Advanced Probabilistic Primality Test Using by Recursive Function

Abstract

In this day and age, public-key cryptography is widely used to secure data. Public-key algorithms contain the usage of prime numbers and of large composite numbers, which have prime factors. Due to this, the security of these algorithms relies on the difficulty to factorize the public keys. For many centuries, mathematic scientists have been fascinated by the subject of prime numbers, have studied their proprietors, and have focused on developing several theories. Many primality tests, deterministic and probabilistic, were suggested to determine whether a number is prime or not. This article describes and analyzes one-sided error probabilistic algorithms, probabilistic runtime algorithms and deterministic algorithms. As a result of the analysis, we have chosen a more efficient algorithm and improve the primality test using a recursive function