This problem is often used to help students see the importance of mathematical proof. If you try many values of n, the expression yields a prime. Can we therefore assume that it will ALWAYS yield a prime?
What happens if n=41?
consider the relation n^2 + n + 41
one person claim that this relation does not apply for primes:
for n=1 it gives 43 : its prime
for n=2 it gives 47:its prime
for n=3 it gives 53 : its prime;etc...
Does this man have a reason for his claim?