A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(7) + 2; g(7) + 3; g(7) + 4; and g(7) + 5?	Choose the correct choice
A) 1
B) 2
C) 3
D) 4
E) none
g(7) is the product of all integers from 1 to 7, so g(7) = 7!   Thus g(7) is a multiple of all the integers from 1 to 7.   Then g(7) is a multiple of 2, 3, 4, and 5.   2 divides g(7)+2   3 divides g(7)+3   4 divides g(7)+4   5 divides g(7)+5   The answer is none.
<result>E</result>
A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(7) + 2; g(7) + 3; g(7) + 4; and g(7) + 5?