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, …, Pn), there must have no LiKe sequence when the terms must be less than 3 × Pn. 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 [3Pn, P2n]. This idea is very important for the study of Goldbach conjecture and twin prime conjecture. It’s worth further study.

Highlights

  • Goldbach conjecture [1] is a mathematical puzzle known all over the world, and has been around for 280 years (1742-2022)

  • This paper briefly introduces the proof process of this method: by indirect transformation, Goldbach conjecture is transformed to prove

  • The method must be right, but how do we prove Goldbach conjecture in this way? We have two paths: A: If when 2N is greater than a certain number, there is no LiKe sequence for all odd prime numbers before N, and make sure the numbers in 2N match the Goldbach conjecture, it can be proved directly

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Summary

A New Method to Study Goldbach Conjecture

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. 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 3Pn , Pn. 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 3Pn , Pn This idea is very important for the study of Goldbach conjecture and twin prime conjecture.

Introduction
The Definition of LiKe Sequence
Why Is It Equivalent to Goldbach Conjecture?
What Is the Proof Path?
Conclusion
Full Text
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