Abstract

LOPEZ SUBIA, Beimar Wilfredo. Formula to find the figure of prime numbers less than a given amount. Rev. Cien. Tec. In. [online]. 2020, vol.18, n.22, pp.125-148. ISSN 2225-8787.

This article presents a formula in order to obtain a totally exact result, in the amount of prime numbers lowerthan a given number. Prime numbers are very important and by conducting an in-depth study, it has been possible to discover a formula that is shown in this article; with the purpose of using it in cryptography (RSA Algorithm) and many applications in mathematics. This research states that: "In science and mathematics everything is possible, and advances can be made by using new mathematics" because it is an unpublished formula discovered through a heuristic method. A characteristic function will be known (function Eit), which helps in numerical accuracy in order to find the amount of prime numbers lowerthan a given number. The formula has been embedded in a theorem, which will be demonstrated, so that every mathematician can verify the process of creating the formula from the ground up. A programming code is created which can be implemented in more powerful software so that very important results can be found, no matter how large the given number is, and in an accurate way. The code is valid in order to find the amount of prime numbers lower than a given number, to know what those prime numbers are, and to identify quickly if a number is a prime number. The amount of prime numbers lower than a given number is verified in a numerical way, up to x = 10²⁵ but, understanding the process of creating the formula, it can be concluded that it is true for any number. Gaps have been studied in the distribution of prime numbers, coming to the conclusion that the formula for counting prime numbers that has been discovered is correct and important for mathematics and much more for cryptography.

Keywords : RSA algorithm; Function (x); Function Eit; Distribution of prime numbers.

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