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Goldbach's conjecture is used when studying computation complexity. [37] The connection is made through the Busy Beaver function, where BB(n) is the maximum number of steps taken by any n state Turing machine that halts. There is a 27-state Turing machine that halts if and only if Goldbach's conjecture is false. [37]
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]
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 mathematical topics covered in these chapters include Goldbach's conjecture that every even number is the sum of two primes, sums of squares and Waring's problem on representation by sums of powers, the Hardy–Littlewood circle method for comparing the area of a circle to the number of integer points in the circle and solving analogous ...
Created Date: 8/30/2012 4:52:52 PM
Chen's theorem is a significant step towards Goldbach's conjecture, and a celebrated application of sieve methods. Chen's theorem represents the strengthening of a previous result due to Alfréd Rényi , who in 1947 had shown there exists a finite K such that any even number can be written as the sum of a prime number and the product of at most ...
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.