Is $545^4 + 4^{545}$ a prime number?

We can go through this using primitive steps. (Proceeding after the two steps given in my approach) Let $545=x$ and $4^{136}=y$. Thus, the expression becomes : $$x^4+4y^4$$ Adding and subtracting by $4x^2y^2$, we get, $${(x^2+2y^2)}^2-{(2xy)}^2$$ This can be written as : $$(x^2+2y^2+2xy)(x^2+2y^2-2xy)$$

Now, since there are two factors to the original expression excluding $1$ and itself, the expression $545^4+4^{545}$ is not a prime.