There are many smart people in this world, and there are many people who claim that they will work hard, but there are very few people who are truly capable of executing. Coincidentally, in the Qiao family, both Qiao Xi and Qiao Yu have very strong execution abilities.

The attitude towards life of being intermittently complacent and constantly eating and waiting for death has nothing to do with either of them.

As long as you make up your mind, the next step is to overcome difficulties and fulfill your mutual commitments.

So just after finishing the meal, Qiao Yu took the wine stored at home and walked out of the house.

After five trips, the living room and balcony at home felt a lot bigger.

Yes, while Qiao Yu was carrying the wine out, Qiao Xi had already sent all the wine cans piled up on the balcony to the grandma downstairs who liked to save all kinds of bottles to sell.

When the eyes are out of sight, the mind will not be troubled.

"I'm going to study." Qiao Yu said.

"Wait a minute, you have to find something for me to do. I can't drink anymore. I can't just stay at home and check my phone every day, right?" Qiao Xi said distressedly.

"Play mahjong?" Qiao Yu suggested.

"I won't go, I don't like it." Qiao Xi shook her head and said, "Well, I'll start learning how to cook tomorrow. You study hard and I'll research recipes for you online. You can also ask Coco to come to your house for dinner on weekends, so in the future Don’t bring food from outside either.”

Qiao Yu hesitated for two seconds, seeming to recall some not-so-good scenes in his mind, but finally nodded firmly: "Okay! But when you cook, you have to set an alarm on your phone to ring every five minutes. "

The biggest problem that hinders Qiao Xi from learning to cook is that she gets distracted easily. This also made Qiao Yu know at a very young age that the final destination of any ingredient after being overheated is carbonization.

Although carbon is edible, it really doesn’t taste good.

But people don't get bored when they have something to do, and don't think about all kinds of things. Even if it challenges one's own weaknesses, Qiao Yu feels that he has to support him.

As for him, it was nothing more than overcoming his fear of difficulties and studying hard.

"Okay, I'll remember to set the alarm."

"It's better if I book it for you."

"oh!"

…

For others, studying hard may be difficult.

When he came to school the next day, Qiao Yu clearly felt that his deskmate's mental state was not very good.

"What were you doing last night?" Qiao Yu asked.

"When I get tired of memorizing words, I memorize formulas until 1 o'clock in the morning." Zhou Shuang yawned and answered casually.

It seems that this guy is serious, but he doesn't know how many days he can last.

Qiao Yu didn't say much, just reminded: "We still need to balance work with rest." Then he didn't bother to pay attention to this guy.

If you can really persist for a week, it means you are really saved.

However, it seemed that Zhou Shuang was really struggling with his studies. After briefly chatting with Qiao Yu, he picked up the English book for the second grade of junior high school and started memorizing it silently.

It was a very smart choice. I was about to take the English test in the morning. As I said, if you sharpen your sword before the battle, it will be useless if you are not happy.

I just hope it’s not an occasional flash of inspiration.

Qiao Yu didn't bother to pay attention to his deskmate's studies, and just lay there to catch up on his sleep.

He was also very tired last night, all because he read the "Introduction to Algebra and Number Theory" given to him by the good old man.

Probably due to a different mentality, things that I thought were difficult to understand before turned out to be quite interesting when I looked at them again. For example, the analysis and properties of prime numbers successfully aroused Qiao Yu's interest in mathematics.

Regarding the issue of prime numbers, this book also briefly discusses the twin prime conjecture and Riemann's conjecture.

This also made Qiao Yu couldn't help but search in detail for the specific contents of these two conjectures, and then once again felt a desire to worship the former mathematics master.

These people worked really hard to solve this problem.

For example, in order to prove the twin prime conjecture, contemporary mathematicians constructed a finite number system. For example, in a finite number system with only 5 elements, 4 plus 3 equals 2. Under this system, other operations

The same rules must be followed.

With this prerequisite theorem, the concept of prime numbers is meaningless. For example, 7 can be directly divided by 3, which is equal to 4. The reason is very simple. In this finite field, 7 and 12 are the same, and they are both on the clock face.

on the 2 position.

Through this series of transformations, the twin prime conjecture of the finite field is related to the direct prime polynomial. Of course, if you really want to understand this concept, you need to understand what a prime polynomial is and what a twin prime polynomial is...

In short, the emergence of this idea allowed later mathematicians to transform integer problems into polynomial problems, and even the simplest finite field can accommodate infinite polynomials.

Under the guidance of this thinking mode, each polynomial is imagined as a point in space, and the coefficients of the polynomial are regarded as coordinates that define the position of the polynomial. For example, the polynomial x3x1 can be represented by the point (1,-3,-

1) means that the polynomial 3x + 2x + 2x2x3x + x2x + 3 can be represented by a point in 8-dimensional space.

Through this method, mathematicians proved that the twin prime conjecture is correct in finite fields: there are infinite pairs of twin prime polynomials that differ by any distance.

This shocked Qiao Yu. It turns out that mathematics can be played like this...

When you don’t have a tool to solve a problem, you create it yourself.

This is just like when playing a game and you are stuck at a certain level and can't pass it. The player can become an artifact builder. As long as he has enough imagination, he can create a stick that can directly deduct 9999 blood drops as long as it touches the BOSS.

…

Of course, the structure of this stick must be reasonable within the larger framework. Isn’t this more interesting than playing games?

Especially when Qiao Yu checked the information and found that prime numbers are closely related to almost all mainstream encryption systems on the modern Internet, it aroused his great interest.

For example, the most widely used RSA encryption algorithm relies on the mathematical property that the product of prime numbers is difficult to factor. The core of encryption and decryption relies on the Euler function?(n)=(p?1)(q?1) and Modular exponentiation.

To put it simply, when two large prime numbers p and q are randomly selected, and others do not know the values ​​of p and q, it is difficult to calculate ?(n) from N.

In addition, Diffie-Hellman key exchange and elliptic curve cryptography are also closely related to prime numbers.

In other words, if he could completely master the secrets of prime numbers, such as finding a way to quickly factorize prime numbers, it would mean that all mainstream encryption algorithms on the world's Internet would be ineffective against him. How much money could he make? , Qiao Yu simply didn’t dare to think about it.

In particular, digital signatures, certifications, and even blockchain technology in the financial field rely on RSA/ECC signatures and a bunch of other encryption algorithms, so the smart contract system can be tampered with.

Really, after seeing this promising future, mathematics that he thought was difficult before suddenly became extremely interesting, so he studied it until three in the morning last night and still felt energetic.

If Qiao Xi hadn't woken up at night and forced him to go to bed, Qiao Yu might have actually studied the prime number problem all night long.
Chapter completed!