Chaotic Distribution of Prime Numbers and Digits of π

4 Pages Posted: 15 Jun 2020

Date Written: March 28, 2020

Abstract

In the paper the distribution of prime numbers and digits of π were presented as chaotic. The analysis was based on the amplitude spectrum plots of the prime number distribution and the amplitude spectrum plots of the π digit distribution. From the chaos of prime numbers a certain regularity emerges, similar to Ulam's spiral. It has also been shown that prime numbers are arranged just above a certain line. A similar analysis was also made for the distribution of digits of the number π. From the distribution of these digits, as well as from the nature of the amplitude spectrum, one can conclude about the chaotic nature of this distribution.

Keywords: prime numbers, chaos, Ulam spiral, periodic, quasiperiodic, amplitude spectrum, harmonics, π number

Suggested Citation

Berezowski, Marek, Chaotic Distribution of Prime Numbers and Digits of π (March 28, 2020). Available at SSRN: https://ssrn.com/abstract=3562793 or http://dx.doi.org/10.2139/ssrn.3562793

Marek Berezowski (Contact Author)

Cracow University of Technology ( email )

ul. Warszawska 24
Krakow, 31-155
Poland

HOME PAGE: http://https://www.researchgate.net/profile/Marek_Berezowski

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