Prime numbers, that is, prime numbers.

Refers to a natural number greater than 1, a number that is not divisible by any natural number other than 1 and itself.

The number of prime numbers is infinite, and the ancient Greek mathematician Euclid gave the classic proof of this as early as his work "Geometric Primitives".

Because the number of prime numbers is infinite, some people will ask, what is the distribution law of prime numbers?

How many prime numbers are there under 100000?

How likely is a random 100-digit number to be prime?

This also promoted the development of number theory, a pure mathematical discipline, and gave rise to the Goldbach conjecture of whether every even number greater than 5 can be written as the sum of two prime numbers.

There are also whether there are infinitely many twin primes, whether there are infinitely many primes in the Fibonacci sequence, whether there are infinitely many Mersenne primes, and whether there are infinite forms such as X?? +1 prime, and so on.

There are problems such as "there must be at least one prime number between a number greater than 1 and twice it", and "there is a sequence of equal differences between prime numbers of any length".

But more than that, it's just a conjecture.

If you want to classify, the Clamel conjecture that Chen Zhou is studying now is probably above the Mersenne prime problem, and under the Jebov conjecture and the twin prime conjecture.

Therefore, Chen Zhou is a little unsure whether his thoughts are right.

A mathematical conjecture that lasted for nearly a hundred years, and no one could come close to proving, he actually found that something seemed to be wrong and needed to be corrected.

In fact, if you say something wrong, the words are inappropriate.

Because Chen Zhou is not falsified, but only found the conjecture of the "improved" prime number spacing.

Just like in 2014, Tao Zhexuan proved the Aitos conjecture.

What Chen Zhou improved was a more modest conjecture.

Even if it is proven, it does not mean that the Kramel conjecture is wrong.

And its value is less than Caramel guesses.

Because of the improved problem, the prime interval is still smaller than Cramel conjecture.

Putting down the pen and reaching out to rub his temples, Chen Zhou's expression was a little strange.

On the scratch paper, it is written:

[Conjecture of the maximum interval between adjacent primes within N, (Pn+1≤N)max(Pn+1-Pn)≈logN(logN-loglogN)+2(N≥7)]

N here refers to any natural number greater than or equal to 7.

"log" is shorthand for natural logarithm.

And the expression of Cramell's conjecture is [limn→∞sup(Pn+1-Pn)/(logPn)?? =1】。

The difference between the two is that (logPn)?? Changed to logN(logN-loglogN)+2 and takes N≥7.

If we can get a little inspiration from the solution of this problem, maybe we can solve the problem of the Cramel conjecture.

Chen Zhou, who was thinking like this, picked up the pen again, and planned to solve this problem of improvement first.

Chen Zhou's solution is based on a simple method for establishing large prime intervals, just like the proof method of the Ertos conjecture.

A large prime interval is equivalent to a long column of non-prime numbers, or composite numbers, between two prime numbers.

As a simple example, let's start with the numbers 2, 3, 4,...... , 101 starts.

Then add a factorial of 101 to each number, which is 101!.

This column of numbers becomes 101!+2,101!+3,101!+4,...... ，101！+101。

Because 101! is divisible by numbers from 2 to 101, each number in this column is a compound number.

That is, 101!+2 is divisible by 2, 101!+3 is divisible by 3, and so on.

This simple method is actually a subtle variation of the high school algebra method.

If it is possible to obtain a list of composite numbers, then it can be used to study the problem of prime number spacing.

In the afternoon, Chen Zhou was in the library, studying the correction of the Kramer conjecture wholeheartedly.

Although it did not solve the problem, the research methods of Tao Zhexuan and other five professors still gave Chen Zhou a lot of gains.

Not like in the beginning, when he tried to solve the Crumell conjecture in this way.

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 returned to the previous rhythm of study and life, Chen Zhou is naturally accompanied by Yang Yiyi.

This state is also the state that Chen Zhou is most familiar with and likes.

Every time I put down the pen, I can see my favorite girl when I turn my head, which is really good.

Originally, he and Yang Yiyi planned to go directly to the cafeteria to eat rice bowls, but they didn't expect Shen Jing's phone call.

Chen Zhou answered the phone: "Senior, are you back?"

Shen Jing said: "Yes, you 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, "Okay, you have nowhere to go except to the library......

Chen Zhou was suddenly unhappy and said: "Who said that, there is also the Institute of Things, and the laboratory of the accelerator, I can go there!"

Shen Jing was silent, he really wanted to say, in addition to the place to study and research, is there anything else?

But Shen Jing didn't say that in the end, he said, "I'll come to you, Dr. Wu has explained something over there." ”

Chen Zhou responded: "Okay, Yiyi and I will go to the cafeteria, you can come over." ”

When Chen Zhou and Yang Yiyi came to the cafeteria, Shen Jing was already waiting at the door of the cafeteria.

As soon as he saw Shen Jing, Chen Zhou smiled and asked, "Senior, what's the matter, doesn't it feel good to stay?"

Hearing this, Shen Jing said angrily: "It's not good!"

Chen Zhou asked in surprise: "How is it possible? I'm leaving, they must have a lot of questions chasing after you? Isn't this your performance time?"

Shen Jing glanced at Chen Zhou and said helplessly: "I thought it was like this, but it wasn'...... fact."

Shen Jing immediately began to complain, and was interrupted by someone before he could start pretending to be forced, and then he also helped Chen Zhou to pretend to be forced and spit it out.

After hearing this, Chen Zhou couldn't help laughing.

Yang Yiyi couldn't help but laugh softly on the side: "Senior, this is an opportunity that you didn't grasp, you can learn more from him, isn't it?"

When Shen Jing heard this, he frowned and looked at the couple, and sighed lightly: "Alas, I think so too, but I can't learn it! He can learn so many things in a week and solve the problem, but I can't......"

Chen Zhou held back a smile and quipped: "Man, how can you say that you can't do it?"

Shen Jing: "......"

Chen Zhou thought that Shen Jing said on the phone that Dr. Wu had something to explain, so he asked, "Senior, you said that Dr. Wu explained something?"

Shen Jing nodded, pondered for a while, and said, "It's something to explain." Dr. Wu hopes that you will not give up your talent in materials science, and she thinks that 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 be finished, he asked, "No?"

Shen Jing looked at Chen Zhou puzzled: "That's all, what's wrong?"

"No, it's nothing ......" Chen Zhou was slightly embarrassed, he thought that Dr. Wu Xinyue had something to explain about the subject, and it turned out to be this matter.

Shen Jing: "What do you think it is?"

Chen Zhou: "It's nothing...... What, thank you Dr. Wu for your concern, but does it need to be said?"

Shen Jing: "......"

A few people chatted a few more words, and Chen Zhou took out his mobile phone to make a call.

In the evening, let's go out for a meal.

Now that Shen Jing came back, he just called Fang Jieming as well.

Fang Jieming agreed to help on this topic without saying a word, and Chen Zhou still remembered it.

When he and Fang Jieming made peace, the four of them went straight out of the school gate and found a nearby grilled fish restaurant.