Publication

A PRACTICAL ANALYTIC METHOD FOR CALCULATING pi(x)

Thorsten Kleinjung
2017
Journal Articles

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/entities/publication/edb37eb0-6c23-4116-ad8c-411f71e55faa

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Thorsten Kleinjung
2017
Journal Articles

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/entities/publication/edb37eb0-6c23-4116-ad8c-411f71e55faa

About this result

Related concepts (21)

Mersenne prime

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p. The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, .

Prime number theorem

In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function).

Euler method

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

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with

f_i:\mathcal{D}\mapsto \mathbb{R}

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minimizing

\sum_{j=1}^nf_j(x)/n

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