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Erdős ProblemsNumber theory

Erdős Problem 1201

Is it true that for every ϵ,η>0\epsilon,\eta>0 there exists a kk such that the density of nn for which P(n(n+1)⋯(n+k))>n1−ϵP(n(n+1)\cdots(n+k))>n^{1-\epsilon} is at least 1−η1-\eta (where P(m)P(m) is the greatest prime divisor of mm)?

Number theoryAMS 11

Mathematical statement

Is it true that for every ϵ,η>0\epsilon,\eta>0 there exists a kk such that the density of nn for which P(n(n+1)⋯(n+k))>n1−ϵP(n(n+1)\cdots(n+k))>n^{1-\epsilon} is at least 1−η1-\eta (where P(m)P(m) is the greatest prime divisor of mm)?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_1201

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_1201 :    answer(sorry) ↔      ∀ ε > 0, ∀ η > 0, ∃ k : ℕ,        atTop.liminf (fun x : ℕ ↦          (((count (Erdos1201Set ε k) x : ℝ) / (x : ℝ)) : EReal)) ≥ (1 - η : EReal) := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References

Pinned Formal Conjectures sourceformalizationerdosproblems.com/1201background