(a) Any > even number =6 can be expressed as the sum of two odd prime numbers.
(b) Any odd number > 9 can be expressed as the sum of three odd prime numbers.
This is the famous Goldbach conjecture. In his reply to him on June 30th, Euler said that he believed this conjecture was correct, but he could not prove it. Describing such a simple problem, even a top mathematician like Euler can't prove it. This conjecture has attracted the attention of many mathematicians. Since Goldbach put forward this conjecture, many mathematicians have been trying to conquer it, but they have failed. Of course, some people have done some specific verification work. For example: 6 = 3+3, 8 = 3+5, 10 = 5+5 = 3+7, 12 = 5+7,14 = 7+7 = 3+1/kloc-. 18 = 5+ 13, ... etc. Someone looked up even numbers greater than 6 within 33× 108, and Goldbach conjecture (a) was established. However, strict mathematical proof requires the efforts of mathematicians.
Since then, this famous mathematical problem has attracted the attention of thousands of mathematicians all over the world. 200 years have passed and no one has proved it. Goldbach conjecture has therefore become an unattainable "pearl" in the crown of mathematics. People's enthusiasm for Goldbach conjecture lasted for more than 200 years. Many mathematicians in the world have tried their best to solve it, but they still can't figure it out.
It was not until the 1920s that people began to approach it. 1920s, proved by Norwegian mathematician Brown with an ancient screening method, and reached a conclusion that every even number with a large ratio can be expressed as (99). This method of narrowing the encirclement is very effective, so scientists gradually reduce the prime factor in each number from (99) until each number is finally made.
At present, the best result is proved by China mathematician Chen Jingrun in 1966, which is called Chen Theorem: "Any large enough even number is the sum of a prime number and a natural number, while the latter is only the product of two prime numbers." This result is often called a big even number and can be expressed as "1+2".
Before Chen Jingrun, the progress of even numbers can be expressed as the sum of the products of S prime numbers and T prime numbers (referred to as the "s+t" problem) as follows:
1920, Norway Brown proved "9+9".
1924, Latmach of Germany proved "7+7".
1932, Esterman of England proved "6+6".
1937, Lacey in Italy successively proved "5+7", "4+9", "3+ 15" and "2+366".
1938, Bukxitib of the Soviet Union proved "5+5".
1940, Bukhsiteb of the Soviet Union proved "4+4".
1948, Rini of Hungary proved "1+c", where c is a large natural number.
1956, Wang Yuan of China proved "3+4".
1957, China and Wang Yuan successively proved "3+3" and "2+3".
1962, Pan Chengdong of China and Barba of the Soviet Union proved "1+5", and Wang Yuan of China proved "1+4".
1965, Buchwitz of the Soviet Union, George W. vinogradov and Pemberley of Italy proved "1+3".
1966, China Chen Jingrun proved "1+2".
It has been 46 years since Brown proved "9+9" in 1920 and Chen Jingrun captured "1+2" in 1966. In the more than 30 years after the birth of Chen Theorem, people's further research on Goldbach's conjecture has been futile.
The idea of Brownian screening method is as follows: any even number (natural number) can be written as 2n, where n is a natural number, and 2n can be expressed as the sum of a pair of natural numbers in n different forms: 2n =1+(2n-1) = 2+(2n-2) = 3+(2n-3) = 2i and 2i. 3j and (2n-3j), j = 2, 3, ...; And so on), if it can be proved that at least one pair of natural numbers has not been filtered out, such as remembering that one pair is p 1 and p2, then both p 1 and p2 are prime numbers, that is, n=p 1+p2, then Goldbach's conjecture is proved. The first part is a natural idea. The key is to prove that' at least one pair of natural numbers has not been filtered out.
But because the big even number n (not less than 6) is equal to its corresponding odd number series (starting with 3 and ending with n-3), it is the sum of odd numbers added from beginning to end. Therefore, according to the sum of odd numbers, it has all possible correlations with prime number+prime number (1+kloc-0/) or prime number+composite number (1+2) (including composite number+prime number 2+ 1 or composite number+composite number 2), namely/. And the cross occurrence "category combination" of 1+0 can be derived as 1+ 1+1and 1+2,1+and. 1+2 and so on. Because 1+2 and 1+2 do not contain 1+ 1, 1 cannot cover all possibilities ". And 1+2 is excluded, then 1+ 1 is proved, otherwise 1+ 1 is not proved. However, the facts are: 1+2 and 2+2, and 1+2. Or the sum of the products of a prime number and two prime numbers), the basic basis for the existence of some laws (for example, 1+2 exists, 1+ 1 does not exist). So 1+2 and 2+2, and 1+2 (or at least one) "
Because the distribution of prime numbers itself changes in disorder, the change of prime number pairs is not simply proportional to the increase of even numbers. When the even number increases, the value of the prime number pair rises and falls. Can the change of prime pairs be related to the change of even numbers through mathematical relations? Can't! There is no quantitative law to follow in the relationship between even values and their prime pairs. For more than 200 years, people's efforts have proved this point, and finally they choose to give up and find another way. So there appeared people who used other methods to prove Goldbach's conjecture. Their efforts have only made progress in some fields of mathematics, and have no effect on Goldbach's conjecture.
Goldbach conjecture is essentially the relationship between an even number and its prime pair. There is no mathematical expression to express the relationship between an even number and its prime pair. It can be proved in practice, but it can not solve the contradiction between individual even numbers and all even numbers logically. How can an individual be equal to the average person? Individuals and the general are the same in nature, but opposite in quantity. Contradictions will always exist. Goldbach conjecture is a mathematical conclusion that can never be proved theoretically and logically.
However, all over the world, as a mathematician, especially an expert in number theory, who doesn't dream of picking this dazzling pearl? Especially in China, inspired by the spirit of Chen Jingrun, how many mathematicians, like Chen Jingrun, stayed up all night trying to prove this "conjecture", concentrating on thinking and exploring the essence? Even some young non-mathematics professionals are keen to delve into Goldbach's conjecture. Some people send their own "research results" to the Institute of Mathematics of Chinese Academy of Sciences or mathematical academic journals, claiming to prove "1+ 1".
After Chen Jingrun's death, faced with the situation that they claimed to have "proved" Corinthian conjecture, mathematicians such as Academician Yang Le earnestly warned blind young people through the media not to do anything useless.
Every year, the School of Mathematics of China Academy of Sciences receives a large number of letters, claiming that they have completed the demonstration of Goldbach's conjecture. In fact, most of these discussants don't even understand some basic mathematical concepts. They worked hard and sweated for the so-called "proof".
According to legend, Hua, a famous mathematician in China, thought in his later years that he had proved Goldbach's conjecture. Later, when several of his students saw it, they knew it was wrong and it was not easy to say it directly, so they advised him to have a rest. Imagine that even Hua Lao mistakenly thought that he had solved Goldbach's conjecture for himself, and it is not surprising that math lovers mistakenly thought that they had solved Goldbach's conjecture for themselves.
I advise those who dream of proving Goldbach's conjecture, first of all, to find out what a prime number is and what its law is, and give you a natural number at will. Can you quickly judge whether it is a prime number? For example, can 1234567 be divisible by 7?
Forget it, forget it, and do something else!