The Mathematical Modeling and Proof of the Goldbach Conjecture

DOI

10.2991/msam-18.2018.6How to use a DOI?

Keywords

Goldbach conjecture; composite number pair; mapping number; induction to absurdity

Abstract

The Goldbach conjecture declares that any even number 2m=2n+2>4 can be expressed as the sum of two prime numbers. The mathematical modeling of the conjecture is: any even number 2m=2n+2 greater than 4 can be expressed as 2n+2=a+b, 2≤a≤n+1, n+1≤b≤2n. With the modeling, let c be a composite number in 2~2n, a mapping number is 2m-c or 2n+2-c. A complete composite pair is a pair (c, 2m-c) that both c and 2m-c are composite numbers. The composite numbers one-to-one correspond to the mapping numbers. Using an induction to absurdity, suppose the Goldbach conjecture is wrong, so that 2n+2 cannot be expressed as the sum of two primes. With the mathematical modeling for the even number 2n+2, numbers 2~2n are all composite numbers or mapping numbers. A false inequation (C) can be obtained when n≥128. This means that the supposition does not stand when n≥128. Meanwhile, the Goldbach conjecture can be easily verified for the even numbers in 6~256. Hence, the Goldbach conjecture is proved.

Copyright

© 2018, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Yu Wang
PY  - 2018/07
DA  - 2018/07
TI  - The Mathematical Modeling and Proof of the Goldbach Conjecture
BT  - Proceedings of the 2018 3rd International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2018)
PB  - Atlantis Press
SP  - 24
EP  - 31
SN  - 1951-6851
UR  - https://doi.org/10.2991/msam-18.2018.6
DO  - 10.2991/msam-18.2018.6
ID  - Wang2018/07
ER  -