1999 Gauss 8 Problem 23

Kalyn writes down all of the integers from 1 to 1000 that have 4 as the sum of their digits. If \frac{a}{b} (in lowest terms) is the fraction of these numbers that are prime, then a+b is

\textbf{(A)}\ 5\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 15\quad \textbf{(D)}\ 26\quad \textbf{(E)}\ 19

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.