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This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, then this would also be true. For 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).
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.
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 number theory, Vinogradov's theorem is a result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers.It is a weaker form of Goldbach's weak conjecture, which would imply the existence of such a representation for all odd integers greater than five.
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 now-proven statement that Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum).
The truth of Ramaré's result for all sufficiently large even numbers is a consequence of Vinogradov's theorem, whereas the full result follows from Goldbach's weak conjecture. In turn, Ramaré's result was strengthened by Terence Tao who proved in 2014 that every odd number is the sum of at most five primes, and by Harald Helfgott 's claimed ...
Even and odd numbers. Parity; Divisor, aliquot part. Greatest common divisor; ... Goldbach's conjecture. Goldbach's weak conjecture; Second Hardy–Littlewood conjecture;
Gilbreath conjecture: number theory: Norman Laurence Gilbreath: 34 Goldbach's conjecture: number theory: ⇒The ternary Goldbach conjecture, which was the original formulation. [8] Christian Goldbach: 5880 Gold partition conjecture [9] order theory: n/a: 25 Goldberg–Seymour conjecture: graph theory: Mark K. Goldberg and Paul Seymour: 57 ...