Partitioning integers into pairs so that the sum of each pair is prime.

Show that, for every positive integer n, the numbers between 1 and 2n can be partitioned into pairs so that the sum of each pair is a prime number.

I tried a few examples, and I figured that an odd number must be paired up with an even number, which isn't much. You can split the numbers 1 to 2n into {1,3,...2n-1} and {2,4,...,2n}, and then somehow pick one number from each set such that all have prime sums, but I am kind of stuck.