G4.4 The roots of the equation $x^{2}-45 x+m=0$ are prime numbers. Given that the sum of the squares of the roots is $d$, find the value of $d$.
Let the roots be $\alpha, \beta$. $\alpha+\beta=45, \alpha \beta=m$
The sum of two prime numbers $\alpha+\beta=45$ $\alpha=2, \beta=43$ (2 is the only even prime number)
$$
d=\alpha^{2}+\beta^{2}=4+43^{2}=1853
$$