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Erdős problem 1209

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Let A={a1<a2<⋯ }A=\{a_1<a_2<\cdots\} be a sequence of integers which tends to infinity sufficiently fast. If there is an nn such that all n+akn+a_k are primes then must there exist infinitely many such nn?

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6 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

1209.lean

Retained formal statement2 of 6

What if we ask for n+akn+a_k to be squarefree instead of prime?

A similar construction provides a counterexample to the squarefree question.

FormalConjectures/ErdosProblems/1209.leanErdos1209.erdos_1209.parts.ii5 linesExact file
False ↔  ∃ f,    ∀ (a : ℕ → ℕ),      StrictMono a →        (∀ (k : ℕ), f k ≤ a k) → (∃ n, ∀ (k : ℕ), Squarefree (n + a k)) → {n | ∀ (k : ℕ), Squarefree (n + a k)}.Infinite
SolvedStatement only, no proof