Let $p_n$ be the $n$-th prime, so that $p_1 = 2, p_2 = 3,...$ and define $$X_n = \{0\} \cup \{p_1,...,p_n\}$$for each positive integer $n$. Find all $n$ for which there exist $A,B \subseteq N$ such that$ |A|,|B| \ge 2$ and $$X_n = A + B$$, where $A + B :=\{a + b : a \in A; b \in B \}$ and $N := \{0,1, 2,...\}$. (Salvatore Tringali)