From University Lecturer to Chief Academician

The GIMPS forum exploded.

The contents of the posts posted on the forum are all related to the newly discovered Mersenne primes.

Everyone is discussing.

All the news is inseparable from keywords and content such as "new Mersenne prime number", "two Mersenne prime numbers discovered in a row", "Chinese volunteer Wang Hao".

Everyone who understands Mersenne prime numbers and the discovery and detection mechanism feels incredible.

From the establishment of GIMPS to the present, in more than 20 years, only 17 Mersenne primes have been found, 14 of which were discovered 10 years ago, and only 3 Mersenne primes have been found in the past ten years.

This is because the later the Mersenne number, the greater the amount of detection and calculation. The detection requirements of the tens of millions of Mersenne numbers and the million-digit Mersenne numbers are of course not at the same level.

The development speed of computer hardware is very fast, and there will be a replacement every few years, but it is still far behind the expansion speed of the detection demand of Mersenne number.

Now it takes a normal computer to run for several months to detect a Mersenne number. It is already remarkable for GIMPS participants to complete the detection of several Mersenne numbers with a personal computer, let alone find a Mersenne prime number.

However, Wang Hao, a volunteer from China, found two Mersenne primes in just one week.

The members of the GIMPS forum first ruled out the factor of hacking. Many of them are mathematicians and computer experts. Just looking at the website, they know that there is no sign of hacking. Under normal circumstances, there will be no hacking. A distributed computing network where all information is publicly available.

That doesn't make any sense.

Website and software errors can also be ruled out, because someone in charge has come forward to explain that there are no errors in the website or software.

"The news about the new Mersenne prime numbers on the website is the information that the software detection information is automatically reported and updated." Blosser is in charge of website maintenance and software updates. He was also surprised to see the information, so he sent a post to clarify .

Blosser's explanation also completely rules out the possibility of error, in other words, the new Mersenne prime numbers shown are very likely to be true.

Many people find this unacceptable.

How can one's luck be so good?

Someone posted and pointed out, "This Wang Hao from China is a mathematician and has a certain reputation. I checked, and the proof of Artin's constant he completed at an international conference is very influential. Could it be He has cracked the mystery of Mersenne primes, and knows which ones are Mersenne primes?"

Immediately, several mathematicians stood up and retorted, "This is impossible, Mersenne prime numbers have no rules."

"I'd rather believe that he was lucky than that he could decipher the law of Mersenne prime numbers."

"It is possible to find Mersenne primes in a row, but it is absolutely impossible to find the law of Mersenne primes. I have been engaged in mathematical research for more than 20 years, and I have a good understanding of Mersenne primes. In Mersenne numbers, this type of number is like Ordinary prime numbers are the same in numbers, and there is no fixed law of appearance at all."

Many people on the forum started discussing about it.

Curtis Cooper is also a mathematician, and he also expressed his views on this, "I also think it is impossible. This is luck, but there is also a factor of his understanding of Mersenne numbers."

The latter is critical.

People who find Mersenne primes are dentists, couriers, or whatever, but most are mathematicians and computer experts.

Curtis Cooper also discovered Mersenne prime numbers. He relied on his own understanding of mathematics to screen out some numbers and conduct custom analysis and testing.

The discovery of other Mersenne prime numbers is mostly found through custom testing. Only laymen who don't understand at all, or just use the program to do system stress testing, will do the testing according to the numbers assigned by the system.

Curtis Cooper's statement won the support of many mathematicians and computer experts, but at the same time they still believed that Wang Hao's luck was so good that it exploded.

Even if there is a deep study on Mersenne numbers, it should be known that Mersenne prime numbers are very rare among Mersenne numbers.

For example, there are more than 664,500 prime numbers below 10 million. Among the Mersenne numbers corresponding to them as "exponents", only 38 are Mersenne prime numbers, and the probability is not even one in ten thousand. arrive.

If the prime numbers of more than 50 million are screened for detection, the probability of corresponding Mersenne prime numbers will be lower. There are only two or three numbers in hundreds of thousands, or even none at all.

With this probability, it is not an exaggeration to say that it is a needle in a haystack.

On the other side, the night of Xihai University.

