If $p>3$ and $p+2$ are twin primes then $6\mid p+1$ I have to prove that if $p$ and $p+2$ are twin primes, $p>3$, then $6\ |\ (p+1)$. 
I figure that any prime number greater than 3 is odd, and therefore $p+1$ is definitely even, therefore $2\ |\ (p+1)$. And if I can somehow prove $3\ |\ (p+1)$, then I would be done. But I'm not sure how to do that. Help!

Note that for every integer $k$, exactly one of $k,k+1$ is divisible by $2$ and exactly one of $k,k+1,k+2$ is divisible by $3$. What do your hypothesis tell you if you put $k=p$?
