There has been quite a bit of work over the years on trying to find a nice formula that takes many prime values. For example, \(x^{2}+x+41\) is prime for all integers \(x\) such that \(-40 \leq x<40\). (You may like to check this!) However:

Find an integer \(x\) coprime to 41 such that \(x^{2}+x+41\) is not prime.