Prime Number Sums

We prove that it is always possible to find a permutation $p$ on the set $\{1,\mathrm{.}\mathrm{.}\mathrm{.},n\}$ such that $c+p(c)$ is prime for all $c\in \{1,\mathrm{.}\mathrm{.}\mathrm{.},n\}\mathrm{.}$