On the Synthesis of the Distribution amongst the Integers of the Prime Number


Academic Paper, 2023

16 Pages, Grade: 2.00


Abstract or Introduction

A method is devised in which the prime number counting function, pi(k) is viewed as having the properties of a staircase. The terminology appropriate to a staircase is used to describe the parts of the distribution amongst the integers.

Strings of limited extent of consecutive numbers which may contain prime numbers are generated from an iterative equation which contains Gauss' prime number counting function. In honour of Gauss we call these strings of numbers, Gauss strings. , and they are used in the construction of the staircase.

Further, we show that the prime number counting function may be represented in number space by an infinite set of connected trapezia, the individual areas of which are numerically equal to the gap between the primes that are situated on two of the borders of any given trapezium.

Details

Title
On the Synthesis of the Distribution amongst the Integers of the Prime Number
Grade
2.00
Author
Year
2023
Pages
16
Catalog Number
V1336494
ISBN (Book)
9783346835666
Language
English
Keywords
synthesis, distribution, integers, prime, number
Quote paper
William Fidler (Author), 2023, On the Synthesis of the Distribution amongst the Integers of the Prime Number, Munich, GRIN Verlag, https://www.grin.com/document/1336494

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