For an 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 options.
A) 1 B) None of the above C) 2 D) 3 E) 4
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 and 6! +7, inclusive. Which means that there are no primes in this range.   Answer: None of the above
<result>B</result>
For an 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 ?