The top student must be diligent

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

Most of the students nodded.

"Very good, then I will select two people to come up and give it a try." Liu Bin nodded, and then called his name: "Ye Cheng, Zhang Zhilan."

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

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

"Well, very good. Zhang Zhilan used the simplest method, which is to use Stolz's theorem to solve the problem. He simplified 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 hard is indeed a strength."

"That's right, I'll give you a regular score."

"Oh yeah!"

Ye Cheng returned to his seat and shook his fist.

Liu Bin continued at this time: "Well, I believe you all have seen Xiao Yi come to this class. Recently, Xiao Yi solved a conjecture related to prime numbers in mathematics, so next I will also come up with another one related to prime numbers. The extreme question is also 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.

Challenge questions related to prime numbers?

[Record w(n) as the number of different prime factors of the positive integer n, record the prime number sequence as pn, and record the sequence an=n∏k=1(pn).

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

"Well, let's see who of you can do this question." Liu Bin said.

Most of the students present immediately masked their pain.

Is this challenge a bit too challenging?

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

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

And Xiao Yi...

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

However, his idea is slightly different...

"If you use the sieve method..."

His eyes narrowed slightly.

A flash of inspiration suddenly flashed in his mind.

On a certain gap, the shadow of a bridge seemed to flash.

…

Chapter 93 The third method

"It's still the same rules as the previous question. There is an average score. Well...if you can solve this question, I will give you a guaranteed average score of 90 at the end of the semester."

While the students in the audience were thinking, Liu Bin continued.

Naturally, he knew the difficulty of this question very well, so he also gave a heavy reward.

There must be a brave man under the heavy reward!

Then the next moment, a hand was raised.

Everyone looked confused. This question seemed extremely difficult. Who raised their hands so quickly?

They looked over, and then they all showed expressions of realization. It turned out to be Xiao Shen!

I almost forgot that Xiao Yi also came to class with them.

At this time, Xiao Yi raised his hand with eagerness on his face.

The usual minimum is 90.

Although it is not a perfect score, it is worth raising his hand. Besides, the first class he takes must have a sense of participation!

Of course, the most important thing is that such a question suddenly gave him the inspiration to unravel the possibility of the twin prime number conjecture.

Maybe, if you ask him to do this question, it will bring some surprises?

However, after seeing Xiao Yi raise his hand, Liu Bin said with a smile: "Except you."

Xiao Yi's expression suddenly fell. Why?

"Didn't I tell you before that your score has nothing to do with your class performance? You're not in class anyway."

defamation!

Absolute slander!

How can someone be innocent out of thin air?

He defended: "I'm in class right now!"

"Sorry, classmate Xiao, I have the right to explain."

Liu Bin spread his hands and said.

There was a burst of laughter in the classroom.

Xiao Yi's eyes widened, good guy, I really didn't expect that Professor Liu is also a humorous person!

However, Liu Bin changed the topic next: "Of course, if you just want to do this question, then I am very welcome, but I have a prerequisite."

"You have to solve this problem in at least two ways."

Xiao Yi's eyes twitched, how could there be a class like this!

The students took the initiative to raise their hands to answer the questions, but in the end they even had to ask for conditions!

but……

If your hands are raised, let’s do it!

Although it is the same wherever he does it, he sometimes feels metaphysically that facing the wide blank space of the blackboard can inspire some inspiration in his heart.

This is probably why top mathematicians still love blackboards and chalk, right?

However, he still said with a look of resentment: "Well, who made you a professor?"

Liu Bin laughed and then said: "Then you can come up now."

Xiao Yi shook his head helplessly, then left his seat and walked to the blackboard.

The students below also stopped laughing and looked at their Xiao Shen with bated breath.

If Xiao Yi published some awesome top journals before, or if he proved a conjecture that has stumped the mathematics community for a long time, or if he came up with any heavyweight theory, to them, it was just like a castle in the air. I know it's awesome, but I don't know how awesome it is.

But now, they could see a very difficult question at a glance. When they had no idea how to solve it, Xiao Yi not only raised his hand immediately, but even faced Professor Liu's request to use two methods to solve the question. conditions, and there was no nervous expression at all.

They can see this awesomeness.

But, can Xiao Yi really come up with two methods?

…

"the first method."

After getting on the podium, Xiao Yi didn't have any time to think and started writing directly.

"Considering this formula, we can easily see that it is actually equivalent to proving——"

【lim(n→+∞)[nln(n)]/ln(an)=1】

As soon as this equation came out, the students below were immediately confused.

Do you think this is equivalent?

How do you equate this? ?

Only a few students showed expressions of enlightenment after thinking for a while.

So that's it.

Liu Bin next to him also nodded with satisfaction. Although it was not unexpected, Xiao Yi's amazing observation skills always amazed him.

Of course, this question cannot be easily solved after finding the equivalence relationship.

[First of all: pn\u003en, so lim(n→+∞)inf(lnpn)/lnn≥1]

[It can be seen from the prime number theorem: for l\u003e1, lim(n→+∞)sup(pn)/n^l=0. 】

[It can be known from the arbitrariness of l\u003e1...]

[Finally, according to Stolz’s theorem, we can get: lim(n→+∞)……=1]

[Certificate completed. 】

Seeing this prime number theorem, and then adding the Stolz theorem that was used in the previous question, more than half of the students immediately surrendered.

I can’t do it, I really can’t do it.