While discussing problem 27 in office hours today, Andy mentioned Germain Primes. I was not sure what these were, so I did some research. And I found this:

"In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, also prime. These numbers are named after French mathematician Marie-Sophie Germain.

A Sophie Germain prime p > 3 is of the form 6k−1 or, equivalently, p ≡ 5 (mod 6) — as is its matching safe prime 2p+1. We note that the other form for a prime p > 3 is 6k+1 or, equivalently, p ≡ 1 (mod 6), and that 3|(2p+1) — thus excluding such p from the Sophie Germain prime domain. This is trivially proven using modular arithmetic."

So now when you are doing problem number 27 in the homework, you can think of Germain Primes. :)