Goldbach’s conjecture

The conjecture states that every even integer n>2 is expressible as the sum of two primes.

In 1966 Chen proved that every sufficiently large even number can be expressed as the sum of a prime and a number with at most two prime divisorsPlanetmathPlanetmathPlanetmath.

Vinogradov proved that every sufficiently large odd number is a sum of three primes. In 1997 it was shown by J.-M. Deshouillers, G. Effinger, H. Te Riele, and D. Zinoviev that, assuming a generalized Riemann hypothesisMathworldPlanetmath, every odd numberMathworldPlanetmath n>5 can be represented as sum of three primes.

The conjecture was first proposed in a 1742 letter from Christian Goldbach to Euler and still remains unproved.

Title Goldbach’s conjecture
Canonical name GoldbachsConjecture
Date of creation 2013-03-22 12:13:43
Last modified on 2013-03-22 12:13:43
Owner drini (3)
Last modified by drini (3)
Numerical id 11
Author drini (3)
Entry type Conjecture
Classification msc 11P32
Classification msc 11-00
Related topic Prime