Research starts with PhD students

Chapter 112: $15! My Lost Youth

Finding a prime number with 100 million digits...

This was Zhang Shuo’s first time doing this kind of research, and he discovered that it was not easy to find a starting point for the research.

A prime number with 10 million digits must first of all be a number with digits over 99 million, and among the numbers with digits over 999 million, the smallest number is 999 to the power of .

The numbers are so large that the amount of calculations involved in determining primality using conventional methods would be immeasurable, and the performance of the most advanced computers would be simply a drop in the bucket.

So, we have to find special numbers.

Mersenne numbers are the easiest "special numbers" to measure primality. So far, the top few numbers in the list of the largest known prime numbers are all Mersenne primes.

Mersenne numbers, or '2 to the power of n - 1', can be tested for primality using the Lucas-Lehmer test because of their special properties.

The Lucas-Lehmer test is a method specifically for detecting cycles in Mersenne numbers.

This method greatly simplifies the primality test of Mersenne numbers. For example, to test the primality of the number '2 to the power of n - 1', only 'n-2' cycles of calculation are needed to get the result.

Of course, when it comes to digits in the billions, each calculation requires a huge amount of computing power, and it is impossible to perform analysis on the digits in the billions themselves.

"So, we can only study the power n..."

Among all the Mersenne numbers, Mersenne primes account for a very small proportion, and there is no regular pattern in their appearance. The only starting point for research is analysis from the power n.

First, in order for the Mersenne number to be higher than 3.32192 million, the power n must be greater than 2 (log10 ()) billion.

Secondly, n must be a prime number. Only if n is a prime number can the corresponding Mersenne number be a Mersenne prime number.

then……

"Krypton Coins!"

【Scientific research coin - 1.】

After carrying out the Kebi operation, I immediately knew the next general direction - probability screening!
Use the probability judgment method to screen prime numbers greater than '3.32192 million'. If the probability of a prime number n corresponding to a Mersenne prime is low, it is directly excluded.

There is no regularity in Mersenne primes, so the screening method is naturally full of subjectivity.

In other words, the screening process is not rigorous.

Of course, it has no impact at all. The goal of the research is to find "a billion-digit prime number". As long as the n that is not the one corresponding to the billion-digit prime number is screened out, it has no impact.

……

Zhang Shuo began to "retreat".

He was bored in the office all day.

Tan Youming and Su Bingkang stood at the stairs together. Tan Youming said with some concern, "Zhang Shuo is a little too devoted to his research. He has been staying in the office alone for a long time recently."

"Maybe he hasn't adapted to the life of a researcher yet?"

Su Bingkang stared at the door of Zhang Shuo's office and frowned, "I just went to check it out. He was indeed doing research. He was so engrossed in it that he ignored me. He probably didn't even know I went in and out."

He pondered and said, "Is it because I graduated too quickly? The transition from studying to working might be a little difficult to adapt to."

Sun Xingli walked over from a distance. He followed their gazes and asked, "Dean Tan, Professor Su, what are you looking at?"

"Zhang Shuo!"

Tan Youming said worriedly, "He has been stuck in the office for two days."

"What's the big deal?" Sun Xingli touched the back of his head, a little confused, "I've been staying in the office all the time, isn't that normal?"

"Are you doing research?" Tan Youming was a little skeptical.

"Of course!"

Sun Xingli immediately emphasized loudly, "I am preparing to apply for a project next year and have already started writing a plan!"

"I gonna go see!"

After he finished speaking, he walked quickly towards Zhang Shuo's office without waiting for Tan Youming to say anything.

"Enter!"

There was a shout from inside.

When Sun Xingli pushed the door open and walked in, he saw a lot of manuscripts on the table and on the floor, making the room look a little messy.

Zhang Shuo was staring at the computer screen.

Sun Xingli leaned over to take a look and found that there was an analytical curve chart on the screen with a lot of densely packed points on it. He looked at it for a long time but couldn't understand it.

He picked up a manuscript on the table, held it in front of his eyes and looked at it again and again, and found that it contained a large number of numbers, as well as some symbols, formulas and the like.

He stared at the manuscript for a long time, then suddenly realized what was happening and shouted in surprise, "Are you studying Mersenne primes?!"

"Definitely is!"

Zhang Shuo nodded and said, "Last time you mentioned Mersenne primes, I thought it was very interesting, so I wanted to find a prime number with 100 million digits."

Sun Xingli immediately laughed, "You are following my old path!"

"When I was 25, I was in the same situation as you, studying a lot of numbers every day, but it seems that you are more persistent than me..."

"I understand. This day will come!"

He patted Zhang Shuo's shoulder in understanding and said, "But I advise you to be prepared for the possibility of not finding anything. Otherwise, when you find nothing, you will cry alone at night and be laughed at by your girlfriend. That will be very uncomfortable."

Zhang Shuo was stunned for a moment, then turned around and asked, "You cried secretly because of this night? And your girlfriend laughed at you?"

