Research starts with PhD students

Chapter 98: Jebov conjecture, proved!

On the stage.

Zhang Shuo finished explaining the last part of the prime number distribution test method.

He put down his pen and walked back to the center, facing the audience, and said, "This part is Professor Sun Xingli's research on 'Testing the distribution of prime numbers starting with square numbers', which is also the core method for proving the Gerbov conjecture in the future."

The reaction in the lecture hall was lukewarm.

Most people, especially those at the back, looked at each other in bewilderment.

There were a lot of people in the lecture hall, but they were all there to watch the fun. They were not professional scholars in the field of number theory, and they simply could not understand the complex logical arguments involved.

Not to mention, many people come from the middle.

Everyone in the back row looked towards the judges' table, but no one there said anything.

Zhu Hao, Shen Yuan and others listened from beginning to end. They did not find any problems. The other judges did not understand some parts and did not want to ask questions.

The purpose of review is to ensure the correctness of the research.

Zhu Hao and Shen Yuan have both confirmed it. Some people feel that it is a bit embarrassing to ask questions, so it is better to ask others later, or simply study the published papers.

Qiu Chengwen and Peng Ruochuan had just arrived not long ago. They only listened to the latter part and naturally did not ask any questions.

Some of the scholars who came later also listened from beginning to end.

A middle-aged man sitting nearby stood up and asked, "Professor Zhang Shuo, this test method seems to have only made a judgment, and has not determined the prime number interval, or the test range. Is there any problem with my understanding?"

Zhang Shuo pondered the question carefully and said with a smile, "There is nothing wrong with your understanding. It's just a judgment."

"You're probably asking what he has to do with proving the Gerbov conjecture, right? That's what I'm going to talk about later."

The middle-aged man sat down after listening.

Soon another person stood up and said, "Professor Zhang Shuo, I didn't understand what Professor Sun just said, that A to B is a sequence of consecutive positive integers, but why is it different from 1 to B? Can you explain it again?"

He was asking about the part where Sun Xingli was stuck in the front.

Zhang Shuo looked down at the paper, found the corresponding part, and asked the staff to bring a new whiteboard. Then he explained, "I will explain it again."

"There are two boundary lines from A to B, one above and one below A and B, but there is only one boundary line from 1 to B. If all its boundaries are divisible by p, the number of times the curve passes through is the least..."

"We can compare the border lines first..."

"Let's analyze the upper and lower limits again. When N is sufficiently large..."

He spoke for about five minutes, going over this part again and making it clear to those who had questions about it.

At this point, everyone in the lecture hall discovered that Zhang Shuo was standing on the stage not giving a report, but as a teacher giving a lecture to students.

That kind of casual and unhurried manner makes people feel very confident.

Many people have already confirmed that there is nothing wrong with the part just explained.

Sun Xingli let out a long sigh and a smile appeared on his face. Zhang Shuo's explanation on the stage until now was actually to make amends for him.

This part is his content.

He was so nervous when he went on stage to speak that his mind was a little confused for a moment and he couldn't understand the logic of his own research.

Now that he was sure there was no problem, Sun Xingli felt very relaxed. He smiled and said, "I was just saying, is there any problem with my research?"

Luo Yongjun turned his head and said disdainfully, "How dare you say that! There is nothing wrong with the research, but you found a problem with it?"

"Isn't this nervous..."

Sun Xingli muttered quietly, "Everything was fine at the beginning, but I was too nervous when I saw Academician Qiu. If I had known, I would not have talked about the Debov conjecture and let Zhang Shuo do it."

"Professor Zhang Shuo's lecture was really good."

Wu Lining praised him, and then asked, "Professor Sun, the research you two did together, the part just now was yours, is the next part Professor Zhang Shuo's research?"

"To be precise, I was also involved."

“How much involvement?”

"There are some," said Sun Xingli, stretching out his hands to indicate an area, then thinking for a moment and narrowing it down a little.

Luo Yongjun stretched out his arm and pointed at his fingertips. "This thumb, the nail on it is his. It doesn't matter if you cut it off."

Wu Lining covered her mouth and laughed when she heard this.

Sun Xingli looked at Luo Yongjun with eyes full of resentment. If possible, he really wanted to pin Luo Yongjun to the ground and kick him hard in the face with his feet.

back row.

Zhou Kaijun looked at the young figure on the stage and felt extremely absurd.

He recalled the young graduate student who asked him questions about his thesis more than a year ago, and then compared it to the young man on the lecture hall who explained his research content confidently like a famous scholar...

The changes are too huge!
Zhou Kaijun did not understand the content of the report, he did not even listen carefully, but from the situation at the scene it was clear that there was no problem with the content.

From the tone of voice used in the explanation on stage, one can hear a strong sense of confidence.

Such a report can only be produced by scholars of high caliber.

Zhang Shuo's mathematical level is beyond doubt.

But when he thought about the situation a year ago, he couldn't help but feel a strong sense of contrast in his heart, "Could it be that Zhang Shuo is really a genius like Peter Scholz?"

"One year, such a big difference..."

……

Zhang Shuo answered the questions and walked down from the podium to rest for ten minutes.

This is the reporting interval.

There was an empty seat in the judging panel, so Zhu Hao pulled Zhang Shuo over to sit down and introduced him to several expert judges.

Zhang Shuo shook hands with several people separately.

Qiu Chengwen also shook hands with Zhang Shuo and said with admiration, "You speak much better than the young man before."

"Professor Sun is a little nervous because this part is all about his research." Zhang Shuo spoke on behalf of Sun Xingli.

