|Table of Contents|

Some Improvements of Chebyshev'ss Bound(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2022年03期
Page:
15-19
Research Field:
数学
Publishing date:

Info

Title:
Some Improvements of Chebyshev'ss Bound
Author(s):
Chen Gang; Wu Bin
(Public Teaching Department of Nantong Vocational University,Nantong 226007,China)
Keywords:
Chebyshev'ss bound; control function; improvement; combinatorial number; continued product of prime numbers; downward sequence of integer
PACS:
O156.1
DOI:
10.3969/j.issn.1001-4616.2022.03.003
Abstract:
This paper shows some improvements of Chebyshev'ss Bound(i.e. upper control function)and presents the control area and algorithm of key parameters. Some combinatorial number better than the traditional one is chosen and estimated upper bound of continued product of prime numbers on half-length interval is optimized. Finally,all prime numbers in the given interval are covered by an infinite half-length sequence.

References:

[1]华罗庚. 华罗庚文集(数论卷Ⅱ)[M]. 北京:科学出版社,2010:87-90.
[2]百度百科. 伯特兰-契比雪夫定理[EB/OL]. [2020-03-18]. https://baike.baidu.com/item/%E4%BC%AF%E7%89%B9%E5%85%B0-%E5%88%87%E6%AF%94%E9%9B%AA%E5%A4%AB%E5%AE%9A%E7%90%86/2053704.
[3]王元. 浅谈素数[M]. 哈尔滨:哈尔滨工业大学出版社,2011:34.
[4]潘承彪. 从契比雪夫到爱尔特希——素数定理的初等证明(上)[M]. 哈尔滨:哈尔滨工业大学出版社,2013:30.
[5]APOSYOL T M.(美)解析数论导引[M]. 哈尔滨:哈尔滨工业大学出版社,2016:73.
[6]MURTY M R.(美)解析数论中的问题[M]. 哈尔滨:哈尔滨工业大学出版社,2014:36,273.
[7]BHAT M A,KOSURU G S R. A generalization of Chebyshev's inequality and its applications[EB/OL]. arXiv:2018.01479v3[math. FA](2021-10-24)[2021-11-03] http://www.xueshufan.com/publication/3190830802.
[8]闵嗣鹤,严士健. 初等数论[M]. 3版. 北京:高等教育出版社,2003:21-22.
[9]LANGEVIN M. Méthodes élémentaires en vue du théorèm de Sylvester[C]//Séminaire Delange-Pisto-Poitou. Théoriedesnombres,1976,17(2):G2-01-G2-09.
[10]吴彬,陈刚. 关于贝朗特假设一般情形的证明[J]. 南通职业大学学报,2020(3):67-69.

Memo

Memo:
-
Last Update: 2022-09-15