Chapter 92 Discovery of new Mersenne prime numbers!
The doctoral students and graduate students in the computer laboratory completed their work faster than expected. Some of them completed their part of the work the next day, and only after asking did they find out that they had stayed up all night to code it.
This kind of enthusiasm for work will definitely be praised by business owners, but Wang Hao is not a business owner, and he does not recommend everyone to do this.
The work of graduate students and doctoral students is progressing quickly, which also gives Wang Hao and Zhang Zhiqiang some headaches because the code part they are responsible for has not been completed yet.
The two simply stayed up late, working until twelve o'clock, and then simply slept in the laboratory.
I woke up the next morning, had a simple breakfast, and started working again.
On the next day, most of the work was to debug the program, including the program packages submitted by others, including the code of their own department, which needed to be debugged and run.
After all the codes are debugged, you can connect them part by part, debug and run them. The process of improvement is slower than the process of coding.
Next, it took another two days for the various parts to be almost completed, and then the first overall operation was carried out.
"The result was successfully output, not bad. What does this '0.03%' mean?" Zhang Zhiqiang is still a little confused. "Does it mean that the Mersenne number corresponding to this number is the probability of a Mersenne prime number?"
"There is no probability for a number. If it is a prime number, it is a prime number. If it is not a prime number, it is not a prime number." Wang Hao said, "However, you understand it correctly. It is just a number output by an evaluation system."
"0.03 is too low."
Wang Hao said, "It's already very high, although I will definitely beat these numbers."
While the two were talking, Li Ming from the Science and Technology Department suddenly came over and said, "Wang Hao, hurry up to the laboratory building of the School of Science. There is a reporter who wants to interview you. I searched all over and couldn't find you. Only after asking did you know.
, so you are here."
"Do I have to be interviewed?" Wang Hao was a little reluctant. He felt that the work at hand was more important.
Li Mingdao, "It's not necessary. The provincial TV station should just deal with it a few words."
"All right."
Wang Hao thought that he should take a short rest. He treated the reporter's interview as a break and followed Li Ming.
The interview took place in a small conference room in the laboratory building of the School of Science.
The reporter from the provincial TV station was already waiting there. Even the background for the interview had been arranged. A brand new desk was moved over. Wang Hao was sitting behind the desk, with a world map in the background.
He sat down for an interview.
The reporter's questions still revolved around Arting's conjecture. The study of Arting's constant has been the hottest mathematical topic in recent times. Many people are talking about it even in foreign countries.
This is the largest achievement in the field of international number theory in recent years.
The last time such an influential result appeared was when Chinese mathematicians in Amriken completed the proof of the ‘weakened twin prime conjecture’.
Wang Hao is likely to win an international-level mathematics award for this research. Some domestic awards can be said to have been booked. Winning is just a matter of time.
The interview centered around the proof of Atting's constant. Wang Hao also talked about the significance of the existence of Atting's constant, "In a certain sense, this shows that there are rules for prime numbers."
"This pattern is not necessarily like other numbers, and what we have to do is to find out the underlying pattern."
"This is important."
Wang Hao gave a simple explanation and also explained the importance of basic mathematical research. "Many people may ask, why do we spend so much time studying these?"
"You may have heard that there is an organization that specifically calculates pi, π, and calculates it to hundreds of billions or trillions of digits. Why?"
"Of course it has no meaning to reality, but it can help humans understand the universe and the world they live in more clearly and clearly."
"This kind of continuous calculation is hoping to see a result, that is, pi can never be calculated completely."
"But what if all the calculations are done? What if it is proved through calculation that π is a finite recurring decimal? Both of these possibilities are very scary. They not only indicate that there is no true circle, but also indicate that our universe may not be a real circle.
The universe is just like the description of some scientists. The universe is probably just a bunch of codes, and we are just virtual ones."
"The research on the distribution of prime numbers is also very similar. The most basic mathematics and numbers are the description of the universe."
"In the most basic areas, we must continue to explore..."
Wang Hao used a simple metaphor to talk about the importance of research. He felt that he had done an extraordinary job in the interview, otherwise he would have explained a lot of content related to Artin's constant.
Although he knows that most people are definitely not interested in this.
The reporter asked the last question, "After completing the demonstration of Artin's constant, do you have any plans for your next research? Can you tell me about it?"
Wang Hao thought for a while and said, "I am currently studying Mersenne prime numbers and hope to gain something in this field."
Then he briefly explained the Mersenne primes, and the interview ended.
…
The provincial TV station still attaches great importance to Wang Hao's interview.
Northern Xinjiang Province is not a big academic province, and there are very few well-known scholars. Even scholars who are from Northern Xinjiang, many of them have gone to eastern coastal cities, or simply gone abroad.
Simply put, Northern Xinjiang Province cannot retain top talents.
Now a young mathematics professor has appeared at Xihai University and has completed world-class number theory results, which is definitely worthy of a special mention.
