SOLUTION: How many positive integers n are there such that nē - 14n + 24 is a prime number?

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Question 550071: How many positive integers n are there such that nē - 14n + 24 is a prime number?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A prime number is an integer greater than 1 
that has no other factors beside itself and 1

nē - 14n + 24

can be factored as

(n - 2)(n - 12)

Therefore unless one of the factors (n - 12) or (n - 2) is 1, and the other
a prime number, (n - 2)(n - 12) will not be prime.

If (n - 2) equals 1 then

    n - 2 = 1
        n = 3

But (3 - 2)(3 - 12) = 1(-9) = -9

But that is a negative number so (n - 2) can't be the factor that is 1.

If (n - 12) equals 1 then

    n - 12 = 1
        n = 13

And (13 - 2)(13 - 12) = 11(1) = 11 which IS prime.

So 13 is the only number n can be such 
that nē - 14n + 24 is prime.

The questios is how many positive integers is that? 
The answer is one, the number 13.

Edwin