Prove by induction.
The case is trivial.
Suppose that for , the integers can be partitioned in pairs s.t.
For , we have the integers . By the Bertrand-Chebyshev theorem s.t. . Therefore we have the following pairs:
This takes care of the integers to . For the rest, note that is an even number (odd-odd=even) and . By the induction hypothesis, we can partition the remaining integers into pairs s.t. the sum of each pair is prime. Q.E.D.