Several proofs demonstrating that there are infinitely many primes, different types of primes, tests of primality, pseudo primes, prime number generators and open questions about primes are discussed in Section 1. Some of these notions are elaborated upon in Section 2, with discussions of the Riemann zeta function and how algorithmic complexity enters into tests for primes. Readers may know segments of what follows, but hopefully this work will help them place their knowledge into richer landscapes.