content:mathematics:goldbach_conjecture

# Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

# Goldbach's conjecture

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

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

The conjecture has been shown (by computerised testing) to hold for all integers less than 4 Ã— 10^{18}, but remains unproven for all possible numbers.

Further reading courtesy Mathematics and Statistics dept. University Tennessee at Martin, US

Goldbach's original letter to Euler in 1742.

Note that Goldbach's *weak* conjecture (a.k.a Goldbach's odd conjecture)

*Every odd number greater than 7 can be expressed as the sum of three odd primes*

is generally accepted to have been finally proved in 2013, by Harald Helfgott

**Show another (random) article**

Suggestions for corrections and ideas for articles are welcomed :

**Get in touch!**

Further resources :