Goldbach's Conjecture

Goldbach conjecture can be roughly divided into two kinds (the former is called "strong" or "double Goldbach conjecture" and the latter is called "weak" or "triple Goldbach conjecture"): 1. Every even number not less than 6 can be expressed as the sum of two odd prime numbers; 2. Every odd number not less than 9 can be expressed as the sum of three odd prime numbers.

The origin of Goldbach conjecture

From 1729 to 1764, Goldbach kept correspondence with Euler for 35 years. In the letter 1742 to Euler on June 7th, Goldbach put forward a proposition. He wrote: "My question is this: Take any odd number, such as 77, which can be written as the sum of three prime numbers: 77 = 53+17+7; Take an odd number, such as 46 1, 46 1=449+7+5, which is also the sum of three prime numbers. 46 1 can also be written as 257+ 199+5, which is still the sum of three prime numbers. In this way, I found that any odd number greater than 7 is the sum of three prime numbers. But how can this be proved? Although the above results are obtained in every experiment, it is impossible to test all odd numbers. What is needed is general proof, not individual tests. " Euler wrote back: "This proposition seems to be correct". But he can't give strict proof. At the same time, Goldbach put forward another proposition: any even number greater than 6 is the sum of two prime numbers, but he failed to prove this proposition. It is not difficult to see that Goldbach's proposition is the inference of Euler's proposition. In fact, any odd number greater than 5 can be written as 2N+ 1=3+2(N- 1), where 2(N- 1)≥4. If Euler's proposition holds, even number 2(N- 1) can be written as the sum of two prime numbers. But the establishment of Goldbach proposition does not guarantee the establishment of Euler proposition. So Euler's proposition is more demanding than Goldbach's proposition. Now these two propositions are collectively called Goldbach conjecture.

A brief history of Goldbach conjecture

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. 1742 On June 7th, Goldbach wrote to the great mathematician Euler at that time. In his reply 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 elusive "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. Goldbach conjecture legend is actually the most legendary history in the history of science (see Baidu Goldbach conjecture legend for details). 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: every even n greater than 5 (not less than 6) can be expressed as the product of nine prime numbers plus the product of nine prime numbers, which is called 9+9 for short. It should be noted that this 9 is not an exact 9, but refers to any one that may appear in 1, 2, 3, 4, 5, 6, 7, 8 and 9. Also known as "almost prime number", it means that there are many pixels. There is no substantial connection with Goldbach's conjecture. 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". Professor Chen Jingrun's "sufficiently large" refers to the power of 10 of about 500,000, that is, adding 500,000 zeros after 1 is a number that cannot be tested at present. Therefore, Paul Hoeffmann wrote on page 35 of Revenge of Archimedes that a number that is almost prime enough is a vague concept.

Edit this paragraph Goldbach conjecture to prove the progress correlation

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 "s+t" problem) 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". 1978, Chen Jingrun proved the upper bound formula of "1+ 1". R (n) = "7.8 ∏ {(p-1)/(p-2)} ∏ {1-1{(p-1) 2}} {n The operation of N/(lnN) indicates the number of prime numbers contained in n numbers. Where (lnN) is the natural logarithm of n, which can be converted into 2{ln(√N)}. n/(lnn)^2=( 1/4){(√n)/ln(√n)}^2~( 1/4){π(√n)}^2。 As long as "the square number of prime numbers in the square root number of n" >; 1, the formula solution is greater than.

Questions about editing this paragraph

(Legend of Goldbach's conjecture, Wang Xiaoming 1999, No.3, Legend of China)

First, what Chen Jingrun proved was not Goldbach's conjecture.

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. Make at least one of the following two formulas hold: "n = p'+p" (a) n = p1+p2 * P3 (b) Of course, it does not rule out that (A)(B) holds simultaneously, for example, 62=43+ 19, 62 = 7+5x. "As we all know, Goldbach conjecture means that even number (a) greater than 4 holds, and 1+2 means that even number (b) greater than 10 holds, which 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+. 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.

Second, Chen Jingrun used the wrong form of reasoning.

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.

Third, Chen Jingrun used many wrong concepts.

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.

Fourthly, Chen Jingrun's 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.

5. Chen Jingrun's works seriously violate the law of cognition.

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.

Edit the meaning of Goldbach conjecture in this paragraph.

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. Time is waiting for an immortal hero.