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It was a good show, and the professor sitting next to Selberg was a little bit lost just now.But after Zhuang Weiran said that he really wanted to solve Zhou's conjecture, he raised his eyebrows slightly, and looked at the blackboard with a face full of drama.

Selberg was a little worried instead, "Zhuang, what's going on? Why are you suddenly so reckless today?"

"He's still young." The old man next to him said, "Perhaps when he was discussing something with someone in private, he was agitated, so he did such a thing."

The old man shrugged, "I think it's interesting, isn't it? Professor Selberg, what are you worried about? You seem to be very worried that he won't be able to solve this conjecture and become a laughingstock. Since he made such a decision, if he hadn't Confidence, that is, he does not have the ability to fear mathematics. It is a good thing to fall, isn't it? At least, in the future, he will understand the truth of respecting mathematics. "

"My dear Professor Bulgan, this is not interesting. I am even afraid that a mathematical genius will die from this. Zhuang can be said to be the future star of mathematics..." Selberg did not find it interesting at all.

"No, Professor Selberg." Burgan said with a smile, "For Zhuang, this is an experience and a transformation. Although those of us have read his papers countless times, we applaud his proof ideas. But in fact, he has never given a symposium in public. At least, not any symposium in front of us.”

"He is also proving his strength to those who doubt him at Princeton University, and even the whole world." Burgan sketched a smile, "What did he just say? When he was studying for a bachelor's degree, he had already started to study Zhou's conjecture. Maybe it was because of other things that made him give up Zhou's conjecture. Or maybe he suddenly felt that Zhou's conjecture was meaningless. But anyway, I am actually more inclined. Here, prove yourself."

"Professor Selberg, have you forgotten what is under our feet?"

"This is Princeton University, a sacred place for mathematics. It has always been a top school in global mathematics rankings. It has the most professional mathematics professors and the most talented students."

"As long as he can conquer the professors and students here, his reputation will spread all over the world."

"That's true." Selberg was still a little worried about Zhuang Weiran, and he had a very good impression of Zhuang Weiran.I can't bear to see this future mathematician become a laughing stock at Princeton University at this time.

"So, I don't think Professor Selberg needs to worry too much. I guess Zhuang may have already figured out a countermeasure." Burgan shook his head and said to Selberg, who was showing concern, "Even if you continue to worry , I am afraid that Zhuang will also have to deal with this problem, so it is better to relax and see if Zhuang can solve it."

"You convinced me." Selberg nodded, and Bulgan did convince him.

Professor Zhang Shouwu is now the same as Li Fei, his heart is in his throat.He was afraid that something might happen to Zhuang Weiran, so holding a pen, Zhuang Weiran turned around with a smile and began to write a line of numbers on the blackboard——

【…

Let 1 be an odd number, (, a-1)=1, then the necessary and sufficient condition for divisible z is

ord(a)=

Because it is an odd prime number and ord(a)≠1, so ord(a)=sufficient condition: if ord(a)=, then a≡1(od) deduces |a-1, because (, a-1)=1 , so |z

……

The prime factor q of z can be expressed in the form of q=2k+1, where (q, a-1)=1, k is a positive integer

Prove the cause q|z, according to theorem 21ordq(a)=then

……1】

Zhuang Weiran wrote faster and faster. In less than half an hour, he had finished writing on two blackboards.Many people couldn't even see the previous formulas before they could understand the contents on the blackboard. When Zhuang Weiran pulled out a blackboard, he completely blocked the previous proof content.

Most of the students looked at the blackboard in confusion, unable to keep up with Zhuang Weiran's train of thought.A small number of teaching assistants and associate professors were thinking with their brows slightly frowned, apparently unable to keep up with Zhuang Weiran's rhythm.

But the professors were still able to keep up with Zhuang Weiran's pace, Bulgan raised his eyebrows, "I think, Professor Selberg doesn't have to worry about Zhuang, it seems that I have already seen the possibility of him making a breakthrough."

"Indeed." Feffman, who was silent just now, suddenly said, "I think that Zhuang had already made a breakthrough in Zhou's Conjecture before, and it was because of certain things that he was forced to suspend the research on Zhou's Conjecture. In addition, he has made rapid progress in the field of mathematics in the past few years, and I am afraid that he can really solve Zhou's conjecture."

"I'm suddenly relieved." Jaffe said with a smile, "I'm good at mathematical physics, but I don't know nothing about number theory. At least, in my opinion, Zhuang is very likely to solve Zhou's conjecture directly."

The Viscount Deligne next to him also nodded slightly. He has now seen that even if Zhuang Weiran cannot solve Zhou's conjecture, he may be able to make many breakthroughs. If Zhuang Weiran is given another month, then he must It can be untied.

Zhou's conjecture looks very simple.Since the conjecture was announced in 1992, countless people have tried to solve this mathematically beautiful conjecture, but unfortunately they all ended in failure.

