Chapter 128 From 4200 million to 246
Tang Shihong carefully closed the office door and leaned his back against the wall to digest the information he had just received.

At this moment, my mood seems a little complicated.

He is very clear about the impact of the twin prime conjecture in the mathematical community. If Xu Yuan can really reduce the value based on Lao Zhang's work, it will be equivalent to promoting the progress of twin prime research.

One step closer to winning the crown.

This, together with the previous solution to the Carmichael number problem and the proof of the smoothness of the solution to the Monge-Ampere equation.

Even if he cannot solve the Qiu Chengtong conjecture, it will not affect his reputation in the mathematics community at all.

Although his student's academic achievement was about to surpass that of his mentor, he felt only happiness and pride.

As parents, we all hope our children will become successful. As a teacher, so does he.

Just as he was thinking about all this, expecting Xu Yuan to be able to get one step closer to proving the twin prime conjecture, he suddenly noticed from the corner of his eye that the department head, Liao Fangyi, was walking briskly towards him.

"Old Tang, what are you doing standing outside the door?"

Liao Fangyi stopped at the door with a curious look on his face: "I have something to talk to you about. Let's go in and talk first."

He asked casually and was about to push the door.

However, his hand remained suspended in mid-air while his body was stopped.

"Let's talk about it somewhere else."

Tang Shihong smiled and grabbed Liao Fangyi, then walked towards the window at the end of the corridor.

It was the first time that Liao Fangyi saw Tang Shihong so worried about someone entering his office.

I can't help feeling a little curious.

He immediately stopped and asked with a smile on his face: "Tang, tell me who is in your office?"

"Don't do anything that is immoral. Be aware of the impact." After saying this, he suddenly thought of something and gave a special warning with a stern face.

It was obviously a misunderstanding.

Tang Shihong's face darkened when he heard that, and he immediately retorted in annoyance.

"What are you thinking about? Am I that kind of person?"

Faced with this situation, Tang Shihong couldn't hide anything. Otherwise, if he talked a few more words, his innocence would be exposed. He didn't want his family to hear and come to the school.

So as soon as he finished speaking, he organized his words to explain.

"Xu Yuan and Lao Zhang were in there proving twin prime numbers. I came out because I was afraid of affecting them."

"Which Lao Zhang?" Liao Fangyi asked subconsciously.

Tang Shihong: "You also know..."

"We previously held a number theory conference with Yenching University, and the other party was invited by Academician Ma."

“Currently working as a professor of mathematics at an overseas university.”

After listening to Tang Shihong's words, Liao Fangyi realized the real point of the words a second later, and his whole face became extremely excited almost instantly.

"What did you say?"

"Are they proving twin primes?"

"Yes."

Tang Shihong nodded and said affirmatively: "If nothing unexpected happens, the research on the twin prime conjecture will take a big step forward."

"Isn't Xu Yuan studying Qiu Chengtong's conjecture recently?" Liao Fangyi felt a little puzzled.

"We should be able to find out the situation when they come out." Tang Shihong sighed as he looked at the closed office door: "I don't know how long it will take."

He knew Xu Yuan's character very well and knew that he would never give up easily when faced with problems in mathematical academic research.

So it’s hard to say how long this demonstration will last.

After all, the twin prime conjecture has been proposed for a hundred years, and the fact that no mathematician has solved it so far speaks volumes.

It is not easy for Zhang Yitang to prove the positive number of the twin prime conjecture to 4200 million.

Inspiration, luck and strength are all indispensable.

In this case, the difficulty of the proof increases as the value decreases.

But inspiration is the most important thing for mathematicians, because this kind of inspiration does not always exist, and most of the time it is fleeting, so whenever inspiration is born, it must be firmly grasped.

If you are interrupted in the middle of your work, you might never get the inspiration back.

It is precisely because of this situation that unless Xu Yuan and Zhang Yitang take the initiative to open the door and come out.

Otherwise, no one would dare to go in rashly.

If the proof really fails because of interrupted thinking, it will be a huge loss to the entire mathematics community.

This is not a responsibility I can take.

But Tang Shihong and Liao Fangyi wanted to know the result first and were afraid of being disturbed by others, so they had to stand outside the office and even had someone move two chairs from the office next door.

However, this also attracted the attention of other people, and they came over to ask about the situation.

So much so that almost all the professors and lecturers in the entire mathematics department who had no classes gathered there.

Everyone wants to witness the birth of this major event in the mathematical world.

Among them, a professor who mainly studies number theory was extremely excited when he learned that there had been substantial progress in the twin prime conjecture.

This is a great event for the field of number theory.

After all, the twin prime conjecture and the Goldbach conjecture are both known as the ultimate problems in the field of number theory. Their influence and importance are not comparable to the problem of infinite Carmichael number intervals proved by Xu Yuan.

As everyone was looking forward to it, time passed by minute by minute.

First the sun sets in the west and darkness covers the earth, then the bright moon hangs high in the sky and the night deepens.

