On the primes with \(p_{n+1}-p_n=8\) and the sum of their reciprocals
type: Item
instance of: scholarly article
title: On the primes with \(p_{n+1}-p_n=8\) and the sum of their reciprocals
zbMATH Open document ID: 1112.11045
DOI: 10.1007/BF02896492
author: Heon Soo Lee
author: Yeon Yong Part
published in: Journal of Applied Mathematics and Computing
publication date: 2006-12-04T00:00:00Z
review text: Let \(\mathbb P\) be the set of prime numbers, and let \(\pi_{2,8}(x):=\sum_{p\leq x: p\in {\mathbb P},p+8\in {\mathbb P}}1.\) Theorem 1. \(\pi_{2,8}(x)=O\left(x\left(\frac{\log\log(x)}{\log(x)}\right)^2\right) .\) Theorem 2. The series \(\sum_{p\in {\mathbb P}:p+8\in {\mathbb P}}\frac{1}{p}\) is convergent.
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11N05
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11A41
Mathematics Subject Classification ID: 11L20
zbMATH DE Number: 5076966
zbMATH Keywords: distribution of primes
MaRDI profile type: Publication
cites work: Evaluation of Artin's Constant and the Twin-Prime Constant
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cites work: Q4003406
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full work available at URL: https://doi.org/10.1007/bf02896492
OpenAlex ID: W2050187263
description: scientific article; zbMATH DE number 5076966