This article on Wikipedia: http://en.wikipedia.org/wiki/Bunyakovsky_conjecture says:
In fact, it can be shown that if for all natural number $ n $, there exists a natural number $ x > 1 $ such that $ \Phi_n(x) $ is prime, then for all natural number $ n $, there are infinitely many natural number $ x $ such that $ \Phi_n(x) $ is prime.
(Where $ \Phi_n(x) $ is the $ n $-th cyclotomic polynomial)
However, there is no reference to the proof. Could you please post the proof or a link to it?
I'm not sure where this claim originally came from or what the intended proof of it was, but it follows quite easily from one property of cyclotomic polynomials (Wikipedia link): $$\Phi_n(x) = \Phi_q(x^{n/q}),$$ where $q$ is the largest square-free factor of $n$. From this property, we see that if $p$ is a prime dividing $n$, then, since the largest square-free divisor of $p^k n$ is also $q$, $$\Phi_{p^k n}(x) = \Phi_q(x^{p^k n/q}) = \Phi_q((x^{p^k})^{n/q}) = \Phi_n(x^{p^k}).$$ Suppose that, for all $n$, we can find an integer $x>1$ such that $\Phi_n(x)$ is prime. Then, in particular, we can find integers $x_1, x_2, \dots$ such that $\Phi_{p^k n}(x_k)$ is prime, for each $k$. But this means that $\Phi_n((x_k)^{p^k})$ is prime, for each $k$. So the sequence $$(x_1)^p, (x_2)^{p^2}, (x_3)^{p^3}, \dots$$ is an infinite sequence of values at which $\Phi_n$ is prime. (Some of these values might happen to repeat, but that's okay, since each value can only repeat finitely many times.)