How many integers \(n\) can be used such that the quantity \(|2n^2+23n+11| \) results in a prime number?
How many integers "n" can be used such that the quantity abs[2n^2+23n+11] results in a prime number?
n =0, -10, -12 gives the following prime numbers =11, 19, 23
+118608 \(|2n^2+23n+11|=|(n+11)(2n+1)|\)
If this is to be prime then one of the factors must be +/-1 and the other must be +/- a prime number.
so either
\(n+11=\pm1\qquad and \qquad |2n+1|\;\;is \;\;prime\\ or\\ 2n+1=\pm1 \qquad and \qquad |n+11|\;\;is \;\;prime\\\)
solve and you will have your answer,
