For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between #6 +2 and #6 +6 , inclusive? Choose the correct choice from the following answers:
A) None B) One C) Two D) Three E) Four
Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.   Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes in this range.   Nonenswer: None.
<result>A</result>
For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between #6 +2 and #6 +6 , inclusive?