Source labels openChecked July 26, 2026

Erdős Problem 942

Is there some constant $c > 0$ such that $h(n) < (\log n)^{c + o(1)}$ and, for infinitely many $n$ , $h(n) > (\log n)^{c - o(1)}$ .

Number theory AMS 11

Mathematical statement

Is there some constant $c > 0$ such that $h(n) < (\log n)^{c + o(1)}$ and, for infinitely many $n$ , $h(n) > (\log n)^{c - o(1)}$ .

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_942

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_942 : answer(sorry) ↔ ∃ c > 0, ∃ (o : ℕ → ℝ), o =o[atTop] (1 : ℕ → ℝ) ∧    (∀ᶠ n in atTop, erdos_942.h n < (Real.log n) ^ (c + o n)) ∧    {n | erdos_942.h n > (Real.log n) ^ (c - o n)}.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/942background