Zhu Hao smiled and said, "I was just saying that Academician Qiu has affected Professor Sun's performance, but Professor Sun still needs to adjust his mentality."

"This is normal. After all, you are young."

Peng Ruochuan followed up with another sentence.

Qiu Chengwen asked, "Are there more proofs to come?" Zhang Shuo estimated the time, "We should be able to finish it before six o'clock. If we go faster, forty minutes will be enough."

"That's all?"

“There’s not much left, but it’s a little harder to understand,” Zhang Shuo said.

Zhu Hao laughed and said, "I just said that your report is just like giving a lecture. Do you really treat it as a lecture? Are you so confident?"

Zhang Shuo affirmed, "It should have been proven."

“We hope you will succeed too.”

Shen Yuan said, "If you complete the proof, this will be the greatest research result ever published by the Chinese Mathematical Society!"

The break is over.

Zhang Shuo walked back onto the podium and said, "Next is my research, using the primality test of square numbers to prove the Jebov conjecture."

He operated the computer and projected the proof process onto the screen.

That only contains the proof steps, which are the content of the paper, and each step needs to be explained in detail.

Zhang Shuo's research content is not extensive, and about three pages of paper are enough to cover it all.

However, it is more difficult and not easy to understand.

At the beginning, it is the mapping and projection of the solution set of the equation, which involves the research methods of differential equations and also involves some content of function theory. The mapping and projection of the solution set connects and transforms the steps, and is used to test and prove the prime numbers behind the square numbers.

This part takes about ten minutes.

Each step is very clever, especially the connection and conversion part, which is like turning the locomotive around. Many people subconsciously think it will make a big turn, but they find that the tail becomes the front and the head becomes the tail, which immediately feels very delicate.

After this part of the demonstration, the research has been completed by 90%.

All that remains is to connect the beginning and the end.

During the question-and-answer session on Sun Xingli's research, a middle-aged scholar asked a key question.

Zhang Shuo also talked about this issue. "The test of square numbers is just a judgment. The first part is a judgment, and the second part is a judgment. It does not involve the interval or range of prime numbers."

"That's a good question."

"The next step is to connect the beginning and the end and carry out the proof from zero to one..."

The square number test is just a judgment on whether to put prime numbers in the front or the back, not to determine the range within which prime numbers exist.

Connect the front and the back, that is, connect the front part of N and the back part of (N+1) together, and then prove that there is at least one prime number, thus realizing the proof from zero to one.

This part of the argument is very difficult.

Zhang Shuo explained each transformation and each logical argument slowly and calmly, trying to make as many people as possible understand. However, this part is very difficult to understand. Professional scholars can understand part of it, and only top scholars can understand it more thoroughly.

The prerequisite is that you must have a very flexible brain.

These contents have gone beyond the limitations of the field of number theory and have become logical arguments that integrate content from multiple directions.

The main core is based on equations and functions, supplemented by number theory methods.

The experts and scholars on the jury all felt that they could not keep up, and only a very few people could understand it. This prerequisite was that they had sufficient breadth of knowledge and a very clear mind.

At this time, everyone in the judging panel was listening very carefully, fearing that they would not understand or be able to keep up if they were distracted.

The people in the back row also held their breath.

Most people didn't understand, but they knew that the argument had reached a critical moment, and completing this part of the argument would mean completing the proof of the Jebov conjecture.

Otherwise, all previous efforts will be wasted.

Zhang Shuo's tone was still neither hurried nor slow, and there was no difference from his previous explanation. His expression was very calm, just like a teacher giving a lecture.

After explaining a change, ask, "Do you understand?"

Then, continue explaining.

The equation formulation, derivation, solution proof and other parts have been completed, and the final part is all about logical argumentation.

"The part approaching a is equivalent to a+a. If there is no prime number from a to a, according to ②, a+a+1..."

“趋近（a+1）的部分，等价（a+1）-（a+1），若是（a+1）-（a+1）到（a+1）不存在素数，根据③可知，（a+1）-（a+1）-1……”

"Obviously, the number between a and (a+1) is divided into two parts. If there is no prime number in either part, then based on the above conclusion, combined with ①, ④, and ⑤, we can know that the number in the middle must be a prime number."

Zhang Shuo finished speaking in one breath, put down his pen, turned around and walked to the middle.

The lecture hall was silent.

The judges in the front row, as well as the scholars who heard the entire presentation, all listened carefully to the proofs on the whiteboard and the projection screen.

The others were staring at the front row of judges.

They didn't understand what was said, and didn't know whether the proof was complete, so they could only look at the reactions of the experts in the front row of judges.

Time, half a minute passed.

Qiu Chengwen made a move, his eyes still fixed on the whiteboard. He slowly raised his hands and then put his palms together, "Pah~~"

A very light sound.

Snap, snap, snap...

Once, twice, three times...

Zhu Hao also stretched out his arms and clapped his hands. His action seemed to have a spreading effect, first to the judges, then to the scholars nearby, and then quickly to the entire lecture hall.

"Hulala~~~"

Everyone clapped.

The applause grew louder and louder, reaching the entrance of the lecture hall and could be heard clearly in the nearby small garden.

Everybody was clapping, everybody was amazed.

Applause was heard, accompanied by shouts of "Academician Qiu has affirmed it, and the review has confirmed that the proof is perfect!"

"No problem, the report is complete, the Jebov conjecture has been proved!"

"The proof of the Jebov conjecture is a major breakthrough in the study of prime number distribution. It's right here in Hall 4!"

"Go and see, the Jebov conjecture has been proven!"

(End of this chapter)