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There is a 27-state Turing machine that halts if and only if Goldbach's conjecture is false. [37] Hence if BB(27) was known, and the Turing machine did not stop in that number of steps, it would be known to run forever and hence no counterexamples exist (which proves the conjecture true).
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. [2] [3] [4]
The Conjecture is that this is true for all natural numbers (positive integers from 1 through infinity). ... Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two ...
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.
1.2 Expert opinion on methods required for proof of Goldbach's Conjecture. 13 comments. 1.3 Perimeter that is tangent to a circle. 3 comments.
Goldbach Conjecture is true — Preceding unsigned comment added by 84.135.35.142 11:14, 13 May 2014 (UTC) If tightened up a little, you are showing that the sum of two odd primes is an even number. This shows nothing about every even n. If you think it does then it's original research and doesn't belong in Wikipedia.