I really just want to be a scholar

Chapter 421 Gilbreth Conjecture

There was another commotion in the room. Academician Wang Lao came up with a question in person, and the one who paid attention was the winner of this year's Chern Mathematics Award!
This kind of situation is rare, and everyone's interest is greatly increased. Those scholars and professors who thought they have the ability to compete for the Chern Mathematics Prize are even more eager to move.

What if the two young awardees on the stage failed to solve the problem proposed by Academician Wang, but I did it... Although it will not overthrow the award result, it will undoubtedly make me famous In a wave, the chances of winning the Shiing-shen Chern Mathematics Award in the next competition will undoubtedly increase greatly!
Only Academician Wang said to Hao Jianchang next to him: "This question-and-answer session will be extended for one hour until 12:[-] noon, is that okay? President Hao."

Hao Jianchang hurriedly said: "Of course there is no problem. Qin Ke and Ning Qingyun's academic report will be the last one in the morning. It was originally scheduled to end at 11:30. Now there is nothing wrong with extending it by an hour, right, Qin Ke ?”

Qin Ke was a little stunned, an hour extension?This Academician Wang won't plan to come up with any problems to trick us, will he?

In fact, he didn't know any of these three bosses, except Mr. Qiu's photo can often be seen on the school website, he recognized it, but today was the first time they met.

When Old Professor Zhou mentioned Zhou's conjecture before, Qin Ke could also guess his identity.

As for Academician Wang...Qin Ke really doesn't know who it is. After all, there are too many bigwigs in mathematics in Xiaguo. Qin Ke can only be regarded as a "newcomer", and he has been in school all the time. How can he know many bigwigs?However, seeing Professor Tian Jianlan sitting beside him, he must be the top leader in the field of number theory.

He glanced at Old Mr. Qiu and Director Wei Yuanfu next to Academician Wang, and saw that they were all smiling, so he said with a smile: "Of course, if I have the opportunity to listen to your teachings, Mr. Wang, a few more hours will be fine." worth it."

Academician Wang couldn't help laughing, shook his head and said, "You kid, you are really as slick as the rumors. Come on, don't scold me for being scheming if you get stumped by my question later."

After he finished speaking, he looked around at everyone: "Because the time will be extended, if anyone has other arrangements, you can leave first."

No one moved. Everyone was very curious about what question Old Academician Wang was going to ask, and they actually reserved an hour for answering?

Moreover, Academician Wang has "retired" for many years and rarely shows up in public. No one knows if he has researched any new theories in the past few years. Who would miss such a rare opportunity?

Academician Wang took out a piece of paper, and Hao Jianchang next to him took it, handed it to the staff, and asked the staff to project it.

Soon the first question appeared on the big screen.

This topic looks very simple at the beginning, it is a few lines of numbers:
"2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31..."

"1, 2, 2, 4, 2, 4, 2, 4, 6, 2..."

"1, 0, 2, 2, 2, 2, 2, 2, 4..."

"1, 2, 0, 0, 0, 0, 0, 2..."

"1,..."

"Define d0(n) as the nth prime number, dk + 1(n) = |dk(n) dk(n + 1)|, where k is a non-negative integer and n is a positive integer. Prove: For all positive integers j , dj (1)≡1."

Everyone stared at this topic dumbfounded, feeling a little familiar but couldn't remember what it was for a while.

However, those present were basically the outstanding figures in Xia Kingdom's mathematics field, and soon someone recognized them, and said in a voiceless voice, "Gilbreth's conjecture?"

Everyone gasped in unison.

Any mathematics professor with more than 20 or [-] years of experience, even if they are not in the field of number theory, will have heard of this Gilbreth conjecture more or less.

If all the prime numbers are written out, and then the difference between adjacent prime numbers is calculated to obtain a new sequence, if the person repeats this action infinitely, except for the prime number sequence in the first row, the first numbers of all other sequence are it's 1.

This is Gilbreth's conjecture, written in mathematical expressions, which is the last line of calculation in the title.

This is a prime number conjecture in stacking. It is not well-known, and it is even inferior to Brocar's conjecture and Jebov's conjecture.

This is not difficult to understand. Although it describes the interval between adjacent prime numbers and belongs to one of the external forms shown by the distribution of prime numbers, even if it is proved that the first number of the sequence is 1, it does not involve the core of the distribution of prime numbers. The law is much less important than Zhou's conjecture, let alone the twin prime conjecture.

This makes its research significance not great, and there are ninety if not one hundred similar conjectures, so there are not many mathematicians who are really willing to invest time and energy to prove it.

But no matter what, it is still a world-class problem that has been over the mathematics world for 60 years. So far, no one has successfully cracked it and proved it.

Could it be that Academician Wang wants Qin Ke and Ning Qingyun here to prove Gilbreth's conjecture on the spot?

Impossible, absolutely impossible, how can this be considered a world-class difficult conjecture, how can it be overcome without spending a few years?Even if you are a genius, it will take a month or two, right?

Unless academician Wang Lao communicated in advance, let these two young people think about it for a year or so in advance.

