Authors : Mehroz Mir; Jyotiraditya Jadhav

Volume/Issue : Volume 8 - 2023, Issue 12 - December

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DOI : https://doi.org/10.5281/zenodo.10454159

Abstract : Prime number distribution is a fundamental concept in multiple areas such as cryptography and statistical analysis. In this paper, we have developed a highly close approximation of the probability of primes in a finite integral domain for higher order range of [0,10000]. Through rigorous mathematical derivations, we have established up- per bound and lower bound probability limits. Linear regressions observed through graphical representations showcase prime prob- ability distributions between the respective modular differences of upper and lower limits of probability with the actual probabilistic values. The observed convergence between the actual probability of primes and the developed relation represented by graphs val- idates the propositions. This convergence of the proposed limits contributes a deeper understanding of prime number distribution in finite integer domains which is being reported for the first time in this study.

Keywords : Prime Distribution, Probability Limits, Linear Re- Gression, Approximation, Order Ranges.