Quadratic that yields the longest prime sequence?

Question

The quadratic $n^2+n+41$ yields prime numbers all the way up to $n=40$ before it fails (pretty cool!).

My question is: Do you know of a quadratic that can 'last even longer'?

Answer 1

$$36n^2-810n+2753$$

is prime for $n\le44$ (source).

Answer 2

$$n^2-81n+1681$$ is prime for all natrual numbers $\le 80$. (This is of course an unfair answer)

Answer 3

From Sierpsinski's prime sequence theorem http://mathworld.wolfram.com/SierpinskisPrimeSequenceTheorem.html you can find arbitrarily many primes (but maybe not consecutive values of the quadratic).