Goldbach's conjecture

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:

Every even integer greater than 2 can be written as the sum of two primes.

Origins[change | edit source]

On 7 June 1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII) [1] in which he proposed the following conjecture:

Every integer greater than 2 can be written as the sum of three primes.

He considered 1 to be a prime number, a convention subsequently abandoned. A modern version of Goldbach's original conjecture is:

Every integer greater than 5 can be written as the sum of three primes.

Euler, becoming interested in the problem, answered by noting that this conjecture would follow from a stronger version,

Every even integer greater than 2 can be written as the sum of two primes,

adding that he regarded this a fully certain theorem ("ein ganz gewisses Theorema"), in spite of his being unable to prove it.

Other websites[change | edit source]