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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).
The best known result currently stems from the proof of the weak Goldbach conjecture by Harald Helfgott, [15] which directly implies that every even number n ≥ 4 is the sum of at most 4 primes. [16] [17]
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.
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.
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 Goormaghtigh conjecture: number theory: René Goormaghtigh: 14 Green's ...
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).
Goldbach's conjecture, one of the oldest unsolved problems in number theory; Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem; Goldbach's comet, a plot of the so-called Goldbach function; Goldbach–Euler theorem, also known as Goldbach's theorem
Goldbach's conjecture. Goldbach's weak conjecture; Second Hardy–Littlewood conjecture; Hardy–Littlewood circle method; Schinzel's hypothesis H; Bateman–Horn conjecture; Waring's problem. Brahmagupta–Fibonacci identity; Euler's four-square identity; Lagrange's four-square theorem; Taxicab number; Generalized taxicab number; Cabtaxi ...