The study of prime numbers and their properties has always been an intriguing and fascinating topic for mathematicians. Primes can be considered the “basic building blocks,” the atoms, of the natural numbers. They play a significant role in number theory. Also, prime numbers, in this current world of computers and digitalization, have paramount significance for the computer programmers and scientists to tackle relevant real-life problems. Since long time, many studies and researches have been conducted regarding prime numbers pattern. In this paper, a squaring prime pattern is presented. Moreover, fifteen different types of primes with their Python code to generate them is included within. In cryptographic encryption system, prime numbers play a major role for security systems in which prime factorization is necessary. Therefore, prime factorization of composite numbers using Sieve of Eratosthenes algorithm on different platforms and time analysis based on that has been presented in the paper. Also, factorization analysis of primes by five different algorithms has been shown and comparison of prime factorization of composite numbers vs time taken graph has been plotted. Two major applications of primes are also covered.
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