The top student must be diligent.

Chapter 92: Flash of Inspiration

Time passed quickly.

With only five minutes left before the math analysis class was to start, Liu Bin, a substitute teacher, appeared in the classroom.

I took a quick glance at the students in the classroom, mainly to see if the number of students matched my impression. Hua Luogeng's class has devoted so many resources to it, so naturally we don't want students to be inattentive in their studies or even skip classes.

However, it seems that there is no shortage of people.

Suddenly, his eyes stopped at the third row and he showed a little surprise.

Xiao Yi actually came to his class?
Then he smiled and nodded at Xiao Yi.

It was he who discovered Xiao Yi and brought him to USTC. At first, he just thought that this was a very talented student. However, he never expected that this kid would start to stir up a storm in the entire mathematics community not long after he showed his talent.

He is deeply moved that she has now become a rising star in the mathematics world.

Xiao Yi noticed Liu Bin's gaze, and then nodded to the professor who had provided him with a lot of help.

Of course, he was very grateful to Liu Bin. To some extent, it was Liu Bin who formally brought him into the major of mathematics. The many books Liu Bin gave him were also the key to his ability to achieve such a level in multiple areas of mathematics.

This is a respectable elder.

Five minutes passed quickly.

As the bell rang, Liu Bin stood on the podium.

"Today's class begins."

"Let's continue with the discussion of sequence limits from the last class. This class will discuss the existence criteria of sequence limits."

"First, we need to consider whether a certain sequence has a limit..."

When the class started, every student in the class quieted down and began to listen to the lesson attentively.

As students of Hua Luogeng's class, they often prepare in advance before class, which is considered the most basic requirement for being the "elite" among mathematics students.

There are also some students who have already finished reading the entire book.

However, even if they have finished learning, they will still listen to the class carefully. After all, maybe they can get some other insights from the teacher's explanation?
However, for Xiao Yi, what was taught in this class was still too simple for him.

Perhaps any idea in his mind about the existence criteria of the limit of a number series, if expanded a little, could be turned into an SCI article.

However, he still listened carefully, and at the same time was thinking about his next goal in his mind - doing two things at the same time was not difficult for him now.

The solution to the Elliott-Halberstam conjecture did not satisfy him, because the completion of this problem, and even the [Automorphic Theory of Étale algebraic varieties], were, to some extent, by-products of his efforts to achieve his ultimate goal.

And his ultimate goal has never changed.

That is the twin prime conjecture.

Probably 99.9% of scholars in the mathematics community have never thought about it, nor would they think about it. The twin prime conjecture is Xiao Yi's ultimate goal.

Perhaps, only Faltings could guess this.

After all, he had approached Faltings about the twin prime conjecture in Faltings' office at the Max Planck Institute for Mathematics.

The Elliott-Halberstam conjecture also came from Faltings' suggestion.

Today, the Elliott-Halberstam conjecture has become a theorem, and with this result, the progress of the twin prime conjecture has come to the number "6".

But what to do next?

Xiao Yi felt that he had touched the final gap in the twin prime conjecture.

But this gap was too far, so he couldn't even find a bridge across it for the time being, let alone other things.

"Sure enough, my understanding of mathematics is not deep enough."

He couldn't help but sigh in his heart.

Of course, he was not discouraged by it.

After all, no mathematician had ever developed a method to directly prove the twin prime conjecture under the assumption that the Elliott-Halberstam conjecture was true, and it could only be advanced to within 6.

This fully shows that there are still some difficulties. Shaking his head slightly, he pulled his mind away from the twin prime conjecture and focused on the class again.

"... Then, I will give you an example question and explain it."

At this time, Liu Bin on the stage said.

He has finished teaching the knowledge in this class and is ready to use the questions to consolidate the knowledge he has just taught.

Soon, he wrote a question on the blackboard.

A classic question.

【If lim(n→+∞)xn=a, prove that lim(n→+∞)(x1+x2+…+xn)/n=a.】

"Everyone, think about this question and see how to solve it." Liu Bin said.

After about a minute, he asked, "Does anyone know how to do this?"

Most of the students nodded.

"Very good, then I will pick two people to do it." Liu Bin nodded, and then called out the names: "Ye Cheng, Zhang Zhilan."

Ye Cheng immediately stood up and went on stage with Zhang Zhilan.

Soon, the two people started writing on the blackboard, and two completely different proof methods appeared on the blackboard.

"Well, very good. Zhang Zhilan used the simplest method, which is to use Stolz's theorem to simplify the whole problem, and then it can be easily solved."

"As for Ye Cheng... Although I don't agree with his method of hard evidence, being able to prove it is indeed a sign of strength."

"Yes, I'll give you a score for the usual time."

"Oh yeah!"

Ye Cheng returned to his seat and waved his fist.

Liu Bin continued at this time: "Well, I believe everyone has seen Xiao Yi coming to this class. Recently, Xiao Yi solved a conjecture related to prime numbers in mathematics. So next I will also give another limit problem related to prime numbers, which can be regarded as a challenge question. Let's try it."

Then he began to write the challenge question on the blackboard.

The students in the class immediately paid attention.

A challenge related to prime numbers?
[Let w(n) be the number of different prime factors of the positive integer n, let the prime number sequence be pn, and let the sequence an=n∏k=1(pn).

Proof: lim(n→+∞)[w(an) lnw(an)]/ln(an)=1.】

"Well, let's see who can solve this problem." Liu Bin said.

Most of the students present immediately wore masks of pain.

The challenge of this question...isn't it a bit too great?

Of course, there were also students like Ye Cheng who started thinking immediately.

Although it is difficult, you still have to think about it!

As for Xiao Yi...

When Liu Bin finished writing this question, he already had an idea.

However, his thinking was slightly different...

"If you use the sieve method..."

His eyes narrowed slightly.

A flash of inspiration suddenly occurred to his mind.