smc

We are given that $p,q$ and $r$ are primes. In order for $p$ and $q$ to sum to another prime, either $p$ or $q$ has to be even, because the sum of two odd numbers would be even, and the only even prime is $2$ (but $p+q=2$ would have, as the only solution in positive integers, $p=q=1$, and $1$ is not prime). Thus, with one of either $p$ or $q$ being even, either $p$ or $q$ must be $2$, and as $p<q$, we deduce $p=2$ (as $2$ is the smallest prime). This means the answer is $\boxed{2}$.