Before today's report began, the Chinese Mathematical Society and Li Mu did not announce what the title of the report Li Mu was going to do.

So before the report began, people were also puzzled why Li Mu also made a report.

Let Fan Pairen go up and talk about it, and prove whether he understands it or not?

What can Li Mu say when he goes up?

Therefore, there are also many mathematicians who have asked the Chinese Mathematical Society before.

To this, the Chinese Mathematical Society only replied with one sentence: a report related to the twin prime conjecture.

因为他们怕提前说了报告主题，到时候就把范湃仁给吓跑了。

The protagonist didn't show up, so isn't this report a little less interesting.

After other scholars learned about the content of Li Mu's report, what else could they say, although they don't know what else is worth reporting about the twin prime conjecture, but this is also Li Mu's report after all, maybe there will be something more important?

So, these scholars came over as if they were opening a blind box.

Otherwise, just one Fan Pairen is not worth so many of them coming, just go back and learn about the follow-up on the Internet.

And now it proves that they are full of expectations for Li Mu and have not been disappointed.

As soon as the theme of this report came out, the audience was stunned, and then there was an uproar.

Polygnac conjecture!

Hardy Littlewood conjecture!

Sure enough, it has something to do with the twin prime conjecture, but isn't this a bit too much......

Forget about Polygnac's conjecture, after all, Li Mu said before that he had a wonderful proof of this conjecture.

But what about the Hardy-Littlewood conjecture that popped up out of nowhere?

If the Polignac conjecture and the twin prime conjecture still have some inheritance, then the Hardy-Littlewood conjecture is somehow different.

Because the latter is about progressive distribution, if you want to solve it, it is not necessarily similar in method.

As a result, it has only been about ten days, and Li Mu is going to solve these two conjectures in a row?

Did you really kill the twin prime conjecture family neatly?

For a while, these scholars were even a little hard to believe.

Immediately, however, some scholars began to pick up their mobile phones and contact other scholars who had good relationships but had left Beijing to tell them the news.

Although there are still many scholars who have come to see the report, some scholars have already left Beijing.

After all, they only took a few days off from the meeting.

That is, it is still in the summer vacation, so there are so many scholars left.

And those scholars who have already left, after receiving the news, immediately beat their chests and regretted it.

Scald!

The last time they were able to witness the proof of the twin prime conjecture, they were glad to be able to do so, but now they missed the proof of the other two conjectures with a single thought.

Of course, soon, these scholars suddenly remembered that the report was live-streamed, so a group of people poured into the live broadcast room.

Seeing the title on the PPT, in addition to being shocked that Li Mu really wanted to prove these two conjectures at the same time, he was also glad that he was not late.

Catch up on the live stream!

At the same time, there were some people who reacted quickly, and suddenly remembered the intention of Li Mu's report.

This is to give Fan Pairen a hard blow.

你一个民科，跑过来碰瓷连续解决孪生素数猜想及其他版本三大猜想的牛人，这种巨大的对比之下，就算这个范湃仁真的懂一点，那也显得弱爆了。

Not to mention, he was really hammered because he didn't know how to pretend to understand.

For a while, a lot of attention from the audience turned to the position of the first row.

Today, as an invited speaker, Fan Pairen is "honored" to be arranged in the first row.

In the past, those who could sit in the first row were all leaders in the domestic and international mathematical community.

Therefore, many mathematicians present ridiculed this, and this time this Fan Pairen can be regarded as a glorious ancestor.

And at this moment, Fan Pairen, who was sitting in the first row, even if he didn't turn his head, could feel countless piercing eyes coming from behind.

Let him sit on pins and needles.

He never thought that Li Mu would not only report with him, but also prove it on the spot, the other two conjectures.

On his own, he still doesn't even have a clue what to say in the report later.

Although Shi Lei asked him to speak for ten minutes of useful content, for now, he may not be able to speak for even three minutes.

As for talking about life experience and the tragic past, he understands the truth, but he can't pull it out, he doesn't have that eloquence.

Not everyone is a master of success.

Although he is a professor, every class in the school is a 45-minute class, but his second private school is very simple, 99% of the students do not listen to the class, and the teachers who can still give serious lectures are almost extinct, and the work is done according to the book.

So he really can't do it, and he talks nonsense for forty minutes.

Thinking of this, his heart floated again, or did he slip away?

This thought, which had arisen to him a few days ago, became more and more agitated at this time.

But now that he was sitting in the first row, it would be too obvious even to leave his seat, so he had to give up the idea for the time being.

只不过，实际上他有些想当然了，在场并没有多少人太过关心他。

Compared with Li Mu's report, he is no longer worth caring about.

Even Yuan Xiang and the others, who were sitting in the first row, listened to Li Mu's report seriously.

……

主席台上，又一次穿上了之前那身西装的李牧，打开了PPT后，看着现场的吃惊的表情，微微一笑。

Everyone's expressions were all visible to him, including Fan Pairen.

The surprise of the crowd, he could have imagined before.

"As I said last time here, there wasn't enough blank space on the blackboard, and the time left was gone for me to finish the proof of the Polliniac conjecture."

He said with a smile: "But today, I will have a lot of time, blackboard, I just saw it in the backstage lounge, the Chinese Mathematical Society and Shanghai Beijing University have prepared 20 small blackboards, it seems that I can't run away today." ”

Everyone present smiled.

Yuan Xianghe couldn't help but laugh out loud even when he was doing it.

If you can still let your kid run away today, they won't mess around in the Chinese math community.

