erdos_463

Is there a function $f$ with $f(n)\to\infty$ as $n\to\infty$ such that, for all large $n$, there is a composite number $m$ such that $$ n + f(n) < m < n + p(m) $$ Here $p(m)$ is the least prime factor of $m$.

theorem erdos_463 : answer(sorry) ↔ ∃ (f : ℕ → ℕ) (_ : Tendsto f atTop atTop),
    ∀ᶠ n in atTop,
      ∃ m, m.Composite ∧
        n + f n < m ∧ m < n + m.minFac

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