The chirping of summer cicadas is getting louder and louder. The entire Qingmu University is already in the middle of summer. All we can see are male and female students wearing short sleeves, shorts and skirts. Occasionally, strictly dressed faculty members will walk by and undress.

The top button of the white shirt.

The pace of time has entered late May unknowingly, and the temperature has soared to 29 degrees Celsius. The scorching sun in the sky is hard to remind people of the time that almost froze the world a few months ago.

Cold wave.

However, for Qin Ke and Ning Qingyun indoors, there was comfortable air conditioning, and their minds were entirely focused on the subject of Goldbach's conjecture, and they did not notice the cicadas and the heat outside.

It was Friday. Both of them had only the first professional class in the afternoon, and then there were no classes. So they returned to their new home in Xingguang Mingyuan Community and sat in the study to work on the final sprint of Goldbach's conjecture.

.

"Every even number greater than 2 can be written as the sum of two prime numbers." - Goldbach's conjecture in the eighth question of Hilbert 23. It can be described in such a simple sentence, but it is recognized by the mathematical community.

, one of the most difficult mathematical problems besides the seven millennium problems, it is also a mathematical crown that has hung in the world of analytic number theory for more than 300 years, and no one has ever been able to take it off.

With the development of computers in modern times, very large even numbers have been verified by computers, but no counterexamples have been found.

In other words, Goldbach's conjecture is correct with a high probability, but for mathematics, only if it is proved 100% can it be promoted to a theorem, otherwise it can only be a guess or conjecture.

The current mainstream proof method is to prove "ab", which is equivalent to the fact that for every large even number N, it can be written as the sum of two almost prime numbers, B, where the number of prime factors of A and B does not exceed a respectively.

and b, whether it is "99" proved by Brown in 1920 or "12" proved by Mr. Xia Guochen, they all follow this pattern, and their ultimate goal is to prove "11".

Every progress in this direction is mainly achieved through the continuous improvement of the large screening method. The most famous one is naturally Mr. Chen's "12".

However, Qin Ke came to the conclusion through repeated research that the big sieve method has evolved to the extreme in the hands of Mr. Chen, that is, "12" is the limit of the big sieve method, and this direction will not work.

In addition, there are several different directions such as the exception set, the three prime number theorem, and almost Goldbach's problem. Breakthroughs can always be achieved, but similar to the big sieve method, at the last moment, the most critical step cannot be taken.

It is also the step that finally succeeds.

Qin Ke chose a brand-new method, which is based on stochastic differential equations and introducing random factors into the deterministic model, which can simultaneously combine the deterministic model (i.e., mathematical equations) and the stochastic model (i.e., probability theory and mathematics).

Statistics), its most basic starting point is the prime number theorem, that is, "If an integer m is randomly selected, the probability that it is a prime number is 1/ln(m)."

The bridge between prime numbers and probability theory emerged, and then random factors were added. Starting from the "Goldbach conjecture graph", nonlinear dissipation was combined with graph theory, construction method, reduction method and other mathematical methods to form a unique "

"Random function chaotic structure system", and ultimately aims to prove that "the probability that every even number greater than 2 can be written as the sum of two prime numbers is 100%". Once this 100% probability is proved, it is equivalent to an equivalent proof.

Goldbach Conjecture.

This idea is extremely unconstrained, and its core is the stochastic function system and chaos system, which requires high levels of nonlinear stochastic differential equations.

From February to late May, for nearly four months, Qin Ke and Ning Qingyun spent almost all their energy on the Goldbach conjecture project on perfecting this "nonlinear structural method of lime number theory".

This mathematical treatment method was established for Goldbach's conjecture, but it can be used not only for Goldbach's conjecture.

Today, this extremely complex mathematical processing method has been announced to be 99% complete, leaving only the last 1%.

After more than half a year of repeated thinking and research, and the past two months of continuous focused study, Qin Ke's thinking was extremely clear. He glanced at Ning Qing next to him who was also concentrating on writing calculations with a frown on his face.

Jun, thinking that Xiao Baicai was under a lot of pressure, so he had to work harder. Then in the next moment, maybe because it was natural, maybe because he was high-spirited to fight, he miraculously did not need the external force of running or exercise.

function, it enters a state of "inspiration amplification".

The door to mathematics suddenly opened in front of me. There were countless documents related to Goldbach's conjecture. I had repeatedly discussed it with Ning Qingyun in the past six months. All the details of the deduction were clearly visible.

Brand-new ideas are readily available, and sparks of thinking are constantly emerging.

This is the world of inspiration, the most fascinating realm for scholars!

Qin Ke held the pen in his hand and started writing. Lines of difficult and difficult mathematical calculations flowed out and turned into gorgeous rays of light, converging on the "Qing Qing Dynasty" that had cost him and Ning Qingyun countless efforts.

"Nonlinear Structural Method of Lemon Number Theory", and finally smooth out all imperfect edges and remove all flaws.

A new and perfect "nonlinear structure method of lime number theory" clearly appeared in his mind.

Holding this newly forged sharp blade in his hand, he easily broke through the defense of Goldbach's conjecture and went straight to its core.

The pages of draft paper quickly filled up and then fell from his side.

Ning Qingyun, who was also focused on perfecting the last piece of the "Nonlinear Structural Method of Green Lemon Number Theory", breathed a sigh of relief with some reluctance, stood up and prepared to move around, adding some tea to both of them.

She didn't disturb Qin Ke, and went to the kitchen on the first floor to make tea and serve it.

While walking on the winding staircase, the girl felt a little melancholy. She wanted to share the Goldbach's conjecture with Qin Xiaoke as much as possible so that he could focus more on the Riemann conjecture. However, she wanted to perfect several mature systems.

