In the next few days at Princeton University, Qin Ke was even busier than when he was in China.

During the day, he insisted on attending the entire lecture. On the one hand, he could earn some academic points, and on the other hand, he could learn the latest academic achievements in the international mathematics community and improve his own mathematical theory system.

After the report meeting, Qin Ke didn't even attend the dinner. He returned to the hotel without stopping, took a few bites of the food prepared by the hotel, and then immersed himself in studying some prime number problems.

Ning Qingyun's idea of ​​proving Zhou's conjecture did give Qin Ke endless room for imagination. He suddenly discovered that the "geometric number theory matching approximation method" was better than the "function transformation hypergeometric system" and the "group theory functional equation method".

It's simpler, but it does have more flexibility and creativity in dealing with some less difficult prime number problems.

It is like a multifunctional saber. As long as you repeatedly transform between the four mathematical methods of geometry, algebra, approximation, and matching, you can combine different uses.

Qin Ke handed over the proof of Zhou's conjecture to Ning Qingyun, while he sharpened his skills and set his sights on other prime number conjectures that were similar to or lower in difficulty than Zhou's conjecture.

Of course, the so-called "lower" is only relative. Prime numbers are originally a difficult sub-subject in mathematics, and the conjectures related to them are basically world-wide problems.

However, there are countless conjectures about prime numbers. Qin Ke must select targets to start with. The reason why many prime number conjectures have not been proven is because they are not meaningful and difficult. Who would waste time on them?

prove?

Naturally, Qin Ke was not interested in caring about those poorly-known prime number conjectures.

He first noticed two propositions: "Whether there are infinitely many Mersenne primes" and "whether there are infinitely many Fibonacci numbers".

The two propositions are not conjectures, because no one can give reasonable guesses, but they are of great significance, comparable to the twin prime number conjecture, but they are very difficult. If Qin Ke wants to kill them, he must first come up with his own guesses.

and prove it.

In addition, there are several alternative goals, such as the New Mersenne Prime Conjecture, which is a conjecture about prime numbers. For any odd natural number p, if two of the following statements are true, the remaining one will be true:

=(2^k)±1 or 4^k)±3

2.(2^p)-1 is a prime number (Mersenne prime number)

3.[(2^p)

1]/3 is a prime number.

There is another famous "Krammel conjecture", its mathematical expression is:/(logpn)^, where pn represents the nth prime number.

The above two are basically at the same level or similar in difficulty and meaning as Zhou's conjecture.

In addition, there is the "Brocard Conjecture", that is, "there are at least 4 prime numbers between the squares of two prime numbers"; and the "Depov Conjecture", that is, "there is a certain number between n^2 and (n 1)^2

"There are prime numbers" is also a well-known conjecture about the distribution of prime numbers.

Qin Ke decided to start with the "Brocard Conjecture" and "Jebov Conjecture" which are closest to Zhou's conjecture.

Facts have proved that his choice was correct. He repeatedly disassembled and used the "Geometric Number Theory Matching Approximation Method", plus a little Merlin Transform and Fourier Transform in the "Group Theory Functional Equation Method", and once again transformed the "Brocard Conjecture"

"The problem is simplified into a complex problem and transformed into an algebraic geometry problem, and then through linear transformation...

Lines of difficult and difficult mathematical formulas flowed out under the tip of his pen, turning into sharp swords and slashing at the little boss named "Brocard's Conjecture". Each of the interlaced and changing mathematical symbols and combinations

They are mysterious rays of truth that penetrate directly into the core of the "Brocard Conjecture".

Qin Ke only spent two nights before the little boss "Brocar's Conjecture" wailed and turned into countless experience points, falling under Qin Ke's pen.

"It's done!" Qin Ke breathed a sigh of relief and looked happy.

The basic idea of ​​overcoming the "Brocard Conjecture" is similar to that of proving Zhou's conjecture. Faced with the sharp and changeable saber of the "Geometric Number Theory Matching Approximation Method", the "Brocard Conjecture" cannot escape the ending of collapse.

As for "Jepov's Conjecture", which is of the same level and has similar attack methods, Qin Ke is a bit too lazy to do it himself.

On the morning of the third day, corresponding to late night of Xia Kingdom time, Ning Qingyun sent a message, telling Qin Ke that she had completed about 60% of the proof process of Zhou's conjecture, only some details and key points, because of experience and knowledge

She has never been able to overcome the deep reasons.

This has surprised Qin Ke enough. Ning Qingyun's resilience and creative thinking during the proof process are very good. For difficult problems, she can repeatedly use various methods she has mastered to make countless boring attempts. Several times

This difficult problem was solved by her seemingly clumsy but yet exquisite method.

Qin Ke feels that Ning Qingyun's talent in mathematics is more like water. It moistens things silently, but can penetrate into every crevice. With the tenacity and patience that water can penetrate a stone, it resolves many problems that cannot be overcome by force.

This forms a very good complement to Qin Ke. Qin Ke has always been quick and resolute, taking the "quick, accurate and ruthless" route, getting straight to the core of the problem, and then refining the remaining parts like peeling off the cocoon.

Zhan Wubu: "Jun'er, leave the next proof of Zhou's conjecture to me. Take a look at the proof process of 'Brocard's conjecture' that I wrote and help improve the details. And here is

Regarding the ideas and key points of proving the 'Jebov Conjecture', it is similar to the proof of the 'Brocard Conjecture'. I have written down the most difficult key points of transformation, and the 'Jepov Conjecture' is left to you.

, I hope you can prove it 100%."

Xiao Qingzhu wants to grow taller: "Yes! I will work hard!"