But this is even more impossible. Academician Wang has always been upright and never cheated. Even if Qin Ke and Ning Qingyun are his grandchildren, it is absolutely impossible for him to do such a thing against his heart. .

And seeing the surprised expressions of the two young people on the stage, they probably didn't know it.

Ning Qingyun even asked Qin Ke in a low voice: "Qin Xiaoke, what is Gilbreth's guess—ah!" The last "ah" was when he realized that his voice had come out, and he blushed quickly and stopped it .

The two of them stood on the stage with the microphone on all the time. Although Ning Qingyun lowered his voice, he still uttered it through the loudspeaker.

Everyone was startled, then laughed and shook their heads.

Ning Qingyun's reaction, which was so real that it couldn't be more real, could never be a fake.

But it's strange, isn't this old academician Wang here to support the young couple?But Ning Qingyun has never even heard of this conjecture!Did the car overturn on the spot?
Those teachers and friends who cared about Qin Ke and Ning Qingyun, such as Professor Tian, ​​Coach Deng Hongguo, and Chairman Hao Jianchang, all straightened up nervously, secretly worried for the two children.

Under countless odd gazes, Qin Ke quickly regained his composure, and briefly introduced Gilbreth's conjecture to Ning Qingyun.

It was also thanks to his knowledge of most of the world's famous number theory conjectures in order to choose a suitable "offensive target", so he knew this Gilbreth conjecture.

Just when everyone in the audience was whispering and discussing, Academician Wang spoke again, and he said with a smile:

"Qin Ke, I heard that when you were at Princeton University, you went to the bar and solved two prime number propositions in half an hour. Of course, now that time is limited, you may not immediately have inspiration, but you can think of it within an hour. Even if I pass my first test, what do you think about the way of proof that convinces me? Of course, everyone here who is interested can also think about it together.”

Having an idea for an hour is already remarkable.

Everyone present asked themselves for an hour to figure out their ideas, but they were really not sure that they could do it, so they all nodded in agreement.

Only Academician Wang said again: "Okay, let's start."

The audience quickly fell silent, and those ambitious mathematicians immediately took out pens and paper, eager to challenge this world-class problem.

Not to mention whether it can be proved in the end, as long as Qin Ke and Ning Qingyun have a more feasible proof idea one step ahead of Qin Ke and Ning Qingyun, and get the approval of Dean Wang, then he can show his face once.

Qin Ke was also thinking about the topic on the projection screen, but unlike most people who frowned and pondered, he quickly found a way to prove it.

This Gilbreth conjecture is extremely difficult in the eyes of others, but it is indeed not that difficult in Qin Ke's eyes. At least it is inferior to Zhou's conjecture. It is a number theory game, and it is really broken. In essence, it has a certain internal connection with Brocar's conjecture and Jebov's conjecture.

With the basis of proving the last two conjectures with the "fourth-order transformation method of lime number theory" as a foundation, it is much easier to figure out the proof idea and even prove the Gilbreth conjecture. Qin Ke asked himself that it would not take much Three 10 minutes.

Even if Ning Qingyun was to prove it alone, it would probably take about two hours.

He couldn't help raising his head, and seeing the three old gentlemen looking at him with a smile, he suddenly understood.

These three old gentlemen must have carefully studied the video of their previous academic reports at Pudong University, and even thought of how to use the "lime number theory fourth-order transformation method" to prove the Gilbreth conjecture, but they valued their identities and did not want to Take the academic achievements of the two juniors to claim this honor, and then throw it out in this "question and answer" session, let the two juniors prove it in front of everyone, so as to completely stop everyone's criticizing mouths.

At the same time, they are also worried that they will be self-defeating. If the two juniors are nervous on the stage and fail to prove it within an hour, they will easily fail to get off the stage. That's why they have the so-called guarantee requirement of "passing the proof idea within an hour". Come.

Wanting to understand this, Qin Ke couldn't help but lament that these three old gentlemen really worked hard.

He looked at Ning Qingyun, smiled and asked softly: "How, Yun'er, do you have any ideas?"

Ning Qingjun glanced at the microphone, leaned closer to his ear, and said in a voice that only the two of them could hear: "I think it should be possible to prove it with the 'lime number theory fourth-order transformation method', so I will use similar proofs for Brocar guesswork."

The girl exhaled like blue, and the familiar lime-like body fragrance made Qin Ke's heart itch. He smiled and gave a thumbs up: "That's right. Let's work together to prove it. I will leave the transformation of the first two levels to you. I will be responsible for the transformation of the third and fourth stages later on, and all the assumed naming rules follow our usual rules, no problem?"

It is not the first time that the two have collaborated to write a thesis, and they study together every day. In terms of tacit understanding, there is no third person in the world.

Ning Qingyun nodded to indicate that there is no problem.

"The difficulty of this question is too low. I will give you another request to increase the difficulty. Your first second-order transformation is relatively simpler and needs to be completed within 20 minutes. Are you confident that you can do it?"

Ning Qingyun clenched her small fists: "I will do my best!"

"Don't worry, you can do it. Come on, let those who are not convinced see our level!"

　Thanks to "Hunter who doesn't like to climb trees" and "Book Friends 20201125200250231" for their rewards!

　　
　
(End of this chapter)