Twin primes refer to pairs of prime numbers that differ by 2, such as 3 and 5, 5 and 7, 11 and 13, and so on.

The twin prime conjecture, which was proposed by Hilbert in his report to the International Congress of Mathematicians in 1900, can be described as follows--

There are infinitely many prime numbers p, such that p + 2 is prime.

A pair of prime numbers (p, p + 2) is called a twin prime.

Once this conjecture was proposed, it became one of the world's mathematical problems and one of the classic number theory conjectures.

Over the past hundred years, countless mathematicians have studied the twin prime conjecture and provided many proof ideas, one of which is the weakening of the twin prime conjecture, "find a positive number so that there are infinitely many pairs of prime numbers that are less than the difference between this given positive number", in the twin prime conjecture, this positive number is 2.

A few years ago, mathematicians, represented by Daniel Goldes, proposed a conjecture that "there are infinitely many pairs of prime numbers with intervals less than 16".

This is the Daniel Godes conjecture.

In the past three days, Zhao Yi was bored in the dormitory, studying the relationship between the two sets of prime solutions of the three-dimensional tremor waveform and the twin primes, and he found out the reason why the waveform has more twin prime solutions, and thus came to the conclusion that 'the waveform has an infinite number of twin prime solutions'.

In reaching this conclusion, he incidentally proved that there are "infinitely many pairs of prime numbers with intervals less than 246", while the Daniel-Goldes conjecture is that "there are infinite pairs of prime numbers with intervals less than 16".

Therefore, Zhao Yi just said that "part of the Daniel-Goldes conjecture has been proved", but he doesn't think there is much significance, because proving the Daniel-Goldes conjecture is not very famous in the field of number theory research, but only a part of it has been proved, and there is still a long way to go to prove the twin prime conjecture.

For Zhao Yi, the most important thing is to study the relationship between the two sets of prime solutions of the three-dimensional tremor waveform diagram and the twin primes.

That's the fundamental.

Anyway, the research was done, and he felt relieved, but the paper was not finished yet.

In fact, Zhao Yi can finish the paper in one go, but he feels that the first day of class is also very important.

On the first day of college, it felt a little weird to skip class.

In the morning, it is advanced mathematics.

Zhao Yi didn't have advanced math on his class schedule, but he still felt that he should go to class, and it was too strange that there was no math class in college.

After breakfast, he glanced at the class schedule recorded on his phone and found classroom 302 in the Faculty of Science.

It's a good time to come.

It was less than five minutes before class, Zhao Yi was depressed and had a delay in breakfast, he observed at the door, thought about it or went around in a circle, and quietly walked in through the back door when the teacher turned his head.

His steps were so light that few of his classmates noticed him.

Enter the classroom and take a seat.

The last row.

The first and second classes of biological sciences are taught math together, and there are a total of 100 students in the two classes, which does not seem to be too crowded in the large classroom, and there are many students in the front rows, but there are also some students sitting in the back rows.

Zhao Yi happened to sit next to Fan Lei, and next to him was Li Renzhe, sitting with three people in the dormitory, and there were only three of them in the last row.

"Zhao Yi, here!"

"You're still in high math class!"

Fan Lei and Li Renzhe waved hello to Zhao Yi.

Fan Lei looked left and right, and said, "They are all good students, just sit in the back of our brothers." ”

"Is there one more me?" Zhao Yi said with a smile, "This is the first class, and if there are too many classes, the back will soon be crowded." ”

"Hahaha, you seem to be very experienced. ”

"A must!"

The two laughed a few words and began to listen carefully.

Even if you sit at the end, it doesn't mean that you don't pay attention to the lecture, after all, it's the first class after going to college, and everyone in the classroom is very serious.

Hu Zhibin was standing on the podium, he didn't notice Zhao Yi walking in, turned his head and continued the class.

The first lesson certainly doesn't go straight to the content, and he's emphasizing the importance of mathematics.

"Mathematics is a very rigorous subject and the foundation of all disciplines. ”

"Whether it's science or engineering, mathematics must be learned, and it must be studied very deeply. ”

"The mathematics requirements of your biology department are lower, such as the School of Information, there are four or five mathematics subjects alone, not to mention the mathematics department. ”

"But you can't think that mathematics is useless for biology. Mathematics is the foundation of all subjects, as long as you are good at mathematics, other subjects will not be difficult for you at least in terms of computational analysis. ”

"On the other hand, if you are not good at mathematics, you will find that whether it is biology or chemistry, when it comes to the step of calculation and analysis, it will not work at all, because the biochemistry teacher will not teach you how to solve calculus, will not teach you how to solve functions......"

