• Mit Patel
• Alok M. Patel
• R.B.Gandhi

Prime numbers have always remained a matter fascination to the mathematicians, and many scientific and technical communities. Also, it has paramount applications for computer engineers to solve myriad real problems. In this paper, twenty different types of prime numbers have been covered and Python programs to generate them are given, with the Python library. Asymmetric algorithm has been used for key exchange between client and server; it is significant because of the prime factorization NP-problem. In the encryption system, prime number play the major role to crack security system where prime factorization is necessary, so the analysis for the same has been shown in this paper, by generating prime numbers on various platforms (Windows, Os X, and Ubuntu) and by prime factorization using three different algorithms. In prime factorization, the comparison between Composite numbers vs. the time it takes to Factorize is plotted on the graphs. Two of the major applications of prime numbers which are Cryptography and Cicada have also been covered in this paper.

Python, Python Library, Cryptography, Cicada, Brute Force, R programming, Asymmetric Cryptosystem and Factorization

"Prime numbers and their analysis", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.7, Issue 2, page no.466-470, February-2020, Available :http://www.jetir.org/papers/JETIR2002273.pdf

"Prime numbers and their analysis", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.7, Issue 2, page no. pp466-470, February-2020, Available at : http://www.jetir.org/papers/JETIR2002273.pdf