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Let us in front of the conjecture Goldbach and try to understand, from a purely algorithmic point of view, what is the question. Suppose we have an even number, denoted by 2n such that p and q that do not exist the first two added together give just 2n. Imagine that the Goldbach conjecture is verified for a given 2n.

say this is like saying that n is not in the middle of the first two, namely that the symmetry with respect to n, for every prime less than n is a number made the other side.

The point is that, in this case, each of these numbers can only be made by the same compound that the first child of n. Indeed, a prime greater than n, multiplied by any other first (even doubled) makes a greater number of 2n and clearly the numbers in question are between them 2n. In addition, these compounds can not be among their prime factors which are also factors of n, for obvious reasons.

So everything is summarized in the following way:

If for any even number p = 2n Goldbach not true, then the primes less than n (and first with n!) Must compose, combine only with each other, all the numbers the results in the symmetry with respect to n.

To be more precise, ik first under its first coat should combine it with a producer ik places equidistant from them n the other hand, those who give them added up to 2n.

The conjecture then says that those k may not hold each of the first k places that are symmetrical with respect to at least one of the jump ..... No!

speech is a very difficult course to be pursued in an attempt to extract a proof from this account. Just think how many possible combinations of k prime numbers, how difficult it is to define the restrictions on those combinations in order to bring these products in the range of its 2n ...

A vision that makes us understand how other results (to Chen, for example) do not fall completely on that interpretation.

This is not to assess the likelihood of achieving results apparently near you .... Goldbach question is whether you can show that given any number n, ik first child early with it and it will not be able to cover all ik places that are symmetrical with respect to n.

Kylie Wilde And Jessie James

Goldbach's conjecture - Presentation

E 'known to the mathematician Christian Goldbach left (in 1742) is an open problem in number theory, a problem faced primarily by Euler and later generations of mathematicians, problem now solved. The wording, and perhaps a sense, the conjecture is very simple and understandable to most people

every even number greater than 2 is the sum of two primes

That is, given any even number is always possible to determine (at least) a pair of primes such that their sum that would lead to an even number of departure. Although not yet produced a proof of this fact, certainly in the last century there has been progress. Although on that 'ahead we would have to get some clarification.

In fact, the problem has never been addressed from a structural point of view, or at least, though never with partial results. A mathematical approach has been followed by the strictly statistical and probabilistic, which led to the conclusion that the conjecture is true , although not proven, based on the principle that the greater the even number in question, the more likely to find that the first two added together are equivalent to it . Combining this theorem (called of prime numbers, source wikipedia) the results of electronic computers, have come to probe the validity dell'asserto for all numbers up to values \u200b\u200bthat are important, as there is content on one side and is considered the conjecture, if proved, at least assimilated. On the other hand, in the course of this century, the emphasis was to turn around all'asserto Goldbach, attacking, and partly showing, seemingly related.

Examples include Vinogradov, who in 1937 proved that every odd number greater than 3 high 3-15 is elevated to a sum of three first, or even Chen, who in 1966 showed that every even number big enough or is the sum of two first or a first and a semiprime or a number consisting of only two primes.

Oliveira e Silva, with powerful computers, have verified the validity of the conjecture up to 1,200,000,000,000,000,000 (results as at March 2008).

And then?

The question we ask is whether the attitude of mathematicians who deal with the problem is perhaps made a silent before it. How can the streets followed are now checking with the computer to ever larger numbers, the study of the problem on probabilistic bases, while making these numbers large enough or worse, the deviation of the problem on other related but that in mock do not really have anything to do with Goldbach's conjecture? It 's the sign that, unlike Fermat's Last Theorem, it'll be really hidden in the great book, without ever leaving?