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No.

Given any positive integer N, the set of N consecutive numbers

from (N + 1)! + 2

to (N + 1)! + N + 1

are composite.

This is because, for 2 ≤ k ≤ n+1,

(n + 1)! is divisible by k and so (n + 1)! + k is also divisible by k.

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