New Discrete Metric Space of Natural Numbers: Discovery of New Possibilities in Number Theory

J. K.  Abdurakhmanov

J. K. Abdurakhmanov Senior Lecturer, Department of Information Technology candidate of physical and mathematical sciences (i.e. PhD) Andijan State University

Keywords: set, finite set, discrete set, distance, metric, Hamming distance, metric space

Abstract

In this article, the main emphasis is on the importance of the recently discovered by the author of the first in the history of mathematics metric criterion to be prime for a natural numbers. In his recent article, the author discovered a new discrete metric space, where, as it turned out quite unexpectedly, the distance between points is exactly two times less than the Hamming distance between the corresponding binary vectors. Extending this new distance in a natural way to the set of natural numbers, the author formulated a truly remarkable metric criterion for natural numbers to be prime.

References

1. R.W. Hamming. Coding theory and information theory: Translated from English. – Moscow, “Radio and communication”, 1983. – 176 p.
(Р. В. Хэмминг. Теория кодирования и теория информации: Пер. с англ. – Москва, “Радио и связь”, 1983. – 176 с)
2. Abdurakhmanov, J. K. . (2022). A NEW, MORE FRUITFUL, DETERMINATION OF THE METRIC (DISTANCE) IN A SET OF FINITE SETS, AND A METRIC CRITERION FOR THE SIMPLICITY OF A NATURAL NUMBER. International Bulletin of Applied Science and Technology, 2(11), 104–109. Retrieved from
https://zenodo.org/record/7344968#.Y4Hm5HZBy3C
https://researchcitations.com/index.php/ibast/article/view/263