# Goldbach conjecture

 Importance: Outstanding ✭✭✭✭
 Author(s): Goldbach, Christian
 Subject: Number Theory » Additive Number Theory
 Posted by: Benschop on: November 20th, 2007

\begin{conjecture} Every even integer greater than 2 is the sum of two primes. \end{conjecture}

This famous conjecture is one of the oldest unsolved problems in mathematics. It arose originally out of a correspondence (1742) between Goldbach and Euler. See \Def[Wikipedia's Goldbach's conjecture]{goldbach's conjecture} for more.

### Weak conjecture now solved

Note that Harald Helfgott has proved the ternary version of Goldbach's conjecture, that every odd number greater than 7 is the sum of three odd primes. See http://arxiv.org/abs/1205.5252 (minor arc estimates) and http://arxiv.org/abs/1305.2897 (major arc estimates).

### Goldbach conjecture

Those interested in a suggestion for a proof via semigroup theory and carry extension, see: "Additive structure of Z(.) mod [\prod first k primes], with carry extension to prime pair sums". - http://home.iae.nl/users/benschop/ngb0203.pdf (10 pgs, submitted for publication)

### Goldbach conjecture

In addition to the above link to the paper with Goldbach-Conj. proof, the abstract and links to an intro-article are at http://home.iae.nl/users/benschop/ng-abstr.htm