Hello,

huh

2 divides $\displaystyle 2^{66}$, therefore it is not prime

Another way :

$\displaystyle 2^{66}-1=(2^{33}-1)(2^{33}+1)$

$\displaystyle \implies 2^{66}=(2^{33}-1)(2^{33}+1)+1$

But since $\displaystyle 2^{33}$ is an even number, $\displaystyle 2^{33}-1 \text{ and } 2^{33}+1$ are odd numbers. Thus their product is an odd number.

If we substract 1 to it, we get an even number. Hence $\displaystyle 2^{66}$ is an even number (and different from 2), so it is not prime.

But that's finding the most complicated way...