I really just want to be a scholar

Chapter 455 Therefore, the Polignac conjecture is proved

In the next five Qiusai exams, Qin Ke was basically invincible and easily handled them. After finishing the papers, the rest of the time was devoted to the research of Polignac's conjecture.

Qin Ke's biggest gain from Wang Lao's notebook is not the improved big sieve method, circle method and group theory, but mastering the mathematical thinking method revealed by Academician Wang Lao in the process of optimizing and improving these three mathematical methods.

As I said before, Qin Ke is used to the vigorous and vigorous mathematical thinking method. He takes the "quick, accurate and ruthless" route, goes straight to the core of the problem, and then makes up for the rest of the problem. The peaceful route is pushed forward and gradually deepened. Once it becomes a trend, it can almost be destroyed.

Now Qin Ke has integrated the advantages of Academician Wang Lao's mathematical thinking, and has a stronger view of the overall situation. While maintaining the style of "quick, accurate and ruthless" straight to the core, he has a more "gradually progressive, flat push past" style. .

Thanks to this higher-level mathematical thinking, Qin Ke has a new idea of ​​integrating "function transformation hypergeometric system" and "group theory function equation method", and gradually formed a set of methods that is better than "lime" The new mathematical method of the fourth-order number theory transformation method.

The "lime fourth-order number theory transformation method" is exquisite and mysterious, and the essence lies in "transformation", simplifying the complex and then simplifying the complex, transforming the four rounds, with many changes, like a Swiss army knife, very suitable for small-scale number theory problems.

Its disadvantage is that it is very cumbersome and difficult to master, and it is easy to cause overall errors due to small mistakes, so it is not suitable for "big projects" such as Polignac's conjecture.

The new mathematical method that Qin Ke has come up with now is called "function group hypergeometric method" for the time being. From point to line and then to surface, starting from the overall perspective, starting from function theory, combining group theory and topology principles, Transform the prime number problem into a hypergeometric problem, and prove or falsify the prime number problem by solving hypergeometric functions and hypergeometric equations.

Such a combination of points, lines and surfaces, and the idea of ​​progressive layers are extremely effective for extending k=1 to any natural number.

However, because it is progressing layer by layer, difficulties will naturally be encountered. This requires the courage to "build bridges when encountering mountains and rivers". As long as the core key difficulties are overcome, the final conclusion will come naturally.

Qin Ke listed the five most difficult key points, and pushed them with Ning Qingyun.

After finishing the Qiu Sai exam, Qin Ke had solved three difficulties, and Ning Qingyun also used the old mathematical method improved by Academician Wang to solve the fourth difficulty. , only the last difficulty remains, which is "the problem of the Möbius transformation group on the Riemann sphere".

This problem involves complex mapping space and holomorphic function and meromorphic function, which is very difficult.

Ning Qingyun is in charge of the complex analysis of Riemann surfaces, and Qin Ke is in charge of the rest.

The two-day Qiu Han semi-finals ended in a blink of an eye, because there were too many candidates participating in the semi-finals this time, and it would take at least half a month before the final promotion list for the finals would be announced.

Neither Qin Ke nor Ning Qingyun paid much attention to the results of Qiu Sai. As far as their strength is concerned, participating in such a college student competition is not a difficult challenge. If it is not for the request of the school, they may not even participate.

On the second day after the Qiu Sai exam, which happened to be Saturday, Qin Ke drove Ning Qingyun back to the new home of "Starlight Mingyuan" early in the morning.

Originally, the two planned to watch a new movie and have a date this weekend, but both of them were full of the last key difficulty of Polignac's conjecture, and they had no interest in leisure and entertainment, so they went together Nest in the new home to do their own calculations.

There is a big desk and two chairs in the study room, it looks like they usually share the same desk in school.

When the two meet what needs to be communicated, they will talk directly. More often, the two will study the part they are responsible for.

Time passed bit by bit, and in the blink of an eye, it was past ten o'clock in the evening. Qin Ke went to the balcony to answer a call from home, and chatted with his parents, mother, and younger sister for about ten minutes. When he came back, he saw him in pajamas. Ning Qingyun was still sitting at the desk and writing seriously.

The girl put on a pure white nightgown, and her black hair, which was slightly moist with moisture, cascaded down like a waterfall, exuding the fragrance of shampoo.

Apparently, while Qin Ke was talking on the phone with his family, Ning Qingyun had already taken a shower.

The young girl's pretty face, as pure as a lotus in water, could hardly hide her tiredness, but she was still completely immersed in the study of difficult problems, and she didn't notice her tiredness at all.

Qin Ke thought that from the morning to this time it was almost eleven o'clock in the night, except for a midway meal and occasional getting up for activities, the rest of the time was almost devoted to this subject, and he felt both admiration and distress in his heart.

