What is the smallest degree of a reducible polynomial \(f\) with integer coefficients, such that \( \lvert f(n) \rvert \) is a prime number for at least \(10\) different integer values of \(n?\)

**Details and assumptions**

A polynomial with integer coefficients is called **reducibl**e if it can be written as a product of two non-constant polynomials with integer coefficients.

You may refer to this List of 1000 Primes.

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