green_58

Suppose $A, B ⊆ \{1, \dots, N\}$ both have size at least $N^{0.49}$. Must the sumset $A + B$ contain a composite number?

theorem green_58 :
    answer(sorry) ↔
      ∀ᵉ (N ≥ (1 : ℕ)) (A ⊆ Finset.Icc 1 N) (B ⊆ Finset.Icc 1 N),
        (N : ℝ) ^ (0.49 : ℝ) ≤ (A.card : ℝ) →
        (N : ℝ) ^ (0.49 : ℝ) ≤ (B.card : ℝ) →
        ∃ m ∈ (A + B), m.Composite

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