At this time of day, they would have basically gone home to rest, but now the lights are still brightly on.

There were more than a dozen people gathered in the corridor, pacing back and forth, waiting patiently.

Even at night, he asked his students to deliver meals to him, fearing that he would miss any news related to the twin prime conjecture. However, seeing that there was still no movement in the office, Tang Shihong and Liao Fangyi began to worry.

Xu Yuan is young and strong and it is okay for him to not eat for a long time, but Zhang Yitang is old after all, and mental exertion is also very energy-consuming.

If someone accidentally faints.

That's not good.

"Still no movement, why don't I go in and take a look."

Tang Shihong looked at the watch on his wrist and couldn't help but say something to Liao Fangyi who was standing next to him.

Liao Fangyi was also quite conflicted upon hearing this.

After holding it in for a long time, he uttered a few words: "Why don't we wait a little longer?"

The other professors around also started talking in low voices, thinking that Xu Yuan was being a bit too aggressive in wanting to reduce the positive value.

"It is probably very difficult to find a positive number less than 4200 million that satisfies the twin prime conjecture. How can we prove a smaller number in such a short time?"

"Xu Yuan does have his own understanding of number theory, and the sieve method he improved is very ingenious, but the time is still too short at the moment."

"Why don't we just let them out? Health is the most important thing."

"Positive numbers less than 4200 million have already caused a sensation in the academic community, and smaller values ​​can be studied slowly in the future."

……

While everyone outside was discussing whether to go in and call for help, Xu Yuan and Lao Zhang in the office were excited.

For several hours, neither of them had even a sip of water.

There were a lot of draft papers filled with formulas scattered on the table in front of him.

But if we really talk about the condition of the two people, it is Lao Zhang who looks better.

You have to know that Xu Yuan has been in a deep learning state for a long time, which consumes a lot of physical energy. It can be said that he was so hungry that he had to stay awake.

On the other hand, because of his age advantage, Mr. Zhang has much less metabolic problems than young people.

Eating a few hours later has no effect.

But Xu Yuan still had no intention of stopping.

On the contrary, his hands moved faster and faster, and he wrote mathematical symbols on the draft paper.

Even with Zhang Yitang's help in the calculations, my hands felt so sore.

At the beginning, Xu Yuan did not have any clear ideas, but combined with Lao Zhang's proof method and process, his mind was working rapidly in the state of deep learning, which led to constant collision of inspiration.

It didn't take long for the number to reach 1300 million.

Under normal circumstances, Xu Yuan's ability to shorten the distance from 4200 million to 2 to 1300 million to 2 so quickly is enough to be called a miracle in the field of number theory.

You can take this result and publish this academic paper together with Zhang Yitang.

But he felt that the positive number of 1300 million was not the limit, at least not his current limit.

So I chose to continue proving it.

When Lao Zhang saw that Xu Yuan had really reduced the number by 2900 million, he was very excited and naturally supported Xu Yuan to continue proving it.

Although smaller numbers are more difficult to prove, even a slight reduction is progress in number theory.

With more and more confidence, Xu Yuan further improved and optimized Lao Zhang's screening method.

After specific application, the value obtained will become smaller as time goes by.

500 million

40 million

……

"We made it!"

I don’t know what time it was, but after Xu Yuan wrote the last mathematical symbol on the draft paper, his face suddenly became excited and happy, and he couldn’t help shouting out loud.

Upon hearing the sound, Old Zhang, who had just laid down on the sofa, did not have time to rest. He sat up abruptly and put on his glasses to look at the draft paper.

Immediately, a result announcement jumped into my eyes, causing my pupils to tremble.

"Iim inf(pn+1-pn)<246"

"246?!"

Lao Zhang subconsciously shouted out these three numbers, even raising his voice a lot with disbelief.

He never imagined that he had only just made a start in the research on twin prime numbers, but Xu Yuan directly increased the positive value from 4200 million to 246.

"It can only go this far."

"There are infinitely many pairs of twin primes whose difference is less than 246."

Xu Yuan didn't care about Lao Zhang's expression at the moment. He slowly exhaled and spoke to himself with some regret.

From 246 to 2 seems to be very close, but the road to continue proving it is becoming more and more difficult.

There is no way of knowing when the crown will be won.

But at least he is trying his best now.

After hearing this, Lao Zhang paused for a few seconds before coming back to his senses. He looked at Xu Yuan with complicated eyes and said from the bottom of his heart: "If other scholars in the field of number theory heard what you just said, I'm afraid no one would dare to study twin prime numbers from now on."

Xu Yuan smiled, showing his neat teeth, stood up, said something and walked towards the office door.

"That's not something I'm considering. Nothing is more important than having a full stomach right now."

And when Xu Yuan opened the office door from the inside, suddenly more than a dozen heads came into his sight, and the eyes they looked at him were full of hot and excited.

……

(End of this chapter)