It can be seen that Ning Qingyun's confidence and motivation are increasing day by day. Qin Ke smiled softly, opened and closed his lips, and the "shimmer" quickly transformed the lip words into words:

This chapter is not finished yet, please click on the next page to continue reading the exciting content! Zhan Wubu: "Work hard, don't stay up late, come on, video, I want to check if you have any dark circles."

Xiao Qingzhu wants to grow taller: "No... I'm in the dormitory, wearing pajamas. Yan Fei and Xiao Hui are also wearing pajamas..."

Zhan Wubuke: "When you say that, I become more interested."

The little green bamboo wants to grow taller: "(Chop Knife) (Chop Knife) Qin Xiaoke, what are you interested in?"

Zhan Wubuke: "Of course I am interested in the way you look in pajamas. Do you think I would be interested in your roommates? Together they are not half as beautiful as you. You have to believe my critical eye and get used to it.

If you don’t see the dazzling gems and pearls, how can you look down on the stones on the roadside?”

Xiao Qingzhu wants to grow taller: "Rogue. Also, don't talk about other girls like this, okay? By the way, last time I saw the photos of the dinner party you sent, there were several beautiful foreign girls. Did you go with them?

Dance?"

Zhan Wubuke: "No, as I said before, other women are just clouds in my eyes. What's more, I only attended the dinner party for one day, and I never went there again. I want to prove two worlds more

level problem, and then apply for a stall and 'set up a stall' on the seventh day. If you don't talk about this, why don't you take a selfie and show it to me? I haven't seen you in three days."

The little green bamboo grows tall: "No, and the lights have just been turned off. I turned on the small desk lamp, so the photo is not clear."

Zhan Wubu Ke: "If you don't want to post a selfie, then just call me 'husband' and let me hear it. Choose one of the two."

Little Green Bamboo grew taller: "I...I'm going to bed."

Qin Ke raised the corners of his mouth and said "But I miss you very much" several times in a row.

After a few minutes, the other person finally sent me a selfie. It was taken while hiding in bed with a flash. The girl's hair was a little messy, her pretty face was flushed, and she looked particularly cute.

Qin Ke chuckled. His little cabbage was always too soft-hearted.

He also sent a handsome selfie of himself, with the following sentence: "Honey, I'm leaving for the report. Sweet dreams, good night."

…

After listening to the report meeting, Qin Ke was familiar with the process. It only took him one night to complete the proof process of Ning Qingyun's Zhou conjecture. After sending it back to Ning Qingyun, he set his goal on "whether there are infinite Mersenne primes."

", and "Does the Fibonacci sequence have infinite prime numbers?" are two propositions that are no less difficult than the twin prime number conjecture.

In this foreign country, snowflakes fall and stop, and the wind howls outside the window. The pile of manuscript paper in Qin Ke's hands is getting thicker and thicker. Often at two or three o'clock in the night, the lights in his room can still be seen.

Relying on his excellent physical fitness and insisting on practicing Eastern Mysteries every day to refresh his energy, Qin Ke only slept for three hours, and devoted the rest of his rest time to studying mathematical problems.

When he was tired and bored, he would chat with Ning Qingyun, or look up his previous chat records, especially the "husband" voice that Ning Qingyun sent him on his birthday last year. It was shy and sweet, Qin Ke

I specially collected it and listen to it whenever I feel tired or bored, and I immediately regain my energy.

Time passed quickly with the stroke of Qin Ke's pen tip.

However, the difficulty of these two propositions exceeds Qin Ke's imagination. With his "professional-level" mathematical ability, even if he has such a sharp tool as the "Geometric Number Theory Matching Approximation Method", his progress is still slow, and many difficulties are stuck halfway.

Enough inspiration to break it.

Inspiration...inspiration.

Qin Ke looked at the "Inspiration Amplification" icon on the system interface, but there was no sign of it being activated.

Looking at the time again, today is the fifth day of the academic lecture, and it is past eight o'clock in the evening. Tomorrow at ten o'clock in the morning will be his keynote lecture on the twin prime conjecture.

But at this time, Qin Ke's mind was full of unresolved Mersenne prime numbers and Fibonacci sequence propositions. It felt like there was something accumulated in his heart that he wanted to spit out but couldn't, and he wanted to swallow it but couldn't. It was like "something stuck in his throat."

, which made him quite uncomfortable.

Qin Ke opened the window and saw that the snowstorm outside had stopped and the wind was not strong, but the cold air that blew in still cheered him up.

When you encounter a problem, run for inspiration!

He put on a light down jacket, sent a message to Ning Qingyun, saying that he was going for a run and that he didn't have to worry if he couldn't be contacted, so he opened the door and walked out.

Chen Ming, who lived next door, pushed out the door almost ten seconds later and followed him like a shadow without asking Qin Ke where he was going.

He didn't ask, but Qin Ke took the initiative to turn around and said: "Brother Chen, I want to go for a run, is that okay?"

Chen Ming was stunned for a moment, looked at the weather outside, and then nodded.

Qin Ke pushed open the door of the hotel, and under the surprised eyes of the little girl at the front desk, he simply completed the warm-up, then opened his legs and ran into the night.

The lights on the campus of Princeton University were bright, and Qin Ke was already familiar with this ancient school, which occupies a small area. He kept a steady speed along the centuries-old school road, relaxed his mind and body, and ran forward.

Chen Ming ran behind him silently, always keeping a distance of about three meters.

Qin Ke ran past European-style, Roman-style or Greek-style buildings, ran past large iconic statues everywhere, and ran past countless bright lights...

The originally thin snow was crushed by the soles of the shoes, causing snow foam to splash.

The cold wind blowing on the body that was hot due to exercise felt indescribably comfortable and made my mind sober.

As he ran, Qin Ke's mind slowly returned from a relaxed state to the problems of Mersenne prime numbers and Fibonacci sequences. He began to enter a state of selflessness, and running became a subconscious mechanical action...
To be continued...