Chapter 247

Yandong Garden.

The sizzling sound in the living room disappeared.

Xu Qingzhou was satisfied and left, smacked his lips, happily laid out the materials, and prepared to continue delving into great mathematical knowledge.

School Beauty Song is very feminine every time she kisses.

One second she was staring and shouting to beat someone, the next second she softened, that lingering little look... Song-Ao-Jiao-Yao.

Saying no on her lips, but enjoying it more than anyone else after being forced. Xu Qingzhou thought again, if she kisses like this when she is angry, will she also stop firing? Of course, he is just thinking, he is not stupid.

If Song Yao is really angry, she might be able to dismantle his arm, let alone kissing and hugging.

"They will arrive at 3 PM, so let's go buy groceries together then."

Read! {

Thinking clearly, Xu Qingzhou didn't waste time anymore and started writing.

"???"

Just now she was still looking spring-like, now... this emotional fluctuation is a bit big.

Returning to his seat in the library, took a sip of water, his eyes focused on the content of the conjecture: For all natural numbers k, there exist infinitely many prime pairs (p, p+2k).

However, what surprised Xu Qingzhou was that on Thursday, he received a call from Professor Zhao Shengwen. Outside the library, Xu Qingzhou exhaled, covered the scorching sun at 2 PM with his hand; entering June, the weather is a bit hot, and even staying in the living room is a bit stuffy.

She didn't bother to pay attention to him, now she just wants to calm down.

"I just thought of calling to ask you, we can be considered old acquaintances. But I know you are busy with Polignac's conjecture; if you are too busy, I will ask Old Gu again."

Song Yao straightened her face, shuffled into the bathroom in slippers, gargled, and sat opposite Xu Qingzhou reading a book, but after not reading for a while, she felt the boyfriend's feet poking her legs.

Xu Qingzhou was a bit confused.

Xu Qingzhou naturally wouldn't refuse: "I have no problem here, whenever you need, I will come over."

"Tomorrow morning, 9 o'clock."

Hanging up the phone, Xu Qingzhou exhaled a long breath; what he thought of came, a few days ago he was still thinking about how to rub off some experiments.

Tuesday, June 16th.

"Xiao Xu, didn't I disturb you?" Zhao Shengwen's voice came from the receiver.

This date is neither here nor there, far from the time her period comes and goes.

This means that when n≤pz, there is: 【π2(pz, z)=∏. 3≤p≤z(p2)=pz2∏3≤p≤z(12p)】

Xu Qingzhou's expression was strange: "Are you very hot?"

By piecing together, first make the product on the right side of (9) become a convergent quantity, that is to say, find a product ∏3≤p≤xf(p) with a known asymptotic expansion such that the product ∏p≥312/pf(p) converges.

"It's all your fault."

【π2(x)kxlog2x.】

According to this method, the necessary and sufficient condition for the Twin Prime Conjecture is that π2(x) is strictly monotonically increasing.

Polignac's conjecture, also called the Generalized Twin Prime Conjecture.

Keep it on the account, and clean it up together later.

According to his past habits, Xu Qingzhou still went through all the calculation steps during this period, and only after having a clear and complete context in his mind did he start to think about where to start.

Thinking about it this way, she found that she seemed strange; why would she like Xu Qingzhou to be a bit tougher on her... Seeing Song Yao sitting on the sofa, her crystal-clear eyes flashing, not knowing what she was thinking, Xu Qingzhou teased: "Still savoring it?"

Next, one can try to find the specific expression for k.

Zhao Shengwen: "I won't beat around the bush, the data for the first stage of our research group has come out, but the effect is not particularly ideal; we need to find someone to help with the analysis, preferably to produce a complete theoretical model."

"Good." Song Yao was indifferent.

But it's a bit different.

Xu Qingzhou narrowed his eyes, his attention returned to the speculation on the number of twin primes. In this place, make corrections, use π2(x) to represent the number of twin primes not exceeding x... Thinking, he picked up his pen and wrote a row of formulas.

Hiss~ murderous aura! In the next few days, before the Dragon Boat Festival arrived, Xu Qingzhou was completely immersed in the library, devoting himself to the proof of Polignac's conjecture.

Song Yao glared threateningly at her boyfriend who was asking for a beating, but because of this, she suddenly associated it with what Jiahui told her before—M attribute.

