Consider the polynomial \(P(x) = x^3 - 7x^2 + 14x - k\), where \(k\) is an integer. Given that the roots of the polynomial are all prime numbers, and one of the roots is 2, find the value of \(k\). Verify if \(k\) is a prime number. Let's think step by step and output the final answer within \boxed{}.
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