Proof of the Triple and Twin Prime Conjectures by the Sindaram Sieve Method

Zhixuan Yan; Kuiying Yan

doi:https://doi.org/10.14445/22315373/IJMTT-V68I9P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 9 | Year 2022 | Article Id. IJMTT-V68I9P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I9P513

Proof of the Triple and Twin Prime Conjectures by the Sindaram Sieve Method

Zhixuan Yan, Kuiying Yan

Received	Revised	Accepted	Published
10 Aug 2022	12 Sep 2022	22 Sep 2022	30 Sep 2022

Citation :

Zhixuan Yan, Kuiying Yan, "Proof of the Triple and Twin Prime Conjectures by the Sindaram Sieve Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 9, pp. 87-103, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I9P513

Abstract

Since Dr. Yitang Zhang proved in 2013 that there are infinitely many pairs of prime numbers differing by 70 million, it has been proved now that there are infinitely many pairs of prime numbers differing by 246. In this paper, we use the sieve method invented by Snndaram in 1934 to find out the solution of triple prime numbers and twin prime numbers, and find the general solution formula of the subset, i.e, an1+b which is result of each subset, such as 3n+1, 5n+2, 7n+3, 9n+4, 11n+5, 13n+6, 15n+7, 17n+8, ... in 2mn+n+m, modulo x respectively (x≥3 takes prime). This general solution formula is used to prove the triple prime conjecture and the twin prime conjecture.

Keywords

Prime numbers, Twin prime numbers, Triple prime numbers, Sindaram sieve method.

References

[1] Wichao Li , “Extension of the Sindaram Sieve Method, “ Mathematical Bulletin , vol. 3, pp. 38-39, 2001.
[2] Kuiying Yan , Wenna Wang, “A Discussion on the General Solution of Odd Combinations and Odd Prime Numbers,” Journal of Xuchang Teachers College, vol. 15, no. 4, pp. 49-50, 1996.
[3] Kuiying Yan, “Study on the Infinity of Twin Primes by Applying Sundaram's Sieve Method,” Sciencelnnovation, vol. 7, no. 2, pp. 48-58, 2019.
[4] Wenna Wang ,Ling Yan ,and Kuiying Yan. KUIYING, “Exploring Twin Prime Infinitesimals with Sindaram Sieve Method,” Journal of Xuchang College, vol. 33, no. 2, pp. 31-36, 2014.
[5] Jingrun Chen, “Elementary Number Theory,” Beijing: Science Press, pp. 3-20, 1983.
[6] Fuzhong Li , “Selected Lectures on Elementary Number Theory,” Jilin:Northeast Normal University Press, pp. 9-85, 1984.
[7] Xianghao Wang, Jiwen Kan, and Xuehua Liu, “Discrete Mathematics ,” Beijing: Higher Education Press, pp. 2-13, 1987.