It is really difficult to combine them into a new mathematical method that can be used for Goldbach's conjecture.

This chapter is not over yet, please click on the next page to continue reading the exciting content! She couldn't do it alone, so she had no choice but to ask Qin Ke to help. Even so, the two of them have joined forces to this day, and there are still some key points.

The point was not conquered.

Work harder!

Ning Qingyun put the brewed black tea next to Qin Ke, but Qin Ke didn't even raise his head.

Ning Qingyun was startled. No matter how serious he was, Qin Ke would habitually raise his head and smile at her, saying something like "Thank you, my wife" or "It smells so good. It is indeed the tea made by my wife, but it's different."

Her words.

But at this time, Qin Ke was just writing something quickly with a focused and empty expression, completely turning a blind eye to her action of putting down the tea.

He was focused because his entire mind was focused on the mathematical equations that were being written in front of him.

It is empty because apart from this concentration, there is "nothing else" in his eyes.

This is concentration to the extreme!

Ning Qingyun's heart skipped a beat. She was very familiar with Qin Ke, and she immediately saw that Qin Ke was in a state of burst of inspiration. It had appeared when he wrote the three papers on the Riemann Hypothesis, proving the twin prime number conjecture.

It has appeared in time, and it has also appeared in time to prove the hail conjecture!

Ning Qingyun was surprised and happy. Could it be that Qin Xiaoke had new inspiration?

She quietly put her tea cup on the bookshelf next to her, and then gently and carefully picked up the manuscript papers that fell on the ground for Qin Ke and put them away.

"Eh... this is..." When Ning Qingyun's eyes fell on a piece of manuscript paper she picked up, she immediately noticed something was different.

If the draft paper that Qin Ke dropped earlier is a real calculation draft, starting from this piece of paper, there is an incomparable rigor and solemnity.

Taking a closer look at the content, Ning Qingyun, who is extremely familiar with the nonlinear structural method of lime number theory, recognized it at a glance. Qin Ke used the nonlinear structural method of lime number theory to prove Goldbach's conjecture!

But isn’t there still a few key points that are not perfect in the nonlinear structural method of lime number theory, so it can’t be used to prove Goldbach’s conjecture?

Ning Qingyun was arranging the manuscript while reading it carefully. The more she read, the stronger the shock, admiration and even worship flashed in her eyes.

Because she discovered that all the imperfections in the nonlinear structural method of lime number theory that had hindered her and Qin Ke had been repaired, and she was working with unstoppable momentum to break through the layers of Goldbach's conjecture.

Mist!

She looked at Qin Ke's profile, eyes filled with intoxication.

This Qin Xiaoke is truly a unique mathematical genius in the world!

His talent in mathematics is unparalleled!

Suddenly, on a whim, she bit her pink lips, took out her mobile phone, and quietly took a close-up of Qin Ke's profile.

In the light and shadow, a young boy with a straight waist and a strong and handsome profile is writing something quickly with his head down and his face focused.

The photos were very beautiful and moving. Ning Qingyun put away her phone with satisfaction and then continued to look at the compiled manuscripts.

The line-by-line argumentation process that in the eyes of outsiders was extremely complex and difficult to understand, in Ning Qingyun's eyes was like a miraculous work of art, exquisite and perfect, which made her mesmerized.

I don’t know how long it took, but the sun was setting outside, and the red sunset glow illuminated the study room with the curtains drawn brightly.

But neither Qin Ke nor Ning Qingyun noticed the beautiful sunset. All their thoughts were focused on the nearly forty pages of manuscript paper.

Qin Ke's pen tip glowed with golden light under the afterglow of the setting sun, and this golden light finally outlined this line:

"Quoting the calculation in line 32 above, substituting it into it, combining Lemma 18 and Lemma 25, it is proved that the probability that every even number greater than 2 can be written as the sum of two prime numbers is 100%. This conclusion can be equivalently converted

is: Every even number greater than 2 must be written as the sum of two prime numbers."

"Goldbach's conjecture, proved."

Qin Ke slowly put down his pen, his forehead was covered with sweat from excessive mental exertion, and his face was a little pale, but his eyes showed indescribable joy and pride.

This mathematical conjecture, which ranks among the top ten most difficult in the world, finally turned into a theorem in his hands!

What countless people cannot do has become a reality in his hands!

Qin Ke turned his head and looked at Ning Qingyun, who was covering his mouth with a look of joy and excitement. He braced himself and grinned: "Jun'er, we did it. I'll leave the paper to you next... I have to

Have a good sleep."

He stood up unsteadily, and Ning Qingyun hurriedly supported him and helped him to the big bed in the master bedroom. Qin Kefu fell into a deep sleep the next second as soon as he was next to the bed.

Ning Qingyun struggled to move his legs to the bed, and like a virtuous little wife, took off his shoes and socks, found a towel and gently wiped the sweat from his face and forehead, and then

He covered him with a thin air-conditioned quilt, kissed him gently on the face, and said with both distress and pride: "Good night, have a good rest, my most powerful math prince, leave the rest to me.

"

The girl turned around and sorted out all the drafts again, then opened her laptop and began to turn the argumentation process in these drafts and the new mathematical methods reflected in them into two complete papers.

Ning Qingyun has completely understood the whole process of Qin Ke's proof of Goldbach's conjecture. Although Qin Ke did not directly write a perfect version of the "nonlinear structural method of lime number theory", Ning Qingyun already knows that "the nonlinear structure method of lime number theory" is

How did the original missing 1% of "Linear Structure Method" be filled in?

This perfect "nonlinear structural method of lime number theory" alone is enough to be written as a paper published in the four top journals.
To be continued...