Research starts with PhD students

Chapter 113 The 52nd Mersenne prime, the first billion-digit prime number!
Computer Architecture Laboratory, Supercomputing Group Office.

Liu Haibin and Dong Hao were sitting together discussing the work issues of the supercomputing group.

Liu Haibin is less than 40 years old, but he is already a full professor at the School of Information at Soochow University. He is also a researcher in the Computer Structure Laboratory and the leader of the supercomputing group.

Dong Hao is a little older, almost 45 years old. He is the laboratory director and is responsible for all the work in the laboratory.

As they were talking, they heard a shout from the door, "Professor Liu, someone's looking for you!"

Liu Haibin took a look at the door and saw three people walking in one after another.

The one in the front is... staggered!

Dong Hao stood up only after seeing someone coming in. He also avoided the first person and immediately walked over and shouted enthusiastically, "Professor Zhang Shuo!"

"I have long admired your great name!"

"You're welcome."

Zhang Shuo is really too famous.

He is an academic star on the Internet. Even if you have never seen him in person, you can recognize him, let alone at Soochow University.

Dong Hao shook hands with Zhang Shuo, and then shook hands with Luo Yongjun, "Professor Luo!"

Liu Haibin also shook hands with Zhang Shuo and Luo Yongjun respectively.

The two of them looked at Sun Xingli again.

"Who is this……"

"Sun Xingli, Professor Sun!" Zhang Shuo also helped to introduce him, "A researcher at the High Court."

Dong Hao suddenly realized what was going on. He took the initiative to reach out and said, "Sorry, this is Professor Sun who worked with Professor Zhang Shuo on the Jebov conjecture!"

Sun Xingli had no choice but to accept it with resentment. The good news was that the other party told him his research results.

After a few people exchanged pleasantries, Sun Xingli, who considered himself experienced, directly stated his purpose.

“Do you want to use a server?”

Liu Haibin nodded and said, "Of course, no problem. We charge by the hour, and the normal fee for one hour is one thousand yuan."

Zhang Shuo looked at Sun Xingli.

Sun Xingli nodded slightly and whispered, "That's the price. It took me five hours and cost me 5000."

"Five hours? So slow?"

Zhang Shuo frowned slightly after hearing this.

"slow?"

Liu Haibin was a little unhappy. He immediately said, "Our server cannot catch up with the supercomputer, but it has 1200 processors installed, and its regular computing power exceeds that of 1000 ordinary computers."

Dong Hao quickly said, "Professor Zhang Shuo is doing important research, so it's normal that he needs a lot of computing power."

"Professor Liu's quotation is for external research projects within the school. The usage fee is 200 per hour, which is relatively low."

He then explained, "Some computing centers are open to the public, and the computing power they provide for individual projects is comparable to that of our servers."

"It's not a major research." Zhang Shuo shook his head.

Sun Xingli said, "It's not a school project, it's a personal hobby, just like me last year."

"Just like you?"

Dong Hao was a little confused and asked doubtfully, "Professor Sun, have you done any calculations?"

As soon as he finished speaking, Liu Haibin suddenly realized something and said, "I remember, Professor Sun, you did a calculation here last year, the Mersenne number verification, right?"

When this sentence was shouted, people passing by the door stopped and even tilted their heads to take a look inside.

Dong Hao also reacted.

Last year, someone came to rent a server to do primality testing of Mersenne numbers, and everyone in the lab knew about it.

This is extremely rare.

The servers in the laboratory are generally used for scientific research projects or personal research.

Some people rent servers specifically to run Prime and test the primality of several Mersenne numbers. Their behavior can be described as "rich people with plenty of money."

joke!

Who would do that?
Sun Xingli said shamelessly, "Let's not talk about my glorious history. This time we are still verifying the primality of Mersenne numbers!"

Everyone else saw Zhang Shuo.

Zhang Shuo didn't care too much and said directly, "We are indeed here to verify the Mersenne number."

Dong Hao and Liu Haibin looked at each other and didn't say anything else about this matter. Instead, they asked, "What number is it?"

He added, "If it is a large eight-digit number like Professor Sun, just count one and use a few small servers to calculate it."

"You don't have to pay. Our laboratory will calculate it for you."

