my scientific age

Chapter 212 Elementary Proof of Prime Number Theorem!
What is the prime number theorem?
As the first disciple of Hua Luogeng in name, of course Yu Hua knows what this thing is. After all, he has just read his master's hard work.

The prime number theorem is one of the most important problems in the distribution of prime numbers. The central pillar theorem of the whole prime number distribution theory is mainly oriented to the study of prime numbers. number of.

Does it seem simple?
It's really simple.

After all, this is a problem that can be solved with elementary proofs, and anyone with a little knowledge of elementary mathematical systems can give elementary proofs of the prime number theorem.

However, this primary proof appeared in 1949.

On the historical line, in 1972, the prime number theorem was born in the hands of Prince Gauss. Later Legendre also proposed the prime number theorem conjecture, but the two failed to prove it, and there was no progress in the following 50 years.

Until 1850, the Russian mathematician Chebyshev made the first record and successfully proved the prime number theorem conjecture, but the process was very complicated.

In the past 46 years, in 1896, the French Adama and the Belgian mathematician Poussin proved the prime number theorem with the extremely advanced complex variable whole function theory and the zeta function created by the grandfather Riemann.

However, the proof process is still extremely complicated, and the methods for proving the prime number theorem in this period all used advanced number theory knowledge points and complex variable functions, which were very 'deep'.

At the beginning of the twentieth century, the time span was nearly a century, and the international mathematical community believed that the prime number theorem could no longer be proved by elementary methods.

Hardy, the mentor of his own master, once gave a speech at the Copenhagen Mathematical Society in 1920: "If anyone can give an elementary proof of the prime number theorem, then he will prove what we are talking about in number theory and analytic function theory. What is depth? and
The idea of ​​'what is superficial' is extremely wrong, and I hope someone can prove it. "

However, with the passage of time, the efforts of a famous mathematician were finally in vain. Hardy's attitude towards the elementary proof of the prime number theorem changed from expectation to abandonment. It was expressed that the prime number theorem must be proved by complex analysis to show the depth of the results of the theorem. , he believes that only using real numbers is not enough to solve some problems, and complex numbers must be introduced to solve them.

Today, the mainstream views and attitudes in the international mathematics community are basically the same - the prime number theorem must be proved with advanced mathematical knowledge, and elementary number theory cannot prove the prime number theorem.

At this point, the situation is very clear. Yu Hua's abacus is to use the "elementary number theory to prove the prime number theorem" to shake the mainstream view and cognition of the prime number theorem proof in the international mathematics community.

When a pebble is dropped on the calm water, there will be waves.

'Proving the prime number theorem by elementary number theory' is exactly the stone that Yu Hua is going to throw at the international mathematics community.

As for the significance of the movement of the stone under the head...

For mathematicians, there is no meaning or practical value to measure mathematical research. For Yu Hua, it is fame and academic achievements.

And to ask how valuable this stone is, for the current era, the result of this elementary proof is undoubtedly a blockbuster, a heavyweight mathematical achievement second only to the advancement of Goldbach’s conjecture.

It is conceivable to imagine how much this result will cause waves when the international mathematical community thinks that the elementary proof of the prime number theorem is impossible.

The most important thing is that the results of the elementary proof of the prime number theorem not only satisfy the close relationship and important influence with the prime number research, but also can raise their own identity and academic status to a higher level.

"Thank you to so many people on the Internet who want to prove Goldbach's conjecture. I am fortunate to see the elementary proof of the prime number theorem and the twin prime number conjecture. I am really grateful." Thinking of this, Yu Hua quietly sent a thank you, as a future scholar The scumbag, the reason why he understands the elementary proof of the prime number theorem is that he has to rely on the people who are enthusiastic about proving Goldbach's conjecture on the Internet.

If it weren't for the behavior of these civil science tycoons, it aroused Yu Hua's interest and gave him a general understanding of Goldbach's conjecture and the related prime number theorem and twin prime number conjecture, which he would never have imagined.

As far as the second transitional result is concerned, the elementary proof of the prime number theorem is completely qualified.

"Then it's decided, academic achievements and identity strength are equal, this is the foundation, step by step, consolidate the foundation, do whatever it takes, I'm sorry..." Yu Hua's eyes flickered, and he sent an apology in his heart, in order to realize the plan, he has nothing to do choose.

Academic achievements and identity strength are equal, this is the principle of conduct that Yu Hua has pursued since the change.

As a genius, you can surpass your peers, but you cannot come up with world-class academic achievements out of thin air. You must have accumulation and precipitation.

The current identity is the most suitable for asymmetric cryptography. When the academic achievements of asymmetric cryptography are completed, a primary proof of the prime number theorem will be able to attract the attention of others, and at the same time improve one's own identity status.

When you have a new round of titles and halo, and then give out the results of promoting Gecha, you will be able to completely stabilize your identity in the mathematical world.

This is one step at a time.

"Boom!" There was a soft knock on the bedroom door.

"Please come in." Yu Hua heard the knock on the door, closed the precious notebook, and shouted towards the door.

The door slowly opened, and Xu Xue's figure appeared. She was wearing inconspicuous gray clothes, and her eyes showed a sense of agility. After several months of self-cultivation and conditioning, the Jiangyou girl has fully recovered. The feeling of a small home jasper.

"Xiao Xue, what's the matter?" Yu Hua asked when he saw that it was Xu Xue.

These days, I basically live at home and teach Xu Rui and Xu Xue to read and write. Although Xu Xue is a girl, she is not stupid at all, she is smart and smart, she has mastered nearly a thousand words, and has a good talent in medicine.

This brother and sister is very interesting. Xu Rui has an unusual alertness and vigilance. He has a good memory, ordinary appearance, and excellent marksmanship talent.

Xu Xue's talent lies in medicine. I don't know if it is because of a serious illness that her talent in the field of medicine surpasses ordinary people. She has steady hands, sharp eyes, and a good memory.

As for why it is so certain, it is because the current Xu Xue is the young apprentice of Mr. Tan of Xuanjitang. After learning with Mr. Tan for more than a month, he can already identify the acupuncture points of the human body, know the medicine and pick the medicine, and it is not a problem to cure a fever and cold.

I also became a veterinarian the day before yesterday and mastered the craft of barrows.

For more than a month, while literate, learning the characteristics of human acupuncture points and various medicinal materials can cure colds and fever. Isn't this a medical genius?
You know, this is the most difficult Chinese medicine to learn.

After discovering Xu Xue's excellent talent, Mr. Tan valued Xu Xue very much. He came to visit him the day before yesterday, and planned to officially accept Xu Xue as a direct disciple.

According to the development of this situation, there will be no problem for Xu Xue to become a top doctor in the future.

By the way, according to the time, the barefoot doctor's manual should be published.

"Sir, just now the postman has sent an email. Today is June [-]st. You said yesterday that if there is a postman delivering mail today, I will notify you immediately." Xu Xue came to the table with a respectful face and eyes full of eyes. Respect, take a step forward, put the unopened email on Yu Hua's desktop, and say softly.

"Okay, I got it, by the way, what about Ruiziren?" Yu Hua glanced at the email on the desktop, guessed what it was, smiled, and asked.

Today, June [-]st, is the day when the first batch of recommended students in the country received their admission notices.

This email, if nothing else, should be his admission letter from National Tsinghua University.

"Brother said he went to the second location." Xu Xue replied.

Location [-], Dongjiaomin Lane, Beiping, Japan Pavilion.

(End of this chapter)