Print sequences with prime sum

Question

Given an integer n, I want to find two permutations of the numbers 1 to n (inclusive) such that the sum of numbers from the two permutations at any given index is always prime.

For example:

   n = 5

      1 2 3 4 5
      1 5 4 3 2

   n = 8

      1 2 3 4 5 6 7 8
      2 1 4 3 8 7 6 5

Answer 1

Construct a bipartite graph on {0,1} x {1...n} such that (0, i) and (1, j) are connected if and only if i+j is prime.

Find a perfect matching using any standard technique, and then produce the sequences so that the matching numbers are at the same index.