erdos_695

Let $q_1 < q_2 < \cdots$ be a sequence of primes such that $q_{i + 1} \equiv 1 \pmod{q_i}$. Is it true that $$ \lim_{k \to \infty} q_k^{1/k} = \infty? $$

theorem erdos_695 : answer(sorry) ↔
    ∀ {q : ℕ → ℕ},
      StrictMono q →
      (∀ i, (q i).Prime) →
      (∀ i, q (i + 1) % q i = 1) →
      Tendsto (fun k => (q k : ℝ) ^ (1 / k : ℝ)) atTop atTop

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