After class on Friday, I went and searched for functions that generate prime numbers. Most of the websites I found said that there were such functions that can generate prime numbers and some that generate only prime numbers. I found one function by W. H. Mill (1947) that says, “There exists a real number A= 1.30637788386308069046… so that the following function is prime for all n, n>=1: g(n)= [A^{3}^{^n}], where [ ] is the floor function!

I also found a nice function that produces lots of primes. In 1772, Euler’s function: f(n) = n^{2}+ n + 41 not only produces primes, but says, “There is no non-constant polynomial in one variable with integer coefficients which produces only prime values for integer inputs."

I also found that currently there is no formula that can tell if a number is a prime number.