This thesis examines the role of prime numbers in cryptography and information security through prime number generation methods and the cryptographic algorithms that utilise them. It presents a detailed evaluation of various prime number generation methods, such as prime sieves and primality tests, as well as cryptographic protocols such as the RSA, AES, and DES. It also analyses the performance of these algorithms in terms of speed and computational efficiency when used in securing today's technology, as well as the emerging quantum technology. Furthermore, it also goes over their practical applications in securing digital communication and data protection. The aim of this study is to investigate how these cryptographic protocols influence the efficiency of information and network security and how that will change with the rise in quantum computing.