Can all even numbers greater than 2 be expressed as the sum of two prime numbers?

(Note that the so-called "China's latest development, which has been confirmed as 1+ 1" at the bottom of this article belongs to the category of malicious pseudoscience added by boring people, so readers need not pay attention to it. "This problem has yet to be solved." For the last sentence. )

This question was put forward by the German mathematician C Goldbach (1690- 1764) in a letter to the great mathematician Euler on June 7th, 742, so it is called Goldbach conjecture. On June 30th of the same year, Euler replied that this conjecture may be true, but he could not prove it. Now, the general formulation of Goldbach conjecture is: every even number greater than or equal to 6 can be expressed as the sum of two odd prime numbers; Every odd number greater than or equal to 9 can be expressed as the sum of three odd prime numbers. In fact, the latter proposition is the inference of the previous proposition.

Goldbach conjecture seems simple, but it is not easy to prove, which has become a famous problem in mathematics. In 18 and 19 centuries, all number theory experts did not make substantial progress in proving this conjecture until the 20th century. 1937 Soviet mathematician vinogradov (ииногралов, 189 1- 1983).

It is directly proved that Goldbach conjecture is not valid, and people adopt circuitous tactics, that is, first consider expressing even numbers as the sum of two numbers, each of which is the product of several prime numbers. If the proposition "every big even number can be expressed as the sum of a number with no more than one prime factor and a number with no more than b prime factors" is recorded as "a+b", then the Coriolis conjecture is to prove that "1+ 1" holds. Since the 1920s, some mathematicians from abroad and China have successively proved the propositions of "9+9", "23", "1+5" and "L+4".

1966, Chen Jingrun, a young mathematician in China, successfully proved "1+2" after years of painstaking research, that is, "any big even number can be expressed as the sum of a prime number and another number whose prime factor does not exceed 2". This is the best achievement in this research field so far, and it is only one step away from picking up this "jewel in the crown of mathematics" that has caused a sensation in the mathematics field. "1+2" is also called Chen Theorem.

Goldbach's problem can be inferred from the following two propositions. As long as the following two propositions are proved, the conjecture is proved:

(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 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. It was not until the 1920s that people began to approach it. 1920, the Norwegian mathematician Bujue proved by an ancient screening method that every even number greater than 6 can be expressed as (9+9). This method of narrowing the encirclement is very effective, so scientists gradually reduce the number of prime factors of each number from (99) until each number is a prime number, thus proving Goldbach's conjecture.

At present, the best result is proved by Chinese 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, 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".

The most difficult problem in Goldbach's conjecture, 1+ 1, has yet to be solved.