Every odd integer greater than 5 is the sum of three primes

You need to know: Even and odd integers, prime numbers.

Background: An integer n is the sum of three primes, if there exist prime numbers $p_1, p_2, p_3$ such that $n=p_1+p_2+p_3$ .

The Theorem: On 30th December 2013, Harald Helfgott submitted to arxiv a paper in which he proved that every odd integer $n>5$ is the sum of three primes.

Short context: In 1742, Goldbach conjectured that every integer $n>5$ is the sum of three primes. Goldbach’s conjecture became one of the best-known unsolved problems in number theory and all of mathematics. In 1937, Vinogradov proved the conjecture for all odd integers greater than some (large) constant $n_0$ . In 1956, Borozdkin proved that one can take $n_0=e^{e^{16038}}$ . In 2002, Ming-Chit improved this to $n_0=e^{3100}$ . The Theorem proves the conjecture for all odd integers. The case of even integers remains open.