"yes, after four months of keeping a low profile, it's time to swell up again. Pen? Interesting? Pavilion wWw. ｂiquge。 info" Zhou Chen joked with a faint smile.

Yang Xi nodded, and also joked: "Well, I think it's okay, I don't have you in the TV news, and I'm still a little uncomfortable." ”

You must know that people are not good for a thousand days, and flowers are not red for a hundred days. No matter how popular a person is, it is impossible to dominate the headlines all the time, there are so many things happening every day in the world, Zhou Chen has not made any new moves for several months, so naturally there is no chance to be on camera.

Some people are scrambling to make headlines, in fact, it is not unreasonable, mainly to get acquainted, don't wait until one day to appear in public, no one else knows, then it will be embarrassing.

On the morning of the next day, in a classroom in the School of Mathematical Sciences of Beijing Normal University, Professor Wang Yun, the instructor of the "Hua Luogeng Class" of the University of Science and Technology of China, who was specially invited to give a lecture on mathematics, was giving a lecture to the students.

The audience was packed with students, and the seats were full.

"At the Second International Congress of Mathematicians in Paris in 1900, the famous mathematician Hilbert delivered a speech entitled "Problems of Mathematics", in which he proposed 23 questions that he considered to be the most important in mathematics based on the results and development trends of mathematical research in the nineteenth century.

Professor Wang Yun gave an off-script speech, standing on the stage with his back to the huge screen behind him, which was very similar to that of some experts and scholars.

"These twenty-three problems can be divided into four major parts, the first to the sixth are mathematical foundation problems; The seventh to twelfth questions are number theory problems; Questions 13 to 18 belong to algebra and geometry; Questions 19 to 23 belong to mathematical analysis. ”

In the more than 100 years since these questions were raised, mathematicians have followed one after another, and many of them have been overcome by later mathematical geniuses, such as Genz's use of the transcendent induction method in 1936 to prove that there is no contradiction in the axiomatic system of arithmetic in the second problem; In 1973, the Soviet mathematician Bogrelov solved the fourth problem, in the case of symmetrical distance, a straight line is the shortest line between two points; In 1953, Hidehiko Yamamai of Japan obtained a completely positive result for the fifth question, "Topology becomes a condition for Lie groups (topological groups)". ”

"But there are still some issues that have only been partially resolved or there has been no progress at all, and these will be the ultimate questions left to all of you...... Hopefully, one day some of you will be able to fix them. ”

The math students in the room listened attentively, and their eyes lit up, but they quickly went out again.

It's not that they're arrogant, it's that it's far beyond their means.

These are world-class problems, and people with the slightest bit of self-knowledge should know that they are not able to solve them.

However, there are really people among them who are not self-sufficient, I saw Hu Yuchen, who was sitting in the middle, clenching his fists hard, and the whole person was full of fighting spirit, as if he had found a way to prove himself.

"I'm going to challenge you!"

So on a hot afternoon, Zhou Chen suddenly saw a young man running in front of him to give him a war letter.

"Challenge what?" Zhou Chen looked at him with some surprise. This quasi-yaman has been silent for a few months, and Zhou Chen thought that he had given up, but he didn't expect to come to him at this time.

"The eighth of the twenty-three most important mathematical problems proposed by Hilbert, the 'Prime Number Problem.'"

Hu Yuchen looked at Zhou Chen with an inexplicable nervousness, the other party was the one who won the Dirac Medal, there are few other honors in China that can defeat him, Hu Yuchen thought about it and felt that the only way to beat him was to find a heavyweight problem to the same level, although it was a bit difficult to find a mathematical problem to challenge him, but if he won the grand prize in mathematics that was no less than the Dirac Medal, then at least he was on the same starting line.

"The eighth question...... Riemann conjecture, Goldbach conjecture or twin prime conjecture? Zhou Chen smiled slightly and asked with interest.

"It's all right!" Hu Yuchen was stunned for a moment, and immediately reacted. He didn't expect that Zhou Chen actually knew something about the eighth question "Prime Number Problem", and actually knew that this question included three prime conjectures: the Riemann conjecture, the Goldbach conjecture and the twin prime conjecture.

This made him cautious, could it be that he would not be able to lose in the major of mathematics?

No way! Can't be overwhelmed by him in momentum!

"We'll see, I'll be sure to solve the prime problem before you do." Hu Yuchen's handsome face was a little distorted, and he yelled hysterically at Zhou Chen. After speaking, he didn't wait for Zhou Chen's reply, turned around and left in a hurry.

"What a weird guy......" Zhou Chen muttered as he looked at his back as he walked away. Obviously, you can eat with your face, but you have to delve into mathematics, which is really funny.

However, Hu Yuchen's battle book was very interesting to him, and he was planning to establish a new mathematical system but had nowhere to start, Zhou Chen felt that maybe this "prime number problem" could be used as an appetizer to guide him into the field of mathematics, and maybe it could also activate the understanding of mathematics of the Odo civilization in the chain database.

Back at his residence, Zhou Chen told Yang Xi about the matter, and then calmed down and began to study hard.

The first is to find information, understand what is the prime number problem, what is the current progress in the mathematical community, and then refer to the experience of predecessors after looking for information, and summarize and sublimate on their basis.

It is better to look at the problem by standing on the shoulders of the predecessors than fooling around without knowing anything, and you can also avoid many detours.

Seeing Zhou Chen's serious look, Yang Xi pursed his lips and sat quietly next to him.

