TITLE: Is there more than one occurrence of a power of two between twin primes?
QUESTION [9 upvotes]: $2^2$ is between the twin primes $3$ and $5$.  Are there any other instances of a power of two between twin primes?  If so, how many?  
That there are Mersenne primes (primes of the form $2^n-1$) makes this a little more tantalizing, but a brief search didn't spit out any results right away.

REPLY [2 votes]: Just some basics.  Twin primes use the last digits of 1 & 3, 7 & 9, and 9 & 1 5 is and exception to the general rule.  The powers of 2 use the last digits of 2, 4, 6, and 8.  The only valid powers of 2 will have the last digits of 2 and 8.  2^2 = 4 and 2^3 = 8.  Lots of luck trying to find more of them.