erdos_370

Are there infinitely many $n$ such that the largest prime factor of $n$ is $< n^{\frac{1}{2}}$ and the largest prime factor of $n + 1$ is $< (n + 1)^{\frac{1}{2}}$. Steinerberger has pointed out this problem has a trivial solution.

theorem erdos_370 : answer(True) ↔
    { n | Nat.maxPrimeFac n < √n ∧ Nat.maxPrimeFac (n + 1) < √(n + 1) }.Infinite

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