Source labels openChecked July 26, 2026

Erdős Problem 385: I

Let $F(n) := \max\{m + p(m) \mid \textrm{$ m < n $composite}\}\}$ where $p(m)$ is the least prime divisor of $m$ . Is it true that $F(n)>n$ for all sufficiently large $n$ ?

Number theory AMS 11

Mathematical statement

Let $F(n) := \max\{m + p(m) \mid \textrm{$ m < n $composite}\}\}$ where $p(m)$ is the least prime divisor of $m$ . Is it true that $F(n)>n$ for all 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_385.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_385.parts.i : answer(sorry) ↔ ∀ᶠ n in atTop, n < F n := 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/385background