The ability to transmit and exchange vast amounts of information, as a result of the tremendous and widespread development in information and communications technology in our current era, has revealed a wonderful harmony and coherence between prime numbers, which are difficult to predict, decode, and distinguish, and the algorithms for encrypting that information and the methods for storing, encoding, and distributing it across communication networks. Today, prime numbers represent one of the cornerstones of mathematics, number theory, and modern applied sciences such as Information and Communications Technology (ICT), computer science, and Artificial Intelligence (AI). They are used in cryptographic systems such as RSA and Duffy-Hellman, and in calculating hash codes due to the difficulty of partitioning and factoring them into non-unit pairs, and their random occurrence in number sequences, making developing an equation to predict them a nearly impossible task. Although Fermat, Mersenne, and Euler used various formulas for calculating prime numbers that were applicable to limited applications, in this paper, researchers present a new mathematical approach to calculating and predicting prime numbers, using modern programming. This approach will open a new horizon for most applications across all fields.