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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.
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]
Much of Pogorzelski's research concerns the Goldbach conjecture, the still-unsolved problem of whether every even number can be represented as a sum of two prime numbers. [3] [4] Born in Harrison, New Jersey, [5] Pogorzelski served in the U.S. Army in World War II. [2]
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]
Uncle Petros and Goldbach's Conjecture is a 1992 novel by Greek author Apostolos Doxiadis. It concerns a young man's interaction with his reclusive uncle, who sought to prove a famous unsolved mathematics problem, called Goldbach's Conjecture , that every even number greater than two is the sum of two primes .
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 ...
The Waring–Goldbach problem is a problem in additive number theory, concerning the representation of integers as sums of powers of prime numbers. It is named as a combination of Waring's problem on sums of powers of integers, and the Goldbach conjecture on sums of primes. It was initiated by Hua Luogeng [1] in 1938.
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).