Goldbach's weak conjecture

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In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, is the proposition that every odd number greater than 5 can be expressed as the sum of three (not necessarily distinct) primes. This conjecture is called "weak" because it is implied by Goldbach's strong conjecture concerning sums of two primes: indeed, if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2 + 2 + 3). However, you cannot work backward to prove the strong conjecture from the weak one. In 2013, Harald Helfgott released a supposed proof of Goldbach's weak conjecture. The proof was accepted for publication in the Annals of Mathematics Studies series in 2015, and has been undergoing further review and revision since; fully refereed chapters in close to final form are being made public in the process. If the proof...

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