, Erdos1203.F, HSub.hSub, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
19 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1203.variants.lower_bound :
    ∀ ε > 0, ∀ᶠ n in atTop, F n ≥ 1 - ε := by
…
```
Mentions: Erdos1203.F