Is it prime?

$2^{999} - 1 = (2^{333})^3 - (1)^3 = (2^{333} - 1) × (2^{666} + 2^{333} + 1)$

Hence, our answer should be:

$\boxed { \text {No} }$

$\large \color{#3D99F6} \text{As a matter of fact:}\ 2^x \ -1 \text{ will never ever be a prime number, where x is not a prime integer.}$