For any integer $n$ greater than $1$,how many prime numbers are there greater than $n!+1$ and less than $n!+n$? For any integer $n$ greater than $1$,how many prime numbers are there greater than $n!+1$ and less than $n!+n$ ?
By trying different values of $n$ for $n=2,3,4,5,6$ I get a feeling that the number of primes in the interval is $0$,of course this might be wrong as $n$ can be any number.
I've not been able to do much progress on this problem...one idea I had was to prove the above conjecture by proving it by picking up first smaller intervals and prove it works for  those intervals.
My feeling is also that Wilson's Theorem might be applicable here.

Hint:  Let $a = n! + 7$.  Does $7 \mid n!$?  Does $7|7$?  Does $7 \mid n! + 7$?  Is $n! + 7$ prime?  
If it isn't what number greater than $n! + 1$ and less than or equal to $n! + n$ might be?  
Can you factor anything out of the number $n! + k$? 
