Source labels openChecked July 26, 2026

Erdős Problem 1072: Ii

Is it true that $f(p)/p \to 0$ for $p \to \infty$ in a density 1 subset of the primes?

Number theory AMS 11

Mathematical statement

Is it true that $f(p)/p \to 0$ for $p \to \infty$ in a density 1 subset of the primes?

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_1072.parts.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1072.parts.ii :    answer(sorry) ↔ ∃ (P : Set ℕ), P ⊆ {p | p.Prime} ∧ P.HasDensity 1 {p | p.Prime} ∧      Tendsto (fun p => (f p / p : ℝ)) (atTop ⊓ principal P) (𝓝 0) := 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/1072background