Power of 2 containing no Digit 2

Theorem
$2^{168}$ contains no $2$ anywhere in its decimal representation.

Proof

 * $2^{168} = 374 \, 144 \, 419 \, 156 \, 711 \, 147 \, 060 \, 143 \, 317 \, 175 \, 368 \, 453 \, 031 \, 918 \, 731 \, 001 \, 856$