The provincial TV station broadcast the entire interview as a science program, and also selected excerpts from it for news broadcast.
At the same time, Weibo, an online news media affiliated with the provincial TV station, also published relevant reports and released them.
Provincial TV stations attach great importance to news, but in fact, it did not cause much trouble, because many media have already reported it, and this is not the first time Wang Hao has been interviewed.
However, some people who paid attention quickly grasped the key points after reading the report.
"Wang Hao is studying Mersenne primes." Many people feel it is a pity.
Someone even commented online, "Wang Hao went to study Mersenne prime numbers, and another mathematical genius is about to disappear."
"Look at those mathematical geniuses in the past. It would be great if they could have one achievement in the field of number theory. If they continue to study, they will not achieve any more results."
"Wang Hao should learn from the great master Tao Zhexuan, don't touch number theory, don't touch number theory."
"I remember Terence Tao was interviewed once and said that he was going to study the twin prime conjecture. It didn't take long for someone to complete the proof of weakening the twin prime conjecture... Luck followed him."
"..."
Wang Hao was not in the mood to pay attention to public opinion issues. After accepting the interview, he immediately returned to the computer laboratory and worked with Zhang Zhiqiang on the final improvements to the entire program.
It’s another day.
They waited until the afternoon of the next day to confirm that the program was complete and could be put into the computer to run normally.
After a brief discussion, they went directly to Dean Chen Qinghua and applied for the use of the two newly purchased large servers.
The computer laboratory recently purchased two servers, which cost 8 million. To put it bluntly, they are a large collection of processors, hard disks and other hardware. The computing power is quite strong. The computing power of each server exceeds
More than three hundred desktop computers worth ten thousand yuan.
These two servers are intended to be used as core equipment in the computer laboratory.
When Chen Qinghua heard that they applied to use the server, he was a little hesitant at first. What they were doing was not a computer laboratory project, and the most important thing was that he didn't think that a group of people could find Mersenne primes by writing a program.
But after careful consideration, he agreed.
Chen Qinghua's main consideration is Wang Hao. Zhang Zhiqiang is not within the scope of care at all. Wang Hao is a top algorithm expert and works at Xihai University. Even if it is just to make friends with Wang Hao and let them use the server, it doesn't matter.
He agreed generously and issued an agreement for use, writing down the specific usage conditions and signing and sealing it.
The server in the computer laboratory is the public property of the laboratory and was purchased by the school with funds for the development of the laboratory. It is not like an ordinary computer and can be used whenever you want.
After Zhang Zhiqiang got the right to use it, he immediately took Wang Hao there with great excitement. He had always been thinking about the two servers, but because he had no projects on hand that required the use of the servers, he unfortunately never used them.
You can try it this time.
The two new servers are in the so-called central laboratory, which is actually a converted conference room on the sixth floor.
They turn on the computer, enter the program, and with the support of powerful hardware, let the program run quickly.
At the same time, each data is also output to the file and classified.
The input value of this program is more than 60 million numbers. It can quickly detect the prime numbers among them and enter the real analysis program. The output is the 'prime number' and 'the probability that the corresponding Mersenne number is a Mersenne prime number'.
Probability is the decision data of a program.
The highest probability setting is 10%, the lowest probability is only 0.01%, and most of the output prime numbers correspond to 0.01%.
However, the accuracy of the determination is not that high. For example, for the known 49th Mersenne prime number, M74207281, the probability of the program determining that it is a prime number is only about 8%.
The 50th one, M77232917, has a probability of about 6%.
The 51st Mersenne prime number found by Patrick Roche, M82589933, has a probability of determination of less than 9%.
Although the program's judgment is not so accurate, it is obvious that the probability of judging several numbers is much higher than that of other numbers.
The first file output by the program contains all prime numbers with a probability above 1% and the decision probability.
The second file contains 0.1% to 1% of prime numbers.
The third file contains 0.05 to 0.1% of prime numbers.
Other prime numbers are discarded and output to the last file.
"Let's first detect numbers below 100 million." Wang Hao made the settings.
Zhang Zhiqiang is writing a program to connect the output file to the custom entrance of the Prime software, so that the prime numbers of "File 1" can be input into the custom detection.
In this way, you don't have to keep looking at the program and perform input operations one by one.
Wang Hao looked at the server host carefully and asked curiously, "We use these two servers to do primality testing for a number with tens of millions of digits. How long does it take to calculate a number?"
"This is not necessarily true." Zhang Zhiqiang said, "If it is fast, a few seconds will be enough. For example, this number can be directly divisible by a very small number, such as 3 or 7, but these are only extreme special cases. Most of them still use Lu.
The Cass-Lehmer test, which runs all the way to the end, would take more than ten hours at best."
"……so slow?"
"This is already very fast." Zhang Zhiqiang grinned vigorously. That was a number in the tens of millions, and the amount of calculation was simply beyond imagination. It only took ten hours, which was already very fast. If it weren't for the Lucas Lemer inspection
method, it is simply impossible to detect it.
