I'm curious, I see all kinds of crazy mathematicians inventing all kinds of formulae for some pretty complex stuff. Why can't the same be done for prime numbers? Is it simply that prime numbers are completely random and do not follow any such pattern? Why is it so difficult? Have people given up trying or are people still adamant that a formula does exist it's just a case of finding it?
You might find the following link useful and while there is no closed formula for primes, primes do closely follow an asymptotic distribution, and so we can calculate the approximate probability that a number is prime. Also, you can consider looking online for projects that use a network of computers to compute whether or not very large numbers are prime.