G1.2 Let $p$ and $q$ be prime numbers that are the two distinct roots of the equation $x^{2}-13 x+R=0$, where $R$ is a real number. If $b=p^{2}+q^{2}$, find the value of $b$.
$x^{2}-13 x+R=0$, roots $p$ and $q$ are prime numbers. $p+q=13, p q=R$
The sum of two prime numbers is 13 , so one is odd and the other is even, $p=2, q=11$ $b=p^{2}+q^{2}=2^{2}+11^{2}=125$