Title: On primes, semiprimes and their applications

Authors: Yegnanarayanan Venkataraman; Y. Gayathri Narayana; Veena Narayana

Addresses: Department of Mathematics, Kalasalingam Academy of Research and Education, Deemed to be University, Krishnankoil, Tamilnadu, 626126, India ' Department of Electronics and Communication Engineering, SSN College of Engineering, Chennai – 603110, Tamilnadu, India ' Department of Mathematics, Kalasalingam Academy of Research and Education, Deemed to be University, Krishnankoil, Tamilnadu, 626126, India

Abstract: The existence of hidden symmetries in the distribution of prime numbers and the open problems such as given a semiprime, how fast we can find its prime factors and all even integers that are adequately large could be realized as a sum of either two prime numbers or a prime and a semiprime has driven us to probe the significant role of the Catalan numbers in semiprime decomposition. We proved some results concerning distribution of primes and semiprimes in terms of functions of primes.

Keywords: primes; semiprimes; Euler totient function; Catalan numbers; cryptography; RSA algorithm; prime factorization; semiprime decomposition; MATLAB.

DOI: 10.1504/IJAIP.2023.133257

International Journal of Advanced Intelligence Paradigms, 2023 Vol.26 No.1, pp.73 - 95

Received: 10 Nov 2019
Accepted: 18 Mar 2020
Published online: 04 Sep 2023 *

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