Sum of prime values of Cyclotomic Polynomials of an integer evaluated at an integer

Question

$\Phi_n(x)$ is the nth cyclotomic polynomial evaluated at a specific integer $x$. The prime indicator function $\mathrm{Id}(n)$ is $1$ when $n$ is a prime number, $0$ otherwise.

What is the value of this sum?

$$\sum_{n=1}^\infty \mathrm{Id}\left( \Phi_n(x) \right) $$