Prime pairs six apart

Statement

How many pairs $(p,q)$ of primes with $p<q<50$ satisfy $q-p=6$?

Solution

Scan the primes $p$ and check whether $p+6$ is also prime (and less than $50$): $(5,11),\;(7,13),\;(11,17),\;(13,19),\;(17,23),\;(23,29),\;(31,37),\;(37,43),\;(41,47).$ There are $\boxed{9}$ pairs. (For example $29\to 35$ and $43\to 49$ do not give primes.)