This is one of those silly ideas that you have on a Sunday afternoon. 

Most of the times our computers are idle - this is unfortunate. On the other hand, we don't know, and maybe never will know, a formula for prime numbers that is computationally efficient. 

It is puzzling that it requires very little mathematical development to get to the prime numbers, but this ancient mystery lingers. How can you find the nth prime, in a simple closed form formula?

So why not generate random mathematical expressions that could generate the prime numbers, and test them? The odds are slim at best, but what is the harm of another program running in the background, among thousands. 

This is what this idea is all about. it is sort of trying the lottery of Science.