Feng Yao's gaze passed through the corridor of time, and in that year, his Olympiad Mathematics Enlightenment teacher, under the same circumstances, said an indelible word.

"When we were in elementary school, we learned about prime numbers, what do you think about their nature?"

Ye Haoran had few words, and he was even more reluctant to speak after being hit, Yang Fan replied: "2, 3, 5, 7, 11...... Prime numbers, also known as prime numbers, are divisible by one and itself, which is actually useless, and has nothing to do with applied mathematics, as if it were a simple concept. ”

Hearing the student's contempt for numbers, and the sacred professional field involved, Feng Yao's tone was cold, and he said: "The discovery of any mathematical law is a flash of inspiration in the thousands of failures of mathematicians. ”

Euler used the Riemann function to prove that the sum of the reciprocals of all prime numbers is divergent, and Harry Furstenberg used topology to prove the infinity of prime numbers. Could it be that those mathematicians are well fed? ”

"Master Chen Jingrun proved that 1+2 is a sufficiently large even number, which must be written as a prime number plus a composite number composed of at most 2 quality factors. ”

"Yang Fan, if you want to prove a conjecture, you must pay attention to any mathematical laws that may exist, which will benefit you for life. ”

"Okay, Mr. Feng, I see. Yang Fan humbly accepted that Lao Feng was good, when it came to mathematics, he was all lofty, and he did not allow others to oppose it, and he had a bad attitude.

Maybe it's this kind of person who can go far.

In this state, Feng Yao knows that the attention is not enough, but today is not mainly to talk about the history of the masters, but to adjust the mentality of the students.

"Let's move on to prime numbers, which are prime numbers. In the infinite sequence of natural numbers, they are in their place, like all other numbers, squeezed by two numbers before and after, but they are one step further away from each other than the others. ”

"They are suspicious and lonely numbers, they have strayed into this sequence, they are imprisoned there like small pearls strung on a necklace. Sometimes it makes people wonder if they want to be as ordinary as all the other numbers, but for some reason they can't. ”

Feng Yao's quiet voice spread throughout the office, and he said this passage extremely sacred, even anthropomorphizing prime numbers.

It's too emotional, and it's not at all like what an engineering man should say. Not to mention that Yang Fan was surprised, even Ye Haoran, who was expressionless, was slightly eccentric.

"Well, that's not what I said, it's the words of other masters. Feng Yao felt that it was not well combined, and this paragraph really did not match his character.

"The important thing is that there are some more special members of prime numbers, which mathematicians call twin primes, and what kind of phenomenon can you call that?

"Twin prime numbers?"

Yang Fan whispered, aren't twins twins, they have similar attributes. He counted down a few numbers until 11 and 13, and there was a little inspiration and a plausibility.

He continued to count, and at 17 and 19, he understood, both near and far.

Ye Haoran and Feng Yao both heard the sound of counting, Feng Yao smiled slightly, and said, "You should have found out that these are two prime numbers with an even number apart." ”

"So Mr. Feng, are they of any use? Prime numbers are endless, there must be a lot more. Yang Fan said.

"Can't you feel that loneliness now that you've found out? they're a pair of prime numbers that are so close together, almost next to each other. There is only an even number between them, blocking their true intimacy.

"If you have the patience to keep counting, you will find that such twin primes will become more and more difficult to encounter, and it is common to encounter lonely single primes, who are lost in the silent and rhythmic space composed of pure numbers. ”

At this point, you have an uneasy premonition that, up to this point, the appearance of those twin prime numbers is only an accident, and that loneliness is destined to be their true fate. Then, just as you are about to give up, you come across a pair of twin prime numbers that hug each other tightly.

Therefore, mathematicians have a common belief that they should count as hard as they can, and sooner or later they will come across a pair of twin prime numbers, and although no one knows that they will appear there, one day, they will be found again. ”

"That's the ...... of mathematics Lonely. ”

The office was silent, Yang Fan was silently counting, and prime numbers were passing through his mind, they were quietly arranged there, and the distance between them and the same type of numbers was getting farther and farther away.

After the number was counted to five hundred, the twin quality was very rare, and when it reached 809,811, Yang Fan's eyes lit up again, and there was hope.

It's hard and hard to come back later, so keep counting, there will be.

The two students were looking for that kind of epiphany in their hearts, and Feng Yao smiled, as if he saw himself back then.

"Yang Fan, the road of mathematics is really lonely, after arriving at the university, except for your classmates, it is difficult for you to communicate with others about professional things, so you can only study alone. Chemistry applies medicine, physics changes technology, only mathematics, and theory is everywhere. In solitude, go on, hold on. ”

"Teacher Feng, I understand. Yang Fan responded seriously.

Feng Yao was relieved, nodded to him, patted Ye Haoran on the shoulder again, and said, "Ye Haoran, don't look like the whole world has abandoned you, I received the news, the physics group, you have entered the training list." ”

The surprise came too suddenly, Ye Haoran lost his stretch slightly, and almost fell down again.

Yang Fan was happy for the shortlisting of this science genius, and said: "Work hard, give up other disciplines, and take physics to the top first." ”

High school mathematics is the best, and after college, physics is the master, and it is simply the world's leading science.

Ye Haoran, who had been expressionless for a long time, squeezed out a smile, and this facial action showed that he was really very happy.

"How's Linear Algebra and Its Applications going?"

Just as the two students were about to leave, Feng Yao stopped Yang Fan.

"It's ok, looked at a small part. Yang Fan didn't tell the truth, the progress of this book had already passed 50%, and he was afraid of scaring Feng Yao.

"You're running out of time, so enjoy high school. Feng Yao smiled mysteriously, didn't say anything, and changed the topic, "On March 2nd, the national team will train intensively." After the end, at the end of March, I will take you to the capital. ”

Going to the capital is to solve the relevant matters of admission, as well as to visit Feng Yao's teacher.

This has been said a long time ago, Yang Fan nodded: "Teacher Feng, I will hurry up and read the math book." ”

Of the textbooks for the three years of mathematics, only two in the third semester of high school are at 82%, and they are perfect in one or two weeks, and since then they have been proficient in high school mathematics without omission.