Question 34
Consider $S=\{1,2,3,\ldots,2010,2011\}$. A subset $T$ of $S$ is called a $k$-element RP-subset if it has exactly $k$ elements and every pair of its elements is relatively prime. Find the smallest positive integer $k$ such that every $k$-element RP-subset of $S$ contains at least one prime number. (For example, $\{1,8,9\}$ is a 3-element RP-subset containing no prime.)