A New Method to Study Goldbach Conjecture

Abstract

This paper does not claim to prove the Goldbach conjecture, but it does provide a new way of proof (LiKe sequence); And in detailed introduces the proof process of this method: by indirect transformation, Goldbach conjecture is transformed to prove that, for any odd prime sequence (3, 5, 7, … , P n ), there must have no LiKe sequence when the terms must be less than 3 × P n . This method only studies prime numbers and corresponding composite numbers, replaced the relationship between even numbers and indeterminate prime numbers. In order to illustrate the importance of the idea of transforming the addition problem into the multiplication problem, we take the twin prime conjecture as an example and know there must exist twin primes in the interval [3 P n , P 2 n ]. This idea is very important for the study of Goldbach conjecture and twin prime conjecture. It’s worth further study.