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 to hold up through 4 × 1018, but remains unproven.
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