Wang Chao took the two of them to the guest house of the University of Science and Technology, Huang Minghai pulled Wang Chao down and said, "You brought us here!" Although the school guest house is in the school, we can't live in it! You don't know the school's regulations on our young school? ”

"Hehe, you'll see it!" Wang Chao said with frowns next to him.

After saying that, he walked in first.

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

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

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

Wang Chao didn't sell it anymore, and said directly: "Didn't you come back last time and couldn't live in it?" And I wasn't allowed to live outside, I thought to myself, doesn't our school have its own guest house? It's in school, right? So then I made friends with the manager here. Although it is stipulated that we can only live in the dormitory, it is always possible to be accommodating occasionally. ”

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

Wu Zhe's mind has been echoing the sentence that the boss Huang Minghai said: "The Hilbert space problem is not only a problem in the field of physical quantities, but also a mathematical problem. ”

It was that sentence that exploded in his brain like thunder.

The Hilbert Space is a direct promotion of the Euclid Space. The study of Hilbert space and the operators acting on Hilbert space is an important part of functional analysis.

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

The inner product can help people to study Hilbert space from a "geometric" point of view, and to describe Hilbert space using the geometric language of finite-dimensional space. Of all the infinite-dimensional topological vector spaces, the Hilbert space has the best nature and is the closest to the finite-dimensional space.

Wu Zhe is interested in the topological algorithm inside, the proof of twin primes 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 it was not a matter of concept at all. But this would tell him directly that this was the key he had been looking for.

[Let {ek} be a family of vectors in the inner product space H that are different from each other, and if any two vectors are orthogonal, i.e., when k≠j, (ek,ej)=0, then {ek} is said to be an orthogonal system; If the norm of each of these vectors is again 1, i.e. for everything k, (ek,ek)=1]

【------】

【x=Σ(x，ek)ek-----】

【------】

At this time, Wu Zhe had already devoted himself to the proof process, and brainstorming began in his mind.

Time passes imperceptibly.

Fortunately, he has been studying mathematical conjectures recently, and there is not much else in the dormitory, but the blank paper has prepared enough for him.

By this time, it would be the afternoon of the next day.

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

When you only need to make complex calculations, you can turn on the full power.

The previous part of the writing is all about expanding from Hilbert's inner product space, and finally turning to the Fourier formula for derivation, and then turning to the most classic sieve method.

When Wu Zhe put pen to pen and wrote:

【s（α）=Σane（nα）； m，n∈ζ……】

The corners of his mouth were already smiling.

After this line of calculations, it is the road of light.

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

【……】

Therefore, there are an infinite number of twin prime pairs. 】

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

And the twin prime of K=1 naturally holds true.

At the time of writing, Wu Zhe had already solved the Polignac conjecture and the twin prime conjecture at the same time.

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

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

Grab another stack of scratch paper.

Start writing:] When 2 2 n ? 1 < p < 2 2 n 2^{2^{n-1}}

2 n?1 2 n,】

【------】

【M p M_{p}M p has 2 n ? 1 2^{n}-12 n ?1 is prime]

【-------】

【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 n?1 )=2 n ?1......】

Wu Zhe's thinking is the most active time, and when he uses the sieve method, he has an idea of Zhou's conjecture, which will, and the proof process can be described as a thousand miles.

Sieve first, then reverse mathematical induction. The key is that a large part of the process of proving twin primes is also universal to the Mersenne prime distribution, which saves a lot of trouble!

Wu Zhe, who was immersed in mathematical formulas, did not feel the passage of time at all, nor did he feel tired, only excited.

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

When Wu Zhe finally wrote

【n=k+1, 2 k < p < 22 k + 1 , p 2^{2^{k}}

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}}

2 n 2 n+1, M p M_{p}M p has 2 n + 1 ? 1 2^{n+1}-12 n+1 ?1 prime】

[2^(2^n)

Writing this, Wu Zhe threw the pen away. All the spirits relaxed.

That's when he felt his temples pounding.

The brain felt a little groggy and hungry and thirsty.

But only he knows that his heart is content.

After looking at the time, it was already the afternoon of the third day. Wu Zhe proved three world-class conjectures in three days, and this efficiency is no one, which is equivalent to one a day.

rubbed his eyebrows with one hand, and turned on his phone with the other. He was afraid of being disturbed, so he turned off his phone.

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

This will be Wang Chao's exam, and this is the last day of the final exam. There are two days left to go on vacation, and Ah Zhe doesn't know what to do? It didn't come out for three days, and it didn't come to us with any news. I don't know what happened to him?

This exam is chemistry, and Wang Chao didn't spend his energy on chemistry, but he finished it early. It's going to be a bit boring.

This person is really careless, and when Wang Chao really thought of Wu Zhe, his mobile phone shook. After sneaking a glance, it was Wu Zhehou, Wang Chao stood up with a spirit, and as soon as he felt that something was wrong, the invigilator shouted there: "This classmate, what do you want to do?" ”

Wang Chao reacted quickly, and immediately replied loudly: "Teacher, I'll hand in the papers." ”

pencil