* Goldbach's conjecture

Because many outstanding problems in number theory, such as Goldbach's conjecture are equivalent to solving the halting problem for special programs ( which would basically search for counter-examples and halt if one is found ), knowing enough bits of Chaitin's constant would also imply knowing the answer to these problems.

He is remembered today for Goldbach's conjecture.

Goldbach is most noted for his correspondence with Leibniz, Euler, and Bernoulli, especially in his 1742 letter to Euler stating his Goldbach's conjecture.

For instance, Goldbach's conjecture is the assertion that every even number ( greater than 2 ) is the sum of two prime numbers.

Thus to Brouwer, we are not justified in asserting " either Goldbach's conjecture is true, or it is not.

Many questions around prime numbers remain open, such as Goldbach's conjecture, which asserts that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, which says that there are infinitely many pairs of primes whose difference is 2.

To be considered a conjecture, a statement must usually be proposed publicly, at which point the name of the proponent may be attached to the conjecture, as with Goldbach's conjecture.

* Christian Goldbach formulates Goldbach's conjecture.

In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture.

Goldbach's conjecture states that every even integer greater than 2 can be expressed as the sum of two primes.

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

Therefore, another statement of Goldbach's conjecture is that all even integers greater than or equal to 4 are Goldbach numbers.

A modern version of Goldbach's marginal conjecture is:

Goldbach's third version ( equivalent to the two other versions ) is the form in which the conjecture is usually expressed today.

* The television drama Lewis featured a mathematics professor who had won the Fields medal for his work on Goldbach's conjecture.

* Isaac Asimov's short story " Sixty Million Trillion Combinations " featured a mathematician who suspected that his work on Goldbach's conjecture had been stolen.

* In the cartoon The Adventures of Jimmy Neutron: Boy Genius ( 2003 ), Jimmy stated that he was in the middle of proving Goldbach's prime number conjecture.

* Goldbach's conjecture, part of Chris Caldwell's Prime Pages.

* Online tool to test Goldbach's conjecture on submitted integers.

* Goldbach Weave showing a graphical representation of Goldbach's conjecture.

** Goldbach's conjecture, one of the oldest unsolved problems in number theory

Many abstract problems can be solved routinely, others have been solved with great effort, for some significant inroads have been made without having led yet to a full solution, and yet others have withstood all attempts, such as Goldbach's conjecture and the Collatz conjecture.

In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that:

Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem ; also, a version of Goldbach's conjecture has been extended to them.

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.

His work on the twin prime conjecture, Waring's problem, Goldbach's conjecture and Legendre's conjecture led to progress in analytic number theory.

In 1997, Deshouillers, Effinger, te Riele and Zinoviev showed that the generalized Riemann hypothesis implies Goldbach's weak conjecture for all numbers.

He also proved a result concerning Fermat numbers that is called Goldbach's theorem.

See Goldbach's comet.

* To generate publicity for the novel Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis, British publisher Tony Faber offered a $ 1, 000, 000 prize if a proof was submitted before April 2002.

From the last equation, we can deduce Goldbach's theorem ( named after Christian Goldbach ): no two Fermat numbers share a common factor.

Goldbach's conjecture states that every even integer greater than 2 can be represented as a sum of two prime numbers.

This conjecture is called " weak " because if Goldbach's strong conjecture ( concerning sums of two primes ) is proven, it would be true.

His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.

Conditional proofs exist linking several otherwise unproven conjectures, so that a proof of one conjecture may immediately imply the validity of several others.

If the four-color conjecture were false, there would be at least one map with the smallest possible number of regions that requires five colors.

The answer to this question turned out to be negative: in 1952, Gleason, Montgomery and Zippin showed that if G is a topological manifold with continuous group operations, then there exists exactly one analytic structure on G which turns it into a Lie group ( see also Hilbert – Smith conjecture ).

In fact, whether one can smooth certain higher dimensional spheres was, until recently, an open problem — known as the smooth Poincaré conjecture.

A conjecture developed by Cumrun Vafa, Amer Iqbal, and Andrew Neitzke in 2001, called " mysterious duality ", concerns a set of mathematical similarities between objects and laws describing M-theory on k-dimensional tori ( i. e. type II superstring theory on T < sup > k − 1 </ sup > for k > 0 ) on one side, and geometry of del Pezzo surfaces ( for example, the cubic surfaces ) on the other side.

" And while the conjecture may one day be solved, the argument applies to similar unsolved problems ; to Brouwer, the law of the excluded middle was tantamount to assuming that every mathematical problem has a solution.

One conjecture holds that " Nazareth " is derived from one of the Hebrew words for ' branch ', namely ne · ṣer, נ ֵ֫ צ ֶ ר, and alludes to the prophetic, messianic words in Book of Isaiah 11: 1, ' from ( Jesse's ) roots a Branch ( netzer ) will bear fruit.

The Poincaré conjecture, before being proven, was one of the most important open questions in topology.

For dimensions greater than three, one can pose the Generalized Poincaré conjecture: is a homotopy n-sphere homeomorphic to the n-sphere?

The Collatz conjecture: one way to illustrate its complexity is to extend the iteration from the natural numbers to the complex numbers.

An unproven statement that is believed to be true is called a conjecture ( or sometimes a hypothesis, but with a different meaning from the one discussed above ).

By explaining past changes by analogy with present phenomena, a limit is set to conjecture, for there is only one way in which two things are equal, but there are an infinity of ways in which they could be supposed different.

This variation might suggest the early rulers came from a hybrid Anglo-British dynasty or that the rule of early Wessex shifted between more than one royal clan, but this is conjecture.

Both questions have remained unsolved ever since, although the weak form of the conjecture appears to be much closer to resolution than the strong one.

Statistical considerations which focus on the probabilistic distribution of prime numbers present informal evidence in favour of the conjecture ( in both the weak and strong forms ) for sufficiently large integers: the greater the integer, the more ways there are available for that number to be represented as the sum of two or three other numbers, and the more " likely " it becomes that at least one of these representations consists entirely of primes.

This precept, from one of Bacchylides ' extant fragments, was considered by his modern editor, Richard Claverhouse Jebb, to be typical of the poet's temperament: " If the utterances scattered throughout the poems warrant a conjecture, Bacchylides was of placid temper ; amiably tolerant ; satisfied with a modest lot ; not free from some tinge of that pensive melancholy which was peculiarly Ionian ; but with good sense ..."

She is one of the handful of people whom certain scholars conjecture may have been the true author of the plays attributed to William Shakespeare.

( Gauss ' conjecture was proven more than one hundred years later by Heegner, Baker and Stark.

As with the Hilbert problems, one of the prize problems ( the Poincaré conjecture ) was solved relatively soon after the problems were announced.

Roughly speaking, the Langlands reciprocity conjecture is the special case of the functoriality conjecture when one of the reductive groups is trivial.

While this theory is in one sense closely linked with the Taniyama – Shimura conjecture, it should be understood that the conjecture actually operates in the opposite direction.