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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 conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.It states that every even natural number greater than 2 is the sum of two prime numbers.
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. [2] [3] [4]
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 ...
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 ...
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.
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Goldbach's conjecture; Goldbach's weak conjecture; Grimm's conjecture; H. Hilbert–Pólya conjecture; L. Landau's problems; Legendre's conjecture; Legendre's constant;