If $\displaystyle f(x) = \sum_{j=0}^{n}a_{j}x^j\in\mathbb{Z}[x]$ is such that $\displaystyle f(10) $ is prime and $\displaystyle 0\le a_{j} \le 10^{15}a_{n}$ for $\displaystyle j\in\left\{0, 1, \ldots n-1\right\}$, prove that $\displaystyle f(x)$ is irreducible.