Three Solutions of the Goldbach Problem

• 1、College of Science, Shenzhen University

Abstract：he term of “Proposition {1, b}” means that every large even number can be expressed as a sum of a prime and a product of at most b primes. The sieve method for Goldbach problem is always claimed to sift out every composite number, which generally made a huge trouble for itself. In fact, this claim is not necessary. The author has found that there at least exist three methods which can solve the Goldbach problem under the condition that only partial composite numbers have been sifted out. The first one is “partition sieve”. In fact, the Proposition {1, 1} has already been solved at the moment when any Proposition {1, b} is proved to be true because there are a mass of primes in the residual integers of in the Proposition {1, b}, where the residual integers not exceeding N^(2/(1+b)) are all primes; as long as these primes or even all residual primes can be separated from the residual integers and prove the number of them to be greater than zero, then the Proposition {1, 1} is true! This

Keywords： Partition sieve Integer classification sieve Ethereal sieve Goldbach problem Problem of twin primes