Question 29
Let $\mathbb{N}$ denote the set of positive integers, and let $S$ be a set. There exists a function $f: \mathbb{N} \rightarrow S$ such that if $x$ and $y$ are a pair of positive integers with their difference being a prime number, then $f(x) \neq f(y)$. Determine the minimum number of elements in $S$.