A PRACTICAL ANALYTIC METHOD FOR CALCULATING pi(x)

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

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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)

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

A new elementary proof of the Prime Number Theorem

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

A new elementary proof of the Prime Number Theorem

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

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