Chapter 472 - 152: Proof of the Infinity of Prime Pairs with a Difference of 6_4

Words : 1474 Updated : Nov 22nd, 2025

Chapter 472 of "Top Student at Their Peak" starts the action: The third part involves the final homomorphism transformation, where through these mapping relationships, the characteristics... Find out what happens!

The third part involves the final homomorphism transformation, where through these mapping relationships, the characteristics of the geometric model are reconverted into the language of number theory...It sounds simple, but in practice, it was quite challenging for Qiao Yu, taking a full ten days to complete the first draft. In the end, Qiao Yu reduced 246 down to 6. In other words, Qiao Yu proved that there are infinitely many pairs of prime numbers with a gap of 6. The completion of proving the twin prime conjecture is not far off. Actually, Qiao Yu felt that he could further narrow the range a bit, but he thought it was unnecessary. Further narrowing the range would introduce more technical details, even reducing it to 4 would take an extra dozen pages, which would obviously make the proof lengthy. It’s just a conference paper, that’s about enough. Then he spent five more days carefully checking the paper for any issues, almost step by step. This has become an obsession for Qiao Yu. Since reviewing the draft of Senior Brother Qin from Yujiang University, Qiao Yu realized he truly couldn’t allow even a small oversight that might lead to a laughable mistake in the paper. The final paper was twenty-one pages long, with a simple title: "Proof of the Infinity of Prime Pairs with a Gap of 6". After the checking was done, Qiao Yu promptly sent it via email to Director Tian and Elder Yuan on October 25th. In any case, no mistakes could be tolerated this time. Once the paper was sent out, there was no further news. However, Qiao Yu didn’t worry about it; he had completed the paper, and whether it could be presented at the Mathematics Society was up to the mentors to decide. So he could relax for another two days. ... October 30th, Huaqing, Qiuzhai, multifunctional conference room. If someone barged in here today, they would find the conference room filled with prominent figures. A bunch of academicians were seated around the conference table. Yuan Zhengxin, Tian Yanzhen, Pan Yuedong, Li Luhe... Not just from Yanbei and Huaqing University, but also from the Hua Science Academy, the nearby Star City Nanjin University, Beijing Normal University... In fact, just the ten or so professors seated in this conference room essentially represented half of Huaxia’s mathematical community. Not only that, there were three internationally renowned Chinese mathematicians participating in this meeting via remote video: Zhang Yuantang, Zhang Shuwen, and Tao Xuanzhi. Everyone had a copy of Qiao Yu’s latest paper. The situation was indeed quite special this time, so five days ago when Qiao Yu sent his paper to Tian Yanzhen and Yuan Zhengxin, the two prominent figures met to discuss it. During which, they even made a phone call to Lott Degen. Afterwards, the two prominent figures listed the names of Huaxian and Chinese mathematicians qualified to review Qiao Yu’s paper, and began calling them one by one. After the paper was sent out, today’s meeting materialized. However, after discussing, Tian Yanzhen and Yuan Zhengxin decided not to let Qiao Yu attend this meeting today. Mainly because some things were hard to explain. For example, Qiao Yu secretly sent out two papers to Ann.Math without telling his advisor. This led to his advisor being unable to deliver a presentation at the annual mathematics conference, thus rushing out a paper at the last minute. The whole event was too sensational; its background could be included in a memoir later, but both felt it wasn’t necessary to let the peers know all the details just yet. Of course, even in Qiao Yu’s absence, many academicians on the scene found the paper hard to evaluate. After all, the paper was filled with a series of novel concepts, like the modal axiom system, which many in the mathematical community hadn’t heard of yet. However, the proof process seemed quite plausible, which felt rather peculiar. But Tao Xuanzhi’s speech resolved much of the confusion for some people. "Over the past five days, I carefully reviewed this paper and didn’t find any errors. Of course... he referenced some new theories that haven’t been publicly disclosed yet..." Saying this, Tao Xuanzhi paused for a moment, perhaps feeling unsure how to evaluate the situation, and then continued, "Coincidentally, a while ago I was invited by Ann.Math