That is, liking to be ×××.

Up to here, Xu Qingzhou finished the first step; next, it is to refine the core method used when exploring the distribution of prime numbers and twin primes, and obtain the original form of the sieve method to prove Polignac's conjecture. First, simplify the sieve method; on the basis of the sieve method of the Twin Prime Theorem, introduce techniques from complex analysis, L-functions, etc., in analytic number theory, as well as combinatorial mathematics, algebraic geometry, etc., to construct a tool that is powerful enough and capable of accurately screening prime numbers.

"Is your physiological cycle messed up?"

Similar to kissing Xu Qingzhou in a crowded place, nervous, heartbeat accelerating.

"A little small achievement, not worth mentioning." Xu Qingzhou said modestly.

"No, just resting." Xu Qingzhou replied.

When the weather gets hotter, he can apply to move to School Beauty Song's room to blow the air conditioner.

The difficulty of proving or falsifying increases linearly with the two words "generalized".

No no no, impossible.

Xu Qingzhou asked helplessly: "Guo Ziyang and Ding Jiahui are coming on Saturday, shall we cook hot pot at home?"

But soon, the other party's hoof stretched out again, rubbing against her calf.

Seeing Xu Qingzhou so formal, Song Yao stopped writing and looked up at him.

"Fine, I'll shut up." Xu Qingzhou saw this posture; if he was cheap again, he would really be beaten; the cold School Beauty Song of the past was indeed gone forever.

"Good."

【k=2∏p≥312/p(11/p)2=2∏p≥3【11(p1)2】】

Song Yao looked up and glanced at Xu Qingzhou lightly, "If you move around again, I'll chop off your feet."

"I'm disgusted with you." Song Yao said muffledly, still struggling with her strange hobby.

Xu Qingzhou echoed and smiled.

"Hmm." Song Yao nodded.

He simply bought a fan to blow when it was hot.

Xu Qingzhou thought happily, while walking to the shade of the big tree in front of the library, and called back Professor Zhao.

"..."

Finally, use the properties of the logarithmic function to transform the problem into proving that the expression converges.

It's like originally having to fish for a needle in a lake, now suddenly changing the lake to the sea, becoming a real needle in a haystack.

Could it be because of half-pushing and half-yielding? Song Yao touched her lips and realized. Oh, it turns out this is not right, because she didn't want to at first, and even resisted, threatening to beat him, but was still "forced" and then felt very exciting.

"Xu Qingzhou!" Song Yao raised the pillow to hit him, but didn't throw it in the end, worried that the pillow would get dirty on the ground.

Complete on this basis, hoping to get a brand new and more powerful sieve method.

Opposite, Xu Qingzhou felt it was necessary to re-confirm the date.

Zhao Shengwen smiled and said: "I heard from Professor Chang that you kid has done a lot of big things in the Quantum Research Institute."

Expression for k:

【π2(x)=#{p≤x: p+2isprime}】

Up to here, the asymptotic formula is relatively important.

Song Yao felt her face was a bit hot, fanned herself with her hand, quickly stopped this dangerous thought, and self-deceivingly said in her heart: "I am very normal, Xu Qingzhou is the big pervert, I was just slightly influenced."

Xu Qingzhou reminded leisurely: "You were the one who stuck your tongue out first."

Xu Qingzhou's expression was serious, and he said in a deep voice: "There is another very important problem."

"Your mature mentality, worthy of being brought out by Old Gu, is exactly the same."

On the sofa next door, Song Yao was holding a pillow in a daze, with a faint blush on her fair cheeks; this guy is getting bolder and bolder, but this time there seems to be an indescribable comfort, which makes people indulge.

!.

At the same time, it is necessary to develop an efficient algorithm to assist in calculation, so as to quickly process large-scale data and improve the efficiency and accuracy of the sieve method.

This point probably still needs to use the supercomputing resources of the Supercomputing Center.

Up to here, Xu Qingzhou temporarily put away the materials for Polignac's conjecture and called up the lithium-ion battery paper he hadn't finished reading; he had been calculating for two days, and he was indeed a bit tired now.

Too much is as bad as too little; calculating blindly is easy to get into a dead end, and wanting to prove a conjecture cannot be done overnight; it is still necessary to combine work and rest.

(End of chapter)