"Then we won't talk much nonsense, so let's start with the Polygnac conjecture."

Li Mu bowed slightly towards the audience, then turned his head and came to the first small blackboard.

There will be a lot of small blackboards that you need today.

So even if he had twenty dollars, he had to save a little.

God knows if the twenty small blackboards will be able to open up the rostrum.

"To save time, I'll continue to start with what I discussed about the Polygnac conjecture at the end of my last report."

He then wrote on the blackboard what had been deduced from the last half of the previous report.

For him, even if all this time had passed, he remembered them clearly.

"Last time I introduced, when k is from 1 to 50, there are infinitely many pairs of primes of the shape (p, p+2k)."

“而接下来，我们要如何将k拓展到正无穷？ ”

"Actually, the next step is very simple."

Li Mu said, and then began to write a line on the blackboard.

【H1(GK， Z/pZ)Z……】

When the people present saw it, those who understood it suddenly showed sudden expressions.

"Kummer Theory!"

"I've probably thought of it, but how?"

"Is it necessary to improve the Kummer theory? The original Kummer theory alone should not be able to solve the problem. ”

While all the scholars were in thought, they also looked more attentively at Li Mu's proof.

In this way, as Li Mu's proof went down step by step, everyone really found the difference between it and the original theory.

"Sure enough, he's improved!"

Those scholars who understood it were all lit up in their eyes, and they couldn't help but admire it in their hearts.

但仍然还是有绝大多数的人面露茫然。

Can this be considered an easy step?

Is simplicity a concept that everyone understands?

For a moment, they felt as if they had become Muggles.

Obviously, not all scholars who come here have extremely high mathematical qualities.

The simplicity in Li Mu's mouth is completely another world for them.

Of course, among these people is Fan Pairen.

He looked at what Li Mu was talking about in confusion.

上一场的报告，李牧一开始讲的内容他还能稍微听懂一点，哪怕只是皮毛，但是这场报告，他从开头到现在就没有不是懵逼的。

He studied the twin prime conjecture for nearly 20 years, but it did not bring him much knowledge.

Because, like the vast majority of civil sciences, he always hopes to use some relatively simple methods to prove it.

As for why, it probably has something to do with their ability to learn.

When they are completely incapable of learning those difficult contents, they can only rely on the constant permutations and combinations of simple methods to seek a breakthrough.

Even this "glimmer" of possibility, it only stems from the fantasy in their hearts.

And in the end, it became a joke.

At this moment, Fan Pairen's thoughts about slipping away in his heart are becoming more and more firm.

It became clearer and clearer that there was no point in staying any longer except for being embarrassed.

Anyway, even Peng Chuan can't be contacted.

As for the professor of Shanghai Beijing University who was promised before, I am afraid that it has become an extravagant hope.

Don't you see that the deans of the School of Mathematics of Shanghai Kyoto University next to you are all there?

Thinking of this, he once again observed his surroundings.

However, his small actions on this side did not attract the attention of others.

In other words, since Li Mu's report entered a more in-depth stage, no one cared about him anymore.

哪怕是那些听不懂的人，也都在认真的记着笔记。

After all, Fan Pairen is just an inconsequential person.

At best, it can only bring people a little fun.

……

As time passed, Li Mu's proof began to enter a critical stage.

The scholars present also became more attentive.

Even the scholars who were watching the live broadcast were taking notes while listening carefully to Li Mu's explanation.

"At this point, we have successfully substituted the k value into our original prime polynomial."

"The next step is to use one of our most classic proof methods, mathematical induction."

Li Mu's pen turned and began the well-known mathematical induction.

At this time, all the scholars have already seen the results.

"Sure enough, it's a mathematical induction, but I don't know how Li Mu wants to deal with this prime polynomial."

As a classical method in number theory, mathematical induction is often used to solve integer problems, and is commonly used to prove that a propositional function P(n) is true for all positive integers.

And this question has been written here, and most mathematicians can see that mathematical induction is needed.

It's just that this mathematical induction method is not so simple to use.

Because that complex prime polynomial can give them all a headache.

But then, Li Mu's proof process made them panic.

"When n = 1, it becomes our twin prime conjecture, and it has already been proven by me, so this case is true."

"Now let's assume that P(n) is true, then P(n+1)=......"

"In the form of P(n+1), because this prime polynomial is more troublesome to deal with, we need to construct another formula to help us topple this domino."

When the mathematicians on the scene saw this step, they all entered into concentration.

That's right, this step is the most troublesome point.

How did Li Mu construct another formula?

However, Li Mu just said: "Observe the original form, and then we can easily construct this new form......"

Then, in the midst of everyone's incredulous gazes, he constructed a completely new polynomial that could be integrated into the P(n+1) equation.

Once the two are substituted, the last step of mathematical induction, the infinite number of the two formulas completes the cancellation, just like the dominoes are overthrown.

Subsequently, P(n+1) was formed.

Li Mu didn't even stop long, as if there was nothing to say about this new polynomial he constructed.

Usually.

He goes on to take the next step: "Thus, we have succeeded in proving that there are infinitely many pairs of primes of the form (p,p+2k) for any positive integer where k is a positive integer. ”

"At this point, it is obvious that the Polygnac conjecture holds."

Li Mu simply wrote the word "Certification" on the blackboard, and then turned around elegantly and looked at the audience.

At this moment, the audience has fallen into silence.

It was so quiet that I could hear the sound of a needle falling on the ground.

They were all numb.

…………

[4k words in this chapter]

(End of chapter)