关于广义孪生素数的几个结论

涂象初; 涂承宇; 涂承媛

关于广义孪生素数的几个结论

1. 北京工业大学电子信息与控制工程学院, 北京 100022;
2. 北京工业大学机械工程与应用电子技术学院, 北京 100022

详细信息

作者简介:
涂象初(1929-),男,江西九江人,教授.

中图分类号: O156.1
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出版历程
- 收稿日期: 2004-11-01
- 网络出版日期: 2022-12-29

Some Conclusions About the Generalized Primes-twin and Others

1. College of Electronic Information& Control Engineering, Beijing University of Technology, Beijing 100022, China;
2. College of Mechanical Engineering & Applied Electronic Technology, Beijing University of Technology, Beijing 100022, China

摘要

摘要: 基于Chebyshev不等式以及对所有相关子集平均浓度的计算,提出并证明了下列引理、定理,以及4条推论:[引理1]至少有1个广义孪生素数集合(或称2素数组子集)是无限集合;[定理1]全部的或无限多的广义孪生素数集合是无限集合;[推论1]至少有1个3生素数集合(或称3素数组子集)是无限集合;[推论2]全部的或无限多的3生素数集合是无限集合;[推论3]普遍地说,至少有1个h生素数集合(或称h素数组子集)是无限集合(h是≥2的整数);[推论4]普遍地说,全部的或无限多的h生素数集合是无限集合(h是≥2的整数).
- 广义孪生素数集合 /
- 3生素数集合 /
- h生素数集合 /
- Chebyshev不等式 /
- 平均浓度
Abstract: Basing on Chebyshev inequality and on the computation of average concentration of all related subsets, the authors put forward and proved the following lemma, theorem, and the four corollaries: [Lemma 1] There exists at least one of the sets of generalized prime-twins (namely one subset of the set of 2-primes group), which is an infinite set. [Theorem 1] All the sets of generalized prime-twins or infinitely many ones among these sets are infinite sets. [Corollary 1] There exists at least one of the sets of primes-triplet (namely one subset of the set of 3-primes-group), which is an infinite set. [Corollary 2] All the sets of primes-triplet or infinitely many ones among these sets are infinite sets. [Corollary 3] There exists at least one of the sets of h-primes-tuplet (namely one subset of the set of h-primes-group) which is an infinite set, where h is an inte ger≥2. [Corollary 4] All the sets of h-primes-tuplet or infinitely many ones among these sets are infinite sets, where h is an integer≥2.
- set of generalized primes-twin /
- set of primes-triplet /
- set of h-primes-tuplet /
- Chebyshev inequality /
- average concentration

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参考文献(6)

[1]	YANDELL B H. Hilbert's problems and their solvers [M]. Natick, Massachusetts: A K Fetters Ltd, 2002: 203-206.
[2]	GUY R K. Unsolved problems in number theorem Vol. 1[M]. 2nd ed. New York: Springer-Verlag Inc, 1994: 10-25.
[3]	SHANKS D. Solved and unsolved problems in number theorem Vol. 1 [M]. Washington D C: Spartan Books, 1962: 30-31.
[4]	SONG Y Y. Number theory for computing[M]. 2nd ed. New York: Springer-Verlag, 2000: 4-5.
[5]	CRANDALL R, POMERANCEC. Prime numbers, A computational perspective [M]. New York: Springer-Verlag, 2001: 9-15, 74-75.
[6]	潘承洞,潘承彪.素数定理的初等证明[M].上海:上海科学技术出版社,1988:38-41.

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关于广义孪生素数的几个结论

作者简介: 涂象初(1929-),男,江西九江人,教授.

计量

出版历程

Some Conclusions About the Generalized Primes-twin and Others

计量

出版历程

目录

作者简介:
涂象初(1929-),男,江西九江人,教授.