Chapter 185 Challenging the Twin Prime Conjecture
Lecture Hall.
The audience was full, and there were even many people standing in the aisle. Xu Qingzhou felt that he had underestimated the appeal of Kramer'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 basic problem in number theory. The determination of this property is related to the construction of all number systems. Euclid proved that if natural numbers want to be extended, prime numbers must be extended."
Xu Qingzhou focused on the theorem proof, from how to use the Erberg sieve method 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 Kramer's theorem, we must first find out the functional adjacent iteration expression of the prime difference interval."
"This is also the key point for the success of the proof - the f(p) function, which may seem strange to everyone. Yes, this is a function I constructed myself, which can give a certain determination of the "density" of prime numbers less than p. measure."
"With this function, I successfully relaxed the upper bound to C×(logp)^α. By the way, α here is a real number greater than 1 but less than 2."
Looking at the young man talking eloquently on the stage, Academician Xu felt that his previous worries were completely unnecessary. The aura of this little guy on the stage was not inferior to that of the mathematicians who held the report meeting in front of him.
Zhao Zhenglai sighed secretly, having a junior brother who was too awesome would be too stressful.
Katherine also stared at Xu Qingzhou closely, finding this person more and more interesting. Perhaps it was because she had a strong mentality?
In addition to these, in the corner, the Indian guy had a dark face and was extremely jealous. This Xia man was a bit scary.
But he took a deep breath and looked down in front of him. Proof of the twin prime conjecture.
I believe it won’t be long before the person standing on the podium giving a report will be him, Salman Khan!
On the podium, Xu Qingzhou has already entered the state and found the feeling of giving lectures, explaining how to construct a mathematical model, and then how to use statistical theory, graph theory, etc. in physics to improve the entire proof process.
The 60 minutes passed quietly and the question-and-answer session has begun.
"Mr. Xu, in the third paragraph of page 5 of your paper, it is mentioned that 'the square of both sides can be transformed (lnpn)^2≈ (pn/n)^2, and the difference between pn and the subsequent prime number pn+1 is set to 2k', here The logic behind it doesn’t make sense.”
Regarding this problem, Xu Qingzhou was well prepared and said with a smile: "pn/n)^2 is divergent, that is to say, the larger n, the larger the corresponding prime number."
While he was explaining, he wrote down the formulas on the blackboard.
After 5 minutes, the man said thank you and sat down thoughtfully.
Someone else raised their hand and said, "Mr. Xu, during the proof process, you relaxed the upper bound to C×(logp)^α"
All the questions were within Xu Qingzhou's expectations, so he could basically answer them quickly.
The last questioner was Professor Maynard.
"Xu, I think of freefandyson's famous metaphor."
Professor Maynard had no doubts about Kramer's theorem, but said: "Mathematicians may be divided into birds and frogs. Birds can overlook the overall situation and think about macro mathematical structures, while frogs like to delve into specific details. Very capable of solving specific problems.”
"In my case, you belong to the latter group, able to find traces of mathematical truth with a keen eye."
After saying that, Professor Maynard started to applaud, and the hall immediately burst into loud applause.
Birds and Frogs
Compared with everyone's excitement, Xu Qingzhou was stunned, as if he had been hit by a bullet, and stayed there, 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 whole and cannot be like a "bird" The same overall view.
His habit is a double-edged sword for solving problems. It allows people to quickly find the key points, and it also makes people forget to look at the road ahead.
Professor Maynard's words were like a key, opening the door to his thoughts. The originally vague and hazy inspiration was clearly visible at this moment.
To put it more vividly, the feeling he had before was like his head was filled with particles moving in a disorderly manner. He could see it, but he couldn't capture its traces.
But at this time, suddenly, a "boson" condensed into a "Bose-Einstein condensate", and all the distracting thoughts were instantly aligned, pointing to the shining light of inspiration.
It's as if the entire universe of symmetry and simplicity opens up to you at that moment.
Xu Qingzhou's brain was running rapidly. Yes, he had indeed been blinded by 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) in the manuscript to obtain an asymptotic formula for the number of twin primes by "guessing" first. Xu Qingzhou squinted his eyes, picked up the chalk amidst everyone's surprised gazes, 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 report meeting has ended, so what did he write?
Everyone was very quiet, staring at the young man who wrote another series of formulas on the podium.
【π(x)~L(s，\chi)=\sum_{n=1}^{\infty}\frac{\chi(n)}{n^s】
Some young scholars have not yet reacted, "What is this?"
"This is the sieve method." Mathematicians who focus on the study of prime numbers have already figured it out and answered this person's question.
Someone else said: "Well, it's the sieve method, a mathematical tool specially used to study the distribution of prime numbers."
Professor Maynard stared at the screen with a solemn expression and said slowly: "Is he thinking about the twin prime conjecture?"
"I'm afraid so." Another mathematician nodded slightly.
"What! Challenge the twin prime conjecture?!"
As a result, everyone in the audience basically knew Xu Qingzhou's plan, and their expressions were filled with surprise.
At such large-scale mathematics seminars, there are people who advertise that they have proved a certain mathematical conjecture. Everyone is used to these wishful thinking behaviors, but the person in front of you is the prover of Kramer's theorem, and the meaning is a little different. .
2 minutes passed.
On the podium, Xu Qingzhou stopped writing and did not continue writing. The source of inspiration has been opened, and the next path is very clear, but the workload is still not small. At least it will not be finished here, and he has to go back to the hotel to think slowly.
Well, failed?
Still finding it doesn’t work?
Everyone in the audience couldn't help but feel doubtful. Even Professor Maynard was very curious. The process of proving the twin prime conjecture was very complicated, and Xu Qingzhou only wrote down a certain part.
Others can infer the twin prime number conjecture based on the sieve method, but it is still the same as reading a book from heaven.
If it fails, it must be a failure! The Indian boy shouted in his heart that the honor of proving the twin prime conjecture belongs to him!
“Hoo~”
Xu Qingzhou breathed out, looked at the quiet crowd in the audience, and said: "Gentlemen and ladies, the report meeting is over."
After saying that, he started to pack his things.
Someone asked impatiently: "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 the research materials!"
Regarding these questions, Xu Qingzhou smiled lightly and left everyone with a suspense: "The truth will appear in front of us soon."
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.
After leaving the noisy and complicated lecture hall, Xu Qingzhou slowed down again.
At this moment, he did not feel the ecstasy he imagined. On the contrary, he felt very calm. He walked slowly back to the hotel and even let his mind wander.
At the same time, some scholars walked out of the lecture hall.
"Hi~ Mr. James, big news, Xu Qingzhou from Xia Kingdom 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 is crazy. However, it seems we already have front-page news today!"
(End of chapter)