Source labels openChecked July 26, 2026

Ben Green's Open Problem 62

Let $p$ be a large prime, and let $A$ be the set of all primes less than $p$ . Is every $x \in \{1, \ldots, p-1\}$ congruent to some product $a_1 a_2$ where $a_1, a_2 \in A$ ?

Number theory AMS 11

Mathematical statement

Let $p$ be a large prime, and let $A$ be the set of all primes less than $p$ . Is every $x \in \{1, \ldots, p-1\}$ congruent to some product $a_1 a_2$ where $a_1, a_2 \in A$ ?

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_62

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_62 :    answer(sorry) ↔      ∀ᶠ p in atTop, p.Prime →        let A := (Finset.range p).filter Nat.Prime        ∀ x : ℕ, 1 ≤ x ∧ x < p →          ∃ a₁ ∈ A, ∃ a₂ ∈ A, (x : ZMod p) = (a₁ * a₂ : ZMod p) := 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 62background