The discovery of a new Mersenne prime number is not an academic achievement. Knowing one more Mersenne prime number with tens of millions of digits will not promote the research of mathematical theory and scientific development, but its influence is greater than that of general academic achievements.
many.
This influence is mainly reflected in "shocking" many people.
That is a very large number with tens of millions of digits, it is tens of millions of 2 raised to the power, not to mention tens of millions to the power, it is just tens or hundreds of powers, the number is already hard to imagine.
There is a very classic story that says that the emperor's daughter unfortunately fell into the water and was rescued by a farmer. The emperor asked the farmer what he wanted in return for saving his daughter.
The farmer pointed to a chess board next to him and said to the emperor: "You put one grain of rice in the first grid, 2 grains in the second grid, 4 grains in the 3rd grid, and 4 grains in the 4th grid."
Put 8 grains in each grid, and so on, the number of rice grains in each grid is twice that of the previous grid. After placing all 64 grids in this way, I will need so many rice grains."
After hearing this, the emperor felt that the farmer's request was easy to satisfy, so he agreed with a smile. However, a smart minister told the emperor that even if he took all the rice produced in the country, he would not be able to fill in the 64 boxes.
Later, mathematicians calculated that the total weight of rice exceeded 281.4 billion tons.
This is already an astonishing number.
But in fact, it is just 2 raised to the 64th power. How big 2 raised to the power of tens of millions has long exceeded our understanding of real things.
If you think about it, you will know how incredible it is to prove that such a number is prime.
This is not something that can be done by ordinary means, and not all numbers can be tested. If it were other numbers with tens of millions of digits, it would be impossible to detect primality at all.
Mersenne numbers are a special case.
The Lucas-Lehmer test can only be used to test Mersenne numbers. In other words, if the number is not a Mersenne number, it is impossible to detect whether it is a prime number.
It is precisely because of the incredible things contained in it that the academic community and even the media attach so much importance to the discovery of Mersenne primes.
Just like more than ten years ago, computer expert Edson Smith discovered Mersenne prime numbers with more than 10 million digits, which was also the largest prime number discovered by mankind at that time.
Many people know very well that finding the Mersenne prime numbers is not an academic or scientific research achievement, but the achievement of the new Mersenne prime numbers was rated as one of the 50 inventions of the year by Amerikan's Time magazine, ranking 29th.
Therefore, the most attractive thing about finding Mersenne primes is that it can greatly increase your reputation.
The same goes for Patrick Roche.
His name appears in major media reports, as if he has become a heavyweight scientist. In fact, he is just an otaku hiding at home, and can be regarded as an algorithm engineer at most.
exactly.
Sokai University's computer lab really wants to be famous.
If a university wants to develop, if a department wants to develop, reputation is a must, and the best way to gain fame is academic achievements, but academic achievements cannot be achieved through hard work.
Wang Hao's research is regarded as a key task.
Dean Chen Qinghua personally went to the battle and stayed by the computer for more than an hour, just waiting for the test result of a Mersenne number.
Later, he found that his energy could not keep up, so he handed over the work to Zhang Zhiqiang, and then opened another laboratory, connected two servers with slightly inferior performance, including all the computers in the two computer rooms, and used them all
To test the Mersenne number.
Now everyone who understands Wang Hao's research knows that the determination procedure he performed must have a certain probability of obtaining Mersenne prime numbers.
With the full support of the computer laboratory, the calculation speed has at least doubled, and the detection speed of the "File 1" number has been accelerated a lot.
Wang Hao did not stay in the central laboratory all the time, and Zhang Zhiqiang became the real protagonist. Many people visited the central laboratory when they had time, and Zhang Zhiqiang, who operated the execution files and calculations, would also proudly explain to them how to find the Mersenne prime numbers.
the process of.
Occasionally, regretful shouts came from the central laboratory, "Why isn't this one?"
"What about this time?"
"The one I tested in the afternoon was not the same. It took more than five hours!"
"This probability is too small, only 2%. It is normal if it is not a Mersenne prime."
"This is already the most probable of the remaining numbers."
"I feel like you guys are thinking too much. Isn't this just normal?"
