Source labels openChecked July 26, 2026

Erdős Problem 18

Conjecture 2.* Is it true that $h(n!) < n^{o(1)}$ ? That is, for all $\varepsilon > 0$ , is $h(n!) < n^\varepsilon$ for sufficiently large $n$ ?

Number theory AMS 11

Mathematical statement

Conjecture 2.* Is it true that $h(n!) < n^{o(1)}$ ? That is, for all $\varepsilon > 0$ , is $h(n!) < n^\varepsilon$ for sufficiently large $n$ ?

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_18b

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_18b : answer(sorry) ↔    ∀ ε : ℝ, 0 < ε → ∀ᶠ n : ℕ in atTop, (practicalH n.factorial : ℝ) < (n : ℝ) ^ 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

Pinned Formal Conjectures sourceformalization erdosproblems.com/18background