The aim of this expository article is to introduce the reader to some of the fundamental milestones in the study of prime numbers across several centuries. Among the important developments in the study of prime numbers, we review the history of the prime number theorem, the Riemann zeta function (in relation to prime number theory), and some recent investigations into spacings between consecutive primes. We also present an important application of prime numbers in safe data transmission, namely the ‘RSA public key cryptosystem’.