"I'm not talking about me, I'm talking about you!" Sun Xingli corrected immediately.

"I don't have a girlfriend."

"...Anyway, I'm talking about you!"

Sun Xingli said the next sentence harshly, and walked out of the room quickly. Just as he closed the door, he saw Luo Yongjun coming towards him.

Luo Yongjun heard that Zhang Shuo was alone in the office, so he came over to check on him. He asked in a low voice, "How is it? What is Zhang Shuo doing?"

"What can we do?"

Sun Xingli said seriously, "He is repeating my mistakes. This is what people like us will inevitably experience!" "People like you? You and Zhang Shuo?"

"correct."

Luo Yongjun glanced at Sun Xingli with disdain, "You better speak up. I don't think you two are the same kind of people anyway."

Sun Xingli explained with a depressed look.

Then, he looked up at the sky at a 45-degree angle and sighed, "Zhang Shuo is in the same situation I was in a few years ago, naively wanting to find a Mersenne prime number and win a $15 prize."

"In the end, nothing will be gained. I have seen his future, just like my youth that has passed away..."

Luo Yongjun curled his lips and said sarcastically, "I remember you said that when you graduated with your master's degree, you had a white girlfriend, but you broke up not long after dating."

"Youth that's gone? Your youth is a breakup, forget it now!"

"..."

in the office.

Zhang Shuo continued his research.

He found 'finding numbers' very interesting.

The research we did before was all about proofs, algorithm research, implementation methods, etc. If there is progress in the research, there is progress. Once the direction is right, the progress of the task will be improved.

Current research is different. It uses mathematical methods to make probability judgments, and the judgment process is very subjective.

It's like picking out the best-looking one among a group of strangers.

How to choose?

"Short people are disqualified, tall people are inappropriate, and those with long hair are eliminated..."

"You have a pimple on your face, get out of here!"

"Those wearing glasses can leave now..."

After a series of 'seemingly related and seemingly unrelated' judgments, a large number of numbers were eliminated.

The growth of task progress is also very interesting. It seems that as long as the numbers are filtered out, the progress will increase. After eliminating most of the numbers, the task progress has increased a lot.

"No matter what method you use, as long as there is an n in the remaining numbers that is related to a billion-digit Mersenne prime, your progress will increase."

Then he began to cull numbers on a large scale.

The progress of the task is increasing rapidly.

For a moment, Zhang Shuo felt that he had found a bug in the system task, until there were only 31 numbers left. No matter how many numbers he eliminated, the task progress did not move.

Open the task system——

【Task 1】

[Research project name: Searching for a billion-digit prime number (difficulty assessment: C).]

【Progress: 70.000%.】

(The task can be canceled. The current number of research coins required to cancel the task is 65.)
(The remaining progress requires 30 scientific research coins.)
"70% exactly?"

"The remaining 30 research coins are needed..."

He got it.

The task system can help eliminate most of the numbers, and the remaining ones must be checked by computer or by purchasing task progress.

He spent one scientific research coin, and the task progress became '71%'. He then tried to eliminate a number, and the remaining number became 30.

"Among the remaining 30 numbers, there must be one that is associated with the billion-digit Mersenne prime."

"If you buy the progress directly, you will have to spend 29 research coins, but the final settlement of the task will only give you 20 research coins."

"The best way is to do the test directly with a computer?"

"30 numbers are still a bit too many..."

Zhang Shuo wrote down the numbers one by one, then stood up and walked out of the office.

He went to find Sun Xingli.

Luo Yongjun was also in Sun Xingli's office. He was sitting on the sofa drinking coffee, while Sun Xingli was sitting on a chair, tiptoeing and browsing his mobile phone.

Zhang Shuo walked in and asked directly, "Brother Sun, where did you find the large server?"

"Mersenne number?"

Sun Xingli sat up straight abruptly, looking at Zhang Shuo with shining eyes. He walked over with a smile, "Do you want to do a calculation verification?"

"Correct."

Zhang Shuo showed Sun Xingli the manuscript paper with numbers written on it and said, "Calculate these numbers."

Sun Xingli smiled even more happily.

He pulled Zhang Shuo out, clearly impatient, "Computer Architecture Laboratory, Supercomputing Group, their laboratory has large servers."

"They have cooperation with the Donggang Computing Service Center and can remotely borrow the computing power of the Donggang Computing Service Center."

When he reached the door, he turned around and called Luo Yongjun, "Old Luo, let's go together. Someone is about to retrace my path to youth..."

"How interesting!"

Luo Yongjun ignored Sun Xingli. He walked over to Zhang Shuo and whispered, "Why don't you reconsider it? Using the supercomputing group's servers costs money, and it's not cheap."

"It's ok."

Zhang Shuo shook his head nonchalantly and said with a smile, "If you find the first billion-digit prime number, you'll get a $15 prize."

Sun Xingli nodded in agreement, "That's what I thought at that time!"

He said this with a smile on his face and gave a thumbs up.

(End of this chapter)