It is not prime. By Sophie Germain's Identity (see %%HREF%%3863%%), we have \begin{align} &4^{545} + 545^{4}\\ =& 545^4 + 4\times (4^{136})^4\\ =&(545^2 + 2\times (4^{136})^2 + 2\times 545\times 4^{136})(545^2 + 2\times (4^{136})^2 - 2\times 545\times 4^{136}) \end{align}