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Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 30

Is it true that, for every ε>0\varepsilon > 0, $h(N) = \sqrt N + O_{\varespilon}(N^\varespilon)

Mathematical statement

Is it true that, for every ε>0\varepsilon > 0, $h(N) = \sqrt N + O_{\varespilon}(N^\varespilon)

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_30

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_30 : answer(sorry)     ᵉ (ε > 0), (fun N => h N - (N : Real).sqrt) =O[atTop] fun N => (N : )^(ε : ) := 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