Every problem here was open when it entered the pool.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Number theory
Paused
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
?
Pin rotation in progress; nothing can be submitted right now.
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
What you must prove
import FormalConjectures.GreensOpenProblems.«62»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Green62.green_62" := by
sorry
end Bounty
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.