Source labels openChecked July 26, 2026

Erdős Problem 932

Let $p_k$ denote the $k$ th prime. For infinitely many $r$ there are at least two integers $p_r < n < p_{r+1}$ all of whose prime factors are $< p_{r + 1} - p_r$ .

Number theory AMS 11

Mathematical statement

Let $p_k$ denote the $k$ th prime. For infinitely many $r$ there are at least two integers $p_r < n < p_{r+1}$ all of whose prime factors are $< p_{r + 1} - p_r$ .

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_932

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_932 :    { r : ℕ | 2 ≤ (Finset.Ioo (r.nth Nat.Prime) (r.succ.nth Nat.Prime) |>.filter      (fun m => m.maxPrimeFac < r.succ.nth Nat.Prime - r.nth Nat.Prime)).card }.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/932background