$2^2=4$

$2^4={\left(2^2\right)}^2=4^2=16$

$2^8={\left(2^4\right)}^2={16}^2=256$

$2^{10}=2^8\cdot 2^2=256\cdot 4=1024$

$2^{20}={\left(2^{10}\right)}^2={1024}^2=1048576>1000000$