What is Goldbach conjecture? 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 7th, Goldbach wrote to Euler, a great mathematician at that time, and put forward the following conjectures: (a) Any one >; 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 Goldbach 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. But 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 try their best, but they still can't figure it out. It was not until the 1920s that people began to approach it. 1920, the Norwegian mathematician Brown proved by 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 a prime number, thus proving Goldbach's conjecture. 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 problem that even numbers can be expressed as the sum of the products of S prime numbers and T prime numbers ("s+t" for short) progressed as follows: 1920, Norwegian 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, Bukit Tiber of the Soviet Union proved "5+5". 1940, Bukit Tiber 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 Taber and vinogradov Jr. of the Soviet Union and Pemberley of Italy proved "1+3". 1966, China Chen Jingrun proved "1+2". It took 46 years from Brown's proof of 1920 of "9+9" to Chen Jingrun's capture of 1966 of "+2". Since the birth of Chen Theorem for 30 years, it is futile for people to further study Goldbach conjecture. 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 is not filtered out, such as 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 description in the previous part is a natural idea. The key is to prove that' at least one pair of natural numbers has not been filtered out'. No one in the world can prove this part yet. If it can be proved, this conjecture will be solved. However, because the big even number n (not less than 6) is equal to the sum of odd numbers of its corresponding odd number series (starting with 3 and ending with n-3). Therefore, according to the sum of odd numbers, prime+prime (1+ kloc-0/) or prime+composite (1+2) (including composite+prime 2+ 1 or composite+composite 2+2) (Note:/kloc) That is, the occurrence "category combination" of 1+ 1 or 1+2 can be derived as 1+ 1 and 1+2. Because 1+2 and 2+2 and 1+2 do not contain1+. So 1+ 1 does not cover all possible "category combinations", that is, its existence is alternating. So far, if the existence of 1+2 and 1+2 can be excluded, it is proved that 1+ 1 But the fact is that 1+2 and 2+2, and 1+2 (or at least one of them) are some laws revealed by Chen's theorem (any large enough even number can be expressed as the sum of two prime numbers, or the sum of the products of one prime number and two prime numbers), such as the existence of 1+2 and the coexistence of 6542. Therefore, 1+2 and 2+2, and 1+2 (or at least one) "category combination" patterns are certain, objective and inevitable. So 1+ 1 is impossible. This fully shows that the Brownian sieve method cannot prove "1+ 1". Because the distribution of prime numbers itself changes in disorder, there is no simple proportional relationship between the change of prime number pairs and the increase of even numbers, and the value of prime number pairs rises and falls when even numbers increase. 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 pair values. 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 are people who prove Goldbach's conjecture in other ways. 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 number pair, and the mathematical expression expressing the relationship between even number and its prime number pair does not exist. It can be proved in practice, but the contradiction between individual even numbers and all even numbers cannot be solved logically. How do individuals equal the average? 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.