Director's Office.

Wang Hao looked at Qiu Hui'an with eyes full of relief and appreciation. He listened patiently to Qiu Hui'an's explanation, and then asked, "Have you used this method to cover Chebyshev's theorem?"

The Bertrand-Chebyshev theorem is a weakening of Legendre's conjecture.

The content is that if the integer n is greater than 3, then there is at least one prime number p, which is consistent with p being greater than n and less than 2n2.

There is also a weaker statement that for all integers n greater than 1, there is at least one prime number p, which is consistent with p being greater than n and less than 2n.

This problem was first raised by Chebyshev, and later Chebyshev completed the proof himself.

Legendre's conjecture has not been proven yet.

Qiu Hui'an nodded and said, "I have used this method to cover Chebyshev's theorem."

"But if I want to cover Legendre's conjecture, I can't find a good entry point. The range of prime number intervals in Legendre's conjecture is even smaller."

"And operations involving squares are much more difficult than simple addition and multiplication."

Wang Haodao, "Your idea is very good, really very good. I think it is possible to prove Legendre's conjecture using this method, and it can even be used to study Zhou's theorem."

"Let's analyze it together now."

"Your method covers Chebyshev's theorem, so it should be like this..."

As Wang Hao spoke, he began to write on the paper. In just ten minutes, he wrote a complete proof.

Qiu Hui'an sat by and watched dumbfounded. He spent half a month studying to complete this proof, and the previous thinking time was more than a month.

In the end, Wang Hao just listened to the idea and wrote the proof.

"Teacher Wang, you are so awesome!" Qiu Hui'an said with a wry smile, "The idea is exactly the same as mine."

Wang Hao didn't care.

This time he did write the proof based on his own understanding, rather than relying on "The Gift of Teaching".

In related research, he has gone much deeper than Qiu Hui'an. The proof of Chebyshev's theorem is also very simple, and there are even many ways to demonstrate it.

He just thought of the method and completed the proof.

However, in the process of writing the proof, he found that the task inspiration value had increased by '1' point.

Suddenly.

His discussion with Qiu Hui'an became more enthusiastic.

This is discussion, not teaching.

Wang Hao has not studied Legendre's conjecture, but only briefly thought about it when instructing Qiu Hui'an.

He prefers that students can complete their own research, otherwise it will be equivalent to him doing the research instead of the students.

This is very important for students' growth.

At the same time, Qiu Hui'an is indeed very good.

When discussing issues, Qiu Hui'an always came up with ideas and incidentally gave Wang Hao some points of inspiration.

Wang Haodu felt a little incredible. At the same time, he felt that Qiu Hui'an was a genius. He had four times the inspiration boosting effect of "The Gift of Scientific Research", but he still had to be truly inspired, but Qiu Hui'an could have continuous inspiration.

"It seems that he is not far away from proving this conjecture." Wang Hao thought with a sigh.

He and Zheng Yaojun had discussed it before.

Zheng Yaojun felt that it would be extraordinary if Qiu Hui'an could complete the proof of Legendre's conjecture during his graduate studies.

If the proof is completed within one year, it can definitely be described as a genius.

Legendre's conjecture is indeed a small conjecture, but it is only compared to Zhou's theorem. It is a difficult problem in number theory. It is quite amazing that a graduate student can prove it, even if it is completed under the guidance of a tutor.

Wang Hao and Qiu Hui'an discussed for nearly an hour.

After Qiu Hui'an left, he quickly checked the mission.

【Task 2】

[R&D project name: Proof of Goldbach’s conjecture (difficulty: S).]

[Inspiration value: 47.]

"It's 47 o'clock!"

He didn't do serious research on the proof of Goldbach's conjecture. He just had a happy-go-lucky mentality. If his inspiration value could rise a little, it would go up a little. It didn't matter if it didn't.

In this kind of mentality, there is certainly not much inspiration.

My previous inspiration value was only about 20 points, and I had some research ideas, but I didn't really think about it in depth.

Now that he had found the direction of his research, Wang Hao went to the door and hung the "Do Not Disturb" sign. Then he stayed in the office and began to do research seriously.

The general solution he thought of was the ‘covering method’.

Simply put, Goldbach's conjecture proves that any even number can be expressed as the sum of two prime numbers.

The idea behind the 'covering method' is to prove that all prime numbers combined in pairs (including itself) can cover all even numbers. As long as complete coverage can be proven and no even numbers are missed, Goldbach's conjecture will naturally be covered directly.

If it is within a bounded range, the proof is naturally very easy, even for analyzing prime numbers.

However, when the range reaches infinity, it is very difficult to prove. We need to study the process of analysis coverage, and even analyze the problems that arise with prime numbers.

This kind of analysis is much more difficult than proving Legendre's conjecture.

…

Wang Hao was bored in the office for three consecutive days, and even asked students to deliver meals several times during the process.

He has been studying ideas.

Among them, the problem involving the analysis of prime numbers was the most difficult, and this problem remained stuck until the third day.

Of course, three days of research still paid off.

【Task 2】

[Inspiration value: 61.]

The inspiration value is 18 points higher than three days ago.

"This is the limit." Wang Hao thought. He followed Qiu Hui'an's idea to conduct research, but it is difficult for a research idea to directly solve a complex problem. There are many other difficulties in trying to prove it.

However, the inspiration value has exceeded 60.

Wang Hao hoped to complete the research in one go. He thought about it carefully and decided to open a related open class.

Once you have a general direction for research, it is relatively easy to accumulate inspiration points.

It is a good idea to open open classes.

When he walked to the elevator, Wang Hao met He Yi who was coming over.

He Yi held a report in his hand and immediately said when he saw Wang Hao, "Don't leave yet, just in time, I'm here to find you."

"Report?"

"Yes." He Yi pulled Wang Hao back to the office and said, "This is the project settlement report. Take a look at it carefully. If there are no problems, I will submit it."

In the past few days, He Yi and Xiao Xinyu have been doing project summaries and writing results reports. After the reports are completed, they must be given to the project leader for a look.

Wang Hao sat down again and looked through it.

I mainly looked at the introduction and summary of the results at the beginning and at the end. I browsed through it and found that there were no problems, so I handed it over to He Yi again, "Submit it directly."

"Don't you take a closer look?" He Yi said in surprise.

Wang Hao shook his head, "There's nothing interesting to see. Professor He, you said this is more professional than me. If there are no problems, just submit it directly. Submit it earlier, and you can apply for the next project earlier."

He Yi smiled and nodded, "Okay, then I'll submit it."

After handling this matter, Wang Hao went to the School of Science office of the Academic Affairs Office and mentioned that he wanted to open an open class.

"Open class?" The person in charge of the Academic Affairs Office was surprised, "Professor Wang, what public class do you want to teach?"

"Goldbach Conjecture."

"Goldbach's conjecture? Um..."

The content of this open class is really unexpected.

The Academic Affairs Office still recorded it, because it was Wang Hao who was offering an open class, so he was not worried that no one would come to listen. He was even worried that there would be too many people signing up to listen.

soon.

The information is disclosed on the school website.

Many people signed up immediately after hearing the news, especially graduate students who wanted to take more of Wang Hao's courses.

Wang Hao has two courses this semester, one is "Nonlinear Functional Analysis" and the other is "Complex Analysis", both are basic courses for graduate students in mathematics.

"Nonlinear Functional Analysis" is an old course.

"Complex Analysis" is a new course, which is the continuation and in-depth course of the undergraduate "Complex Variable Function" course.

Wang Hao decided to teach this course because an old professor had retired and it was difficult to find a new teacher for difficult mathematics courses.
To be continued...