The top student must be diligent.

Chapter 99: Parity Sieve and Twin Prime Conjecture

Hearing the voice in his mind, Xiao Yi felt it was somewhat pleasant for a moment.

“It’s upgraded!”

The joy of having just proved the twin prime conjecture and the joy of having his Wuqing Lianxue buff upgraded made him feel comfortable.
Moreover, as the buff was upgraded, the bonus increased directly from 14 times to 17 times. He immediately felt that he had made further progress in his understanding of all the knowledge he had learned in the past.

Even for the proof of the twin prime conjecture that he had just completed, he felt that he could optimize some of the steps in it to be more streamlined.

"However, the proof of the twin prime conjecture is only of medium value?"

Recalling the mysterious voice's comment on the twin prime conjecture, Xiao Yi had the expression of an old man on the subway looking at his phone.

After proving the Elliott-Halberstam conjecture, he thought he would be able to upgrade again, but unexpectedly, the voice did not sound.

The result is now...

The worst happened.

No, buddy, if the twin prime conjecture is only considered of medium value, then what are the problems of high value?
Riemann Hypothesis?

Hodge's conjecture?

Or...the proof of the P=NP problem?
At least according to Xiao Yi's understanding, these questions are indeed much more valuable than the twin prime conjecture.

Sighed helplessly.
In this case, God knows how long it will take to upgrade the buff to the next level.

The only hope is that there are other optional upgrade conditions.

"Forget it, don't think about it. At least there is another good news after this upgrade."

[Within 24 hours, if the utilization rate of Ruthless Link is less than 50%, the BUFF will disappear.]

Xiao Yi noticed that after the buff of Wuqing Lianxue was upgraded to level 4, the daily utilization requirement became lower.

It has been reduced from 60% to 50%, which means that he had to study for 14.4 hours a day before, but now he only needs to study for 12 hours.

Well, to some extent, it allows him to have more time to relax every day.

At least……

Can he play a few games with his friends?

"Well... just relax a little today!"

As for the thesis and other things, I will sort them out tomorrow!

After studying the problem for so long, can't you just enjoy yourself?
He stood up from his seat and stretched hard.

Having said that, although he spent all his time studying every day and had almost no time for exercise, he found that his health was still quite good. As long as he got enough sleep, he never had any discomfort.
Maybe it is also related to the buff learned by Wuqing Lian?

Just at this moment, the dormitory door was opened, and Ye Cheng and three others walked in, talking and laughing.

Probably just finished class.

However, after coming in, they were stunned when they saw Xiao Yi in the dormitory.

"Oh my god, Brother Xiao, you didn't go to the library today?"

For the past two months, Xiao Yi's daily routine has been between the dormitory, library and cafeteria, with no change. They almost never see him during the day.

So they never expected to see Xiao Yi during the day.

Xiao Yi nodded and said, "Yes, I solved the math problem I've been studying today, so I didn't go."

“Done…done?”

The three people were shocked and gathered around him, saying excitedly: "Twin prime conjecture... have you proved it?"

"Yes……"

Xiao Yi nodded, but he suddenly reacted the next moment.

Hey, he never said that he was studying the twin prime conjecture?

"How do you know that I'm studying the twin prime conjecture?"

"Brother Xiao, don't you know?" Ye Cheng asked back, "Last month, the video of you using three methods to solve problems in Professor Liu's math analysis class was filmed by Qin Le from our class, and then he posted it on Bilibili, and it became popular. Then..."

Listening to Ye Cheng's story, Xiao Yi was surprised. He simply wrote down his ideas about the sieve method on the blackboard, but others guessed that he wanted to study the twin prime conjecture?
Even now the entire mathematics community knows about it and is paying close attention to it?
Do you want to be so exaggerated?
Well, it is actually quite reasonable and can indeed be connected. After all, the Elliott-Halberstam conjecture he studied before is closely related to the twin prime conjecture.

At this time, Ye Cheng said, "Oh, by the way, there is one more thing. I saw in the news a few days ago that your previous paper on the automorphism theory of Etale algebraic varieties and the proof of the Elliott-Halberstam conjecture have passed the review of the Annals of Mathematics. You are not unaware of this, are you?"

Xiao Yi slapped his head for a moment. During the past two months of research on the twin prime conjecture, he almost forgot that his last two papers were still under review.

But fortunately, it just happened a few days ago, so it’s not too late.

He immediately returned to his seat, turned on his computer and accessed his email.

As soon as he entered his mailbox, he saw that he had more than 100 unread emails.

"I remember that I had processed all the emails that discussed the automorphic theory of Etale algebraic varieties with me before?"

He was overwhelmed. When he clicked on the page, he immediately scratched his hair in madness.

"What the hell..."

In addition to the more than 100 new emails from those who also wanted to discuss the self-protection theory of Etale algebraic varieties with him, there are now many more emails from mathematicians who probably watched his video and want to discuss the classification of parity problems with him.

The vast majority of them were sent last month. There are relatively fewer this month, but there are still some, like one yesterday.

If I were to reply to these emails one by one, I don’t know how long it would take.

not to mention……

He has already solved the classification of parity problems, and has also proved the twin prime conjecture.

There is no need to send these emails to discuss this with him.

He pinched his eyebrows.

It seems that his original plan to have a good rest today will be dashed. He has to organize the paper as soon as possible as a response to these emails.

Otherwise, someone might send him another email in a while.

Just as he was thinking this, he saw a notification pop up on his mailbox, indicating that a new email had been received.

I saw it was indeed the email from a mathematics professor at Trinity College, Cambridge University. I shook my head helplessly and ignored it for now.