Hu Zhibin began a tirade, he talked about the importance of mathematics to advanced mathematics, and then talked about the science of Yanhua University, giving a realistic example, "A few days ago, I saw Professor Zhou Li of the School of Science, and Zhao Yi and Zhao Yi, who majored in biological sciences, all know it, it is a student in your class, and his achievements in mathematics can only amaze me." ”

"What are the two men arguing about? It's the relationship between geometric curves and numbers. Professor Zhou Li believes that numbers can be expressed by solving geometric curve functions, while Zhao Yi believes that numbers are numbers. ”

"The two of them are arguing about this, and you may not understand. What's there to argue about numbers? 1, 2, 3, 4, 5, 6, can you still tell if you are ugly?"

In fact, this is the dispute between mathematics and physics, that is, the principle of mathematics, the understanding of mathematics. When it comes to the study of art, everyone's understanding is different. ”

"I support Professor Zhou Li's view that the analysis of complex mathematics can indeed explain the simplest numbers in turn, and I also argued with Zhao Yi at that time. ”

Of course, it's not a question of right or wrong. ”

"There is no right or wrong in concept, understanding. ”

“......”

Zhao Yi has been listening to the last row, and at first he listened with relish, and felt that what Hu Zhibin said made a little sense, and he explained the concept very clearly.

Then it didn't feel right.

"Was there anyone else that day? I like to see him for the first time, right?"

"At that time, there were a few teachers in the office, but none of them spoke ......"

"This Teacher Hu, has you argued with me?"

In fact, Hu Zhibin just said it casually, he knew that there was a gap between himself and Zhou Li, and even more so with Zhao Yi.

But he still wanted to put himself on the same level as Zhou Li and Zhao Yi, and argued with them about mathematical problems, as if he was at the same level.

He just wanted to elevate himself and let his students know that their math teacher was no worse than a top professor or a student with significant research output.

It doesn't matter if the students understand this meaning or not.

Hu Zhibin was very comfortable after speaking.

Next, let's move on to the formal content, "In this lesson, we're going to talk about functions and limits, and there's a lot of content in it, and I've already talked about it in high school......"

Hu Zhibin still has a lot of teaching experience, and he spoke for more than 40 minutes in one breath, and only let the students take a five-minute break in the middle of the lecture, and then continued to teach the students a few classic topics based on the knowledge he just taught.

After talking about the two questions, Hu Zhibin wanted to find the students to answer the questions.

A question appeared on the projection screen, and he made everyone think for a moment, then raised his head and glanced at it.

Suddenly.

In the last row, the sleeping figure came into view.

Hu Zhibin's myopia was a little serious, he couldn't see who the classmate was, but he slept on his stomach in the first class, which was too shameless, and he immediately shouted, "It's you!"

"In the middle of the last row, the one lying on his stomach, the classmate next to him helped to call. ”

Fan Lei was also a little unenergetic, but when he heard Hu Zhibin's words, he immediately became energetic, and there was even some schadenfreude on his face, and he didn't know if it was Zhao Yi or Hu Zhibin.

"Zhao Yi, wake up!"

"Wake up!"

"The teacher called you!" Fan Lei pushed hard.

Zhao Yi is sleeping with the fragrance.

In fact, he didn't plan to sleep in the first class, but Hu Zhibin talked at length for a long time, and after he started the lecture, the content was only functions and limits.

None of this made sense to him, of course.

Zhao Yi had been doing research for three consecutive days, and he felt very tired all over, and suddenly thought that he hadn't swiped the "rest coin" for a long time, so he immediately fell asleep on the table.

It's not easy!

It's been a few months!

Finally able to seriously brush the "rest coin", he dreamed of falling asleep in his dreams, and the system kept reminding him in his ears, "Learning coin +1, learning coin +1, learning coin +1......"

"Zhao Yi, don't sleep, the teacher called you!"

Zhao Yi was woken up in a daze, raised his head and found that the whole class had looked over, and he stood up in a daze.

"You slept soundly, you just took the first class, and you slept, but there are still four years left in college. ”

Hu Zhibin criticized vigorously, and then asked, "Let's take a look at this question, do you have any ideas?"

Of course, he didn't think that Zhao Yi had ideas, but he just wanted to embarrass the sleeping classmates, which was equivalent to giving a small lesson and maintaining the majesty of being a teacher.

This sentence caused a round of laughter.

Hu Zhibin felt weird when he heard the laughter, it was normal to have laughter, but why was the tone so wrong?

He didn't care.

Zhao Yi finally understood, he looked at the question on the projection screen, thought for about ten seconds, and said tentatively, "Two out of seven?"

"Teacher, the result is two out of seven. ”

Hu Zhibin frowned when he heard this, "I didn't let you tell the answer...... and then asked strangely, "How do you know the answer?"

"Oh, oh. ”

Zhao Yi understood, "I still have to talk about the process, it's ......"

"Remove the numerator denominator with one of the cubic fractions of x, because when x approaches infinity, the limits of the numerator and denominator are infinity. ”

"The disadvantage after removing the numerator and denominator is that two plus three parts of x, plus three parts of x...... In the end, the infinitesimal is divided to find the limit, and the answer is two out of seven. ”

Zhao Yi told the process completely in one go.