to review two papers on this modal axiom framework." From what I know, all six reviewers of these two papers gave positive feedback for publication. So, the likelihood of these papers being published in the last issue of Ann.Math this year is very high. Therefore, I personally think there’s no major problem with the reasoning process in this paper, including the modal space, path existence theorem, modal density function mapping theorem, and the related transformation process he cited." In the conference room, everyone’s expressions varied. Tian Yanzhen and Yuan Zhengxin remained composed; over time, they had come to terms with this unexpected situation. As for others, some were puzzled, some surprised... After a long silence, Academician Pan from the Academy of Sciences asked, "Hmm, although it might seem a bit presumptuous, Professor Tao, may I ask if you know who the reviewers of those two papers were, apart from yourself?" Tao Xuanzhi nodded and replied, "Besides myself, there were Professor Pierre Delini, Professor Andrew Wiles, Professor Richard Taylor, Professor Andrew Granville, and Professor Peter Schultz." Sometimes reviewers are reluctant to let it be known that they reviewed certain manuscripts. But obviously, this situation did not include such concerns. In fact, when these reviewers are willing to give feedback on a paper, it generally means they truly don’t mind letting the outside world know that they are the reviewers. As a result, the eminent figures in the conference room were once again at a loss for words. Impressively, five Fields Medalists, and the other, although not a Fields Medalist, held the only silver Fields Medal in history. If this lineup of reviewers agreed with the other two papers, any potential doubters just closed their mouths. After another long silence, Yuan Zhengxin lightly coughed and said, "Professor Zhang Yuantang, do you think there are any flaws in Qiao Yu’s paper?" This was a very courteous inquiry. After all, an initial key question regarding the twin prime conjecture was whether the minimum gap between prime numbers was finite. Remember, in 2008, a group of top number theory experts from around the world held a conference at the National Institute of Mathematical Sciences in the United States to discuss this issue. But the meeting ultimately ended in failure. And Zhang Yuantang was the first mathematician to answer this question. Even if his result was that the bounded gap between primes was seventy million... But his proof directly addressed this pivotal question. In the milestones of number theory, it could be regarded as a leap from nonexistence to existence. Later reducing it to 246 was based on the tools his paper provided. Saying he laid the foundation for the problem would not be an exaggeration. "In August this year, I went to Yanbei University to give a lecture and met Qiao Yu, who told me he intended to design a brand new axiom framework to address a series of prime number issues. At the time, I thought it was a magical idea. But even more magical was that by October, he had done it, not only constructing a new axiom framework for real. More importantly, when I tried to find unreasonable parts in the proof process, I failed... I couldn’t believe this was achieved by a sixteen-year-old. But one thing I am sure of is that a brand new path in number theory is about to open. Under modal space, we are no longer studying specific numbers but elements containing all possible states. Assigning a geometric significance to every number... I don’t even know how to evaluate this framework, but clearly, he is on the path to success. So if I were to simply evaluate this paper, I think it is correct. As I mentioned, I worked hard to find errors, but I failed. Of course, all this is predicated on the definitions given by the modal space being logically consistent. As for whether the definition of modal space is reasonable, I think Professor Tao Xuanzhi has already given the answer. My speech is over." After listening attentively to Zhang Yuantang’s evaluation, Tian Yanzhen waited a while, letting everyone have ample time to think before formally speaking. "Ahem, so... how about we just vote directly, since Qiao Yu is a joint training candidate for Yanbei and Huaqing, Elder Yuan and I will abstain. If anyone thinks this paper is suitable for a presentation at this year’s annual conference, please raise your hand." Without much hesitation, everyone in the conference room raised their hand quickly.

Chapter 472 - 152: Proof of the Infinity of Prime Pairs with a Difference of 6_4

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