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 $a_1, a_2 \in A$?

This is a problem of Erdős, Odlyzko, and Sárközy [105] from 1987.

Reference: Ben Green's Open Problem 62

theorem Green62.green_62 : sorry ↔ ∀ᶠ (p : ℕ) in Filter.atTop, Nat.Prime p → have A := Finset.filter Nat.Prime (Finset.range p); ∀ (x : ℕ), 1 ≤ x ∧ x < p → ∃ a₁ ∈ A, ∃ a₂ ∈ A, ↑x = ↑a₁ * ↑a₂

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 $a_1, a_2 \in A$?