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, a +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
Citation
Zhixuan Yan, Kuiying Yan(2023). Proof of the Triple and Twin Prime Conjectures Using the Sindaram Sieve Method. SQPreprints, Volume 1, Issue 1, Page 10-36, Publish Date: 2023-05-12
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