Source labels openChecked July 26, 2026

Erdős Problem 18

Conjecture 3.* Or perhaps even $h(n!) < (\log n)^{O(1)}$ ?

Number theory AMS 11

Mathematical statement

Conjecture 3.* Or perhaps even $h(n!) < (\log n)^{O(1)}$ ?

Erdős offered $250 for a proof or disproof.

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_18c

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_18c : answer(sorry) ↔    ∃ C : ℝ, 0 < C ∧ ∀ᶠ n : ℕ in atTop, (practicalH n.factorial : ℝ) < (log n) ^ C := 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