It doesn't matter whether the number is prime or not. The entire series 6n + 1 is contained within 3n + 1. To see this suppose we have a number k = 6n + 1. What is n' for k = 3n' + 1?

k = 6n + 1 = 3n' + 1

6n + 1 = 3n' + 1

6n = 3n'

n' = 2n.

Since there is an n' for every n, thus every number 6n + 1 can be written in the form 3n' + 1.

-Dan