A PRACTICAL ANALYTIC METHOD FOR CALCULATING pi(x)

Thorsten Kleinjung
2017
Journal paper

Abstract

In this paper we give a description of a practical analytic method for the computation of pi(x), the number of prime numbers

Official source

https://infoscience.epfl.ch/record/230460?ln=en

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A new elementary proof of the Prime Number Theorem

Florian Karl Richter

Let

\Omega(n)

denote the number of prime factors of

n

. We show that for any bounded

f\colon\mathbb{N}\to\mathbb{C}

one has [ \frac{1}{N}\sum_{n=1}^N, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). ] This yields a ...

2021

A PRACTICAL ANALYTIC METHOD FOR CALCULATING pi(x)

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A new elementary proof of the Prime Number Theorem

Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions

Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions

A new elementary proof of the Prime Number Theorem

Self-morphing Soft Parallel-and-coplanar Electroadhesive Grippers Based on Laser-scribed Graphene Oxide Electrodes