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upper_bound

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Is it true that $$N(b) \ll \log \log b$$?

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Lean 4 Statement 
theorem upper_bound : answer(sorry) ↔
    (fun b : ℕ => (smallestCollectionTo b : ℝ)) =O[atTop] (fun b : ℕ => Real.log (Real.log b))
ID: ErdosProblems__304__upper_bound
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