A shout suddenly came from the top floor of the computer laboratory building, "Ah~~~"

Several people in the building hurried to the central laboratory to check, and saw Zhang Zhiqiang in a state of excitement, "You are here, come and see! The new Mersenne prime number has been found!"

"I fell asleep just now, and I just dreamed that I found a Mersenne prime number, so I came here to take a look. I didn't expect to find it!"

"This is the second one!"

Zhang Zhiqiang said excitedly with his red eyes. Others could understand his emotions. It was really difficult to find a Mersenne prime number, but he found two within a week.

Although it is not Zhang Zhiqiang's achievement, he can be regarded as the second person to contribute.

Others also talked excitedly, "The second Mersenne prime number, this is really amazing."

"It is estimated that public opinion will explode tomorrow!"

"This time, our computer laboratory is definitely a big hit, not only domestically, but also internationally!"

"Look, the GIMPS forum has gone crazy, and everyone is talking about this topic."

They discussed staying in the computer lab altogether, squatting there all the time, waiting for the arrival of the next day, as if they were afraid that the numbers would run away with long legs.

In the morning, some media had already noticed the news and started reporting.

Most reports are somewhat uncertain, "Professor Wang Hao of Xihai University, suspected to have found two Mersenne prime numbers."

"Shocking news came out of GIMPS. Within a week, two Mersenne primes were suspected to be detected, and they were all discovered by Professor Wang Hao from Xihai University."

"Is this a mistake, or real information? GIMPS announced the detection of the second Mersenne prime number..."

This incident even became a hot search on the Internet, and the public opinion was even hotter than last time.

I discovered a Mersenne prime number before, which is a progress in the search for Mersenne prime numbers. In just one week, I discovered a new Mersenne prime number and found that the person is still Wang Hao. Things have become very unusual.

The same person finds two Mersenne prime numbers, which also happened in history.

For example, the 43rd and 44th Mersenne prime numbers were both discovered by the same team using GIMPS, but the time interval between them was as long as nine months.

Now it is only within a week to quickly discover two Mersenne primes, which is beyond the 'normal range'.

It was asked whether the coverage operation was carried out.

A professional computer expert immediately stood up and pointed out, "Even if a high-performance supercomputer is used, it will take more than 100,000 hours to perform coverage detection for the index corresponding to the 60 million to 70 million range index. .”

"Obviously, that's impossible."

So public opinion paid attention to Xihai University and Wang Hao who discovered two Mersenne prime numbers.

At eight o'clock in the morning, Wang Hao arrived at the computer laboratory on time.

He knew in advance that he had discovered the second Mersenne prime number, but he was not surprised. He just went around and talked with a few familiar people. After writing down the specific number, he hurried to the workshop to verify it. .

Wang Hao has already shaped two functions.

One is a verification function, which can be substituted into a prime number to calculate the coordinates, and the other is a judgment function, which can determine whether the coordinates are within the area or on the edge line. The former indicates that the probability of being a Mersenne prime is high, and the latter indicates that it must be a Mersenne prime. .

After substituting the newly discovered Mersenne prime number, unfortunately, the coordinates of the corresponding function appear in the coverage area of ​​the decision function, but not on the edge line of the coverage area of ​​the decision function.

"It seems that we still need to use computer means to verify, and the next work cannot be solved by mathematical research."

Wang Hao started to write the program after thinking about it. He wanted to do a "function verification" program, that is, to substitute each index into the function, calculate the coordinates corresponding to their corresponding Mersenne numbers, and determine whether the area covered by the function Inside.

Because the two functions are more complicated, the program design is not easy.

Fortunately, the function created by Wang Hao himself is very familiar with the solution method after substituting values. It took him a whole morning to finally complete all the design of the program.

Then he went to the central laboratory.

At this time, the central laboratory was still very lively. Not only people from the computer laboratory, but also people from other colleges came over. Several leaders of the school came to pay special attention to the problem of Mersenne prime numbers. They knew that Wang Hao was busy. He was studying something, and he didn't bother in the past.

In the corridor.

Chen Qinghua, Zhu Jianrong, and Luan Haiping were standing together, discussing the school's announcement.

