1+2=?

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 off the jewel in the crown of mathematics that has caused a sensation in the mathematics field. But this small step is hard to take. "1+2" is called Chen Theorem.

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Proof method

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.

Chen Jingrun's proof of even Cauchy formula implies that the lower bound is greater than 1.

Let r(N) be the representation of an even number as the sum of two prime numbers. In 1978, Chen Jingrun proved that:

r(n)≤《7.8∏{(p- 1)/(p-2)}∏{ 1- 1/{(p- 1)^2}}{n/(lnn)^2}。

Among them, in the first series, the numerator of the parameter is greater than the denominator, and the value is (a fraction greater than one). The limit value of the second series is 0.66 ... and its multiple of 2 is also greater than 1. N/(lnN) is the number of prime numbers contained in the number of n: where (lnN) is the natural logarithm of n and can be converted into 2{ln(√N)}. Because n/(lnn) 2 = (1/4) {(√ n)/ln (√ n)} 2 ~ (1/4) {π (√ n)} 2. The parameters are based on the prime number theorem; The number of prime numbers in the square root number of (√ n)/ln (√ n) ~ π (√ n) ~ n. The formula proved by Chen Jingrun is equivalent to {(number greater than one) (square number of prime numbers in the square root number of n)}. As long as the square number of prime numbers in the square root number of even numbers is greater than 4, even numbers have a solution greater than 1. That is, it is greater than the second prime number.

Let r(N) mean that the number of even numbers is the sum of two prime numbers. The formula adopted by mathematicians is: r (n) 2 {(p-1)/(p-2)} {1-1(p-65438). Known: ∏{(p- 1)/(p-2)}≥ 1. 2∏{ 1- 1/(p- 1)^2}>； 1.32...。 N/(lnn) 2 = {[(√ n)/ln (√ n)] 2}/4, [(√ n)/ln (√ n)] √ The number of prime numbers in the square root of an even number, that is, when the even number is greater than the square number of numbers containing two prime numbers, the even guess solution formula is a number greater than 1.

In the formula for solving Goldbach's conjecture introduced in the book of number theory, let r(N) be the representation that even N is the sum of two prime numbers, including: R (n) ∏ 2 [(p-1)/(p-2)] ∏ [1-65438+] There are two formulas π (n) n ∏ [(p-1)/p], which are known: 1/lnn ∏ [(p- 1)/p], and the p parameter is a prime number not greater than the square root of n, ∏ [n ∏ [(p-1)/p] = (√ n) ∏ [(p-1)/p] (√ n) = (√ n) {(660) Because: (√ n) So the square number of: n/(lnn) 2 ? {(√ n) ∏ [(p-1)/p]} is determined, and the solution is a number greater than (greater than one). The solution of Goldbach's conjecture solution formula introduced in the book of number theory is a number greater than (a number greater than 1). (The value of p in the formula (√N)∏[(P- 1)/p] is not the value of p in the prime number formula for finding the square root of n, and the difference between the two formulas is one coefficient. )

Mathematicians use a formula to solve the problem of "representing the sum of three prime numbers in odd-numbered tables": let T(N) be the representation of the sum of three prime numbers in odd-numbered tables, and t (n) ~ (1/2) ∏ {1-1(p-65438+). ∏ {{1+1(p-65438) is converted into the following formula: t (n) ~ (1/2) ∏ [1-kloc-0/(p-) 1) (n/lnn) (square number of prime numbers in the square root of n numbers /4), which is equivalent to (>; 0.33 ..) (the number of prime numbers in n numbers) (the square number of prime numbers in the square root of n numbers) /4, and the condition that the formula is greater than 1 is obtained. If the odd number is greater than 9, the formula solution is >; (0.33*4)(2*2/4)> 1, odd Goldbach conjecture solution formula solution is greater than one.

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Questioning Chen Jingrun

Deny Chen Jingrun

Chen Jingrun and Shao Pinzong wrote on the page 1 18 of Goldbach conjecture (Liaoning Education Press) that the result of "1+2" of Chen Jingrun's theorem, in layman's terms, is that for any even number n, an odd prime number P', p ",or P 1, can always be found.

N=P'+P" (A)

N=P 1+P2*P3 (B)

Of course, it is not excluded that both (a) and (b) are true, such as 62=43+ 19, 62=7+5X 1 1. "

As we all know, Goldbach's conjecture holds for even numbers (a) greater than 4, and for even numbers (b) 10+2.

These are two different propositions. Chen Jingrun confused two unrelated propositions and changed his concept (proposition) when he announced the prize. Chen Jingrun did not prove 1+2, because 1+2 is much more difficult than 1+ 1.

Note: Logically, if a proof is correct, there is no difficulty in denying it. Anything different can be distinguished and separated. In other words, it is not allowed to "infiltrate" an opinion. When two objects are combined into one object, it can only be understood that one object is destroyed and the other is saved. "1+2" is 1+2, so it cannot be said to be 1+ 1.

Wrong reasoning form

Chen adopts the "positive formula" of compatible substitution reasoning: either A is B or A, so either A or B is combined. 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.

