As soon as this inspiration came, the pen could not stop, and I was not even hungry.

Lu Zhou, whose whole body was already full of spiritual food, only felt that his whole body was full of energy, took the pen, and began to write down lines of equations on the paper.

[Let the finite group G and |G|=p1α1p2α2··· piαi, where pi is a prime number and αi is a positive integer. Let p∈π(G), define deg(p)=|{q∈π（G）|p~q)|

Deg(p) is called the number of times the vertex p. Redefine C(G)=......

……

】

Time passed minute by minute, but the feeling of the wellspring of literature did not stop for a moment.

This feeling is different from last time.

The inspiration last time was borrowed, but this time the inspiration was conceived by himself.

The nib of the pen travels over the paper.

Before you know it, five sheets of scratch paper have been written.

After sorting out the steps and ideas, Lu Zhou rubbed his stomach, leaned back in his chair, and took out his mobile phone.

I thought it wouldn't take long, but when I saw the time, I was shocked.

"Hold the grass, it's five o'clock?!"

People are iron, rice is steel, and if he doesn't eat a meal, he will be hungry, not to mention that he hasn't eaten breakfast yet.

Lu Zhou couldn't hold on in the end, and while the cafeteria had not been occupied by the juniors and sisters in all green uniforms, he hurriedly went to the canteen for dinner, and came back to continue to work hard.

It was half past six.

After returning from class outside, Shi Shang pushed the door in with a boxed lunch, and saw Lu Zhou lying on the table struggling to write, and shouted curiously.

"Elbow, what are you doing? Graduate students still have assignments? ”

Just when he got to the critical place, Lu Zhou didn't look up, and replied casually.

"Write a thesis."

At this time, Huang Guangming and Liu Rui also followed into the door with a boxed lunch.

Throwing the schoolbag on the table, Liu Rui took out his professional homework, and Huang Guangming walked behind Lu Zhou curiously and looked at the paper twice.

It doesn't matter.

After reading it, I was stunned.

"Hold the grass, elbow, I can't read a word of what you write."

Hearing Xiao Bei's voice, Shi Shang stopped eating and walked over curiously.

"It's an exaggeration, little cheap, we're not freshmen now, we're juniors, you can't understand the process, you can always understand the symbols...... Hold the grass, I'm not mistaken, this thing is a group theory, right...... It's overclass! ”

Liu Rui, who was writing his homework for a professional course, turned the pen in his hand, and in the face of various sassy operations on his elbow, he became more and more calm: "It's not too overclass, in the interdisciplinary elective of the special elective course, there is Li Qun Li algebra...... But it doesn't matter what we should do, unless you're going to switch to theoretical physics. ”

Switching from science to science, that's a lot of hard work.

There is nothing to say for the sake of interest, not really interested, everyone is honestly going to the engineering with a vast road of money.

"I can't afford to mess with it." Huang Guangming shook his head and retreated.

"You can't afford to mess with it, or you're the one who makes a big news." patting Xiao Bei's shoulder and sighing, Shi Shang also retreated with an expression of giving up treatment.

Lu Zhou: "......?" ”

……

Rome was not built in a day, and a sound theory requires not only inspiration, but also time.

For several days in a row, Lu Zhou spent almost all of his days in the library, and continued to study after returning to his dormitory at night.

Occasionally, he would take the time to reply to Professor Frank's emails, and although there was no new data coming from CERN for the time being, the work of refining the theory would also require calculations.

Every day, Lu Zhou lived quite a fulfilling life.

Although it seemed incomprehensible to others, he enjoyed it himself.

In the second week of September, on a sunny morning, Lu Zhou, who was sitting in the library, stretched his waist, looked at the more than ten pages of paper sprinkled in front of him, and sighed in his heart.

"It's finally done!"

When the sensitivity is exhausted, all the work is to set the stage for the moment when inspiration comes. And when he really figured out the solution to this problem, finding the exit of the maze seemed to be right in front of his eyes.

Everything fell into place.

At this moment, Lu Zhou's mood was indescribably happy.

Not only because he solved another mathematical problem, but also because he had a deeper understanding of group theory when solving this mathematical problem, and on this basis, he developed a new set of mathematical methods.

And this discovery, even more exciting than the solution of the mathematical conjecture itself.

Hilbert once commented that Fermat's theorem is a chicken that lays golden eggs, not because this hen has fed a large number of mathematicians, nor because this hen has provided many journals with opportunities for water papers, but because many novel mathematical methods are derived from the study of number theory problems.

For example, inspired by Fermat's problem, Kummer introduced the concept of ideal numbers and discovered the only decomposition theorem that decomposes the number of a cyclic domain into ideal element factors, which has been extended to arbitrary algebraic fields by Dedekin and Kronnecke today, occupies a central position in modern number theory, and its significance has gone far beyond the scope of number theory to the field of algebraic function theory.

Lu Zhou's work at the Princeton Conference was the same, applying topology to supplement the sieve theory and ingeniously solving the twin prime conjecture.

The original sieve theory has been used to the extreme by Mr. Chen, and it is generally believed that in order to solve the "1+1" form of Goldbach's conjecture, it is necessary to seek new methods.

But now it seems that there has been some turning point, and the sieve theory still has value worth digging into.

And even Professor Zeerbeck, who was the first to introduce the principle of topology into the sieve theory in 95, did not anticipate this.

This is the value of number theory.

Lu Zhou also completed this work when solving the Polygnac conjecture and found a unique solution to this conjecture.

This new method was called the "overall structure research method of group theory", or "group construction method" for short.

Using the method of group theory, the problem of infinity is studied from the perspective of the whole, and the form of "K=1" is extended to "k is an infinite number of natural numbers", which thoroughly proves the proposition that "for all natural numbers k, there are infinitely many pairs of prime numbers (p, p+2k)".

It may only be a sentence or two to describe it, but if you want to explain this solution in detail, you may need several large blackboards.

It took a whole day to organize all the processes on the computer and convert them to PDF format.

Looking at the finished product on the screen, Lu Zhou finally checked it twice and nodded with satisfaction.

"That's it."

In fact, there is still a lot to write about the detailed theory of group construction, and even to summarize it all, which is longer than the proof process itself.

But that part is no longer the focus of this paper.

So far, the Polygnac conjecture has been proven.

Although it seems that the twin prime conjecture is only generalized to the form of infinite spacing of prime pairs, the difficulty of this is known only to him, the prover.

Lu Zhou thought about it, and at the end of the paper, added a line.

【…… For the sake of space, I will elaborate on the detailed theory of "group construction" in the next paper. 】

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