From University Lecturer to Chief Academician

The discovery of a new Mersenne prime is not an academic achievement. Knowing one more Mersenne prime with tens of millions of digits will not play a role in promoting 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 the 'shock' of many people.

That is a very large number with tens of millions of digits, 2 to the tens of millions of powers, let alone tens of millions of powers, just tens or hundreds of powers, the number is already hard to imagine.

There is a classic story that the emperor's daughter fell into the water and was rescued by a farmer. The emperor asked the farmer what he wanted in return for saving his daughter.

Pointing to a chess board nearby, the farmer said to the emperor, "Put one grain of rice on the first grid, two grains on the second grid, four grains on the third grid, and four grains on the fourth 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. Just put these 64 grids in this way, and I want 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 wise minister told the emperor that even if all the rice produced in the country was brought in, the 64 grids would not be filled.

Later, mathematicians calculated that the total weight of meters exceeded 281.4 billion tons.

This is already a staggering figure.

But in fact, it's just 2 to the 64th power. How big is the tens of millions of powers of 2, it has already exceeded the cognition of real things.

When you think about it, you can see how incredible it is to prove that such a number is a prime number.

This is not something that can be done by ordinary means, and not all numbers can be tested. It is impossible to test the primality of other numbers with tens of millions of digits.

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 incredibleness contained in it that the academic circles 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 a Mersenne prime number with more than 10 million digits, and it was also the largest prime number discovered by humans at that time.

Many people know very well that finding Mersenne primes is not an academic or scientific achievement, but the achievement of new Mersenne primes was named one of the 50 inventions of the year by American's "Time" magazine, ranking 29th.

So finding Mersenne primes, the most attractive thing is that it can greatly increase fame.

Same goes for Padraic Roche.

His name appeared in the reports of major media, as if he had become a heavyweight scientist. In fact, he was just an otaku hiding at home, at best he could be regarded as an algorithm engineer.

exactly.

The computer lab at Xihai University desperately wants fame.

If a university wants to develop and a department wants to develop, fame is a must, and the best way to get fame is academic achievements, but academic achievements cannot be obtained through hard work.

Wang Hao's research was regarded as a key task.

Dean Chen Qinghua went into battle in person and stood by the computer for more than an hour, just to wait 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, connecting two servers with less performance, and all the computers in the two computer rooms together, all using To do the detection of Mersenne number.

Everyone who understands Wang Hao's research now knows that the judgment procedure he made 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 one' 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 went to the central laboratory when they had time, and Zhang Zhiqiang, who operated and executed files and calculations, would also proudly explain to them how to find Mersenne prime numbers. the process of.

Occasionally, a cry of regret came from the central laboratory, "Why isn't this?"

"What about this time?"

"The one tested in the afternoon is not the same. It took more than five hours!"

"This probability is too small, only 2%, and it is normal if it is not a Mersenne prime number."

"This is already the most probable of the remaining numbers."

"I feel like you guys are thinking too much. Isn't it normal, okay?"

Wang Hao is also in the computer laboratory. He is summarizing the content about Mersenne prime numbers. He occasionally takes a break to take a walk around. When he hears the discussions in the central laboratory, he can't help curling his lips hard.

Chen Qinghua came out and saw Wang Hao, and immediately asked anxiously, "Wang Hao, tell me, which number is most likely to be a Mersenne prime number? Let's verify the most likely number first."

"Don't worry, the verification is definitely your result, and the login is your account, and it is impossible for us to grab the result. It is just a name of a computer laboratory verification."

"this……"

Wang Hao grinned vigorously, and said, "Dean Chen, are you paying too much attention to it? I feel that finding Mersenne prime numbers is just a random thing. It is enough to use two servers for detection. If you can find it, you will find it. If you can't find it, you will find it. Never mind……"

"Forget it, this is an opportunity." Chen Qinghua said seriously, "Our university's School of Computer Science has been established for a short time, and subject rating still needs more achievements. Finding achievements such as Mersenne prime numbers is at least a very good invention. ? You can get an invention award in the province."

"Don't talk about rewards or not, think about it, if you can find another Mersenne prime number, then the whole country will know about our computer laboratory."

"After spreading the reputation, the source of students recruited in the future will be better..."

Wang Hao had to admit that what Chen Qinghua said was reasonable. From the perspective of the dean who wanted to develop the college, it must be very important to establish the reputation of 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 it does not make much sense to continue.

"All right."

Wang Hao agreed with Chen Qinghua's statement, and he said, "Actually, there is no good way to verify, and now we start to verify from the high probability."

"But I'm working on this. I'll see if I can improve the analysis program in a few days?"

"Can you continue to improve?"

Chen Qinghua stared at him, pulled Wang Hao into a corner and asked carefully, "Wang Hao, tell me, have you really found the law of Mersenne prime numbers? I don't believe it at all if it were you, or It's possible."

