FormalConjectures.ErdosProblems.«431»

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import FormalConjecturesUtil

Erdős Problem 431

Reference: erdosproblems.com/431

namespace Erdos431open scoped Pointwise

Are there two infinite sets $A$ and $B$ such that $A+B$ agrees with the primes up to finitely many exceptions?

@[category research open, AMS 11]
theorem erdos_431 : answer(sorry) ↔
    ∃ A B : Set ℕ, A.Infinite ∧ B.Infinite ∧
      (A + B : Set ℕ) =ᶠ[Filter.cofinite] {n | n.Prime} := by⊢ True ↔ ∃ A B, A.Infinite ∧ B.Infinite ∧ A + B =ᶠ[Filter.cofinite] {n | Nat.Prime n}
  sorryAll goals completed! 🐙

end Erdos431