InfoGoldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and in all of mathematics.

AM, a computer mathematician that generates new mathematical concepts.It managed to produce by itself the notion of prime number and the Goldbach conjecture.As with Racter, the question is how much the programmer filtered the output of the program, keeping only the occasional interesting output.…

The strong Goldbach conjecture is much more difficult.Using Vinogradov's method, Chudakov, Van der Corput, and Estermann showed that almost all even numbers can be written as the sum of two primes (in the sense that the fraction of even numbers which can be so written tends towards 1).…

He has visited the Institute of Advanced Studies and taught at University of Colorado.Wang's research focuses on the area of number theory, especially in the Goldbach Conjecture.Sieve methods and circle methods are often applied by him.…

All known perfect numbers are even; it is unknown whether any odd perfect numbers exist.Goldbach's conjecture states that every even integer greater than 2 can be represented as a sum of two prime numbers.Modern computer calculations have shown this conjecture to be true for integers up to at least 4 × 10 18, but still no general proof has been found.…

The teacher arranges group discussion amongst the students and may request further modification of conjectures.One successful result by HRL was the independent invention of Goldbach's conjecture.…

Such counterexamples do not disprove a statement, however; they only show that, at present, no constructive proof of the statement is known.One weak counterexample begins by taking some unsolved problem of mathematics, such as Goldbach's conjecture.…

The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem.The twin prime conjecture and Goldbach's conjecture are two unsolved problems in number theory.…

The decidability is still an open question, but there are results on restriction of thoses circuits.Finding answers to some questions about this model could serve as a proof to many important mathematical conjectures, like Goldbach's conjecture.It is a natural extension of the circuits over sets of natural numbers when the considered set contains also negative integers, the definitions, which does not change, will not be repeated on this page.…

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.…

By the Law of Excluded Middle, Goldbach's conjecture is either true or false.If it is true then f is 1, and the required algorithm is just "print 1".…

He is remembered today for Goldbach's conjecture.

The strong Goldbach conjecture implies the conjecture that all odd numbers greater than 7 are the sum of three odd primes, which is known today variously as the "weak" Goldbach conjecture, the "odd" Goldbach conjecture, or the "ternary" Goldbach conjecture.While the weak Goldbach conjecture appears to have been finally proved in 2013, the strong conjecture has remained unsolved.If the strong Goldbach conjecture is true, the weak Goldbach conjecture will be true by implication.…

The subprojects running on the platform OProject@Home are important to science because they address difficult and unsolved problems in physics and theoretical mathematics.For example, Goldbach's conjecture, proposed in 1742 has never been disproven.It is not even clear whether the problem can be solved, as the range of numbers are infinite.…

He was honored with an Academician of the Chinese Academy of Science in 1991.Previously, Wang Yuang made progress toward Goldbach's Conjecture on the distribution of prime numbers.His result was that for any sufficiently large even number, that number is the sum of two numbers -- one a product of at most two primes, the other a product of at most three primes.…

These are like the Goldbach Conjecture, in stating that all natural numbers possess a certain property that is algorithmically checkable for each particular number.The Matiyasevich/MRDP Theorem implies that each such proposition is equivalent to a statement that asserts that some particular Diophantine equation has no solutions in natural numbers.…

In 1995, he sharpened earlier work on Schnirelmann's theorem by proving that every even number is a sum of at most six primes.This result may be compared with Goldbach's conjecture, which states that every even number except 2 is the sum of two primes.…

While the weak Goldbach conjecture appears to have been finally proved in 2013, the strong conjecture has remained unsolved.If the strong Goldbach conjecture is true, the weak Goldbach conjecture will be true by implication.For small values of n, the strong Goldbach conjecture (and hence the weak Goldbach conjecture) can be verified directly.…

Chen's 1973 paper stated two results with nearly identical proofs.His Theorem I, on the Goldbach conjecture, was stated above.His Theorem II is a result on the twin prime conjecture.…

A Goldbach number is a positive integer that can be expressed as the sum of two odd primes.Therefore, another statement of Goldbach's conjecture is that all even integers greater than 4 are Goldbach numbers.The expression of a given even number as a sum of two primes is called a Goldbach partition of that number.…