2001 Gauss 7 Problem 15

A prime number is called a "Superprime" if doubling it, and then subtracting 1, results in another prime number. The number of Superprimes less than 15 is

\textbf{(A)}\ 2\quad \textbf{(B)}\ 3\quad \textbf{(C)}\ 4\quad \textbf{(D)}\ 5\quad \textbf{(E)}\ 6

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.