Ethereal Sieve and Other Methods for the Goldbach Conjecture

There are at least four methods with which to prove the Goldbach conjecture, which contain the "ethereal sieve method", the "comparative sieve method", the "sifting function partition by integer sorts" and the "sifting function partition by intervals"; these are all based on existing results about the research of Goldbach problem. By means of these methods, the number of primes which are propitious to the Goldbach problem can be calculated from existing results, an accurate first order approximation of Goldbach conjecture can therefore be obtained, and the problem of twin primes can also be solved.