The top student must be diligent.

Chapter 94 Theoretical Materials for Building the Bridge of Truth

[Let A be the set of positive integers not greater than x, and let P be the set of prime numbers, then let Ap be the set of numbers in A that are divisible by the prime number p in P...]

Let’s first give a definition - this is also Xiao Yi’s way of taking care of his classmates who may not understand the basic elements of sieving, so he wrote this part.

But in fact, his classmates really knew what sieving was, because when they took the joint entrance examination, the questions posed by the academicians included sieving.

Even if they didn't do it, they still learned about it after returning.

So they were all stunned.

Can this problem be solved by sieve method?
With disbelief in their eyes, they just watched Xiao Yi continue to move forward.

[Let z be any real number, and P(z) be the product of prime numbers in P that are not greater than z, then we have:

S(A, P, z)=|A\p|P(z)∪Ap|……]

[Consider w(n) as the number of different prime factors of the positive integer n, introduce the above formula, and after processing, we can get...]

The students in the class either became more confused the more they looked at it, or became more surprised the more they looked at it.

It seems that this problem can really be solved in this way!
After gradually understanding the role of the sieve method in this problem, they also gradually realized the cleverness of it.

Someone with broad knowledge and quick reactions, like Ye Cheng.

At this moment, his expression was quite excited: "Great!"

"First, use the sieve method to filter out the composite terms in w(n), determine the sequence of prime terms, process them separately, and then classify and discuss the remaining composite terms..."

"And Brother Xiao's method also avoids the parity problem in the sieve method. This sieve method... is definitely not the most original sieve method. From my visual estimation... it should be the Selberg sieve method!"

Song Ziyang and Luo Qiao next to them were stunned.

How did you know that?
And you can guess it by visual inspection?
Could it be that he is the one who laughs and jokes every day but is secretly more extravagant than anyone else?
Damn it, I must torture him severely when I get back.

It’s okay to roll, but it’s inhumane to roll secretly!
Ye Cheng never expected that he would accidentally reveal the secrets of rolling the ball while he was still explaining it.

"We're almost there! Just keep using the previous equivalent formula. With the help of the sieve method, w(n) is just a little kalami!"

But at this moment, Ye Cheng's voice became puzzled: "Eh? Why did Brother Xiao stop?"

Luo Qiao and Song Ziyang were stunned.

Would Xiao Yi also stop while thinking?

Is this still their God Xiao?
At this moment, Xiao Yi in their eyes had just completely completed the classification of w(n) using the Selberg sieve method. Next, just as Ye Cheng said, he had reached the final step.

But Xiao Yi's hand left the blackboard and hung down. Then he looked at the contents on the blackboard for a long time without moving, as if he was lost in thought.

Everyone became confused.

Some of them have already seen the next steps, so how could Xiao Yi not see it?
While everyone was in doubt, they saw Xiao Yi's hand finally raised again. However, he did not calculate according to the steps of the answer just now, but started writing on the blank space on the other side.

【A(x)A(√x)(log x)^2】

[∑_(d≤y)μ^2(d)g(d)=c1·log y+c0+O((log y)^-8)】

Rows of equations that had nothing to do with the current problem appeared on the blackboard.

What followed were 30 pairs of confused gazes.

What is this?

Did they skip some time just now?

Why did he start writing the heavenly book without any reason?

"Do you understand this?" Song Ziyang poked Ye Cheng, who had just explained, and asked maliciously.

If this kid even knows this...

"What do I know about this market?" Ye Cheng rolled his eyes and said unhappily.

"That's good."

Then Song Ziyang breathed a sigh of relief at Ye Cheng's puzzled expression.

Ye Cheng: "I don't understand why you are so happy?"

"You don't understand." Song Ziyang smiled kindly. ...

Liu Bin on the side of the podium might be slightly better than the students below. He could probably see that what Xiao Yi wrote was still about the sieving method, but from the perspective of the sieving method, his content was more advanced.

"This kid, could it be..."

As a knowledgeable professor, Liu Bin had some vague guesses in his mind.

However, Xiao Yi, who was writing the "Heavenly Book" on the blackboard, was not so calm in his heart.

When all the inspirations that had flashed before condensed, he now understood.

Perhaps enlightenment in Longchang was similar?

"The biggest disadvantage of the sieve method is that there is a parity problem."

"Parity problems prevent the sieve method from providing a good estimate of prime numbers."

Xiao Yi was thinking in his heart.

"Just like the idea of ​​using the sieve method to solve this problem, we need to classify, study them by category, and then break them down one by one. This is undoubtedly a good idea."

"Green had linked the parity problem to the distinction between type one and type two information in a sieve, and it turned out that his idea was successful."

"only……"

The corners of his mouth curled up slightly.

“They haven’t gotten to the extreme yet.”

The idea of ​​classification research has a long history in mathematics.

For example, the p-adic Hodge theory he had studied before also aims to classify and study a certain p-adic Galavasan representation.

And now, Xiao Yi has found the possibility of classifying the twin prime conjecture.

"The sieving method can be even more extreme and perfect!"

Write the last line of Legendre's equation on the blackboard and then put a heavy period at the end.

The questions in Xiao Yi's mind were finally answered at this moment, and a sense of relief and pleasure arose in his mind.

This is the thrill of mathematics!
Previously, it was thought that the final difference of "4" from the twin prime conjecture had become an insurmountable gap.

But now, he has found the theoretical materials to build this bridge to the truth!
A bright smile appeared on his face.

The students in the classroom suddenly looked more and more confused.

What happened to their God Xiao?

After suddenly writing a bunch of incomprehensible mathematical formulas, he started laughing. And he laughed so happily?
But Liu Bin probably understood the meaning of Xiao Yi's smile, and walked up to him and asked, "Xiao Yi, do you... have any new ideas?"

Xiao Yi nodded, and suddenly noticed from the corner of his eye that he had not yet finished writing the last step of the third solution to the problem, so he quickly added the last key step below.

Putting down the pen, he said to Liu Bin: "Yes, professor, I think I can take the sieving method to an even more extreme level."

He said a little embarrassedly: "Well...I might need to find a place to write down these thoughts for a while."

Liu Bin shook his head helplessly.

Just now he was trying to argue that "I'm in class now", but now he's planning to slip away before the class is even over.

But what else could he say?

"Go ahead and accomplish something more important."

"Thank you Professor!"

Xiao Yi's face lit up with joy, and he quickly returned to his seat, picked up his books and schoolbag, and left the classroom in full view of everyone.

From the perspective of his classmates, Xiao Yi was like someone who had handed in his exam paper early and left the class earlier than them.

Only Liu Bin knows.

This mathematical genius is about to strive for a greater cause in mathematics!

(End of this chapter)