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erdos_32.variants.log_bound

Specification

Can the bound $O(\log N)$ be achieved for an additive complement to the primes? [Guy04] writes that Erdős offered \$50 for the solution.

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Lean 4 Statement 
theorem erdos_32.variants.log_bound : answer(sorry) ↔ ∃ A : Set ℕ,
    IsAdditiveComplementToPrimes A ∧
    (fun N => (((Finset.Icc 1 N).filter (· ∈ A)).card : ℝ)) =O[atTop]
      fun N => Real.log N
ID: ErdosProblems__32__erdos_32.variants.log_bound
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