How many integers n can be used such that the quantity |2n^2 + 3n + 11 - n^2 + 9n| results in a prime number?

2n^2 + 3n + 11 - n^2 + 9n can be written as n^2 + 12n + 11 which, in turn can be factored as (n + 1)(n + 11).

So what does this tell you, remembering that a prime number has no factors other than itself and 1?