A property of the sequence of primes
type: Item
instance of: scholarly article
title: A property of the sequence of primes
zbMATH Open document ID: 0641.10035
DOI: 10.1007/BF01198628
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: A sequence \((a_ n)\) of integers is called k-periodic (k\(\in {\mathbb{N}})\), if there are positive integers \(\ell\) and \(n_ 0\), so that for \(n\geq n_ 0\), \(a_{n+\ell}\equiv a_ n mod k\). By analytical means, but without using Turán's power sum method, it is shown that the series of primes (in natural order) is non k-periodic for all \(k>2\).
Mathematics Subject Classification ID: 11N05
Mathematics Subject Classification ID: 11N13
zbMATH DE Number: 4043948
zbMATH Keywords: distribution of primes
zbMATH Keywords: non-k-periodic sequence
author: Dieter Wolke
reviewed by: Dieter Wolke
MaRDI profile type: Publication
cites work: Q5772619
cites work: Contributions to the theory of the distribution of prime numbers in arithmetical progressions III
full work available at URL: https://doi.org/10.1007/bf01198628
OpenAlex ID: W2010940902
description: scientific article; zbMATH DE number 4043948