Source labels openChecked July 26, 2026

Ben Green's Open Problem 58

Suppose $A, B ⊆ \{1, \dots, N\}$ both have size at least $N^{0.49}$ . Must the sumset $A + B$ contain a composite number?

Combinatorics AMS 5 AMS 11

Mathematical statement

Suppose $A, B ⊆ \{1, \dots, N\}$ both have size at least $N^{0.49}$ . Must the sumset $A + B$ contain a composite number?

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_58

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_58 :    answer(sorry) ↔      ∀ᶠ (N : ℕ) in Filter.atTop, ∀ᵉ (A ⊆ Finset.Icc 1 N) (B ⊆ Finset.Icc 1 N),        (N : ℝ) ^ (0.49 : ℝ) ≤ (A.card : ℝ) →        (N : ℝ) ^ (0.49 : ℝ) ≤ (B.card : ℝ) →        ∃ m ∈ (A + B), m.Composite := 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 Ben Green's Open Problem 58background