2005 AMC 12A Problem 18

Call a number "prime-looking" if it is composite but not divisible by 2, 3, or 5. The three smallest prime-looking numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many prime-looking numbers are there less than 1000?

\textbf{(A) } 100 \qquad \textbf{(B) } 102 \qquad \textbf{(C) } 104 \qquad \textbf{(D) } 106 \qquad \textbf{(E) } 108

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.