Chen Qinghua wants Zhu Jianrong to mention the computer lab more when drafting a manuscript. It is best to "obfuscate" Wang Hao's affiliation, so that people who read the news think that Wang Hao is the research institute of the computer lab and a professor of the School of Computer Science. .

Next to him, Luan Haiping listened with a dark face, his vicious eyes seemed to reveal that he had the urge to strangle Chen Qinghua to death, and he kept objecting, "Wang Hao is a professor of the Faculty of Science, even if he doesn't talk about the Faculty, he can't say He's from the School of Computer Science? Isn't that a lie?"

"What lie?"

Chen Qinghua immediately questioned Sanlian, "Has Wang Hao been in the computer lab? Did the two Mersenne primes be discovered in the computer lab? So the announcement of the results said, Professor Wang Hao in the computer lab, what's the problem?" ?”

"Ah~~~"

Wang Hao came over and stood by.

Chen Qinghua noticed that Wang Hao was a little embarrassed, and immediately said, "Wang Hao is also here, and I will say bluntly that we are not going to dig him into the computer laboratory, but, for this achievement, we will complete it in our computer laboratory." Yeah, it doesn't make sense for the announcement to talk about the Faculty of Science, does it?"

"Why is it meaningless? It's very meaningful. The School of Science also needs..." Luan Haiping immediately retorted.

Wang Hao was not interested in the School of Computer Science or the School of Science. Anyway, it was just an announcement from the school. He simply pretended that he hadn't seen it, and walked past it lightly.

He came to find Zhang Zhiqiang.

Zhang Zhiqiang still had red eyes, and he hadn't rested since three in the morning.

Wang Hao persuaded, "Hurry up and go back to sleep. Finding Mersenne primes is a pleasure, but don't be like this..."

"Don't worry, you can still hold on!"

Zhang Zhiqiang said nonchalantly that he was indeed very tired and was thinking of going to the office for a while.

There is still something to do now.

"Stop the detection program and calculate this first..."

Wang Hao copied the written code into the computer, and explained briefly, "This is a screening program for Mersenne numbers. It can be said to be an optimization of the previous program, and it may become more accurate."

He was a little unsure.

Before the results are 100% out, he dare not say that the research he has done is correct.

Zhang Zhiqiang immediately regained his energy, stopped the running detection program, and started to execute the code he just copied.

The prime numbers below 100 million are entered as data, and there are three files at the output end.

The first file records the 'exponent P' and the corresponding coordinates at the edge of the decision function.

The second file records the 'exponent P' within the coverage of the decision function, the corresponding coordinates and the closest distance to the edge line.

The third file is the remaining excluded prime numbers, corresponding coordinates, and the shortest distance to the edge line.

The functions are more complicated, and the programs are more complicated, and the amount of calculation required is very large. Even with the existing computing power, it will take more than three hours to execute all of them.

Zhang Zhiqiang was pushed to rest.

Wang Hao simply waited in front of the computer, watching the program execute, waiting for the output result.

...

At two o'clock in the afternoon, Chen Qinghua and Zhu Jianrong went to the central laboratory together, found Wang Hao and handed him a handwritten announcement.

"We discussed and discussed, but I still want to let you see, you are the person involved, how about this announcement?"

"If you say yes, we will post it." Chen Qinghua looked at Wang Hao seriously, and the announcement said that "Professor Wang Hao is working in the computer laboratory and found two Mersenne prime numbers in a row."

This vague statement sounds as if Wang Hao is a researcher in the computer laboratory.

Wang Hao didn't care about this. He just glanced at it, threw the handwritten announcement aside, and said, "Dean Chen, Director Zhu, don't rush to make an announcement, it's just two Mersenne prime numbers."

"...That's all?" Chen Qinghua was puzzled.

Zhu Jianrong also tugged at the corner of his mouth, and found that the two Mersenne primes were just 'just'. Isn't his tone too loud?

Wang Hao ignored their reactions, but opened a file in the computer, which recorded eleven numbers, eight of which were in standard red fonts, and the remaining three were still black.

Pointing to the three black numbers, he said seriously, "These three are the indices of Mersenne numbers, let's verify it."

"If nothing else, they should all be Mersenne primes."