In the next five Qiushe exams, Qin Ke was basically unstoppable and easily passed them. After finishing the papers, he devoted the rest of his time to research on the Polignac conjecture.

Qin Ke's biggest gain from Mr. Wang's notebooks was not the improved large sieve method and circle method group theory, but the mathematical thinking method revealed by Academician Wang in the process of optimizing and improving these three mathematical methods.

As I said before, Qin Ke is accustomed to the vigorous and resolute mathematical thinking method. He takes the "quick, accurate and ruthless" route, getting straight to the core of the problem, and then peeling off the cocoon to make up for the rest, while Academician Wang Lao takes the Zhongzheng route.

The peaceful route advances gradually and gradually deepens. Once it becomes popular, it can almost destroy everything.

Now Qin Ke has integrated the advantages of Academician Wang Lao's mathematical thinking, and has a stronger overall view. While maintaining the style of "quickly, accurately and ruthlessly" going straight to the core, he has added a grand spirit of "progressing layer by layer and pushing forward flatly".

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It is precisely thanks to this higher-level mathematical thinking that Qin Ke has new ideas by integrating "functional transformation hypergeometric system" and "group theory functional equation method", and gradually formed a set of methods that are better than the "green lemon method".

A new mathematical method called "fourth-order number theory transformation method".

The "Green Lemon Fourth-order Number Theory Transformation Method" is exquisite and mysterious. The essence lies in "transformation". Simplify to complex and then complex to simplify. Four rounds of transformations. There are many changes. It is a Swiss army knife and is very suitable for small-scale number theory problems.

The disadvantage is that it is very cumbersome and difficult to master, and it is easy for small mistakes to lead to complete errors, so it is not suitable for "big projects" such as Polignac Conjecture.

The new mathematical method that Qin Ke has now figured out is tentatively called the "function group hypergeometric method". It starts from points to lines and then to surfaces with an overall perspective, starting from function theory, and combining group theory methods and topology principles.

Convert the prime number problem into a hypergeometric problem, and prove or falsify the prime number problem by solving hypergeometric functions and hypergeometric equations.

This idea of ​​combining points, lines and surfaces, and progressing step by step, is extremely effective in extending k=1 to any natural number.

However, because we are progressing step by step, we will naturally encounter difficulties, which requires the courage to "open roads and build bridges over mountains and rivers". As long as the core key difficulties are overcome, the final conclusion will be reached naturally.

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

By the time he finished the Qiu Sai exam, Qin Ke had solved three difficult points, and Ning Qingyun also used the ancient mathematical method improved by Academician Wang Lao to solve the fourth difficult point: "If the interval difference can be listed, it must be an infinite group."

, only the last difficulty is left, which is the "Möbius transformation group problem on the Riemann sphere".

This problem involves complex mapping spaces and holomorphic functions and meromorphic functions, and is very difficult.

Ning Qingyun is responsible for the complex analysis of Riemannian surfaces, and Qin Ke is responsible for the rest.

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

Qin Ke and Ning Qingyun didn't take the results of the Qiu competition too seriously. Considering their strength, participating in such a college competition is no longer a difficult challenge. If it wasn't required by the school, they might not even participate.

The day after finishing the Qiu Sai exam, which happened to be Saturday, Qin Ke drove Ning Qingyun back to his new home in "Xingguang Mingyuan" early in the morning.

Originally, the two of them planned to watch a new movie and go on a date this weekend, but their minds were filled with the last key difficulty of Polignac's conjecture, and they had no intention of leisure and entertainment, so they went together.

Stay in your new home and write and do calculations.

There is a large desk in the study room with two chairs. It looks like two people sitting at the same table in school.

When the two of them encountered something they needed to communicate with, they would talk directly. More often than not, they would each delve into the parts they were 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 and little sister for about ten minutes. When he came back, he saw him wearing pajamas.

Ning Qingyun is still sitting at the desk writing something seriously.

The girl put on a pure white nightgown, and her black hair with a hint of moisture flowed 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 bath.

The girl's pure and pretty face, as pure as a hibiscus, could not hide her tiredness, but she was still completely immersed in her research and did not notice her tired face at all.

Qin Ke thought that from morning to now it was almost eleven o'clock at night, except for a quick meal and the occasional activity, she had almost devoted herself to this topic, and he felt both admiration and distress in his heart.

In fact, he also knew that the final difficulty was difficult to overcome, mainly due to lack of inspiration. It was not a good idea to blindly attack and use fatigue tactics.

"Jun'er." Qin Ke went over and gently hugged 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 her knees and the other on her waist.

"Hey, Qin Xiaoke, you..." Ning Qingyun's face was slightly red, but she still wanted to struggle.

Qin Ke straightened his face: "Be honest and don't even look at the time. It's time to go to bed."

"But... I always feel like I'm still a little bit closer to thinking about it. I want to stay up a little longer..."

"No. We will continue tomorrow. We have plenty of time, and there is no rush." ​​Qin Ke said in a tough tone that could not be questioned, and directly carried the girl to the master bedroom.