Zhang Shuo took out a piece of manuscript paper filled with numbers and showed it to Dong Hao and Liu Haibin.

Sun Xingli and Luo Yongjun also leaned over to take a look.

They were stunned at the first glance.

Sun Xingli shouted exaggeratedly, "Nine digits? And it starts with 3 or 4? Why didn't you tell me earlier... Do you know what this means?"

He said what Dong Hao and Liu Haibin wanted to say.

Zhang Shuo said as a matter of course, "Didn't I say that? To find a billion-digit prime number, n must be a number greater than 300 million to be a billion-digit prime number."

"but……"

Sun Xingli frowned and didn't say anything for a long time.

Liu Haibin also understood Mersenne numbers, and finally understood why Zhang Shuo said that the calculation was slow.

He shook his head and said, "This amount of calculation is too huge. Even if we use our server to calculate it for a month, it would only be one number."

"If we really want to calculate, we must use the computing power of the supercomputing center."

Others also figured it out.

When Zhang Shuo heard Sun Xingli say that he had calculated for five hours, he subconsciously said "slow down". It turned out that he was calculating a nine-digit number!
The amount of computation required to test the primality of Mersenne numbers increases exponentially with the increase in the power n.

The amount of calculation required for a nine-digit number whose power begins with '3' can easily be hundreds or even thousands of times higher than that required for a large eight-digit number.

It took Sun Xingli five hours to calculate several numbers.

Zhang Shuo would spend more than ten days or even more than a month calculating a number. If he charged 1000 yuan per hour, it would cost him hundreds of thousands of yuan to calculate a number.

Zhang Shuo also understood.

He simply picked up the pen on the table and began to mark numbers on the manuscript paper, crossing out numbers one by one.

【Scientific research coin - 29.】

[The task has been completed and can be submitted! ]

He didn't have time to care about the task and quickly crossed out 29 numbers, leaving only the last one on the paper.

"That's it, just count this number!" Zhang Shuo said forcefully.

"Are you sure, Professor Zhang?"

Luo Yongjun pulled Zhang Shuo from behind. He felt that determining the primality of Mersenne numbers was like throwing money.

Hundreds of thousands!

Throw it away?

It's like a part of my heart was cut off...it hurts!
Zhang Shuo still said affirmatively, "Forget it, I've made up my mind." He then asked, "Can we use the computing power of the supercomputing center? One month is too long."

"No problem." Dong Hao nodded. "We have cooperation with the Donggang Computing Center. The unit price of their computing power is cheaper. We only use it when the computing demand is very large."

"Using their computing power, this number will take about a few hours, right? This is my estimate, but I'm not sure yet."

"What about the cost..."

Dong Hao and Liu Haibin looked at each other and continued, "Let's look at the amount of calculations."

He said frankly, "Our agreement with the Donggang Computing Center is to charge based on computing power. I estimate your figure to be... more than 10."

Liu Haibin followed up with, "It's already very low."

Zhang Shuo also had an estimate of the amount of calculation required. After listening, he asked, "Director Dong, Professor Liu, what if the calculation ends halfway through?"

"For example, it only took half an hour."

Dong Hao was stunned for a moment before he understood, "You mean, this happens to be a Mersenne prime number?"

"Correct."

If the power corresponds to a Mersenne prime, the calculation loop will exit halfway, perhaps completing the calculation in an hour.

Dong Hao smiled and said, "Well, Professor Zhang, if it is a Mersenne prime, not only will we not charge you, we will also give you 100,000!"

"Really?" Zhang Shuo asked.

"of course."

Dong Hao laughed, "If we can calculate the 52nd Mersenne prime, then we can say that it was calculated by our structural laboratory. What is 10 yuan worth?"

"Then let's get started!"

Zhang Shuo nodded with satisfaction and was very much looking forward to it.

……

Calculation is to log into Zhang Shuo's Prime account on the computer in the laboratory, thus entering the GIMPS distribution network.

Then, log in to the Donggang Computing Service Center and use their computing power for calculations.

Once everything is ready, the calculation begins.

Zhang Shuo sat in front of the computer waiting.

Sun Xingli and Luo Yongjun sat together. Liu Haibin also came over and asked curiously, "Why did Professor Zhang Shuo insist on calculating that number?"

