Chapter 58 A new way to get rich, this time it’s a beautiful knife!
First review primary school mathematics. Prime numbers, also known as prime numbers, refer to natural numbers greater than 1 that are not divisible by other natural numbers except 1 and itself. For example, 2, 3, 5, 7, 11, 13, etc.
Let’s talk about Mersenne number, 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 1;
The number 31 is 2 raised to the 5th power minus 1;
The number 127 is 2 raised to the 7th power minus 1. These numbers All numbers are Mersenne numbers.
But since 4 is not a prime number, 2 raised to the fourth power minus 1, which is the number 15, cannot be called a Mersenne number.
If the Mersenne number is also a prime number, then this 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 his book "Elements of Geometry".
This research continues to this day and is considered an important part of number theory research since ancient times.
In the mathematical world, whether there are infinite Mersenne primes is a conjecture on the same level as Goldbach's conjecture, Riemann's conjecture, twin primes, etc.
Messenne primes were first used in the field of cryptographic technology. 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, it goes without saying how important algorithms are!
Moreover, studying Mersenne primes requires a lot of calculations. In order to be able 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 have both. 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.
Humanity first relied on manual calculations to search for Mersenne prime numbers. In BC, humans only found four Mersenne prime numbers, 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. Human 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 the Internet era came, 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 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 be sold for money, and calculating Mersenne prime numbers can also be sold for money. In order to encourage netizens to participate in the calculation of Mersenne prime numbers, the Electronic Frontier Foundation of the United States has specially set up a reward mechanism for this.
Find a Mersenne prime number with more than 1 million digits and receive a reward of $50,000. Let me emphasize, it is not 100 digits, nor 10,000 digits, but 1 million digits!
For finding a Mersenne prime number with more than 10 million digits, the reward rises to US$100,000; for a Mersenne prime number with more than 100 million digits, the reward is US$150,000; for a Mersenne prime number with more than 1 billion digits, the reward is US$250,000.
These bonuses are also the reason why Zhang Wei plans to get some Mersenne prime numbers.
Before 2004, humans had just discovered the 40th Mersenne prime number, which was a number of 6.32 million digits. The next Mersenne prime number was a number of 7.23 million digits, worth $50,000!
At the 45th Mersenne prime number, it has exceeded 10 million digits. As long as you take it out, you can exchange it for one hundred thousand 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 bit of egg liquid left in the corner of his mouth, and the strong fishy smell was still lingering 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 be washed away. Get rid of that sick 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, the fishy smell was diluted a lot, but Zhang Wei's psychological effect still felt that the taste in his mouth was very strong.
“Brush your teeth!”
The foam of the toothpaste 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.
< br>"Okay, the notes are ready! The 41st prime number is, M24,036,583! "
"24,036,583, 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 24,036,583 minus 1.
The Mersenne primes have been obtained, and the question now is how to publish them.
Zhang Wei can use the GIMPS software to input this number first 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 is only an Intel Pentium 4 processor, and it takes an unknown amount of time to calculate a number with more than 7 million digits.
And the efficiency of GIMPS is not very good. In history, it took half a year to verify the Mersenne prime number.
Zhang Wei can’t afford to wait for half a year.
"There should be faster computers at Qingdao University!"
Zhang Wei suddenly thought of Professor Zhuge from the Department of Mathematics.
If the Mersenne prime numbers are published through the Department of Mathematics of Tsinghua University, it will 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 to 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)