How to show $\displaystyle (\forall n \in \mathbb{N}*) (2^{2n}+5)$ isn't a positive prime nimber????
$\displaystyle 2^2=4=1\!\!\!\pmod 3\Longrightarrow 2^{2n}=(2^2)^n=1\!\!\!\pmod n$ , and since $\displaystyle 5=2\!\!\!\pmod 3$ , we get $\displaystyle 2^{2n}+5=1+2=0\!\!\!\pmod 3$