Wang Hao shook his head, "You have too high expectations of me. I feel that the Mersenne prime numbers are irregular, and I just found a little correlation."

"That's amazing too!"

Chen Qinghua took a deep breath, "That's a Mersenne prime number!"

...

Work in the computer lab has been busy.

It was big news that a Chinese scholar had found a new Mersenne prime, and a reporter from the provincial TV station soon went over to do an 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 made the reporter puzzled, "After a while, let's interview together."

"??"

Wang Hao didn't explain too much. He felt that finding a Mersenne prime number was nothing worth interviewing, and it was impossible to face the camera and reveal his research on Mersenne prime numbers in advance.

What if there is a problem with the research?

This is not 100% guaranteed. If you find a Mersenne prime by luck, there is no need for an interview.

That's just luck.

It's like winning the lottery, so what's the point of being interviewed? Can you tell me the secret of buying lottery tickets?

Wang Hao continued to do his own research. He was summarizing the relationship between Mersenne prime numbers and the corresponding exponent p, as well as the law of the occurrence of known Mersenne prime numbers.

Regarding the law of Mersenne prime numbers, there is a very famous conjecture called "Zhou's conjecture". He has a set of column intervals to describe Mersenne prime numbers, which can be understood as how many Mersenne prime numbers there are in a certain interval.

The expression of Zhou's conjecture looks simple, but because it involves an exponential increase in numbers, it is very difficult to decipher 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 exponent p, and the other was used as a judgment function.

He does not want to use a function to describe all Mersenne prime numbers, but to substitute the determined prime number values ​​into the function, and the obtained coordinate points, the Mersenne numbers in the area covered by the judgment function, are more likely to be Mersenne Prime number.

If it happens to intersect with the edge of the decision function, it must be a Mersenne prime.

This is a determination of the exponent P corresponding to the Mersenne prime number, rather than actually solving the mystery of the Mersenne prime number.

Although it is just that, it must be quite remarkable. The most direct effect is to help find more Mersenne primes.

...

Two days later, the GIMPS main station released the news --

After two detailed calculations and tests, the M6XXXXXXX Mersenne number found by Wang Hao, a volunteer from China, was determined to be a new Mersenne prime.

Although it is a newly found Mersenne prime, its code name is not 52, but 49. The new Mersenne prime, whose number is between 48 and the original 49, becomes the new '49th Mersenne prime'.

At the same time, the Mersenne Prime Electronic Frontier Foundation announced that they will award $100,000 to Wang Hao, a volunteer who finds a new Mersenne prime.

The GIMPS master station also updated the information.

The introduction of 'Lucky Padrik Rosh' was replaced, and 'Lucky Chinese Scholar' Wang Hao was put in. The introduction was much taller than Padrik Rosh, "This volunteer from China , is an internationally renowned mathematician, he is more fortunate than ordinary people, the record shows that he joined GIMPS for only one week."

"So, anyone can find a Mersenne prime, and as long as they are lucky enough, they may win a $100,000 grand prize..."

University of Central Missouri.

Curtis Cooper sat in the office and watched the news from the GIMPS main station, and couldn't help but sigh for Wang Hao's luck. He always thought that the next Mersenne prime would take two years, and he never thought that it would be so soon.

"Numbers between the 48th and 49th numbers should be randomly assigned by the program."

"Because of this, I'm so lucky!" Curtis Cooper couldn't help but sigh with emotion, "After this number appears, the next one will have to wait for a few years. I don't know if I can wait until I retire?"

This is an uncertain thing.

Curtis Cooper is fifty-seven years old, and his colleague Vince Edmondson, who promoted GIMPS, has passed away.

The other party was not able to share with him the results of finding new Mersenne primes, nor was he able to share the excitement and joy.

This is the place to be sorry.

Curtis Cooper couldn't help shaking his head while thinking, and was about to turn off the computer to take a rest, when he suddenly saw a reminder on the webpage.

Marked in red.

"The new Mersenne prime number is verified, from Chinese user WangHao, the number is M6XXXXXXX."

Is the message delayed?

Curtis Cooper subconsciously thought that the news was delayed that day, but at a glance, he felt that something was wrong. He personally verified the new Mersenne prime number, and verified it twice in a row. It took more than ten hours. The exponential The eight numbers can be memorized proficiently.

In this new reminder, the exponent number after the M is significantly different.

"What's happening here?"

"Could it be that the website was hacked and something went wrong? Impossible?"

Curtis Cooper rubbed his eyes hard, and then opened the forum to look, and found that it could already be described as an 'explosion'. There were related posts everywhere, and exclamations everywhere--

"Did you see it? New Mersenne primes."

"Another new Mersenne prime, still starting with 6, still found by Wang Hao!"

"It feels like buying a lottery ticket and winning 100 million, and then buying another bet and winning another 100 million. What kind of character is this?"

"It's amazing, this volunteer Wang Hao from China!"

"There is no doubt that God is watching him!"

"I'm going crazy with envy!"

"..."