……

The so-called prime number problem mainly refers to the twin prime conjecture, the Goldbach conjecture and the Riemann conjecture, all three of which are world-class difficulties. Probably the simplest and most basic of these is the twin prime conjecture.

The core of these three conjectures is a prime number, so what is a prime number? Prime numbers, also known as prime numbers, refer to numbers greater than 1 that are only divisible by 1 and themselves, such as: 2, 3, 5, 7, 11, 13, 17......

The twin prime conjecture originated from a general conjecture proposed by the French mathematician Alfon de Polignac in 1849: for any natural number k, there are infinitely many p's prime numbers, and p+2k is also prime.

The twin prime conjecture is the case when k is equal to 1, that is, there are infinitely many primes p in the natural number, so that p+2 is also a prime number, and the prime pair (p,p+2) here is the twin prime.

The simplest twin primes are actually pairs of 3 and 5, 5 and 7, and 11 and 13, but the twin prime conjecture requires proof that there are an infinite number of such pairs (p,p+2).

Is there really an infinite number of such prime numbers, right? The prime theorem states the tendency of prime numbers to become scarce as they tend to infinity, while twin primes, like prime numbers, have the same tendency, and this tendency is more pronounced than prime numbers. In this way, the possibility of prime pairs is constantly diluting!

It is indeed a difficult task to prove the twin prime conjecture, and in the history of twin prime research, mathematicians have followed suit, and some have claimed to have proved the twin prime conjecture, but so far there has been no proof that can be examined by professional mathematicians.

It was not until May 2013 that Zhang Yitang made a breakthrough in the study of twin primes, and he proved a weakened form of the twin prime conjecture. In his research, Zhang Yitang proved that "there are infinitely many pairs of prime numbers with a difference of less than 70 million" without relying on unproven inferences, and this research was immediately considered to have made a major breakthrough in the ultimate number theory problem of twin prime conjecture.

Although the interval 2 is a long way from the interval of 70 million, the Nature report called it an "important milestone".

Zhang Yitang's paper was published on the Internet on May 14 and officially published on May 21. But on May 28, that constant dropped to 60 million, and then just two days later, on May 31, it dropped to 42 million, and three days later, on June 2, it was 13 million; the next day, 5 million; June 5, 400,000.

Zhang Yitang's proof has been continuously improved, which has further narrowed the distance between the final solution of the twin prime conjecture. As recently as February 2014, Zhang Yitang's 70 million had been shrunk to 246, that is, it had been proved that there were countless prime pairs (p, p+246).

This seems to be getting closer and closer to the final solution of the twin prime conjecture of 2, and due to Zhang Yitang's outstanding contribution, the twin prime conjecture has become the most likely to be proved among the three prime conjectures.

As for the Goldbach conjecture, it is also called the "1+1" conjecture, which is more difficult than the twin prime conjecture, and is known as the world's three major mathematical conjectures together with Fermat's conjecture (Fermat's great theorem) and the four-color conjecture (four-color theorem). Among them, Fermat's theorem and the four-color conjecture were proved by the British mathematician Professor Wiles in 1995 and the Chinese teacher Yu Chengren in 2016.

The source of Goldbach's conjecture is that on June 7, 1742, the German mathematician Goldbach put forward a bold conjecture in a letter to the famous mathematician Euler: any odd number not less than 7 can be the sum of three prime numbers (e.g., 7=2+2+3). So on June 30, 1742, Euler wrote to Goldbach that any even number not less than 4 could be the sum of two prime numbers (e.g., 4=2+2).

Obviously, the first conjecture is a corollary of the second conjecture, so it is enough to prove only one of the two conjectures.

The latter is organized into the form that every even number greater than 2 can be written as the sum of two prime numbers, which is the Goldbach conjecture, that is, "1+1" - can be written as the sum of two prime numbers.

The main methods used by mathematicians in the 20th century to study Goldbach's conjecture were advanced mathematical methods such as sieves, circles, denseness, and trigonometric sums. The idea of solving this conjecture is like "narrowing the encirclement", gradually approaching the final result.

In 1920, the Norwegian mathematician Brown proved the theorem "9+9", thus delineating the "Great Encirclement" to attack Goldbach's conjecture. The so-called "9+9", that is, any large enough even number can be expressed as the sum of two other numbers, and each of these two numbers is the product of 9 odd prime numbers.

Starting from this "9+9", mathematicians all over the world have concentrated their efforts on narrowing the encirclement, and of course, the final goal is "1+1".

In 1924, the German mathematician Redmacher proved the theorem "7+7". Soon "6+6", "5+5", and "4+4" were captured one after another; It was not until 1957 that the Chinese mathematician Wang Yuan proved "3+3" and "2+3"; Later, the Chinese mathematician Pan Chengdong proved "1+5", and in the same year, he cooperated with Wang Yuan to prove "1+4".

In 1965, Soviet mathematicians proved "1+3".

In 1966, the famous Chinese mathematician Chen Jingrun conquered "1+2", that is, any large enough even number can be expressed as the sum of two numbers, and one of these two numbers is an odd prime number, and the other is the product of two odd prime numbers.

This theorem is known as "Chen's theorem" by the world mathematical community.

Thanks to Chen Jingrun's contribution, mankind is only one step away from the final result of Goldbach's conjecture "1+1". But in order to achieve this final step, it may be a long process of exploration.

There are even many mathematicians who believe that in order to prove "1+1", it is necessary to create new mathematical methods, and the previous path is likely to be impossible.