Question

When does n^2 + n +41 stop being prime (n=0,1,2....)?

Answer 1

PrimeQ is a Mathematica function which is True if the argument is a prime number.
At n=0, 41 is prime. PrimeQ [ 41] -> True
At n=40, PrimeQ [ 1681] -> False. 1681 = 41 x 41
All expression values for n=0 through n=39 are prime.

Answer 2

Right, evidently 41 yields a non prime by inspection so then a case of testing the ones less than that.

Answer 3

A complete case testing solution using Mathematica Home Edition is attached.

Answer 4

Just what computers are good at:-)