Volume 1: Student Life Chapter 271 Is there any need to say this?
Prime number, that is, prime number.
It refers to a natural number greater than 1 , which cannot be divided by other natural numbers except 1 and itself.
The number of prime numbers is infinite. The ancient Greek mathematician Euclid gave a classic proof of this in his book "Elements".
Also, because the number of prime numbers is infinite, some people may ask, what is the distribution pattern of prime numbers?
How many prime numbers are there below 100000?
How likely is it that a random 100-digit number is prime?
This also promoted the development of number theory, a pure mathematical discipline, and led to the Goldbach conjecture that whether every even number greater than 5 can be written as the sum of two prime numbers.
There are also questions such as whether there are infinite twin prime numbers, whether there are infinite prime numbers in the Fibonacci sequence, whether there are infinite Mersenne primes, whether there are infinite prime numbers in the form such as X2+1, and so on.
Among them, there are problems that can be solved using the prime number theorem, such as "there must be at least one prime number between a number greater than 1 and its twice" and "there exists an arithmetic progression of prime numbers of arbitrary length."
But more of it is just a guess.
If we have to rank them, the Cramer conjecture that Chen Zhou is currently studying is probably above the Mersenne prime problem, and below the Gerbov conjecture and the twin prime conjecture.
Therefore, Chen Zhou is now a little unsure whether his idea is correct.
He discovered that a mathematical conjecture that no one had been able to prove for nearly a hundred years seemed to be a little wrong and needed to be corrected.
In fact, if you say something wrong, the words you use are inappropriate.
Because Chen Zhou did not disprove the hypothesis, he just found an "improved" conjecture about the spacing between prime numbers.
Just like the Erdős conjecture proved by Terence Tao and others in 2014.
What Chen Zhou improved was just a more moderate guess.
Even if it is proved, it does not mean that Cramer's conjecture is wrong.
And its value is smaller than the Caramel conjecture.
Because of the improved problem, the prime number interval is still smaller than Cramer's conjecture.
Chen Zhou put down his pen and rubbed his temple with a strange expression.
On the draft paper, it was written:
[Conjecture about the maximum interval between adjacent prime numbers within N, (Pn+1≤N)max(Pn+1-Pn)≈logN(logN-loglogN)+2(N≥7)]
Here N refers to any natural number greater than or equal to 7.
"Log" is the abbreviation of natural logarithm.
The statement of Cramer's conjecture is [limn→∞sup(Pn+1-Pn)/(logPn)2=1].
The difference between the two is that (logPn)2 is changed to logN(logN-loglogN)+2, and N≥7.
If we can get some inspiration from solving this problem, maybe we can solve the problem of Cramer's conjecture.
Thinking of this, Chen Zhou picked up the pen again and planned to solve the improvement problem first.
Chen Zhou's solution is the same as the proof of the Erdős conjecture, which is based on a simple method of establishing large prime number intervals.
A large prime gap is equivalent to a long series of non-prime numbers, or composite numbers, between two prime numbers.
To give a simple example, let’s start with the numbers 2, 3, 4, …, 101.
Then add 101 factorial to each number, which is 101!
The series of numbers becomes 101! +2, 101! +3, 101! +4, ..., 101! +101.
Since 101! is divisible by the numbers from 2 to 101, every number in this sequence is a composite number.
That is, 101! + 2 is divisible by 2, 101! + 3 is divisible by 3, and so on.
This simple method is actually a slight variation of the high school algebra method.
If it were possible to obtain a list of composite numbers, then this could be used to study the prime spacing problem.
Chen Zhou spent an entire afternoon in the library, studying the revised problem of Cramer's conjecture.
Although the problem was not solved, the research methods of five professors including Terence Tao still brought Chen Zhou a lot of benefits.
It was not like the beginning, when he tried to use this method to solve the Cramer conjecture.
At six o'clock in the afternoon, Chen Zhou and Yang Yiyi walked out of the library hand in hand.
Now that he has returned to Yanda and his previous pace of study and life, Chen Zhou naturally has Yang Yiyi by his side.
This state is also the state that Chen Zhou is most familiar with and likes most.
It’s really nice that every time I put down my pen, I can turn around and see my favorite girl.
Yang Yiyi and I had been planning to go directly to the cafeteria to eat rice with toppings, but we didn't expect Shen Jing to call us.
Chen Zhou answered the phone: "Senior, are you back?"
Shen Jing said: "Yes, I just arrived at school. Where are you?"
Chen Zhou replied: "Just came out of the library."
Shen Jing was silent for two seconds before he said, "Well, you have nowhere to go except to the library..."
Chen Zhou was immediately unhappy and said, "Who said that? There's also the Physics Institute and the accelerator laboratory. I can go there!"
Shen Jing remained silent. He really wanted to ask, besides places for study and research, is there anything else?
But Shen Jing didn't say that . He said, "Let me come to see you. Dr. Wu has told me something."
Chen Zhou responded: "Okay, Yiyi and I will go to the cafeteria, you come over."
When Chen Zhou and Yang Yiyi arrived at the cafeteria, Shen Jing was already waiting at the door.
As soon as he saw Shen Jing, Chen Zhou smiled and asked, "Senior, how is it? It feels good to stay here, right?"
Hearing this, Shen Jing said unhappily: "Not happy!"
Chen Zhou asked in surprise: "How is that possible? I'm gone, they must have a lot of questions to ask you. Isn't this your performance time?"
Shen Jing glanced at Chen Zhou and said helplessly: "I thought so too, but it's not true..."
Shen Jing immediately started to complain, telling the whole story of how he was interrupted before he even started to show off, and then helped Chen Zhou to show off.
After hearing this, Chen Zhou couldn't help but burst out laughing.
Yang Yiyi couldn't help but chuckled and said, "Senior, you didn't seize the opportunity. Why don't you learn from him?"
Hearing this, Shen Jing frowned and looked at the couple, then sighed softly: "Alas, I thought so too, but I can't learn it! He can learn so many things in a week and solve the project, but I can't..."
Chen Zhou suppressed his laughter and jokingly said, "As a man, how can you say you are not good enough?"
Shen Jing: “…”
Chen Zhou thought of what Shen Jing said on the phone about Dr. Wu saying that he had something to tell him, so he asked, "Senior, did you say that Dr. Wu told him something?"
Shen Jing nodded, pondered for a moment, and said, "Yes, I explained something. Dr. Wu hopes that you will not give up your talent in materials science. She thinks you will definitely be able to make some achievements in this area."
Chen Zhou waited for a while, and when he saw that Shen Jing seemed to have finished speaking, he asked, "That's all? That's all?"
Shen Jing looked at Chen Zhou in confusion: "That's all, what's wrong?"
"No, nothing..." Chen Zhou was a little embarrassed. He thought Dr. Wu Xinyue had something to explain about the project, but it turned out to be this.
Shen Jing: "What do you think it is?"
Chen Zhou: "Nothing... Well, thank you Dr. Wu for your concern, but do I need to say this?"
Shen Jing: “…”
After a few brief chats, Chen Zhou took out his cell phone and made a call.
Let’s go out for a meal in the evening.
Now that Shen Jing is back, it's a good time to call Fang Jieming along as well.
Fang Jieming agreed to help on this project without hesitation, and Chen Zhou still remembered it.
After meeting Fang Jieming, the four of them went straight out of the school and found a grilled fish restaurant nearby.