Chaotic Distribution of Prime Numbers and Digits of π

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