What is the principle of Goldbach's law?

1742, a German math teacher Goldbach asked Euler, a great mathematician at that time, the following question: Every even number not less than 6 can be expressed as the sum of two odd prime numbers. But Euler failed to give an answer, which is the famous Goldbach conjecture. Gauss, the prince of mathematics, once said: "Number theory is the crown of mathematics, and Goldbach conjecture is the jewel in the crown". In fact, it is also a central topic of an important branch of analytic number theory. Mathematicians in China have made a series of important research achievements here. 1938, the famous mathematician Hua proved that almost all even numbers greater than 6 can be expressed as the sum of two odd prime numbers. In other words, Goldbach conjecture holds for almost all even numbers. Subsequently, China mathematicians Wang Yuan, Pan Chengdong and Chen Jingrun made a series of important progress on the weak Goldbach problem. Especially in 1966, Chen Jingrun solved the problem of Goldbach's conjecture "1+2" by screening. That is, there is a normal number, so that every even number greater than this constant can be expressed as the sum of the products of a prime number and no more than two prime numbers. This result is the best result of studying Goldbach's conjecture so far. It is generally called "Chen Theorem" internationally. Once this achievement was published, it immediately attracted the attention and interest of mathematicians all over the world. At that time, British mathematician Halberstam and German mathematician Li Xite were writing a monograph on sieve number theory. After the original ten chapters went to press, we saw the result of Chen Jingrun's "1+2" and specially printed the eleventh chapter. This chapter is called "Chen Theorem". Although this result is only one step away from Goldbach's conjecture (that is, "1+ 1"), it is very difficult to completely overcome it. Some mathematicians even think that it is almost impossible to solve Goldbach's conjecture without developing new mathematical tools.

Goldbach conjecture (Goldbach conjecture)

One of the three major mathematical problems in the modern world. Goldbach is a German middle school teacher and a famous mathematician. He was born in 1690, and was elected as an academician of Russian Academy of Sciences in 1725. 1742, Goldbach found in teaching that every even number not less than 6 is the sum of two prime numbers (numbers that can only be divisible by themselves). For example, 6 = 3+3, 12 = 5+7 and so on.

1742 on June 7, Goldbach wrote to the great mathematician Euler at that time, and put forward the following conjecture:

(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 thought 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 Fermat put forward this conjecture, many mathematicians have been trying to conquer it, but they have not succeeded. Of course, some people have done some specific verification work, such as: 6 = 3+3, 8 = 3+5, 10 = 5+5 = 3+7, 12 = 5+7,14 = 7+7 = 3+/kloc. Someone checked the even numbers within 33× 108 and above 6 one by one, and Goldbach conjecture (a) was established. However, the mathematical proof of lattice test needs 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. It was not until the 1920s that people began to approach it. 1920, the Norwegian mathematician Bujue proved by an ancient screening method, and reached the conclusion that every even number with larger ratio can be expressed as (99). This method of narrowing the encirclement is very effective, so scientists gradually reduced the number of prime factors in each number from (99) until each number is a prime number, thus proving "Goldbach".

At present, the best result is proved by China mathematician Chen Jingrun in 1966, which is called Chen's theorem? "Any large enough even number is the sum of a prime number and a natural number, and the latter is just 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, Bren of Norway proved "9+9".

1924, Rademacher proved "7+7".

1932, Esterman of England proved "6+6".

1937, Ricei of Italy proved "5+7", "4+9", "3+ 15" and "2+366" successively.

1938, Byxwrao of the Soviet Union proved "5+5".

1940, Byxwrao of the Soviet Union proved "4+4".

1948, Hungary's benevolence and righteousness proved "1+c", where c is the number of nature.

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, Byxwrao and vinogradov Jr of the Soviet Union and Bombieri of Italy proved "1+3".

1966, China Chen Jingrun proved "1+2".