Prime Generating Function!

Number Theory Level 4

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.

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