2. Given is the set $A=\{1,2,3, \ldots, 62,63\}$. A subset $X$ of the set $A$ will be called good if for every element $x \in X$ it holds that $x$ does not divide the sum of the remaining elements of the set $X$. Determine the maximum number of elements that a good subset can have.
2. Let $X$ be a good set. Clearly, $1 \notin X$. Also, the set $\{2,3, \ldots, 63\}$ is not good because $5 \mid 2+3+\cdots+63=31 \cdot 65$. Therefore, $X$ cannot have more than 61 elements. On the other hand, the set $X=\{2,3,5,6,7, \ldots, 63\}$ with 61 elements is good because the sum of its elements is 2011, which is a prime number. Therefore, the answer is 61.