What is the least possible value of $n$ such that $n^2+n+17$ is composite? The question is-


  Find the least $n$ for which $n^2+n+17$ is composite.


I tried to factorize it and show that it has a factor greater than $1$.But I could not factorize it and I also found that it has no real zeroes (roots).Now,how do I solve the problem?

Thanks for any help!!
According to computer:


$19$ is prime.
$23$ is prime.
$29$ is prime.
$37$ is prime.
$47$ is prime.
$59$ is prime.
$73$ is prime.
$89$ is prime.
$107$ is prime.
$127$ is prime.
$149$ is prime.
$173$ is prime.
$199$ is prime.
$227$ is prime.
$257$ is prime.
$289 = 17\times17$.
According to computer:


$19$ is prime.
$23$ is prime.
$29$ is prime.
$37$ is prime.
$47$ is prime.
$59$ is prime.
$73$ is prime.
$89$ is prime.
$107$ is prime.
$127$ is prime.
$149$ is prime.
$173$ is prime.
$199$ is prime.
$227$ is prime.
$257$ is prime.
$289 = 17\times17$.