Reductio Ad Absurdum

Find the largest possible number of distinct integer values \(\{x_1, x_2, \ldots x_n\}\), such that for a fixed reducible degree four polynomial with integer coefficients, \(|f(x_i)|\) is prime for all \(i\).

Details and assumptions

A polynomial with integer coefficients is called reducible if it is a product of two non-constant polynomials with integer coefficients.

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