Chapter 185 Challenging the Twin Prime Conjecture Lecture hall. The seats below the stage were packed, and there were even many people standing in the aisles. Xu Qingzhou felt that he had somewhat underestimated the appeal of Cramer's Theorem. He opened the prepared PPT and briefly stated the content of his report. "Today's report will be divided into three parts: theorem explanation, theorem proof, and theorem significance." "The problem of adjacent prime numbers is a fundamental problem in number theory. The determination of this property is related to the construction of all number systems. Euclid proved that if natural numbers are to be extended, prime numbers must also be extended." Xu Qingzhou focused on the theorem proof part, from how to use the Sieve of Albergo to accurately understand the distribution of prime numbers, to how to use analytic number theory to correct and supplement the distribution of prime numbers. "In the process of studying Cramer's theorem, we first need to find the adjacent iteration expression of the function of the prime number difference spacing." "This is also the key point of the success of the proof - the f(p) function. You may find it unfamiliar. Yes, this is a function I constructed myself, which can give a certain measure of the "density" of prime numbers less than p." "Through this function, I successfully relaxed the upper bound to C×(log p)^α. By the way, α here is a real number greater than 1 but less than 2." Looking at the young man speaking eloquently on the stage, Academician Xu felt that his previous worries were completely unnecessary. The aura of this little guy on the stage was no less than that of the mathematicians who were giving lectures in front of him. Zhao Zhenglai sighed secretly. Having a junior brother who was so awesome was really too much pressure.
Catherine also stared at Xu Qingzhou closely and found him more and more interesting. Perhaps it was because she admired the strong? In addition to these, in the corner, the Indian guy had a dark face, and was extremely jealous. This Xia countryman was so strong that it was a bit scary. but He took a deep breath and looked down at the proof of the twin prime conjecture in front of him. I believe that it won’t be long before the person standing on the podium giving a report will be him, Salman Khan! At the podium, Xu Qingzhou had already gotten into the state, finding the feeling of giving lectures in the past, explaining how to construct mathematical models, and then how he thought of using statistical theory, graph theory, etc. in physics to improve the entire proof process. 60 minutes passed quietly and the question-and-answer session began. "Mr. Xu, the third paragraph on page 5 of your paper mentions 'Squaring both sides can be transformed into (lnp n)^2≈(pn /n)^2, and the difference between pn and the successor prime number p n+1 is set to 2k'. The logic here does not make sense with the following." Xu Qingzhou was well prepared for this question and said with a smile: "pn/n)^2 is divergent, that is, the larger n is, the larger the corresponding prime number is." As he explained, he wrote down the formula on the blackboard. After 5 minutes, the man said thank you and sat down thoughtfully. Another person raised his hand, "Mr. Xu, in the process of proof, you relaxed the upper bound to C×(log p)^α" All the questions were within Xu Qingzhou's expectations, so he was able to answer them quickly. The last questioner was Professor Maynard. "Well, I'm thinking of freefandyson's famous metaphor." Professor Maynard had no doubts about Cramer's theorem. Instead, he said, "Mathematicians can be divided into birds and frogs. Birds can look at the overall situation and think about macroscopic mathematical structures, while frogs like to delve into specific details and solve specific problems. They have strong practical ability." "To me, you belong to the latter, able to find traces of mathematical truth with a keen eye." After saying this, Professor Maynard began to applaud, and loud applause broke out in the hall. Birds and frogs Compared to everyone's excitement, Xu Qingzhou was stunned, as if he was hit by a bullet. He stood there in a daze, lost in thought. Yes, he pays great attention to details. For example, every time he encounters a problem, he likes to go over all the details so that he can always find new ideas. But this also means that he will subconsciously ignore the overall picture and cannot overlook the overall situation like a "bird". His habit is a double-edged sword when it comes to problem solving. It can help people find the key points quickly, but it can also make people forget to look at the road ahead. Professor Maynard's words were like a key that opened the door to my thoughts. The originally vague and hazy inspiration became clear at this moment. To put it more vividly, the feeling before was that his head was filled with disorderly moving particles. He could see it but could not capture any trace of it.
