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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 ...
One weak counterexample begins by taking some unsolved problem of mathematics, such as Goldbach's conjecture, which asks whether every even natural number larger than 4 is the sum of two primes. Define a sequence a ( n ) of rational numbers as follows: [ 9 ]
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [ 1 ] [ 2 ] [ 3 ] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem , proven in 1995 by Andrew Wiles ), have shaped much of mathematical history as new areas of mathematics are developed in ...
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
Born in the Duchy of Prussia's capital Königsberg, part of Brandenburg-Prussia, Goldbach was the son of a pastor. [2] He studied at the Royal Albertus University. [2] [5] After finishing his studies he went on long educational trips from 1710 to 1724 through Europe, visiting other German states, England, the Netherlands, Italy, and France, meeting with many famous mathematicians, such as ...