Chen's theorem

The set of Chen - named after the Chinese mathematician Chen Jingrun - is a set of number theory. It is usually stated as follows:

He is considered the best ever closer to a proof of the not yet proven gold Bach's conjecture states that every even number is the sum of two primes.

Background

See also the article about the Goldbach conjecture

Goldbach's conjecture is unproven to this day. In the twentieth century, however, reach first evidence of "similar " statements. These state for example, that every even number, or a certain subset of even numbers can be written as a sum of at most X prime numbers or numbers with a maximum of X prime factors.

The in this sense, so far the "best" approximation to the actual Goldbach's conjecture has now been achieved Chen Jingrun in 1966 by proof of said set.

The addition of "sufficiently large" means that the rate for all even numbers above a certain minimum number applies.

Content

The theorem in its original formulation deals with the question of how many different ways the even number can be represented as a corresponding sum. For this number, it provides at least the following amount:

With

A summary of the evidence found, for example under

The English translation of 1973 contains another set ( with proof ) from the environment of the twin prime conjecture: at any difference ( for the twin prime conjecture ), there are infinitely many primes for which is a prime number or a product of two primes.

Developments

Published in 1975 P. Ross a simpler proof of the theorem of Chen.

2002 proved YC Cai, that ( at least above another limit) can represent any even number so that the summand, which is the prime number, is less than.