Prime Generating Function!

The function $f\left( n \right)=8n^{ 2 }-488n+7243$ generates primes for certain integer input. Strangely, the function seems to produce a prime for every consecutive integer input.

Starting from $f\left( 0 \right)$ , what is the last integer $n$ such that $f\left( n \right)$ is prime for every non negative integer less than or equal to $n$ .

Details and Assumptions

• The generated primes may not necessarily be distinct.