Use the wrong concept

Chen used two vague concepts in his thesis, namely "big enough" and "almost prime number". 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.

The conclusion is not a theorem.

The characteristics of Chen's conclusion are (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, everything, all, each) propositions, which state the unchangeable relationship between all elements of a given class and apply to infinite classes. And Chen Jingrun's conclusion is not even a concept.

Work violates cognitive laws.

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 pi is clear or not, 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.

Query on "Query"

What does "questioning" mean?

When we see here, it is not difficult to produce the following views:

1, what does "discovery" mean? Is discovery and proof the same thing? Finding it is equivalent to seeing it, isn't it? Chen Jingrun said: In geometric proof, if two angles are found or seen to be equal, can it be said that two angles are proved to be equal?

2. "At least one formula holds" and "It is not excluded that (a) and (b) hold at the same time".

If (a) and (b) are established at the same time, because they are screened out, and then (b) is screened out, doesn't it prove that Goldbach's conjecture is established?

(A)(B) At least one formula is established, which means that a formula is not established or does not exist, which means that a formula is not established. So, which formula doesn't hold?

If (b) is not true, it means that 1+2 is not true; If (a) doesn't hold, Goldbach's conjecture doesn't hold. In fact, whether Goldbach conjecture is established is the best proof of Goldbach conjecture

Some people think that:

At present, many math enthusiasts in China claim to have proved Goldbach's conjecture. Some of them fabricated rumors with ulterior motives, such as "Chen Jingrun's proof in those days was false", "Chen Jingrun, Wang Yuan, and Pan Chengdong stole the concept to declare awards", and distorted the facts to achieve the purpose of speculating their "political 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, the correctness of "Chen Theorem" is still controversial in the international mathematics field, and it is recognized that "Chen Theorem" is the most problematic study of Goldbach's conjecture. "

Discrimination:

1, Chen Jingrun proved that it is not "Goldbach conjecture", so there is no doubt about it. 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. Therefore, Professor Qiu Chengtong thinks this is the result of the media.

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.

There is no other evidence about Chen Jingrun's "forgery".

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. In fact, "almost prime number" is just a noun, which refers to a number p, which is either a prime number or the product of two prime numbers; "Big enough" is a common concept in advanced mathematics.

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Guess the meaning

One thing interests people because we care about it. If the solution of a problem can't arouse human pleasure at all, we will close our eyes. If this question doesn't help our knowledge at all, we will think it is worthless. If this incident can't arouse justice and beauty, sentiment and enthusiasm can't be verified.

Goldbach conjecture is a sequence of numbers. People love it for a long time because without this sequence, people will lose confidence in deeper problems-because disorder is fatal to beauty, and if Goldbach conjecture is wrong, it will limit our observation ability. This makes it difficult for us to appreciate them across some issues. If a problem imposes its chaotic side on our inner life, it will make our feelings ugly and produce inferiority and sadness. Goldbach conjecture actually means that any natural number n greater than 3 has an x, so that n+x and n-x are prime numbers, because (n+x)+(n-x)=2n. This is a symmetry between prime numbers and natural numbers, representing an order. It makes sense because the seemingly chaotic thing, prime number, is symmetrical with the natural number n, just like a shepherd boy calling out sheep running all over the mountain and touching people's hearts, just like biological gene DNA, it turns around the natural number n in a double helix structure, and people see a simple and youthful side from the mysterious prime number. Symmetry is not only a visual aesthetic concept, it means the unity of objects.

Prime number has a romantic temperament, produces an amorphous haze and has mysterious charm. In contrast, pi and natural logarithm. Feckenbaum numbers of imaginary numbers are much simpler, and Euler unified them with a formula. And prime numbers give people more tragic colors and a sacred indifference. When Goldbach conjecture becomes a theorem, we can see the wisdom of the great god. Multiplication is the superposition of addition, while Goldbach conjecture summarizes multiplication by addition. There is profound knowledge in this obscure proposition. It has changed people's view of logarithm: the wheel of multiplication is intuitive and clear at a glance, Goldbach conjecture embodies an exploration function, and the distinction between noble and inferior is obvious. Addition and multiplication are the accumulation of quantities, but multiplication is the generalization of addition, but the control of addition on multiplication embodies two different requirements, the former can be understood through feeling, and the latter needs inspiration-humanity and philosophy. Looking at the former and longing for its opposite (the latter), this ideal realm has become a century-old belief and reflection. The special value of reflection lies in satisfying deep curiosity and is the spiritual path of all major discoveries. For example, recording is the result of reflection on pronunciation, and magnetism is the result of reflection on electricity. . . . Shun thinking and reflection is a kind of symmetry, which indicates a kind of vitality and vigor. Shun thinking is natural, reflection is active, shun thinking produces experience, and reflection produces science. Si Shun's content is often superficial, open and well known. The content of reflection is often hidden and unknown. Reflection is not a simple review of feelings, nor a nostalgia for experience, but the ultimate standard for finding the essence of things-the revelation of historical truth or the truth of things.

