A detailed explanation of Chen Jingrun's theorem. .

Chen Theorem Chen Theorem is a detailed proof method published by China mathematician Chen Jingrun in 1966 and 1973. This theorem proves that any large enough even number can be expressed as the sum of a prime number and a semi-prime number, which is what we usually call "1+2". 1742, the German Goldbach wrote a letter to Euler, a great mathematician living in Petersburg, Russia. In the letter, he raised two questions: First, can every even number greater than 4 be expressed as the sum of two odd prime numbers? Such as 6=3+3, 14=3+ 1 1 and so on. Second, can every odd number greater than 7 represent the sum of three odd prime numbers? Such as 9 = 3+3+3, 15 = 3+5+7, etc. This is Xu Chi's reportage, the famous Goldbach Conjecture. China people know Chen Jingrun and Goldbach's conjecture. So, 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 his teaching that every even number not less than 6 is the sum of two prime numbers (numbers that can only be divisible by 1 and itself). For example, 6=3+3, 12=5+7 and so on. 1On June 7th, 742, Goldbach wrote to Euler, a great mathematician 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. Described in contemporary language, Goldbach conjecture has two contents, the first part is called odd conjecture, and the second part is called even conjecture. Odd number conjecture points out that any odd number greater than or equal to 9 is the sum of three odd prime numbers. Even number conjecture means that even numbers greater than or equal to 6 must be the sum of two odd prime numbers. Correct solution In fact, the correct solution of the first question can lead to the correct solution of the second question, because every odd number greater than 7 can obviously be expressed as the sum of even numbers greater than 4 and 3. 1937, Soviet mathematician vinogradov proved that every odd number big enough can be expressed as the sum of three odd prime numbers with his original "triangular sum" method, which basically solved the second problem. But the first problem has not been solved so far. 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. Question 1: Chen Jingrun didn't prove Goldbach's conjecture. There are five questions about Chen's theorem: Chen Jingrun didn't prove Goldbach's conjecture: Chen Jingrun and Shao Pinzong co-wrote Goldbach's conjecture on page 1 18 (Liaoning Education Publishing House): the result of Chen Jingrun's theorem is "1+2", which means, in layman's terms: for any even number n, p ". It is well known that at least one of the following two formulas holds true. Goldbach conjecture holds true for even numbers (a) greater than 4, and 1+2 holds true for even numbers (b) greater than 10. These are two different propositions. Chen Jingrun confused two unrelated propositions when he declared the prize, stealing the concept (proposition), and Chen Jingrun did not prove 65438+. Question 2: Chen Jingrun used the wrong form of reasoning. Chen Jingrun used the wrong form of reasoning: Chen adopted "affirmative" compatible alternative reasoning: either A or B, A, so either A or B, or both A and B hold. This is a wrong form of reasoning, ambiguous, far-fetched, meaningless and uncertain, just like the fortune teller said, "Mrs. Li gave birth, or gave birth to a boy, or gave birth to a girl, or both boys and girls gave birth to multiple births." Anyway, it's right. This judgment is called falsifiability in epistemology, and falsifiability is the boundary between science and pseudoscience. There is only one correct form of consistent substitution reasoning. Negative affirmation: either A is B or A is B, so there are two rules in B. Consistent substitution reasoning: 1, and denying one part of the substitute limb means affirming the other part; 2. Affirm some verbal limbs but don't deny others. It can be seen that the recognition of Chen Jingrun shows that China's mathematical society is chaotic and lacks basic logic training. Question 3: Chen Jingrun used many wrong concepts. Chen Jingrun used many wrong concepts: Chen used two vague concepts of "big enough" and "almost prime number" in his paper. The characteristics of scientific concepts are: accuracy, specificity, stability, systematicness and testability. And "big enough" means 10 to the power of 500,000, which is an unverifiable number. Almost prime numbers mean a lot of pixels, a child's game. Question 4: Chen Jingrun's conclusion can't be regarded as a theorem, and Chen Jingrun's conclusion can't be regarded as a theorem: Chen's conclusion adopts special names (some, some), that is, some N is (a) and some N is (b), so it can't be regarded as a theorem, because all strict scientific theorems and laws are expressed in the form of full-name (all, all, all, each) propositions, and a full-name proposition states all of a given class. And Chen Jingrun's conclusion is not even a concept. Question 5: Chen Jingrun's works seriously violate the cognitive law. Chen Jingrun's works seriously violate the cognitive law. Before finding the general formula of prime numbers, Coriolis conjecture can't be solved, just as turning a circle into a square depends on whether the transcendence of π is clear, and the stipulation of matter determines the stipulation of quantity. (Legend of Goldbach's conjecture) Wang Xiaoming 1999, Legend of China 3) Editor-in-Chief. Questioning "Questioning" Many domestic math lovers claim to have proved "Goldbach conjecture". Some of them (such as Wang Xiaoming, a pseudo-citizen) fabricated rumors with ulterior motives, such as "Chen Jingrun's certificate was false" and "Chen Jingrun, Wang Yuan and Pan Chengdong stole the concept declaration award", because their "achievements" could not be published, distorting the facts in order to achieve the purpose of speculating their "achievements". These "doubts" lack basic mathematical knowledge, and the concept of stealing is serious, and the argument goes against science. For example, The Legend of Goldbach's Conjecture, which has been reposted constantly, said: "Chen used two vague concepts of' big enough' and' almost prime number' in his paper. In fact, these two concepts have been accurately defined and widely used in mathematics. The words "almost prime number" have never been used in Chen Jingrun's proof, and "big enough" has only been used once; Another example is "Chen's conclusion uses a special name (a, a), that is, a certain n is (a), so it can't be a theorem at all", which shows that the author doesn't understand the scientific meaning of the theorem at all; Another example is "Chen adopted the" affirmative form "of compatible alternative reasoning, which is a wrong form of reasoning, with nothing to say and nothing to be sure", while Chen Jingrun did not use the logical form of "compatible alternative reasoning" at all in his proof, and many of them were subjective judgments and lacked basis. At present, there is no dispute about the correctness of "Chen Theorem" in the international mathematics field, and it is recognized that "Chen Theorem" is the best result of Goldbach's conjecture research. Chen Theorem has been quoted by many foreign number theory works, such as Sieving Method in Britain, Solving the Problem of Prime Numbers, Number Theory in America, Mathematics in the 20th Century, etc. Readers can consult relevant materials by themselves. This also reminds us that in this era of developed information, we must pay attention to judging the source and correctness of information. Discrimination: 1, Chen Jingrun's proof is not "Goldbach conjecture", which needs no doubt. There has always been a public opinion in the international mathematics community. Chen Jingrun's proof of "1+2" is only the "best achievement", not the proof of "1+ 1", and the two cannot be equated. This has always been clear in the past. 2. "Chen Theorem" is an independent theorem, which only proves the result that Chen wants to prove. So the judgment of "compatible word selection" does not apply here. Because Chen doesn't want to use his own achievements to launch other achievements. As long as there is no problem with Chen's other steps before reaching this result, there is no problem with the proof itself. In other words, what Chen wants is the result of "either A or B". Before Chen, no one could prove this result. Chen got this result through strict proof. Although this result can't solve other problems at present, it can't be said that there is a problem with the proof itself. 3. From the point of view of 2, the relevant "query" did not produce sufficient evidence and reasonable logic to explain that Chen Jingrun's work "violated the cognitive law". So the conclusion is not valid for the time being. The proposition that Chen Jingrun's conclusion can't be called a theorem, like Goldbach's conjecture, is still unsolved. There is no other evidence about Chen Jingrun's "forgery". It is also a proposition that has no solution for the time being. 5. The skeptics pointed out that Chen Jingrun's use of the concepts of "almost prime number" and "large enough" is against the laws of mathematics, and there is no specific argument. On the other hand, defenders have presented evidence that the concepts of "almost prime number" and "large enough" have been widely recognized internationally. For this evidence of the defender, at present, the skeptics have not produced strong negative evidence. 6. Defender thinks that Chen Jingrun has never used the concept of "almost prime number", but the fact that this word has not appeared does not mean that this concept has not been used. Because according to the definition of "almost prime number", Chen Jingrun's achievement of "1+2" itself serves "almost prime number". But this little mistake of the defender has no influence on the merits of the whole question. The key is 5. 7. There is insufficient evidence to say that the questioner has "ulterior motives". At present, it is also a proposition with no solution for the time being.