Study on the Infinity of Twin Primes by Applying Sundaram’s Sieve Method

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.