Up to now, around the world, Dr. Zhang Yitang from the University of New Hampshire offers the best research results of the infinity of twin primes. In 2013, Dr. Zhang proved the infinity of twin primes that are 70,000,000 apart and received the 2014 Frank Nelson Cole Prize in Number Theory. This study suggests new ways to find prime numbers, twin primes, and triplet primes by applying Sundaram’s Sieve Method and finds the general solution and character of the an+b subset of matrix 2xy+x+y. Besides, by studying the problem that 3n+2 is not the subset of K∪L with three methods, the author finds the way to prove the infinity of twin primes and detailed proofs are presented in this paper. It offers new way to study triplet primes and n-plet primes conjectures.
| Published in | Science Innovation (Volume 7, Issue 2) |
| DOI | 10.11648/j.si.20190702.11 |
| Page(s) | 48-58 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
Prime Number, Twin Prime, Triplet Prime, Sundaram’s Sieve Method
| [1] | 李维超。辛达拉姆筛法的推广[J]。数学通报，2001,（3）:38—39。 |
| [2] | 李复中。初等数论选讲[M].吉林:东北师范大学出版社，1984：85。 |
| [3] | 华罗庚。数论导引[M].北京：科学出版社，1979。 |
| [4] | 闫奎迎。勾股数组的排列顺序及应用[A].中国初等数学研究文集（二）[C].香港：中国科学文化出版社，2003:135—138。 |
| [5] | 王文娜，闫亮，闫魁迎. 用辛达拉姆筛法探讨孪生素数无穷多[J].许昌学院学报，2014,33（2）:31—36。 |
| [6] | 王元. 谈谈素数{M}.上海：上海教育出版社，1978.2-10。 |
| [7] | [美]G.波利亚.数学与猜想[M[.北京:科学出版社,2001：64-70。 |
| [8] | 潘承洞，潘承彪,哥德巴赫猜想[M].北京 科学出版社,2001。 |
| [9] | 吴在渊.数论初步[M]北京 商务印书馆，1931。 |
| [10] | 闵嗣鹤，严士键. 初等数论[M}.北京:高等出版社，1958。 |
| [11] | 柯召，孙琦 谈谈不定方程[M].上海:上海教育出版社，1960。 |
| [12] | 闫奎迎,王文娜.关于奇合数和奇素数一般解的探讨[J].许昌师专学报，1996，15（4）:49—50。 |
| [13] | 闫奎迎,王文娜.关于孪生素数无穷多问题的探讨[J] 许昌师专学报， 1998，17（1）:6—10。 |
| [14] | 闫奎迎,王文娜.关于孪生素数猜想证明的探讨[J].许昌师专学报， 2000，19（2）:15—21。 |
| [15] | 闫奎迎.勾股数组的排列顺序[J].河南教育学院学报：教育教学研究专辑，1996：7—11。 |
| [16] | 闫奎迎.猜想. 信阳师范学院学报[J].1997，10(3):8。 |
| [17] | 闫奎迎.关于费尔马定理证明的探讨 [J].许昌师专学报， 1991.10（2）: 26—37。 |
| [18] | U. Dudley, EIEMENTARY NUMBEB THEORY (W. H. Freemen and Co. 1969)（有中译本《基础数学》，周仲良译，上海科学技术出版社）。 |
| [19] | R. P. Burn. A Pathway into Nnmber theory. (Cambridge University Press 1982). |
| [20] | Hasse. H. Zahlentheorie (Berlin Akademie-Verlag, 1949). |
| [21] | Hasse, H. Vorlesungen uber Zahlentheorie (Berlin, Springer, 1950). |
| [22] | 吴在渊，数论初步（商务印书馆，1931）。 |
| [23] | 陈景润.初等数论[M].北京：科学出版社，1978.3-20。 |
APA Style
Yan Kuiying. (2019). Study on the Infinity of Twin Primes by Applying Sundaram’s Sieve Method. Science Innovation, 7(2), 48-58. https://doi.org/10.11648/j.si.20190702.11
ACS Style
Yan Kuiying. Study on the Infinity of Twin Primes by Applying Sundaram’s Sieve Method. Sci. Innov. 2019, 7(2), 48-58. doi: 10.11648/j.si.20190702.11
AMA Style
Yan Kuiying. Study on the Infinity of Twin Primes by Applying Sundaram’s Sieve Method. Sci Innov. 2019;7(2):48-58. doi: 10.11648/j.si.20190702.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.si.20190702.11,
author = {Yan Kuiying},
title = {Study on the Infinity of Twin Primes by Applying Sundaram’s Sieve Method},
journal = {Science Innovation},
volume = {7},
number = {2},
pages = {48-58},
doi = {10.11648/j.si.20190702.11},
url = {https://doi.org/10.11648/j.si.20190702.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.si.20190702.11},
abstract = {Up to now, around the world, Dr. Zhang Yitang from the University of New Hampshire offers the best research results of the infinity of twin primes. In 2013, Dr. Zhang proved the infinity of twin primes that are 70,000,000 apart and received the 2014 Frank Nelson Cole Prize in Number Theory. This study suggests new ways to find prime numbers, twin primes, and triplet primes by applying Sundaram’s Sieve Method and finds the general solution and character of the an+b subset of matrix 2xy+x+y. Besides, by studying the problem that 3n+2 is not the subset of K∪L with three methods, the author finds the way to prove the infinity of twin primes and detailed proofs are presented in this paper. It offers new way to study triplet primes and n-plet primes conjectures.},
year = {2019}
}
TY - JOUR T1 - Study on the Infinity of Twin Primes by Applying Sundaram’s Sieve Method AU - Yan Kuiying Y1 - 2019/06/15 PY - 2019 N1 - https://doi.org/10.11648/j.si.20190702.11 DO - 10.11648/j.si.20190702.11 T2 - Science Innovation JF - Science Innovation JO - Science Innovation SP - 48 EP - 58 PB - Science Publishing Group SN - 2328-787X UR - https://doi.org/10.11648/j.si.20190702.11 AB - Up to now, around the world, Dr. Zhang Yitang from the University of New Hampshire offers the best research results of the infinity of twin primes. In 2013, Dr. Zhang proved the infinity of twin primes that are 70,000,000 apart and received the 2014 Frank Nelson Cole Prize in Number Theory. This study suggests new ways to find prime numbers, twin primes, and triplet primes by applying Sundaram’s Sieve Method and finds the general solution and character of the an+b subset of matrix 2xy+x+y. Besides, by studying the problem that 3n+2 is not the subset of K∪L with three methods, the author finds the way to prove the infinity of twin primes and detailed proofs are presented in this paper. It offers new way to study triplet primes and n-plet primes conjectures. VL - 7 IS - 2 ER -
Email: