3. L et $A$ be an $n$-element subset of $\{1,2, \ldots, 2009\}$ with the property that the difference between any two numbers in $A$ is not a prime number. Find the largest possible value of $n$. Find a set with this number of elements. (Note: 1 is not a prime number.)
3. If $n \in A$, then $n+i \notin A, i=2,3,5,7$. Among $n+1, n+4, n+6$ at most one can be in A. Thus among any 8 consecutive integers, at most 2 can be in $S$. Hence $|A| \leq 2\lceil 2009 / 8\rceil=504$. Such a set is $\{4 k+1: k=0,1, \ldots, 502\}$.