Infinitely many pairs of sexy primes? I recently discovered what sexy primes are, primes of the form (p,p+6), where p is a prime. I have no background in number theory so pardon me if the answer is trivial. 
So are there infinitely many pairs of them? Is there any reading material on them? Or a proof or counter example I can study? Thanks for your time.

We know that there is at least one difference smaller than seventy million (this result may have been improved since) which gives infinitely many pairs of primes. Whether $6$ is one of them we don't know.
