Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers which tends to infinity sufficiently fast. If there is an $n$ such that all $n+a_k$ are primes then must there exist infinitely many such $n$?

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No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

1False ↔2  ∃ f,3    ∀ (a : ℕ → ℕ),4      StrictMono a →5        (∀ (k : ℕ), f k ≤ a k) → (∃ n, ∀ (k : ℕ), Nat.Prime (n + a k)) → {n | ∀ (k : ℕ), Nat.Prime (n + a k)}.Infinite

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