AHSME 1969 Problem 23

For any integer $n>1$, the number of prime numbers greater than $n!+1$ and less than $n!+n$ is: $\text{(A) } 0 \text{(B) } 1 \\ \text{(C) } \frac{n}{2} \text{ for n even, } \frac{n+1}{2} \text{ for n odd} \\ \text{(D) } n-1 \text{(E) } n$