Chapter 210 Elementary Proof of Prime Number Theorem!
What is the prime number theorem?
As Hua Luogeng's first disciple in name, Yu Hua certainly knew what this thing was. After all, he had just read his master's painstaking work. If he didn't understand it, it would be unreasonable.
The prime number theorem is one of the most important issues in the distribution of prime numbers. It is the central pillar theorem of the entire prime number distribution theory. It is mainly oriented to the study of the number of prime numbers. The mathematical language is: assuming x≥1, use π(x) to represent prime numbers not exceeding x.
number of.
Doesn’t it look simple?
It's really simple.
After all, this is a problem that can be solved with elementary proof. Anyone who knows some knowledge of the elementary mathematical system can give an elementary proof of the prime number theorem.
However, this elementary proof appeared in 1949.
On the historical line, in 1972, the prime number theorem was born in the hands of Prince Gauss. Subsequently, Legendre also proposed the prime number theorem conjecture, but the two failed to provide a proof, and there was no progress on this in the following fifty years.
It was not until 1850 that the Russian mathematician Chebyshev set the record for the first time and successfully proved the prime number theorem conjecture, but the process was very complicated.
Forty-six years later, in 1896, French mathematician Adama and Belgian mathematician Poussin used the extremely advanced theory of integral functions of complex variables and the creation of the zeta function by their founder Riemann to prove the prime number theorem respectively.
However, the proof process is still extremely complicated, and the method of proving the prime number theorem in this period all uses advanced number theory knowledge points and complex variable functions, which is very 'deep'.
By the beginning of the 20th century, after nearly a century of hard work, the international mathematical community believed that the prime number theorem could no longer be proved using elementary methods.
Hardy, the mentor of his master, once delivered a speech at the Copenhagen Mathematical Society in 1920: "If anyone can give an elementary proof of the prime number theorem, then he will have proved our current understanding of number theory and 'what is depth' in analytic function theory"
and
The idea of ‘what is superficial’ is extremely wrong, I hope someone can prove it.”
However, as time went by, the efforts of mathematicians were ultimately in vain. Hardy's attitude towards the elementary proof of the prime number theorem changed from expectation to giving up. He stated to the outside world that the prime number theorem must be proved by complex analysis to show the depth of the theorem result.
, he believes that only using real numbers is not enough to solve certain 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 becomes very clear. Yu Hua’s plan is to use the content of elementary number theory to prove the prime number theorem to shake the mainstream views and understanding of the proof of the prime number theorem in the international mathematics community.
If you drop a pebble into the calm water, it will create waves.
"Elementary number theory proves the prime number theorem" is the stone Yu Hua is preparing to throw to the international mathematics community.
As for the meaning of the behavior of the stone under the head...
For mathematicians, there is no meaning or practical value to measure mathematical research. For Yu Hua, this is fame and academic achievements.
As for the value of this stone, for the current era, the result of this elementary proof is undoubtedly a blockbuster, a heavyweight mathematical result second only to the advancement of Goldbach's conjecture.
You can imagine how big a stir this result will cause when the international mathematical community believes 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 have a close relationship and important influence on the study of prime numbers, but also can elevate one's identity and academic status to a higher level.
"Thank you to so many civil science experts on the Internet who want to prove Goldbach's conjecture. I have the honor to see the elementary proof of the prime number theorem and the twin prime number conjecture. Thank you very much." Thinking of this, Yu Hua quietly sent a thank you in his heart, as a tribute to future generations of scholars.
He is such a scumbag. The reason why he understands the elementary proof of the prime number theorem is because of the people on the Internet who are enthusiastic about proving Goldbach's conjecture.
If it weren't for the actions of these civil science experts that 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, he would never have thought of it.
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 are equal to identity and strength. This is the foundation. Step by step, lay a solid foundation and do whatever it takes. I'm sorry..." Yu Hua's eyes flickered and he apologized in his heart. In order to realize the plan, he had no other choice.
choose.
Academic achievements are equal to status and strength. This is the principle that Yu Hua has pursued since his change.
As a genius, you can surpass your peers, but you cannot produce world-class academic achievements out of thin air. You must accumulate and accumulate.
My current identity is most suitable for asymmetric cryptography. When the academic achievements of asymmetric cryptography are completed, I can come up with an elementary proof of the prime number theorem to attract the attention of others and improve my status.
Once he has a new round of titles and halo, and then gives results that promote his guessing, he will be able to completely consolidate his identity in the mathematics world.
This is one step at a time.
"Dong dong!" The bedroom door knocked softly.
"Please come in." Yu Hua heard the knock on the door, closed his precious notebook, and shouted towards the door.
The door slowly opened, and Xu Xue's figure appeared. She was dressed in inconspicuous gray clothes, and her eyes showed agility. After several months of training and conditioning, this Jiangyou girl has fully recovered her body, revealing
The feeling of Xiaojiabiyu.
"Xiaoxue, what's the matter?" Yu Hua asked when he saw that the person coming was Xu Xue.
These days, I basically live at home, teaching Xu Rui and Xu Xue how to read and write. Even though Xu Xue is a girl, she is not stupid at all, she is smart and smart, she has mastered nearly a thousand words, and she has considerable talent in medicine.
This pair of siblings is very interesting. Xu Rui has extraordinary agility and vigilance, good memory, ordinary appearance, and excellent marksmanship. He is a good material to be a top spy. Being his own experimental assistant is really a bit of an underachievement.
Xu Xue's talent lies in medicine. I wonder if it is because of a serious illness that her talent in the medical field is beyond ordinary people. She has a steady hand, sharp eyes, and a good memory.
As for why he is so sure, it is because Xu Xuenai is now Mr. Tan's apprentice of Xuanji Hall. After studying with Mr. Tan for more than a month, he can already identify the acupuncture points of the human body, recognize and take medicine, and cure a fever and cold without any problem.
The day before yesterday, I also worked as a veterinarian to master the art of castrating pigs.
For more than a month, while literacy, I learned the characteristics of human acupuncture points and various medicinal materials. I can cure colds and fevers. What is this but a medical genius?
You know, this is the most difficult form of Chinese medicine to learn.
After discovering Xu Xue's outstanding talent, Mr. Tan valued Xu Xue extremely highly. He made a special trip to visit Xu Xue the day before yesterday, preparing to officially accept Xu Xue as his direct disciple.
If this situation continues, there will be no problem for Xu Xue to become a top doctor in the future.
By the way, according to the schedule, the Barefoot Doctor's Handbook should be published.
"Sir, the postman just delivered a mail. Today is June 1st. Yesterday you said that if a postman delivers a mail today, I will notify you immediately." Xu Xue came to the table with a respectful face and full eyes.
With respect, he took a step forward, placed the unopened email on Yu Hua's desk, and said softly.
"Okay, I understand. By the way, where are the Ruizi people?" Yu Hua heard this, glanced at the mail on the desktop, roughly guessed what it was, smiled, and asked.
Today, June 1st, is the day when the first batch of recommended students in the country receive their admission notices.
If nothing else, this email should be his admission notice from National Tsinghua University.
"Brother said he was going to location No. 2." Xu Xue replied.
Location No. 2, Dongjiaomin Lane, Peking, Japan Pavilion.