"10 yuan, what a waste!"

"We really didn't charge any extra. If someone else charged this, Director Dong would never agree."

Sun Xingli nodded, "I know that. You just treat me differently. When I came here last year, you charged me one thousand yuan an hour."

"When it comes to Zhang Shuo, the fees are charged based on the research project."

Liu Haibin laughed and said, "Professor Sun, next time you come, I will definitely charge according to the school project, don't worry."

"Again?"

Sun Xingli couldn't help but grin.

Liu Haibin asked again, "Why does Professor Zhang insist on calculating that number?"

"You don't understand this?" Sun Xingli said, "I came here once last year, and he is just reliving my youth!"

"Be stubborn and persistent. You have to fail once before you can face the reality!"

Luo Yongjun rarely refuted. He was still distressed about the computing power cost, feeling as if he had spent his own money.

Liu Haibin still didn't understand. He had been dealing with computers all the time and couldn't understand what the point of calculating Mersenne numbers was.
Does doing mathematical research give you the confidence that you can analyze Mersenne primes?

……

at the same time.

Wang Duoju and Zhou Jianxin accompanied professors Liu Jian, Zhang Chunyang and Xu Jun to the Institute for Advanced Studies building.

Liu Jian, Zhang Chunyang and Xu Jun came on behalf of the Science, Technology and Industry Bureau.

When Professor Li learned about Zhang Shuo's numerical research on the NS equation, he asked several relevant scholars to come to Soochow University to talk to Zhang Shuo, wanting to know the specific progress of the research.

Numerical simulation of NS equations has great application value and significance and must be taken seriously.

The three of them talked about this topic all the way. "It's the news from the Second Academy of Aerospace, but I think it's a bit too much."

"The NS equation is a difficult problem to solve, not to mention numerical simulation."

"Li Jianfeng's team at the Donggang Mathematics Center is studying this and seems to have made considerable progress. Could it be that Zhang Shuo has made even greater progress than Li Jianfeng?"

"Li Jianfeng's team should be the most powerful in the country, right?"

"No matter what the situation is, I came here just to meet Zhang Shuo, he's a famous person."

"Right."

The arrival of the three people was still very low-key. They came on behalf of the Bureau of Science, Technology and Industry, and specifically told Sudong University not to be high-profile.

So only Wang Duoju and Zhou Jianxin accompanied them to find Zhang Shuo.

When they arrived at the Institute for Advanced Study building, they found that Zhang Shuo was not there. They asked several people but no one knew what happened. Finally, they made a phone call and found out that he was in the Computer Structure Laboratory.

Zhang Shuo didn't know who was coming, but he still wanted to wait for the primality test of Mersenne numbers, so he didn't want to meet anyone, so he replied directly, "Come here and talk if you have anything to say."

After Wang Duoju finished explaining the situation, Zhang Chunyang said, "How about we wait here?"

"What are you waiting for?"

Liu Jian said, "Professor Zhang may be doing some research, let's go over and take a look."

"Ok."

The three of them agreed and went to the computer structure laboratory together.

As they arrived at the door of their office, they heard a surprised shout from inside, "The calculation is over!"

"it's over?"

"It can't be that fast. That's a nine-digit number. Did Donggang allocate that much computing power to us?"

This is what Liu Haibin asked.

Liu Haibin, Dong Hao, Sun Xingli, Luo Dayong were all in the room, and two other associate professors also came to join in the fun.

Just now, they were still figuring out how long it would take.

This can be calculated using the allocated computing power and the required computing power.

Then, I found that the calculation was over.

After asking, Liu Haibin went to check and found that the calculation was indeed completed. He was a little confused for a moment.

Dong Hao was also a little confused.

Everyone else also reacted.

If there are no problems in the calculation, and the computing center does not allocate more computing power, the calculation ends early, which means...

"Mersenne primes!"

Sun Xingli shouted in disbelief.

Everyone looked at Zhang Shuo with doubts and surprise in their eyes.

Zhang Shuo smiled calmly. He nodded slightly first, then stood up and said to Sun Xingli, "So I said, Brother Sun, I am here to realize your dream!"

"The calculation is over!"

"I have found the 52nd Mersenne prime, which is also the first prime number with million digits!"

(End of this chapter)