The whole class was stunned.

No one can keep up with the train of thought, including Hu Zhibin, needless to say whether to seek the limit or not, he said the detailed column formula in one breath, and wanted to listen to it while listing the column formula in his head, which must require quite excellent brain thinking.

Most people don't reach that level.

Hu Zhibin only remembered the first and most important sentence, "first use the cubic part of x to remove the numerator and denominator", he looked down and clicked the mouse, looked at the detailed process of the answer, and found that it was the same as what he remembered, it was brought in with the cubic of x.

What Zhao Yi just said was one third of x.

This is the difference.

Hu Zhibin calculated according to what Zhao Yi said, and found that there was one step missing, and his eyes widened in surprise.

Although the questions are not difficult, it is absolutely remarkable that they can be done so quickly and that they are easier than the answers.

"This student is a genius, why did he sign up for the biology department?"

"Could it be that the test score was not enough and was transferred to the Department of Biology?"

"And how is his tone familiar, as if I've heard it somewhere?"

Hu Zhibin looked up with doubts and asked, "This classmate, what is your name?"

"Zhao Yi. ”

"What?"

"Zhao Yi. ”

The other students in the class couldn't help but laugh and said, "Teacher Hu, he is Zhao Yi, you also said Zhao Yi at the beginning." ”

"Yes, you should know Zhao Yi!"

"Didn't you still debate with him......"

“......”

Hu Zhibin was a little dazed, he rushed over a few quick steps, and when he got closer, it was really Zhao Yi, his face turned red with shame, and he quickly asked, "Zhao Yi, when did you come?"

"Sorry, I seem to be five minutes late. ”

"Five-minute ......"

Hu Zhibin recalled it carefully, and was very sure that he said that the debate was five minutes later.

So......

Zhao Yi heard it?

Hu Zhibin's face was suddenly full of embarrassment, he didn't know what to do for a while, and hurriedly asked Zhao Yidao to come to the podium, "Zhao Yi, let's talk about it, you know more than me, the winner of the international award, you come to give a lecture to everyone, it will definitely benefit the students immensely!"

"I won't, I won't. ”

"I really wouldn't!"

Zhao Yi hurriedly shirked it, he was here to listen to the class, but he didn't want to rob the teacher's job.

The two of them have been shirking it, but they can't do it.

Hu Zhibin returned to the podium with tears in his eyes and continued to explain the next math problems, he hoped that he could forget Zhao Yi, but he felt very awkward after standing on the podium.

There's a math boss sitting in the audience!

That's the big guy who won the international prize, and it is said that he is likely to win the next Fields, and even now he is one of the world's top mathematicians.

How else is this class?

Hu Zhibin missed just now, because he didn't know that Zhao Yi was offstage and could give lectures with a normal attitude, and now he hoped that Zhao Yi would continue to sleep.

However, Zhao Yi didn't sleep anymore.

Zhao Yi felt that it was disrespectful to the teacher to continue to sleep, even if the practice questions were very simple, at least he had to pretend to listen carefully.

Then Hu Zhibin was even more depressed.

Fortunately, there was not much time left before the end of class, Hu Zhibin insisted on explaining the two exercises, called out for a long time, and quickly announced the end of class.

"Zhao Yi, don't leave yet. ”

Seeing that Zhao Yi was about to leave with the other classmates, Hu Zhibin quickly stopped him, and he also pushed away other students who wanted to ask questions, telling them to explain the topics in the exercise class.

When only two people were left in the classroom, Hu Zhibin looked at Zhao Yi with complicated eyes, and still had to speak, "Zhao Yi, this, I remember that there is no math in your class schedule, right? ”

Zhao Yi hurriedly shook his head and said very sincerely, "Teacher Hu, it doesn't matter how many points you get in the course, I think the important thing is the learning process." Your course helped me, I was able to learn something in your class, it affected your class, I'm sorry, but I still want to continue the class. ”

"But ......"

Hu Zhibin didn't know if what Zhao Yi said was true or false, but when he thought that in the future, there would be a math boss sitting below, he felt that something was wrong.

Zhao Yi continued, "Teacher Hu, you can just treat me as an ordinary student, I am also a freshman. There is no need to discriminate, I will definitely listen carefully in the future classes. ”

Zhao Yi's sincere attitude made Hu Zhibin not know how to refuse, he opened his mouth for a long time, and wanted to speak several times, but he didn't say a word.

In the end, he could only tearfully agree.

After Zhao Yi left, Hu Zhibin sorted out his things and thought to himself, "He said everything, my class will help him......"

"Yes, it helps. ”

"Helpful. ”

"It's nothing embarrassing for me to be able to help a future Fields Medal winner. ”

That's what I said, but I'm still very depressed!