This paper is a review of prime numbers and their applications in cryptography, discussed in special reference to RSA (Rivest-Shamir-Adleman) cryptosystem. Firstly, we discuss prime numbers and important related theorems, viz. Unique Factorization Theorem and Chinese Remainder Theorem. Then we discuss modular arithmetic and introduce Euler's totient function and discuss Euler's theorem, which forms the backbone of RSA cryptosystem. Next, Cryptography and public key cryptography are introduced and the implementation of RSA cryptosystem is discussed. RSA is widely used because of the difficulty of finding the prime factorization of large composite numbers. Implementation of RSA cryptosystem in real-world applications is also discussed along with the conclusions.

Prime Numbers, Modular Arithmetic, Public-Key Cryptography, RSA Cryptosystem