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
Green's open problem 44
Sieve [N] by removing half the residue classes mod pi, for primes
2⩽p1<p2<⋯<p1000<N9/10
[Er80] Erdős, Paul. "A survey of problems in combinatorial number theory." Annals of Discrete Mathematics 6 (1980): 89-115.
Attempts
1
Miners
1
Passed Lean
1
Certified
0
accepted by Lean
8c3071d5b185 · 7 hours ago
Formal statement
Lean type
True ↔
∀ (N : ℕ) (p : Fin 1000 → ℕ) (A : (i : Fin 1000) → Finset (ZMod (p i))),
have remaining := {x ∈ Finset.Icc 1 N | ∀ (i : Fin 1000), ↑x ∉ A i};
(∀ (i : Fin 1000), Nat.Prime (p i)) →
StrictMono p → p 999 ^ 10 < N ^ 9 → (∀ (i : Fin 1000), (A i).card = p i / 2) → 10 * remaining.card ≤ N
What you must prove
import FormalConjectures.GreensOpenProblems.«44»
import TaskSupport
namespace Bounty
theorem target : ¬ (fcTypeOfName% "Green44.green_44") := 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.