They’re all reborn, what’s wrong with being a little more almighty?

Chapter 58 A new way to get rich, this time it’s a beautiful knife!

先复习一下小学数学，素数也就是质数，是指大于1的自然数中，除了1和它自身外，不能被其他自然数整除的数。比如2、3、5、7、11、13等等。

Let’s talk about Mersenne number again, which refers to the positive integer that can form 2^p-1.

In human terms, it is a positive integer that is 2 raised to the power of P minus 1, where P must be a prime number.

For example, the number 3 is 2 raised to the power of 2 minus 1;

The number 7 is 2 raised to the third power minus 3;

The number 31 is 2 raised to the fifth power minus 5;

The number 127 is 2 raised to the seventh power minus 7. These numbers are all Mersenne numbers.

But since 4 is not a prime number, 2 raised to the fourth power minus 4, which is the number 1, cannot be called a Mersenne number.

If the Mersenne number is also a prime number, then the number is called a Mersenne prime number.

Mersenne primes are the most special of all numbers.

Human research on Mersenne prime numbers can be traced back to the ancient Greek mathematician Euclid in 300 BC. Prime numbers were already mentioned in the "Elements of Geometry" written by him.

This research has continued to this day and has been an important part of number theory research since ancient times.

In the mathematical world, whether there are infinitely many Mersenne primes is a conjecture on the same level as Goldbach's conjecture, Riemann's conjecture, twin primes, etc.

Mersenne primes were first used in the field of cryptography. Since Mersenne primes are difficult to factor, the secret key parameters in the cryptosystem are all based on Mersenne primes.

Later, people discovered that the operation of Mersenne prime numbers could be used to test the speed and stability of the calculation formula.

Because the larger the Mersenne prime number, the more calculations are required. If you want to know the performance of a certain computer, ask it to test a Mersenne prime number, and the performance will be clear at a glance.

The famous "burn-in" software Prime95 uses this principle to test computer performance.

In fact, this software was originally developed not to test computer performance, but to calculate Mersenne prime numbers.

After humans enter the digital age, Mersenne prime numbers have become more and more important.

For example, the blockchain technology used in virtual currency relies on numerical principles and cryptography technology, and the Mersenne prime number happens to be the basis of the secret key parameters in cryptography.

It is no exaggeration to say that everyone involved in algorithms will regard Mersenne primes as their basic research. From the perspective of 2024, there is no need to say how important algorithms are!
Moreover, studying Mersenne primes requires a large amount of calculations. In order to achieve results in the field of research on Mersenne primes, in addition to having a solid theoretical research foundation, it also requires computers with high computing power. Only countries with strong science and technology can possess both of these two factors.

Therefore, the research level of Mersenne prime numbers also reflects the technological level of a country.

(The above introductions are actually all nonsense, just a shameless attempt to make up the number of words. As a human saying goes, Mersenne primes are awesome!)

The study of Mersenne prime numbers is called a shining pearl in the ocean of mathematics. So when Zhang Wei saw the Prime95 software on the CD, he immediately made a decision to pick up a few of this pearl.

Humans first relied on manual calculations to search for Mersenne primes. In BC, humans only found four Mersenne primes, namely 3, 7, 31 and 127. No more could be found.

It was not until the fifteenth century that humans found the fifth Mersenne prime number, 8191. In the following hundreds of years, mathematicians successively found several Mersenne prime numbers. By the twentieth century, humans had found 12 Mersenne primes.

After World War II, computers began to appear. Humanity's computing power has greatly improved, and the search for Mersenne primes has become faster. As of 1996, humans have discovered a total of 34 Mersenne primes.

Then came the Internet era, and Americans launched an Internet-based distributed computing project, which is the Internet Mason Prime Search, or GIMPS for short.

You only need to go to the GIMPS official website and download a free software to participate in the calculation of Mersenne prime numbers. This is equivalent to using the world's computer resources to calculate Mersenne prime numbers.

It is equivalent to dividing a pile of sand containing gold into countless parts and handing them over to gold diggers. As for who can take out the gold, it depends on your luck.

