Before understanding the meaning of Zhou's conjecture, we must first understand a term - Mersenne primes.
The Mersenne prime number is a special kind of prime number. It is named after the famous seventeenth-century mathematician Marin Mersenne and comes from the Mersenne number (^p-1). If the Mersenne number is a prime number, it is called a Mersenne prime number.
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There are infinitely many prime numbers, but only 51 Mersenne primes have been discovered so far. The latest 51st Mersenne prime number discovered is 2^-1, with a total of digits.
How big is the largest prime number? If printed out in size 4 font, A4 paper can cover a length of more than 100 kilometers.
How many Mersenne primes are there? Are they finite or infinite? This is still an unsolved mystery in the mathematical world.
In addition to the significance of mathematicians pursuing academic truth, Mersenne primes are also widely used in modern cryptography because "it is very difficult to decompose a large number into the product of several prime numbers, but it is relatively easy to multiply several prime numbers."
Studying.
Because the exploration of Mersenne prime numbers, especially large prime numbers, has exceeded the scope of human computing capabilities, computers must be used. And when even supercomputers are struggling, distributed computing technology based on the Internet is needed.
This makes the exploration of large prime numbers involve more and more disciplines, mathematics, computers, programming, distributed network architecture... the requirements and difficulty are getting higher and higher.
Every time the latest large prime number is discovered, it will cause huge international repercussions, and its significance is even as great as the discovery of a new element.
Therefore, countries around the world have invested a lot of manpower and material resources in the research of Mersenne prime numbers. This not only represents the country's mathematical research level, but also indicates whether a country's comprehensive scientific and technological capabilities are at the forefront of the world.
Naturally, Xia State is no exception. In order to catch up with the international advanced level, a large number of Xia State mathematicians have devoted themselves to the study of Mersenne prime numbers. Among them, mathematician and linguist Mr. Zhou Lao has achieved the most dazzling academic achievements.
Twenty years ago, he used the method of connected observation and incomplete induction to propose an important conjecture about the distribution of Mersenne prime numbers. This conjecture attracted the attention of the international mathematics community and named it "Zhou's conjecture."
When 2^(2^n) is less than p and less than 2^(2^(n 1)), Mp has 2^(n 1)-1 prime numbers (Note: p is a prime number; n is a natural number; Mp is a Mersenne
number).
This is the mathematical expression of Zhou's conjecture, and it is also the most mathematically beautiful and accurate expression in the international mathematical community's research on the distribution of Mersenne prime numbers.
Including Mr. Zhou himself, many mathematicians in the world are trying to prove this "Zhou's conjecture" and turn it into "Zhou's theorem", which will greatly promote the study of Mersenne prime numbers.
Unfortunately, to this day, no one has been able to successfully prove it.
Zhou's conjecture is still a conjecture. It is like a bright pearl hanging in the palace of mathematics, waiting for real mathematical geniuses to pick it.
So when he heard that Ning Qingyun actually had the idea to prove Zhou's conjecture, Qin Ke couldn't help but jump up from the bed.
This...this is so surprising!
You must know that this is Zhou's conjecture! Even if you just think of the proof idea, it is very remarkable.
Moreover, Qin Ke knows her little cabbage very well, and she will not tell her if she is not more than 50% sure.
Once you have an idea, it's like you have the right direction. It's only a matter of time before you prove it!
Qin Ke hurriedly continued reading.
The little green bamboo will grow taller: "I will explain it to you in detail in the video at noon. I have taken the time to write out most of the specific ideas. I should be able to finish it in the advanced algebra class later. I hope it can inspire you.
Let you prove one more world-class conjecture!"
Qin Ke felt moved in his heart.
This silly girl... if we want to prove it, we can prove it together. Ideas are very important, do you know?
But it won’t be until noon...
Noon in Xia Kingdom was early morning here. Qin Ke looked at the time and saw that there were still two or three hours left.
This long wait made Qin Ke feel like a cat scratching his heart. Not long ago, Academician Wang said that he hoped he could prove Zhou's conjecture. Now Ning Qingyun said that he had an idea, which made Qin Ke vaguely feel...
The feeling of being destined.
Of course, Qin Ke did not want to covet this honor. After all, Zhou's conjecture is less valuable and significant in the international mathematics community than the twin prime conjecture.
But as soon as he thought of being able to prove Zhou's conjecture with Ning Qingyun, signing the paper at the same time, and having their names appear side by side in the international mathematics community, Qin Ke couldn't help but feel excited.
Ning Qingyun said that she wanted to be his second best and always be by his side, but Qin Ke thought even further.
He hopes to hold the little hand of this beloved girl, see the most beautiful scenery in the scientific world together, stand at a height that the world can look up to, and be famous in history together!
Qin Ke took a deep breath, calmed down, lay back on the bed, and opened the photo of Ning Qingyun and himself again.
The girl with a single ponytail in the photo shyly hugged his arm, her face was flushed, and she looked indescribably innocent and cute.
It has been three days since I saw Xiao Baicai. Ning Qingyun should be sitting in the classroom and preparing for class seriously, right?
