Reshaping life starting from the Junior Class of HKUST

Chapter 220 Three days, three world-class conjectures
Wang Chao led the two of them to the guest house of the University of Science and Technology. Huang Minghai pulled Wang Chao down and said, "Just take us here! Although the school guest house is on campus, we can't live there! The school treats us Are you ignorant of the rules of the Junior Court?"

"Hey, just look at it!" Wang Chao said winkingly beside him.

After speaking, he walked in first.

Huang Minghai and Shen Zhiwen shook their heads and could only follow in.

A few minutes later, Wang Chao got the room card.After entering the room, he said to the two of them: "How is it? Follow me, right!"

Huang Minghai asked puzzledly: "I think the manager at the front desk knows you, why are you so familiar here!"

Wang Chao didn't hold back anymore, and said directly: "Isn't it impossible to live in people when I came back last time? I was not allowed to live outside. I thought to myself, doesn't our school have its own guest house? This is inside the school! So later I I made friends with the manager here. Although it is stipulated that our junior hospital can only live in dormitories, it is always possible to accommodate occasionally."

Huang Minghai and Shen Zhiwen also admired Wang Chao's social skills.

Wu Zhe has been echoing the words of the boss Huang Minghai: "The problem of Hilbert space is not only a problem in the field of physical force, but also a problem of mathematics."

It was that sentence that exploded in his mind like a thunderbolt.

Hilbert spaces are a direct generalization of Euclidean spaces.The study of Hilbert spaces and operators acting on Hilbert spaces is an important part of functional analysis.

The infinite-dimensional Hilbert space is an extension of the n-dimensional Euclidean space, which can be regarded as "infinite-dimensional Euclidean space".In three-dimensional Euclidean space, an inner product is specified between any two vectors.

The inner product can help people study the Hilbert space from a "geometric" point of view, and use the geometric language in the finite-dimensional space to describe the Hilbert space.Among all infinite-dimensional topological vector spaces, Hilbert spaces have the best properties and are closest to the situation of finite-dimensional spaces.

What Wu Zhe is interested in is the topological algorithm in it. The proof of twin prime numbers Wu Zhe used a lot of mathematical methods, but found that they were all dead ends.

But he never thought of using topological algorithms, because this is not a conceptual problem at all.But this time he told him directly that this was the key he had been looking for.

[Assuming {ek} is a family of different vectors in the inner product space H, if any two vectors are orthogonal, that is, when k≠j, (ek, ej)=0, then {ek} is said to be a positive Intersection; if the norm of each vector is 1, that is, for all k, (ek, ek)=1]

【--】

[x=Σ(x,ek)ek——]

【--】

Now Wu Zhe has devoted himself to the proof process, and brainstorming has started in his mind.

Time passed unknowingly.

Fortunately, his recent research is mathematical conjectures. There are not many other things in the dormitory, but there are enough blank papers for him.

Now, it's already the afternoon of the second day.

Wu Zhe's face was a little pale, but fortunately, his thinking was still clear, so he didn't need to use his own brain power to calculate.

When you only need complex calculations, just turn on the power at full power.

What was written in the previous part was all expanded from Hilbert's inner product space, and finally turned to the Fourier formula for derivation, and then turned to the most classic sieve method.

When Wu Zhe wrote:
【s(α)=Σane(nα); m, n∈ζ...】

There was a smile on the corner of his mouth.

After this line of calculation, it is a bright road.

[s(2)-(logkx)s(1)>0 is established when k≥2, the acceptable array h=...]

【…】

【Therefore, there are infinitely many pairs of twin primes. 】

Then for all natural numbers k, there are infinitely many pairs of prime numbers [p, p + 2k] established.

And the twin primes of K=1 are naturally also established.

When writing here, Wu Zhe has solved the Polignac conjecture and the twin prime conjecture at the same time.

Wu Zhe's feeling is also correct. If you want to complete the twin prime conjecture, you must solve the Liniac conjecture.

It's just that although this meeting solved two world-class conjectures, Wu Zhe has no intention of stopping at all.

He took another stack of draft paper casually.

Start writing:] When 2 2 n 1 < p < 2 2 n 2^{2^{n-1}}<p<2^{2^{n}}2 <p="">2 n1 2 n hour,】

【--】

[M p M_{p}M p has 2 n 1 2^{n}-12 n 1 which are prime numbers]

【--】

【π M p ( 2 2 n )π M p ( 2 2 n 1 )= 2 n 1( a )\pi_{M_{p}}(2^{2^{n}})-\pi_{M_{ p}}(2^{2^{n-1}})=2^{n}-1(a)π M p (2 2 n )π M p (2 2 n1 )=2 n 1]

Wu Zhe's thinking was at its most active at this time, and when he used the sieve method, he had an idea about Zhou's conjecture. At this time, the proof process can be described as a drastic drop.

First use the sieve method, and then use the reverse mathematical induction method.The key is that a large part of the process of proving twin primes is also common to the distribution of Mersenne primes, which saves a lot of trouble!
Wu Zhe, who was immersed in mathematical formulas, could not feel the passage of time at all, nor did he feel tired, only excited.

By the afternoon of the third day, Wu Zhe finally finished Zhou's conjecture.

When Wu Zhe finally wrote

[It is established when n=k+1, 2 k < p < 22 k + 1, p 2^{2^{k}}<p<2^{2^{k+1}}, p2 <p="" >2 k 2 k+1 ——]

[k — 2 k + 1 2^{2^{k}}—2^{2^{k+1}}2 2 k —2 2 k+1;]

【--】

[When 2 2 n < p < 2 2 n + 1 2^{2^{n}}<p<2^{2^{n+1}}2 <p="">2 n 2 n+1 , M p M_{p}M p has 2 n + 1 1 2^{n+1}-12 n+1 1 prime number]

【2^（2^n）＜p＜2^（2^（n+1））时，mp有2^（n+1）-1个是素数成立。并以此为论据，证明了当p&lt;2^（2^（n+1））时，mp有2^（n+2）-n-2个是素数这一推论成立。】

After writing this, Wu Zhe threw away his pen.All spirits relax.

Only then did he feel his temples beating violently.

Feeling a little groggy in the head, and hungry and thirsty.

But only he himself knows that his heart is satisfied.

Looking at the time, it was already the afternoon of the third day.Wu Zhe proved three world-class conjectures in three days, which is very efficient, which is equivalent to one a day.

Rubbing the center of her eyebrows with one hand, she turned on the phone with the other.He was afraid of being disturbed by others, so he turned off his mobile phone.

After turning on the phone, he called Wang Chao directly.

This meeting, Wang Chao is taking an exam, and this is already the last day of the final exam.There are two days left for the holiday, and Ah Zhe doesn't know what's going on?They haven't come out for three days and haven't given us any news.I don't know what's going on with him?
This test was about chemistry. Wang Chao didn't spend his energy on chemistry, but he finished it early.This can feel a little boring and lazy.

This person really didn't talk about it. When Wang Chao was thinking of Wu Zhe, his phone vibrated.After taking a sneak peek, it was Wu Zhe, and Wang Chao stood up in a jerk. Just when he felt something was wrong, the invigilator shouted: "This student, what do you want to do?"

Wang Chao responded very quickly, and immediately replied loudly: "Teacher, I will hand in the paper."

(End of this chapter)