Erdős Problem 291: Shiu Heuristic Density Zero
In particular, there should be infinitely many , but the set of such should have density zero. Unfortunately this heuristic is difficult to turn into a proof.
Mathematical statement
In particular, there should be infinitely many , but the set of such should have density zero. Unfortunately this heuristic is difficult to turn into a proof.
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_291.variants.shiu_heuristic_density_zero
theorem erdos_291.variants.shiu_heuristic_density_zero : Filter.Tendsto (fun N : ℕ ↦ ((((Finset.Icc 1 N).filter (fun n ↦ Nat.gcd (a n) (L n) = 1)).card : ℝ) / (N : ℝ))) atTop (nhds 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