Erdős problem 1209 · problems.science

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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6 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1209.lean

Retained formal statement2 of 6

What if we ask for $n+a_k$ 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

1False ↔2  ∃ f,3    ∀ (a : ℕ → ℕ),4      StrictMono a →5        (∀ (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

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