I am a math hobbyist working through John Stillwell's book "Elements of Number Theory"

On page 3 Stillwell after pointing out that $\displaystyle n^2 +n + 41$ is prime for all small values of n, poses the following problem:

"Show, nevertheless that $\displaystyle n^2 +n + 41$ is not prime for certain values of n"

Can anyone help me with this problem? I would certainly like to see a rigorous proof.