Number theory
n ≥ 2, between the squares of the n-th and (n+1)-th primes,
there are at least four prime numbers.
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Formal statement
Proof target
import FormalConjectures.Wikipedia.BrocardConjecture
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Brocard.brocard_conjecture" := by
sorry
end Bounty
Original conjecture (Lean type)
∀ (n : ℕ),
1 ≤ n → 4 ≤ (Finset.filter Nat.Prime (Finset.Ioo (Nat.nth Nat.Prime n ^ 2) (Nat.nth Nat.Prime (n + 1) ^ 2))).cardOriginal conjecture source: FormalConjectures/Wikipedia/BrocardConjecture.lean
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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