But at this moment, suddenly, a "boson" condensed into a "Bose-Einstein condensate", and all the distracting thoughts instantly became unified, pointing to the shining light of inspiration. It’s as if the entire symmetry and simplicity of the universe opens up to you at that moment. Xu Qingzhou's brain was working rapidly. Yes, he had indeed been blinded by the details before, and had been struggling to find an accurate formula. But it doesn't have to be this way. Why couldn't he combine M, and the steps (10), (14) and (15) on the manuscript paper to get an asymptotic formula for the number of twin primes by "guessing". Xu Qingzhou narrowed his eyes, picked up the chalk in the surprised eyes of everyone, turned around and started writing on the blackboard behind him. Huh? Everyone was stunned for a moment and looked at the blackboard in confusion. Xu Qingzhou’s lecture has already ended, so what did he write? Everyone was very quiet, staring at the young man on the podium who was writing out another string of formulas. [π(x)~L(s,\chi)=\sum_{n=1}^{\infty}\frac{\chi(n)}{n^s] Some young scholars haven’t reacted yet, “What is this?” "This is the sieve method." A mathematician who focuses on prime number research has already seen it and answered the man's question. Someone else said: "Well, it's the sieve method, a mathematical tool specifically used to study the distribution patterns of prime numbers." Professor Maynard stared at the screen with a serious expression, and said slowly: "Is he thinking about the twin prime conjecture?" "I'm afraid so." Another mathematician nodded slightly. "What! Challenging the Twin Prime Conjecture?!" As a result, almost everyone in the audience knew Xu Qingzhou's plan, and their expressions were filled with surprise and doubt. At these large-scale mathematics conferences, there are always people claiming that they have proved a certain mathematical conjecture. Everyone is used to these wishful thinking behaviors, but the person in front of us is the prover of Cramer's theorem, so the meaning is a little different. 2 minutes passed. On the podium, Xu Qingzhou stopped writing and did not continue. The source of inspiration had been opened, and the way forward was very clear. However, the workload was still heavy, at least it could not be finished here, and he had to go back to the hotel to think slowly. Um, failed? Or find that it doesn’t work? Everyone in the audience couldn't help but feel confused. Even Professor Maynard was curious. The process of proving the twin prime conjecture was very complicated, and Xu Qingzhou only wrote out a part of it. Others can use the sieve method to infer things related to the twin prime conjecture, but it is still like reading a book in heaven. Failed, definitely failed! The Indian guy shouted in his heart, the honor of proving the twin prime conjecture belongs to him! "Whoo~" Xu Qingzhou exhaled, looked at the silent crowd below the stage, and said, "Ladies and gentlemen, the lecture is over." After saying that, he began to pack up. Someone couldn't wait to ask: "Mr. Xu, do you want to challenge the twin prime conjecture?" "Do you have any ideas, Mr. Xu? I have been studying the twin prime conjecture for more than ten years. If you are willing, I have given you all my research materials!" In response to these questions, Xu Qingzhou smiled faintly and left everyone with a suspense: "The truth will soon appear before us." After saying hello to Professor Maynard and Academician Xu, Xu Qingzhou quickly walked out of the lecture hall and prepared to return to the hotel for retreat. Leaving the noisy and busy lecture hall, Xu Qingzhou slowed down again.
At this moment, he did not feel the ecstasy he had imagined. On the contrary, he felt very calm. He walked slowly back to the hotel and even cleared his mind. At the same time, some scholars walked out of the lecture hall. "Hi~ Mr. James, big news, Xu Qingzhou from Xia Country announced that he is about to prove the twin prime conjecture!" "Mr. Tucker, are you crazy?" "No, he's crazy!" "Mr. Tucker, calm down. I don't care who's crazy. But it looks like we already have a front-page news story today!" (End of this chapter)