2021 Gauss 8 Problem 22

The prime numbers 23 and 29 are *consecutive prime numbers* since 29 is the smallest prime number that is greater than the prime number 23. How many positive integers less than 900 can be written as a product of two or more consecutive prime numbers?

\textbf{(A)}\ 14\quad \textbf{(B)}\ 13\quad \textbf{(C)}\ 11\quad \textbf{(D)}\ 12\quad \textbf{(E)}\ 15

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.