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For a given a,n ∈ N², find a d ∈ N such that the arithmetic progression (a + kd) consists entirely of primes for the first n entries.
This is an interesting one. Dirichlet's theorem on APs says that every AP has infinitely many primes
..but there is no guarantee that there exists an AP with the first n being all prime. It isn't obvious that a solution exists for every (a,n).