Wang Hao is also in the computer laboratory. He is summarizing the content about Mersenne prime numbers. He occasionally takes a break and walks around. When he hears the discussions in the central laboratory, he can't help but curl his lips vigorously.
Chen Qinghua came out and saw Wang Hao, and immediately asked anxiously, "Wang Hao, tell me which number in it is most likely to be a Mersenne prime number? Let's verify the most likely number first."
"Don't worry. The results that are verified must be yours. The account used to log in is yours. It's impossible for us to steal the results. It's just a computer laboratory verification."
"this……"
Wang Hao grinned vigorously and said, "Dean Chen, do you pay too much attention to it? I feel that finding Mersenne prime numbers is a matter of chance. It is enough to use two servers for detection. If you can find it, you can find it. If you can't find it, you can find it.
Never mind……"
"Forget it, this is an opportunity." Chen Qinghua said seriously, "The School of Computer Science at our university has only been established for a short time, and the subject rating still needs more results to support it. Finding results like Mersenne primes is at least a good invention.
?You can get an invention award in the province."
"Not to mention rewards or not, think about it, if we can find another Mersenne prime number, then the whole country will know about our computer laboratory."
"After we build up our reputation, the number of students we will recruit in the future will be better..."
Wang Hao had to admit that what Chen Qinghua said made sense. From the perspective of a dean who hopes to develop a college, it must be very important to build a reputation for the department's laboratory.
However, for academic research, he has already verified a Mersenne prime number, which means that there is no problem with his research, and there is little significance in continuing.
"All right."
Wang Hao agreed with Chen Qinghua's statement and said, "In fact, there is no good way to verify it. Now we just start verifying it from the one with the highest probability."
"But I'm studying this. I'll see if I can improve the analysis program in a few days?"
"Can we continue to improve?"
Chen Qinghua stared after hearing this, pulled Wang Hao to the corner and asked carefully, "Wang Hao, tell me, have you really found the law of Mersenne prime numbers? If it were anyone else, I wouldn't believe it at all. If it were you, or
It’s possible.”
Wang Hao shook his head, "You have too high expectations for me. I feel that Mersenne prime numbers have no rules, and I just found a little correlation."
"That's amazing too!"
Chen Qinghua took a deep breath, "That's a Mersenne prime!"
…
The computer lab is always busy.
The discovery of a new Mersenne prime number by a Chinese scholar was big news, and a reporter from the provincial TV station quickly went over to do the interview.
The computer laboratory came forward to accept the interview, but the reporter mainly wanted to interview Wang Hao, who found the Mersenne prime number.
Wang Hao refused.
The reason for his refusal left reporters confused, "Let's do an interview together after a while."
"??"
Wang Hao did not explain too much. He felt that finding a Mersenne prime number was nothing worthy of an interview, and it was impossible to reveal his research on Mersenne prime numbers in advance in front of the camera.
What if there is a problem with the research?
This is not 100% guaranteed. If you find a Mersenne prime by luck, there will be no need to accept an interview.
That's just luck.
It's like winning the lottery. What's the point of being interviewed? Can you tell me the secret of buying a lottery ticket?
Wang Hao continues to do his own research. He is summarizing the relationship between Mersenne prime numbers and the corresponding exponent p, as well as the known rules for the occurrence of Mersenne prime numbers.
Regarding the rules of Mersenne prime numbers, there is a very famous conjecture called "Zhou's conjecture". He has a column interval setting to describe the Mersenne prime numbers, which can be understood as how many Mersenne primes there are in a certain interval.
The expression of Zhou's conjecture seems simple, but because it involves an exponential increase in numbers, it is very difficult to crack the conjecture, and it is impossible to prove it.
What Wang Hao did was to establish two function expressions, one of which was used to describe the index p, and the other was used as a decision function.
He does not want to use a function to describe all Mersenne prime numbers, but to substitute the determined prime number value into the function. The resulting coordinate point, the Mersenne number in the area covered by the decision function, is more likely to be a Mersenne number.
Prime number.
If it happens to intersect the edge of the decision function, it must be a Mersenne prime number.
This is a judgment that the exponent P corresponds to the Mersenne prime number, rather than actually cracking the mystery of the Mersenne prime number.
Although it is only this, it is certainly quite remarkable. The most direct effect is to help find more Mersenne primes.
To be continued...