Is $545^4 + 4^{545}$ a prime number? The main question is :
Is $545^4 + 4^{545}$ a prime number? Explain your answer.
My approach :
I tried writing the expression as, 
$$545^4 + 4*4^{544}$$
Thus we get,
$$545^4 + 4*{(4^{136})}^4$$
I can't proceed any further. Is there some obvious thing or concept I'm missing? This question is a base-level olympiad question, thus there must be some short solution to this. I will appreciate if you can give a detailed answer, along with a shortcut if you have one, so that I understand the concept thoroughly. Thanks! 

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.
