# The Mathematical Modeling and Proof of the Goldbach Conjecture

Authors
Yu Wang
Corresponding Author
Yu Wang
Available Online July 2018.
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.

Open Access

Volume Title
Proceedings of the 2018 3rd International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2018)
Series
Publication Date
July 2018
ISBN
10.2991/msam-18.2018.6
ISSN
1951-6851
DOI
10.2991/msam-18.2018.6How to use a DOI?
Open Access

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  -