Is it like mining in the current virtual currency field? The method tells you that if you want to mine virtual currency, you have to invest in the equipment yourself.

Mining virtual currency can sell money, and calculating Mersenne prime numbers can also sell money. In order to encourage netizens to participate in the calculation of Mersenne prime numbers, the Electronic Frontier Foundation has set up a reward mechanism specifically for this.

Find a Mersenne prime number with more than 100 million digits, and the reward is $100. Let me emphasize, it is not 1 digits, nor 100 digits, but million digits!
而找到一个超过1000万位数的美森素数，奖励上升到10万美金；超过1亿位数的梅森素数，奖励15万美金；超过10亿位数的梅森素数，奖励25万美金。

These bonuses are also the reason why Zhang Wei plans to create several Mersenne primes.

Before 2004, humans had just discovered the 40th Mersenne prime number, which was a number with 632 million digits. The next Mersenne prime number was a number with 723 million digits and was worth $!
By the 45th Mersenne prime number, it has exceeded 1000 million digits. As long as you take it out, you can exchange it for US dollars.

In other words, if Zhang Wei just takes out a few Mersenne primes, he can exchange them for hundreds of thousands of dollars!
A new way to get rich, you can make more money than taking the college entrance examination!
……

"One, two, three..."

Zhang Wei took ten raw eggs and put them on the table.

Then he took out a bowl and cracked five raw eggs into it. After hesitating for a few seconds, he poured it directly into his mouth.

A strong fishy smell instantly filled Zhang Wei's mouth, and then his nasal cavity.

However, Zhang Wei still forced himself to swallow the raw egg. The raw egg slid down his throat. Although it was smooth, it gave him a nauseating feeling.

There was a little egg liquid left in the corner of his mouth, and the strong fishy smell still lingered in his mouth. Zhang Wei quickly picked up a glass of water and drank it in a big gulp. Although the fishy smell was much less, it still couldn't wash away the disgusting feeling.

"There are five more! Fight for fifty thousand US dollars!"

Zhang Wei cracked another five raw eggs into the bowl. This time he pinched his nose and poured the raw eggs into his stomach.

The nasal cavity is not irritated and feels better. At least there is no fishy smell when breathing.

Another sip of water diluted the fishy smell a lot, but Zhang Wei's psychological effect still made him feel that the taste in his mouth was very strong.

"Brush your teeth!"

The toothpaste foam washed through the oral mucosa, and Zhang Wei finally felt better.

"Devil, I have eaten 10 raw eggs. Now you should give me the Merlin prime number. I have checked that the 41st Merlin prime number has not been discovered yet. I want the 41st Merlin prime number.

"Okay, the notes are ready! The 41st prime number is, M24!"

"24, right?" Zhang Wei confirmed the number again.

M plus number is an expression of Mersenne prime number. This number is P in 2 raised to the power of P minus 1.

In other words, the 41st Merlin prime number is 2 raised to the power of 24 minus 036.

The Mersenne primes have been obtained, and the question now is how to publish them.

Zhang Wei can use the GIMPS software to first input this number and let the computer slowly calculate it to confirm that it may be a Mersenne prime number, and then submit it to the GIMPS server for confirmation.

But in this case, it may be a bit slow. After all, his computer only has an Intel Pentium 700 processor, and it takes who knows how long it will take to calculate a number with more than million digits.

Moreover, the efficiency of GIMPS is not very good. In history, it once took half a year to verify the Mersenne prime numbers.

Zhang Wei couldn't afford to wait for half a year.

"There should be faster computers at Qingdao University!"

Zhang Wei suddenly remembered Professor Zhuge from the Department of Mathematics.

If the Mersenne prime numbers were published through the Department of Mathematics of Tsinghua University, it would be equivalent to an academic research!

The most important thing is that Professor Zhuge also said that he has a daughter who is 170cm tall, has long legs, white skin, and has practiced aerobics!
　Thank you all Dehua Yanzu for your monthly votes! Sure enough, I read it right. You old perverts still want to look at those with 170cm long legs.

　　
　
(End of this chapter)