Ask HN: Prime number hunting, techniques to wrestle it down to the ground

Okay I found a small slim sieve that seems to produce primes. Basically take an ordered series of primes and multiply them together and take that subtotal and add the number one and it will always generate primes.

So I am looking at number methods and theories to wrestle it down as its a good way to understand the switching back and forth between deductive and inductive which helps keep my unit testing skills somewhat sharp.

What good books or resources are there for factorials and their distributions and also on cantor dust, bars, and sets?