Authors :
Mehroz Mir; Jyotiraditya Jadhav
Volume/Issue :
Volume 8 - 2023, Issue 12 - December
Google Scholar :
http://tinyurl.com/3ej4uzzr
Scribd :
http://tinyurl.com/4vsvfp8a
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.
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.
