Question 25
Let $p_1, p_2, \dots, p_{n+1}$ denote the first $n+1$ primes. Suppose that $\{A, B\}$ is a partition of the set $X = \{p_1, p_2, \dots, p_n\}$, where $A = \{q_1, q_2, \dots, q_s\}$ and $B = \{r_1, r_2, \dots, r_t\}$. Prove that if $m = q_1q_2\dots q_s + r_1r_2\dots r_t \lt p_{n+1}^2$, then $m$ is a prime.