Source labels openChecked July 26, 2026

Erdős Problem 647: Infinite

Erdős says it 'seems certain' that for every $k$ there are infinitely many $n$ for which $\max_{n−k < m < n}(m + \tau(m)) ≤ n + 2.$

Number theory AMS 11

Mathematical statement

Erdős says it 'seems certain' that for every $k$ there are infinitely many $n$ for which

\max_{n−k < m < n}(m + \tau(m)) ≤ n + 2.

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_647.variants.infinite

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_647.variants.infinite :    answer(sorry) ↔ ∀ k, { n | ⨆ m : Set.Ioo (n - k) n, ↑m + σ 0 m ≤ n + 2 }.Infinite := 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 sourceformalization erdosproblems.com/647background