Why is Goldbach's conjecture attractive? There are absolutely no objective things and factors in the world that can move people. One thing is attractive because it has some quality that can shake the observer's sensibility, and the size of sensibility is the quality of the observer. Touching things are often public. Give people infinite reverie and hints. Goldbach's conjecture conceals its insidious essence in a simple and cheerful form. There is a strong hazy atmosphere around him. He teased people that they started with comedies, but ended with tragedies without exception. He politely refused all her suitors, made them jealous and fought, and watched a poor performance. Corinthian conjecture makes people daydream with an abstract beauty. It created a fairyland, aroused people's desires and ambitions, and made those who thought they had some talents die of hard work, trouble and anger. He ran wildly in the ocean of human spirit, making the boat of wisdom difficult to control and sinking the scientific research Titanic again and again.

The spiritual prestige of human beings is based on the victory of science over superstition and ignorance. The mental health of human groups depends on a kind of self-confidence. Only self-confidence can lead the ideal to the future, and perfect faith can alleviate the hardships and pains of life. Such a soul-stirring disaster and soul-stirring grief can hardly destroy people's faith. Only when they feel incompetent will their beliefs fall apart. Under the guidance of an empty soul, the body melts into an animal, and human beings feel inferior in failure. This is the philosophical significance of Goldbach conjecture.

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status

No substantial progress has been made.

"In the past 20 years, there has been no substantial progress in proving Goldbach's conjecture." Chen Mufa, a professor of mathematics at Beijing Normal University who will give a 45-minute report at this international congress of mathematicians, said, "Its proof is only the last step. If the research makes essential progress, then the conjecture will eventually be solved. " According to Chen Mufa, in 2000, an international organization listed seven Millennium problems in the field of mathematics, and offered a reward of10 million dollars to solve them, but it did not include Goldbach's conjecture. "In recent years or even more than ten years, Goldbach's conjecture is still difficult to prove." Gong Fuzhou, a researcher at the Institute of Mathematics and System Science, Chinese Academy of Sciences, analyzed this, and now conjecture has become an isolated problem, which is not closely related to other mathematics disciplines. At the same time, researchers also lack effective ideas and methods to finally solve this famous conjecture. "Mr. Chen Jingrun has used the existing methods to the extreme before his death." Becker, a professor at Cambridge University and a Fields Prize winner, also said that the progress made by Chen Jingrun in this work is the best verification result so far, and there is no greater breakthrough at present. "It may be difficult to make progress in solving this kind of mathematical problems for one or two hundred years, or it may make significant progress in a short time." In Gong Fuzhou's view, there is a certain contingency in mathematical research, which may make people make progress in conjecture proof in advance.

Corresponding to [1] Baidu Encyclopedia Prime Law, Gong Fuzhou's famous saying has been verified.

Corresponding to this edition of Guess and the number of prime numbers in Baidu Encyclopedia, Goldbach's conjecture proposition has been proved to be valid. The conclusion that the status quo has not made essential progress is an outdated conclusion 10 years ago.

Produce a new theory

I don't want to say more about the difficulty of Goldbach's conjecture. I want to talk about why modern mathematicians are not interested in Goldbach conjecture, and why many so-called folk mathematicians in China are interested in Goldbach conjecture.

In fact, in 1900, the great mathematician Hilbert made a report at the World Congress of Mathematicians and raised 23 challenging questions. Goldbach conjecture is a sub-topic of the eighth question, including Riemann conjecture and twin prime conjecture. In modern mathematics, it is generally believed that the most valuable is the generalized Riemann conjecture. If Riemann conjecture can be established, many questions will be answered, while Goldbach conjecture and twin prime conjecture are relatively isolated. If we simply solve these two problems, it is of little significance to solve other problems. So mathematicians tend to find some new theories or tools to solve Goldbach's conjecture "by the way" while solving other more valuable problems.

Why are folk mathematicians so obsessed with Gothic conjecture and not concerned about more meaningful issues such as Riemann conjecture? An important reason is that Riemann conjecture is difficult for people who have never studied mathematics to understand its meaning. Goldbach guessed that primary school students could watch it.

It is generally believed in mathematics that these two problems are equally difficult. Folk mathematicians mostly use elementary mathematics to solve Goldbach conjecture. Generally speaking, elementary mathematics cannot solve Goldbach's conjecture. To say the least, even if an awesome person solved Goldbach's conjecture in the framework of elementary mathematics that day, what's the point?

Say angry words, can't stop people from solving Goldbach's conjecture. ? The law of Goldbach's conjecture corresponds to the encyclopedia card of Goldbach's conjecture, and the theory that gave birth to it must be expressed as a function:

First, the function object:

1, even number and its number field

2. Odd numbers and their number fields

Second, the main target:

1, at least one pair of prime numbers is the addend factor of the specified even field.

2. In the specified number field, at least three prime numbers are addend factors of specified odd numbers.

Third, the key to the function [1],

1, at least one pair of prime numbers is the addend factor of the specified even field.

2. Adjust the specified odd number in the specified number field.

(1): Converts the specified odd number to an even number.

(2): Even number is decomposed into two prime numbers.

(3): The specified odd number is converted into the sum of a prime number and an even number, and the even number is further decomposed into the sum of two prime numbers.

This is sheer nonsense.