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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 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 ...
English: The even integers from 4 to 50 as sums of two primes. Goldbach's conjecture is that every even integer greater than 2 can be expressed as the sum of two primes in at least one way.
Goldbach's conjecture Goldbach's conjecture is a conjecture that states that every even natural number greater than 2 is the sum of two primes. greatest common divisor The greatest common divisor of a finite list of integers is the largest positive number that is a divisor of every integer in the list.
Goldbach's comet [1] is the name given to a plot of the function (), the so-called Goldbach function (sequence A002372 in the OEIS). The function, studied in relation to Goldbach's conjecture , is defined for all even integers E > 2 {\displaystyle E>2} to be the number of different ways in which E can be expressed as the sum of two primes.
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]
It concerns number theory, and in particular the Riemann hypothesis, [1] although it is also concerned with the Goldbach conjecture. It asks for more work on the distribution of primes and generalizations of Riemann hypothesis to other rings where prime ideals take the place of primes. Absolute value of the ζ-function.
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 ...