There exist a non constant polynomials such that f(Z) contained in set of prime number

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There is no non-constant polynomial f ∈ ℤ[X] such that f(x) is prime for every x ∈ ℤ. There is no non-constant polynomial f ∈ ℤ[X] such that f(x) is prime for every x ∈ ℤ.
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