All open problems
Source labels openChecked July 26, 2026
Green's Open ProblemsNumber theory
Ben Green's Open Problem 7: Positive Density
Does Ulam's sequence have positive density?
Mathematical statement
Does Ulam's sequence have positive density?
Statement source: Green's Open 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
green_7.variants.positive_density
Complete statement target, proof intentionally absentLean 4
theorem green_7.variants.positive_density : answer(sorry) ↔ ∀ a : ℕ → ℕ, Erdos342.IsUlamSequence a → Set.upperDensity (Set.range a) > 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