AMC 12 2005a 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 $1000$?

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