In fact, he also knows that the last difficulty is difficult to overcome, mainly due to lack of inspiration, and it is really not a good way to blindly attack and carry out fatigue tactics.

"Jun'er." Qin Ke went over and gently put his arms around the girl's slender waist.

"Huh?" Ning Qingyun was startled, and turned around: "What's wrong?"

Qin Ke couldn't help but hugged her with one hand on his knees and the other on his waist.

"Hey, Qin Xiaoke, you..." Ning Qingyun blushed slightly, and wanted to struggle.

Qin Ke sternly said: "Be honest, don't look at the time, it's time to go to bed."

"But... I always feel that I'm just a little bit close to thinking about it. I want to stay up late for a while..."

"No. Continue tomorrow. There is plenty of time, and there is no rush." ​​Qin Ke said in an unquestionably tough tone, and directly carried the girl to the master bedroom.

The study room and the master bedroom are both on the second floor of the duplex, which is quite convenient.

Qin Ke carried Ning Qingjun back to the bed and put it down, only to find that Ning Qingjun's face was flushed. She pressed the hem of her nightgown unnaturally, took a peek at Qin Ke, then lowered her eyes, and said weakly : "I...I'm not very convenient today..."

Seeing that Ning Qingyun had clearly misunderstood something, Qin Ke couldn't laugh or cry. He just thought that Ning Qingyun had been tired all day and needed to rest, and he had no other thoughts. thought up.

After pushing the girl to lie down on the bed, she took off her slippers, laid her white jade-like calves flat, and covered her with a quilt, Qin Kecai said: "I know, no matter how busy I am, I will never forget to count the time. It's about whether it's safe or not."

Ning Qingyun blushed even more, and said softly, "Rogue."

"Call me a few more words? I like it when you call me a 'rogue'." Qin Ke smiled, his skin thicker than a city wall.

"..." Ning Qingyun rolled his eyes at him, and covered half of his face with a quilt: "Then you sleep too?"

"Okay, I'll sleep too."

Qin Ke turned over and jumped onto the bed, lifted the quilt and got in, sleeping next to Ning Qingyun.

The familiar lime-like scent of a girl's body exuded from the quilt, which smelled particularly good. Qin Ke suddenly felt refreshed, and the tiredness of studying mathematics for a day disappeared.

"Come to sleep." Qin Ke said carelessly.

Ning Qingjun bit her red lips and glanced at him, but finally leaned over obediently.

Qin Ke put his arms around her and let her rest on his shoulder: "Hey, go to sleep."

"But I still can't sleep."

"If you don't go to bed after eleven o'clock, you will accelerate aging, and you will not be beautiful."

"Bad guy." Ning Qingyun was lying on the bed, her head covered with black hair, which was in stark contrast to the white sheets, and her bright red face was like a ripe apple, extra cute.

Even if she has become intimate with Qin Ke, but sleeping in his arms like this, the tender-skinned girl can't help but blush a little.

"Then turn off the light."

Qin Ke directly ordered: "Twilight, turn off the lights."

The light in the master bedroom went out immediately, and the curtains were pulled open, and the silver-white moonlight poured down like water, like a dream.

"You can sleep now, Your Highness."

"Yeah." Ning Qingyun closed her eyes forcefully, pretending to be trying to sleep, but opened them again soon, and gently held Qin Ke's big hand with her small hand, clasping his fingers tightly.

The girl's fingers were thin and soft, especially comfortable to hold in her hand.

Contrary to others who don't cherish what they get, Qin Ke is just the opposite. It is precisely because he knows that what he has got is a unique treasure in the world, so he cherishes it even more.The closer he was to Ning Qingyun, the more his love and liking for Xiaobaicai went deep into his bones.

He was thinking about how to make this treasured girl in his family happy. In the dark, Ning Qingjun suddenly blushed, and said with attachment and shyness:
"That...kiss...kiss, I haven't kissed tonight..."

Qin Ke was almost overwhelmed by the cuteness.

Generally, according to the usual practice, he would kiss Ning Qingyun before going to bed, but he was afraid that something would happen if he kissed, especially now that Ning Qingyun was tired and just inconvenient.

However, my wife has a life, so Qin Ke still decided to be obedient.

Of course, it's not Qin Ke's style to be too honest.

He rubbed his ears: "Jun'er, what are you talking about? The wind was too strong just now, so I didn't hear it."

"I'm ignoring you." Ning Qingyun turned her face away.

Only then did Qin Ke kiss her warm, soft and smooth face with a smile, and then hugged her tightly into his arms.

Ning Qingyun quietly opened her eyes and glanced at him, just as Qin Ke was also looking at her, her eyes met, her breath smelled, a special warmth and happiness pervaded.

"Qin Xiaoke, do you think we can solve the last critical difficulty tomorrow?" The girl's voice was soft, as if she was acting like a baby.

