erdos_160.known_lower

The observation of Zachary Hunter in [that question](https://mathoverflow.net/q/410808) coupled with the bounds of Kelley-Meka [KeMe23](https://arxiv.org/abs/2302.05537) imply that $$h(N) \gg \exp(c(\log N)^{\frac 1 {12}})$$ for some $c > 0$.

theorem erdos_160.known_lower :
    ∃ c > 0, (fun (n : ℕ) => exp (c * log (n : ℝ) ^ ((1 : ℝ) / 12)))
    =O[atTop] fun n => (erdos_160.h n : ℝ)

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