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

Qin Ke carried Ning Qingyun back to the bed and laid her down, only to find that Ning Qingyun's little face was flushed. She pressed the hem of her nightgown unnaturally, glanced at Qin Ke secretly, lowered her gaze, and said weakly

: "I...I came here today..."

Seeing that Ning Qingyun had clearly misunderstood something, Qin Ke didn't know whether to laugh or cry. He simply thought that Ning Qingyun had been tired for a day and needed to rest. He had no other ideas. Even if he had, he was embarrassed to think of anything else after thinking that she had been tired for a day.

Got an idea.

Pressing the girl to lie down on the bed, he took off her slippers, flattened her white jade-like calves, and covered her with a quilt. Qin Kecai said, "I know, no matter how busy I am, I will never forget to count this time.

It’s about safety and security.”

Ning Qingyun's face turned even redder and she said softly: "Rogue."

"Do you want to scold me a few more times? I like it when you call me a 'hooligan'." Qin Ke smiled, his face thicker than the city wall.

"..." Ning Qingyun rolled her eyes at him and covered half of her face with the quilt: "Then you want to sleep too?"

"Okay, I'll sleep too."

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

The familiar lime-like girly body fragrance emanated from the quilt, and it smelled particularly good. Qin Ke suddenly felt refreshed, and the fatigue from studying mathematics for a day disappeared.

"Get some sleep." Qin Ke said carelessly.

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

Qin Ke put his arm around her and let her rest on his shoulder: "Be good, go to sleep."

"But I still can't sleep."

"Not sleeping after 11 o'clock will accelerate aging and make you look unattractive."

"Bad guy." Ning Qingyun was lying on the bed, her hair spread out in black hair, which was in sharp contrast to the white sheets. Her pretty face looked like a ripe apple, and she was extraordinarily cute.

Even though she was intimate with Qin Ke, the girl with a particularly tender face could not help but blush a little while sleeping in his arms like this.

"Then turn off the light."

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

The lights in the master bedroom immediately went out, the curtains were opened, and the silver-white moonlight poured down, like a dream.

"You can go to sleep, Your Highness Princess."

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

The girl's fingers are thin and soft, and it feels particularly comfortable to hold it in her hand.

Contrary to others who think they don't cherish it, Qin Ke feels that what he got is a unique treasure in the world, so the closer he gets to Ning Qingyun, the more his love and affection for her goes deep into his bones.

He was thinking about how to make this precious girl of his family happy. In the darkness, Ning Qingyun suddenly blushed and said with attachment and shyness:

"Um...kiss...kiss me, I haven't kissed you tonight..."

Qin Ke was almost blown away by the cuteness.

Normally, as a rule, he would kiss Ning Qingyun before going to bed, but he was afraid that something would happen if he kissed her, but now Ning Qingyun was tired and inconvenient.

However, my wife had a fate, so Qin Ke decided to obey.

Of course, being too honest is not Qin Ke's style.

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

"Ignore you." Ning Qingyun turned away.

Qin Ke then smiled and kissed her warm, soft and tender face, and then held her tightly in his arms.

Ning Qingyun quietly opened her eyes and glanced at him. It happened that Qin Ke was also looking at her. Their eyes met and they breathed together. A special kind of warmth and happiness filled the air.

"Qin Xiaoke, do you think we can solve this last key difficulty tomorrow?" The girl's voice was soft, as if she was coquettishly coquettish.

Qin Ke gently rubbed her hair and said: "If you can, it's okay. If you can't, it doesn't matter. We have plenty of time anyway. Isn't that invitation for a scientific breakthrough in June?"

"Yeah, but if you want to publish the proof of Polignac's conjecture in the May Annals of Mathematics, you have to hurry up. It's already the end of March."

"The proof process of Polignac conjecture is so complicated. Even if we finish writing the paper and submit it, it will definitely not be published in the May issue. It will take at least two months of expert review time before it can be published in July.

It will be good when it comes out, so there is no need to rush."

"Is the Kohl Prize awarded in August? It won't be published until July. I'm afraid it won't be in time... I don't want you to lose this grand prize. Obviously that weak Polignac conjecture doesn't count."

Qin Ke felt soft in his heart and hugged Ning Qingyun tightly again: "It doesn't matter, it's just a Kohl Prize, and it's judged by foreigners. It's difficult to be fair and just. It doesn't matter if we don't win. We will give Goethe the prize later."

Both Bach's Hypothesis and Riemann's Hypothesis have been proved, giving them a hard slap in the face, and at the same time, a slap in the face of the guy who used the weak Polignac Hypothesis to fool people."

"It's so difficult for us to solve the Polignac conjecture, let alone Goldbach's conjecture and Riemann's conjecture... However." Ning Qingyun listened to Qin Ke's arrogant and domineering tone, pursed her lips slightly, and said with a smile:

"I believe you can do it sooner or later."

"It's not me, it's us. Okay, go to sleep, be good."
To be continued...