erdos_458

Let $\operatorname{lcm}(1, \dots, n)$ denote the least common multiple of $\{1, \dots, n\}$. Let $p_k$ be the $k$-th prime. Is it true that for all $k \geq 1$, $\operatorname{lcm}(1, \dots, p_{k+1}-1) < p_k \cdot \operatorname{lcm}(1, \dots, p_k)$?

theorem erdos_458 :
    answer(sorry) ↔ ∀ k : ℕ, lcm_upto ((k + 1).nth Prime - 1)
     < k.nth Prime * lcm_upto (k.nth Prime)

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