"All right."
Wang Hao pursed his lips and nodded, "So we just have to wait? Let it run slowly. At this speed, it will take at least a month to finish calculating the first file, right?"
"almost."
Zhang Zhiqiang calculated the time and felt that he should talk to Dean Chen again. It was okay to use the server for a while, but using it continuously for a month seemed a bit excessive.
"Forget it, let's go tomorrow!" He thought and shook his head.
…
Wang Hao and Zhang Zhiqiang went out for a simple meal and agreed to go to the laboratory the next day to distribute money to the participating students.
Then rested.
After being busy for several days, Wang Hao also felt very tired. After filling his stomach, he returned home, lay down on the bed and fell asleep.
Ten hours later.
Opposite the earth.
After a busy day at work, Curtis Cooper, a mathematician at the University of Central Missouri, went to the computer room and routinely opened GIMPS open information to view data.
Curtis Cooper, the discoverer of the 49th Mersenne prime number, had been affiliated with the Electronic Frontier Foundation for Mersenne Primes for seven years.
Since ten years ago, he has been committed to coordinating and promoting GIMPS and hopes that more volunteers will join.
Now whenever he comes to work normally, Curtis Cooper will go to the computer in the computer room to take a look after finishing his work for the day.
GIMPS is a distributed open network. All information is open to the public and can be viewed by anyone who logs in.
The displayed content includes ‘which numbers have been detected’, ‘how many CPUs are involved in the calculation’, ‘number of users online’, ‘what is the total calculation time’, etc.
Of course, the ‘latest verified Mersenne prime number’ is also indispensable.
For the last kind of information, Curtis-Cooper did not consider it at all. He believed that the next Mersenne prime number would have to wait at least more than two years, because as of now, the calculation amount of each number is too large.
, it takes a long, long time for a volunteer's personal computer to verify a number, and the inability to completely verify a number means that the test will be in vain, because unfinished tests will not be reported at all.
It is impossible for any software to monitor all calculation data, otherwise there would be no need for volunteers to participate.
Today seems to be the same as usual, some numbers have been detected, and the number of logged-in users and CPUs are still about the same.
Curtis Cooper looked carefully and suddenly saw a special message——
"The new Mersenne prime number has been verified, from Chinese user WangHao, the number is M6XXXXXX!" The red font is hard to ignore.
Curtis Cooper was immediately shocked. He thought it was due to his old eyesight, so he read it carefully over and over again before confirming that the news was true.
He immediately logged into the forum on the GIMPS website, and sure enough, there were already a lot of discussions on it.
"The latest news, a new Mersenne prime has appeared! Wang Hao from China!"
"He's so lucky!"
"It turns out to be a number starting with 6, which is between the 48th and 49th Mersenne prime numbers. I have always thought that there must be a Mersenne prime number in this interval, but I didn't expect that there really is one!"
"Chinese are very rare. He should be the first Chinese to discover Mersenne prime numbers, right?"
“It’s actually us Chinese, it’s really awesome!”
“Friends, Mersenne primes know no borders!”
"I'm really jealous of him. My computer has been running continuously for seven years, and the result is nothing, nothing..."
"You're only seven years old, I'm fifteen years old, and I've already had four different computers!"
Curtis-Cooper looked at the news and determined that a new Mersenne prime number had appeared. He felt a little incredible and immediately told the other leaders of the Electronic Frontier Foundation of Mersenne Prime numbers.
There are three main people in charge of the Mason Prime Electronic Frontier Foundation. One is responsible for software development, one is responsible for website and forum maintenance, and one is the original sponsor. There is also a small organization that is mainly responsible for publicity and funding.
During the event, we also promoted products related to Mersenne prime numbers, but the promotion effect has always been very poor.
For example, they promoted a T-shirt, but as a result, the selling price of the T-shirt could not keep up with the shipping cost, and there were very few buyers.
Of course, none of this matters.
The important thing is that after learning about the latest Mersenne prime number, they immediately released public information and announced the discovery of the new Mersenne prime number.
"We are excited to announce that WangHao, a volunteer from China, has discovered the new Mersenne prime number M6XXXXXX."
"We also need to repeat the verification of the results, which will be done by Professor Curtis Cooper from the University of Central Missouri."
"Although I dare not say it clearly, this result is a normal report of the software, and it is most likely true!"
Florida, Ocala.
In a somewhat cramped rental house, a disheveled Patrick Roche was watching the battle scene played on the computer screen with excitement.
At some point, everything becomes boring.
Patrick Roche opened the browser indifferently and noticed the information released by GIMPS. He looked at it blankly and said to himself after a long time, "So, my name can no longer be listed on the GIMPS website in the future.
Up?"
"If you go out for a night out, all your capital will be lost?"
"This WangHao is really a lucky bastard who steps on shit..."
"WangHao, WangHao, that's strange. I seem to have heard of this name before?"