Are there any twin primes of the form $2^n − 1$, $2^n + 1$, for $n > 2$? If so, give an example, and if not, prove there aren’t any.
Hint: $k$, $k + 1$, $k + 2$ is a complete residue system modulo $3$, for any choice of $k$.
I've tried to find an example of twin primes of the form specified above, but I can't seem to find any (simply through guess and check). How can I prove that there are no primes of the above form?