Qin Ke gently rubbed her hair and said, "It doesn't matter if it's possible, anyway, we have a lot of time. Isn't that invitation for the Science Breakthrough Award in June?"

"Well, but if you want to publish the proof of Polignac's conjecture in the "Annual Mathematical Journal" in May, you have to hurry up. It's the end of March now."

"The proof process of Polignac's conjecture is so complicated. Even if we finish writing a paper and submitting it, we will definitely not be able to publish it in the May issue. At least two months of expert review time will be required, and it will be published in July." It'll be fine when it comes out, so don't rush."

"Is the Cole Award awarded in early August? It was announced in July, and I'm afraid it's too late... I don't want you to lose this award, since that weak Polignac conjecture doesn't count for anything."

Qin Ke's heart felt soft, and he hugged Ning Qingyun tightly again: "It's okay, a mere Cole Award is judged by foreigners. It's hard to be fair and just. It's okay if it doesn't make it. We will judge Goethe later." Both Bach's conjecture and Riemann's conjecture were proved, and they were severely slapped in the face, and the face of the guy who used the weak Polignac conjecture to fool people was swollen by the way."

"It's so difficult for us to solve the Polignac conjecture, let alone Goldbach's conjecture and Riemann's conjecture...but." Listening to Qin Ke's arrogant tone, Ning Qingyun pursed her lips and said with a smile: "I believe you can do it sooner or later."

"It's not me, it's us. Well, go to sleep, good boy."

Ning Qingjun closed her eyes obediently, and fell asleep after a few minutes.Her sleep quality has always been very good, and she is really exhausted these days. Looking at the faint dark circles under her eyes, she probably stayed up late in the school dormitory a few days ago to delve into Polignac's conjecture.

Qin Ke got out of bed quietly, covered Ning Qingyun with the quilt, and returned to the study by himself.

Ning Qingyun thought that if he won the Cole Award, it would be necessary for Qin Ke to realize his little cabbage's wish.

What's more, he doesn't want to lose to the Eagle Countryman who is eager for quick success. He is determined to win the Scientific Breakthrough Award and the Cole Award!

Qin Ke picked up Ning Qingjun's small notebook on the desk, followed her thoughts, and found that Ning Qingjun actually tried to solve the problem of complex analysis on Riemann surface in five different ways, and each method was well-known. The essence of the number theory method of Tian Jianlan and Academician Wang Lao.

Qin Ke sighed a little. Unknowingly, Ning Qingyun was also growing rapidly. Now when it comes to the level of number theory, she is no less than any graduate student majoring in mathematics in the world.

After reading Ning Qingyun's part, Qin Ke carefully read the part he wrote again.

As the night gradually darkened, Qin Ke flipped through it repeatedly, vaguely feeling that he had touched the edge of inspiration, but he was still a little bit short.Just a little bit!It would be great if it could trigger the "Inspiration Amplification".

But it wasn't easy for him to go out for a run in the middle of the night, so he simply went to the lobby on the first floor to practice the oriental secret classics and Wing Chun boxing. The boxing and gymnastics over and over again made his mind more and more quiet and clear.

I don't know how long it took, maybe an hour, maybe two hours, and finally at a certain moment, Qin Ke entered the familiar and wonderful realm!
The system's "Inspiration Amplification" function is activated again!
Qin Ke rushed back to the study on the second floor, picked up a pen and started writing.

In the world of "Inspiration Amplification", his thinking is sparking, and all the accumulation of studying Polignac's conjecture in the past four or five months, all the books and papers he has read, and all the lectures he has heard are clear. Incomparably floating in front of his eyes, let him use it at his fingertips.

What is thick accumulation and thin hair?

This is the real thick and thin hair!

In this world of inspiration, Qin Ke integrated the essence of number theory methods learned by Ning Qingjun from Professor Tian Jianlan and Academician Wang Lao into the "Function Group Hypergeometric Method", turning the already well-established new mathematical method into a It is more concise and effective, and in the past two months, he and Ning Qingyun have proved all the details of the Polignac conjecture, and they have re-optimized the points, lines and surfaces in this "function group hypergeometric method", and finally It turned into an unstoppable force, and the fifth key difficulty "the problem of the Möbius transformation group on the Riemann sphere" that had troubled him and Ning Qingyun for half a month suddenly turned into ashes!
When the sky was light, Qin Ke had filled more than 40 pages of draft paper.

He let out a long sigh of relief, dropped the pen, staggered back to the master bedroom, fell on the bed, and fell asleep in an instant.

And the last line of the more than 40-page draft paper reads impressively:

"Therefore, for all natural numbers k, there are infinitely many pairs of prime numbers (p, p + 2k). Polyniac's conjecture is proved."

　I was so busy today that I didn't even eat a meal. I updated it first, and then I took a shower and had dinner.Thank you for your recommended monthly tickets!
　　
　
(End of this chapter)