Well, you have to look at all numbers <= to N!+1 to try to find a factor, not just numbers <=N.
Ex) 4! + 1 = 2*3*4 + 1 = 25, and 5 divides 25.
In fact, I'm not even sure if a prime number exists of the form N! + 1 for N >= 4.
However, in reference to the other part of your post, a 10M digit prime does not need to be a Mersenne prime to qualify for the prize.
EDIT: 11! + 1 is prime, but who knows if there are a finite numbers of primes in this form or not? (I'm sure someone knows.)