First, find out if there is any email from the "Annals of Mathematics". Since the two papers have passed the review, he also needs to sign a "Copyright Transfer Agreement" with them so that the papers can be published.

After checking his mailbox, he saw a notification email sent by the Annals of Mathematics four days ago, informing him of the final review results of his two papers.

First there is a big [Accepted], and then below it are comments on his two papers.

As the chief reviewer of the review committee, Enrico Bombieri gave the following evaluation: [Rigorous, innovative, high-value, and major breakthroughs, there is no doubt that these two papers are a gift from a mathematical genius to the entire mathematical community. ]

The other three reviewers also gave similar evaluations.

Tao also added a joke: "I think many people in the mathematics community will have trouble sleeping."

Looking at these comments, Xiao Yi couldn't help but smile. Then he clicked on the copyright transfer agreement link below, signed the electronic agreement, and finally replied to the email with a thank you letter.

The three roommates who had been watching him busying around couldn't help but feel envious.

This is probably what it means, that there are great scholars among whom one talks and laughs, and there is no unlearned common man among them, right?
After doing all this, Xiao Yi began to prepare to organize his paper on the twin prime conjecture and his optimized sieve method.

This is a huge project. He estimated that he would have to organize sixty or seventy pages. He probably used hundreds of sheets of draft paper in the past two months.

Without further ado, I entered LaTex skillfully and started editing the document.

Ye Cheng and the others watched Xiao Yi continuously editing some words and mathematical formulas in the document that seemed like hieroglyphics to them, and they roughly guessed that this was the proof of the twin prime conjecture.

Of course, the title of the paper makes this clear.

Parity Sorting Sieve and the Twin Prime Conjecture

The simple title is completely extraordinary in the world of mathematics.

The three people watched helplessly as a paper that might... should be "definitely" able to go down in the history of mathematics was born.

No one knew what they were thinking, but after a while, Ye Cheng returned to his seat, took out his book and started studying.

A few days passed leisurely.

……

A professor's office in the Department of Mathematics at the University of California, Santa Barbara.

The owner of this office is Zhang Yitang.

The world of mathematics is a rather pure world, or rather, a world where the strong are truly respected.

As long as you have the ability and have made real achievements, you can get everything, no matter how down and out or poor you have been.

And Zhang Yitang is obviously a good example.

Before officially publishing the paper "Bounded Gaps between Prime Numbers" in 2013, he was just an ordinary lecturer at the University of New Hampshire, which is a non-first-class university in the United States and it is not an exaggeration to describe it as a fake university.

Ordinary, just like everyone else.

After that, he went directly to the University of Santa Barbara and became a professor of mathematics. He had his own office. In less than two years, he won four mathematics awards and became a respected master of analytic number theory.

Perhaps the only regret for him was that he was nearly 60 years old when he became famous, so he once said that his favorite poem was: Yu Xin’s life was the most desolate, and his poems in his old age moved the Jiangguan Pass.

Of course, after achieving such outstanding results, he did not devote his energy to enjoyment, but still devoted himself to using his twilight years to solve more mathematical problems, such as the Landau-Siegel zero point conjecture he is currently studying.

The Landau-Siegel zero-point conjecture may not be so famous outside the mathematical community, but for people in the mathematical community, the answer to this question can help them find half of the truth about the Riemann hypothesis.

The purpose is to prove whether the Landau-Siegel zero exists. If it exists, it would be equivalent to finding a counterexample to the Riemann hypothesis, which would directly prove that the Riemann hypothesis is wrong.

Of course, in the mathematical community, it is generally believed that the Landau-Siegel zero does not exist. After all, the mathematical community also generally believes that the Riemann hypothesis must be true.

Standing in front of the blackboard, Zhang Yitang pinched his chin, his eyes behind the black-framed glasses filled with thought.

"The existence range of the real number sequence depends on Cantor's real number continuum hypothesis, but the hypothesis is not a proof. Unfortunately, Gödel had already stated that the continuum hypothesis is unprovable..."

"It's difficult."

Shake his head.

As he gets older, he can no longer find the feeling he had when he broke through the twin prime conjecture.

"If we want to achieve a breakthrough, we may still have to rely on the screening method. How can we push the screening method to a more extreme level?"

As he thought about this, a name flashed through his mind.

Xiao Yi.

He had also watched Xiao Yi's video, but unfortunately, like most people in the mathematics community, even though he saw how Xiao Yi took the first step, he couldn't figure out how to take the second step.

“I don’t know if he got a reply to the email I sent him.”

At this point he returned to his desk, opened his mailbox on the computer and took a look, but there was no email from Xiao Yi.

"I heard that other people haven't received his reply either. I guess they are still studying the twin prime conjecture."

"Forget it, let's go to arxiv to see if there are any papers on this topic."

Thinking of this, he opened arxiv and started browsing.

But after searching just now, he saw a title.

"Parity Sieve and Twin Prime Conjecture", author, YiXiao.

His eyes suddenly widened.

What's this?
He took off his glasses and rubbed his tired eyes, then put them back on and looked refreshed.

"Did Xiao Yi...complete the proof of the twin prime conjecture?"

He immediately clicked on the paper and downloaded the PDF file.

Then he looked at the summary.

【It is proved that lim(n→∞)inf(pn+1pn)=2, where pn is the nth prime number.

The method used in this paper is an improvement on the work of Zhang Yitang, Tao Zhexuan, and J. Maynard on sieve theory. A major component of the proof is a stronger version of the Friedlander-Ivaniec theorem, and a relatively accurate classification of different categories in the parity check problem is completed, so as to achieve an accurate estimate of the number of prime factors of infinite natural numbers. Although the final result is less than 3, it is sufficient to meet the purpose of proving the twin prime conjecture. 】

……

(End of this chapter)