Source labels openChecked July 26, 2026

Erdős Problem 463

Is there a function $f$ with $f(n)\to\infty$ as $n\to\infty$ such that, for all large $n$ , there is a composite number $m$ such that $n + f(n) < m < n + p(m)$ Here $p(m)$ is the least prime factor of $m$ .

Number theory AMS 11

Mathematical statement

Is there a function $f$ with $f(n)\to\infty$ as $n\to\infty$ such that, for all large $n$ , there is a composite number $m$ such that

n + f(n) < m < n + p(m)

Here $p(m)$ is the least prime factor of $m$ .

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_463

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_463 : answer(sorry) ↔ ∃ (f : ℕ → ℕ) (_ : Tendsto f atTop atTop),    ∀ᶠ n in atTop,      ∃ m, m.Composite ∧        n + f n < m ∧ m < n + m.minFac := 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/463background