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Abstract: All sieve methods for the Goldbach problem sift out all the compositenumbers; even though, strictly speaking, it is not necessary to do so and whichis, in general, very difficult. Some new methods introduced in this paper showthat the Goldbach problem can be solved under sifting out only some compositenumbers. In fact, in order to prove the Goldbach conjecture, it is onlynecessary to show that there are prime numbers left in the residual integersafter the initial sifting! This idea can be implemented by using one of thethree methods called sifting function partition by integer sort, siftingfunction partition by intervals and comparative sieve method, respectively.These are feasible methods for solving both the Goldbach problem and theproblem of twin primes. An added bonus of the above methods is the eliminationof the indeterminacy of the sifting functions brought about by their upper andlower bounds.



Author: Fu-Gao Song

Source: https://arxiv.org/



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