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Number theory
Date added
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∈{1,…,p−1}
congruent to some product
a1a2
where
a1,a2∈A
?
$2,390 bounty·nobody has started
week of 18 Sept 2025 · nothing publishedweek of 25 Sept 2025 · nothing publishedweek of 2 Oct 2025 · nothing publishedweek of 9 Oct 2025 · nothing publishedweek of 16 Oct 2025 · nothing publishedweek of 23 Oct 2025 · nothing published
Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
True ↔
∀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
18 Sept 2025nothing published against this one yet10 Sept 2026
Ben Green's Open Problem 62
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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