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This is sometimes known as the extended Goldbach conjecture. The strong Goldbach conjecture is in fact very similar to the twin prime conjecture, and the two conjectures are believed to be of roughly comparable difficulty. Goldbach's comet; red, blue and green points correspond respectively the values 0, 1 and 2 modulo 3 of the number.
In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. [2] The proof was accepted for publication in the Annals of Mathematics Studies series [3] 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. [4] Some state the conjecture as
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, [1] and Harald Helfgott extended this to a full proof of Goldbach's weak conjecture in 2013.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
"There exists a natural number x, such that if an index of a proof of the Goldbach conjecture exists, then the number x is the index of a proof of the Goldbach conjecture." This is classically provable, as follows: Either an index for a proof of the Goldbach conjecture exists, or no such index exists.
Additive number theory is concerned with the additive structure of the integers, such as Goldbach's conjecture that every even number greater than 2 is the sum of two primes. One of the main results in additive number theory is the solution to Waring's problem. [5]
In 2013, he released two papers claiming to be a proof of Goldbach's weak conjecture; the claim is now broadly accepted. [4]
1.2 Expert opinion on methods required for proof of Goldbach's Conjecture. ... 1.4 Decidability and Goldbach's Conjecture. 9 comments. Toggle the table of contents.