Although this conjecture formula is very simple, it is very difficult to make the distribution of Mersenne prime guesses.Everyone knows that if you want to solve Zhou's conjecture, you must use the sieve method. The so-called sieve method is the sieve method to find prime numbers.

用筛法求素数的基本思想是：把从2到n的一组正整数从小到大按顺序排列。从中依次删除2的倍数、3的倍数、5的倍数，直到根号n的倍数为止，剩余的即为2~n之间的所有素数。2

This is something that is easy to say but very difficult to do.Countless mathematicians are trying to solve this problem. Unexpectedly, a few years ago, in a junior class of a university in Huaguo, a teenager almost solved the prime number problem of Zhou's conjecture without telling anyone. .

Everyone doesn't know why, Zhuang Weiran suddenly gave up Zhou's conjecture that was about to be solved, and turned to study nonlinear partial differential equations.But they knew very well that if Zhuang Weiran had been able to persist until the unraveling, perhaps this young man would have become a world-renowned academic genius three years ago, or even earlier.Instead of waiting until last year - he was proven to unravel the Yang-Mills existence and mass gap to become a world-famous mathematical genius.

In fact, the professors at Princeton University are very heartbroken.It is the biggest loss in the history of Princeton University for such a talented boy not to be able to study for a doctorate at Princeton University.

In fact, Princeton University hardly recruits students in Asia, unless the student's grades are outstanding enough to impress those arrogant professors at Princeton University.

Zhuang Weiran's grades obviously didn't just move the heart of these arrogant professors, it was heartache.

Why didn't they discover this genius who almost solved Zhou's conjecture a few years ago.If I knew earlier, I am afraid that there are countless professors here who would rather stay in China every day and bring Zhuang Weiran to Princeton University.

Mathematics is a subject of genius, and a genius like Zhuang Weiran is the best seed for doing mathematics research.Who would turn down the best seed for mathematics? !The answer is obviously no.

"The above is the result I calculated before." Zhuang Weiran paused for a while, "Next, I made it after sorting out my previous thoughts..."

"What?" The people below have already begun to discuss in low voices. This is really too scary, no, it's something they couldn't even imagine.The steps that Zhuang Weiran did before are almost visible to the naked eye and can solve Zhou's conjecture.

Why doesn't he continue?Why since he abandoned Zhou's conjecture that he had almost made, he turned to study the Yang-Mills existence and quality gap.

Huge doubts breed in everyone's hearts, what kind of person is Zhuang Weiran?

"Interesting." Bulgan said with a smile, "He was able to make Zhou's conjecture several years ago, I believe he should be very clear, as long as he persists for a while, Zhou's conjecture can be solved by him. But he gave up Zhou's conjecture at this time."

"What is Professor Bulgan's opinion?" Fefferman didn't quite understand what Zhuang Weiran was thinking, and he didn't think it was very interesting.As a professor of number theory, he spent a lot of time researching Zhou's conjecture. Obviously, he has not seen the results yet.But Zhuang Weiran was about to solve this conjecture several years ago, and finally he gave up this conjecture.

Feffman was a little sick, and a little hurt.

"Great opinion... I can't talk about it, I'm just thinking, since Zhuang was about to solve Zhou's conjecture a few years ago, does it mean that maybe, someday in the future, the last jewel in the crown of mathematics—— Riemann assumes that he can also make it?" Burgan shrugged, "Of course, I'm just guessing."

"If he can really make the Riemann Hypothesis, he will undoubtedly be the greatest mathematician of this century. Even after thousands of years, people will still recite his achievements."

"He will be one of the greatest people in the history of mathematics." Jaffe said in a deep voice, "Zhuang's surprise for me is really too great."

Selberg said very calmly now, "Actually, we should have thought a long time ago that a mathematician who solved the Millennium Prize problem cannot be ignorant of number theory. Although the Yang-Mills equation and number theory seem to be Irrelevant. To be precise, as a mathematics student, he must learn number theory."

"I even doubt that he has been learning mathematics since he was born. Otherwise, it cannot be explained, how could he be able to solve Zhou's conjecture when he was thirteen or fourteen years old."

【…

证得：当2（2n）＜＜2（2（n+1））时，有2（n+1）－1个是素数

同理可证：当＜2（2（n+1））时，有2（n+2）－n－2个是素数】

Zhuang Weiran put down the pen in his hand, looked at the people in the classroom, "Does anyone have any questions?"

His expression was very confident, Zhang Shouwu was taken aback for a moment, and then laughed.It seems that he still underestimated this genius from China, he actually solved Zhou's conjecture.

Li Fei's beating heart also slowly calmed down, it was too scary, he was almost scared to death just now.

No one spoke, the professors closed their eyes and began to think, most of the students looked confused, and a small number of students muttered something in their mouths.

The author has something to say: 1: Excerpted from China National Knowledge Infrastructure "Research on Mersenne Number, Wagstaff Number Extension and Their Integer Factors"

2: Excerpted from Baidu Encyclopedia: Sieve method to find prime numbers