Goldbach Conjecture

In 1742, mathematician Christian Goldbach wrote a letter to Leonhard Euler claiming that every integer greater than 2 can be written as the sum of 3 primes and that every even number is the sum of 2 primes. At the time of this letter, Goldbach considered 1 to be a prime number, so a modernized version of this conjecture would be: 

1. Strong Goldbach Conjecture: Every even integer greater than 2 can be written as the sum of two primes.

2. Weak Goldbach Conjecture: Every odd integer greater than 5 can be written as the sum of three primes

Although this problem sounds fairly simple, the strong conjecture has only shown to hold through 4 x 10^18. Despite many attempts, no one has been able to to prove a full solution yet. The weak conjecture was proved in 2013 by Harald Helfgott.