Qin Ke gently touched Ning Qingyun's photo with his fingers. Even though he hadn't seen her for three days, the longing accumulated in his heart seemed to be overflowing.
In the past two years, Qin Ke has become accustomed to having a girl with a single ponytail next to him. Whenever he looks back, he can see her shy and gentle eyes.
At this time, Qin Ke was alone in the empty hotel room. The feeling of being empty and missing something important was very obvious.
Suddenly, the phone vibrated and a new message was received.
The little green bamboo grew taller: "There will be a class soon. This is Professor Cui's advanced algebra class. Yan Fei, Xiao Hui and Jia Nan are sitting together. It's snowing here again today. I wonder if it's snowing over there.
Are the same snowflakes fluttering? And..."
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Xiaoqingzhu grew taller: "I miss you."
Just four words, all of a sudden the overflowing emotions in Qin Ke's heart burst out of the shell, and the heat flowed through his body, straight into his nose and eye sockets, making his nose sore and his eye sockets warm.
"What, a mere Ning Qingyun actually dares to attack suddenly..." Qin Ke muttered to himself, an indescribable sweetness filling his heart.
The corners of his mouth curled up, and he lay on the bed and replied quickly: "Hey, I'm so busy today."
…
In the distant Xia Kingdom, in the classroom of Qingmu University, Ning Qingyun was getting ready for class. Remembering the message she had just sent, the girl's face turned red.
For the tender-skinned Ning Qingyun, she was really not good at saying such sweet love words. But when she saw that the person sitting next to her was her roommate instead of Qin Ke, she couldn't control the longing in her heart, and then she made such a mistake out of nowhere.
One word passed.
I wonder if the bad guy will roll around happily?
Thinking of this scene, Ning Qingyun felt shy but also a little sweet.
At this time, the phone vibrated slightly. Seeing that the professor who was giving the lecture had not yet arrived in the classroom, Ning Qingyun bit her red lips, secretly picked up the phone from the drawer, and glanced at it expectantly.
Zhan Wubuke: "Hey, I'm so busy today."
Huh? That’s it?
The girl couldn't help but opened her mouth in disappointment, Qin Xiaoke, you just said this to me? Aren't you the best at saying those messy and obedient things?
She pressed the phone quickly.
Little Green Bamboo wants to grow taller: "What are you busy with? Listening to the report meeting?"
Zhan Wubuke: "I'm too busy missing you (smiley face)."
Ning Qingyun's initial grievance immediately turned into sweetness, and she couldn't help but laugh out loud. This bad guy, as expected, has a familiar taste and familiar formula, which can make girls happy.
Ning Qingyun was originally the focus of countless boys' peeks. At this moment, the girl with a single ponytail showed a sweet and shy smile. The cold and reclusive temperament on her body suddenly disappeared. I don't know how many boys looked at it and were disturbed and panicked.
I looked away, fearing that my soul would be taken away if I continued to look at it, but soon I couldn't control myself and looked back again quietly.
Ning Qingyun didn't notice the gazes around her. She bit her lip lightly, blushing and was about to reply, but Qin Ke sent the message first.
Zhan Wubu Ke: "I have been studying a very interesting word recently."
Ning Qingyun knew Qin Ke was teasing her again, but she still asked curiously: "What word?"
Invincible: "Play."
The little green bamboo wants to grow taller: "Wan? What is there to study about the word "play"?"
Zhan Wubu Ke: "What is the pinyin of Wanzi?"
The little green bamboo wants to grow taller: "WAN".
Zhan Wubu Ke: "Thank you, I (W) love (A) you (N) too."
Isn't the meat numb?
But such flirting words made Ning Qingyun feel as sweet as drinking honey.
She tried hard to hold back the smile on her lips, and her face turned red.
On the left of Ning Qingyun was Gu Yanfei, and on the right was Ximen Hui. The two girls looked at each other, and they were both a little envious. They could make Ning Qingyun, who is usually as cold as a bamboo, smile so sweetly and cutely. It goes without saying that the other person must be Qin Ke.
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Gu Yanfei sighed: "Ah, every time I see Qingjun like this, I want to fall in love."
Ximen Hui nodded in approval: "Me too, but it's so difficult to find a good boyfriend."
The "air talk" between the two made Ning Qingyun's face blush even more. She hurriedly replied: "I have to go to class, bad guy. I will video chat with you at noon." Then she put away her phone and dialed.
Brushing the hair around her ears, she took out the book again.
At this time, the professor had come in and started teaching, and the surrounding area became quiet.
Ning Qingyun didn't plan to listen to this class. She wanted to perfect her idea of ​​proving Zhou's conjecture, so she told Qin Ke at noon, hoping to give him some inspiration.
But looking at the white paper, I always think of Qin Ke's words just now, and also think of the distant, dreamlike future.
Her pen moved subconsciously and wrote two words on the white paper.
When she came back to her senses, the girl hurriedly crossed out the words with a blushing face.
Under the messy handwriting, the word "husband" can still be faintly seen.
Chapter completed!