Goldbach's conjecture
Goldbach's weak conjecture, every odd number greater than 5 can be expressed as the sum of three primes, is a consequence of Goldbach's conjecture. Ivan Vinogradov proved it for large enough "n" (Vinogradov's theorem) in 1937, and Harald Helfgott extended this to a full proof of Goldbach's weak conjecture in 2013.