Research starts with PhD students

Chapter 114: International excitement! Coincidence or luck? For mathematicians, it can't be a coincidence!

in the office.

Everyone saw Zhang Shuo, with extreme shock in their eyes, "You are not kidding, right? That's a Mersenne prime number!"

"is that true?"

“Are you sure it’s a Mersenne prime?”

Zhang Shuo nodded slightly and smiled, "It should be confirmed."

Liu Haibin looked at the computer screen, took a deep breath and said, "The calculation of the platform connection has been terminated, and the loop has been exited. The software prompts that a Mersenne prime number has been found..."

"it is true!"

He was very sure.

Others were even more surprised.

Before the calculation, no one would believe that the number Zhang Shuo came up with would correspond to a Mersenne prime.

Mersenne primes are not a new study.

Over the past few decades, countless scholars have specialized in studying prime numbers and then inputting them into computers to calculate whether the corresponding numbers are Mersenne primes.

Some people or teams succeed, but the reason for their success is not accurate analysis, but a lot of calculations.

Those calculations are not just one or two numbers, but rather a comprehensive calculation using a large amount of computing power, targeting tens of thousands or hundreds of thousands of numbers.

No one and no team would do that now, because the power of Mersenne number detection has reached the 'billion-digit' level.

The GIMPS maintenance team has determined that there are no other Mersenne primes among the Mersenne numbers with a power N below 90 million.

If the power N is above 90 million, or even over 100 million, the primality test of each number will require a huge amount of computation.

Computing power costs a lot of money.

In short, it is almost impossible to analyze which number corresponds to the Mersenne prime simply by mathematical means.

In this regard, luck is more important than analysis.

Many mathematical studies believe that the probability of Mersenne primes appearing is related to the distribution (density) of prime numbers. The larger the number, the sparser the distribution.

When the power n is set to a prime number between 300 million and 400 million, what is the probability that the corresponding Mersenne number is a Mersenne prime?

“No more than one in a hundred thousand!”

Liu Haibin said excitedly, "I also know about Mersenne primes. From 1996 to now, GIMPS has only discovered 16 Mersenne primes."

"The last Mersenne prime was a few years ago, and it was a number with a power of more than 80 million."

"The chances are too small!"

"What we have discovered now is a Mersenne prime with a power of 300 million to 400 million, and the corresponding number has exceeded 100 million digits."

“It means a lot!”

Dong Hao was also very excited, as he knew too well the impact of discovering the super-large Mersenne prime.

That will be reported by media all over the world!
The Computer Structure Laboratory is just a municipal scientific research unit of the School of Information at Soochow University and has no fame or influence at all.

Once the news is confirmed, they will be reported internationally, and possibly extensively.

By then, you will be famous!

Is development still far away?

He immediately said, "Calculate again and reconfirm!"

"it is good!"

Liu Haibin asked Zhang Shuo, then took the initiative to operate the computer to connect to the computing power platform and started a new calculation.

Others gathered around Zhang Shuo and asked, "How did you find that number?"

"Isn't this amazing?"

"It's definitely not luck!"

"This is amazing! The first prime number with 100 million digits, a super large Mersenne prime. I can imagine how surprised others would be if they knew about it..."

Liu Jian, Zhang Chunyang and Xu Jun stood together at the door.

They came here to discuss with Zhang Shuo some research issues on numerical simulation of NS equations, but when they arrived, no one paid any attention to them.

Now they know that Zhang Shuo has made a major discovery, the 52nd Mersenne prime?
The largest prime number with billion digits?

Of course, they knew what Mersenne primes were, and what the new discovery represented, and they were also very shocked.

"It looks like it was really discovered!"

"Isn't this too lucky? The chance of winning a Mersenne prime number is even lower than the chance of winning a lottery ticket!"

"They only calculated one number and determined it was a Mersenne prime. Could it be Zhang Shuo's latest research? He proved the Gerbov conjecture, so it's normal for him to study prime numbers."

"Even if we solve the Gerbov conjecture, it doesn't mean we can find Mersenne primes, right? The two are totally unrelated."

"Let's wait and see. I don't think we can talk about it today."

They came to talk to Zhang Shuo about research, but Zhang Shuo had just done another very important thing and couldn't possibly be in the mood to talk about other research.

The three of them simply sat aside and waited, and found a few computers to browse the Internet.

Liu Jian logged into the domestic GIMPS forum and posted a special message: "Important news: The 52nd Mersenne prime has been detected!"

A large number of comments quickly appeared below, "The poster is a professor? How dare you spread fake news!"

"Grandstanding!"

"After I read the post, I went to the official website to check, but there was nothing there."

"The original poster should be aware that spreading rumors is illegal, so don't be too happy about going to the detention room for a few days."

"You're lying. A Mersenne prime with a power of more than 3 million? Now the number has just exceeded 3 million. When did it reach more than million?"

"..."

Liu Jian was so angry that he started cursing and immediately started to respond with insults.

at the same time.

The sun is rising on the other side of the ocean.

Curtis Cooper, a former mathematics professor at the University of Central Missouri, discovered a total of four Mersenne primes through the GIMPS project, which earned him the title of "King of Prime Numbers".

After retirement, Curtis Cooper joined the GIMPS main team and was responsible for website maintenance and information updates.

All information from the GIMPS distributed computing system will be transmitted to the main platform.

Curtis and others will compile the information and publish it on the website, including verified numbers, new discoveries, related cooperation information, and so on.

At 6:30 in the morning, Curtis was already sitting in front of the computer. He logged into the main site as usual and immediately noticed a report message.

"A new Mersenne prime has been verified, M(3XXXXXXXX)."

He was stunned when he saw the message, and his first reaction was that the information was wrong.

Mersenne numbers with powers of 30 to 40 million have been verified more than twice, and there cannot be other Mersenne primes.

He looked at the string of numbers carefully and found that it was a nine-digit number.

Curtis took a deep breath and clicked on the message - M (3XXXXXXXX) has been verified, and the IP is from Sudong City, China.

Volunteer (user): ZhangShuo, last login time...

Registration time...

"New user? Chinese user? Only logged in twice?" "Discovered it on the third time?"

Curtis was filled with surprise.

M (3XXXXXXXX) is a very large Mersenne prime with a power of more than million, and it is also the first Mersenne prime discovered with more than million digits.

The information of the discoverer is also very interesting. The account has only been logged in twice, that is to say, the new Mersenne prime number was detected when logging in for the third time.

This is big news!
“The biggest breakthrough in a few years. No, maybe the biggest breakthrough in a decade!”

"The first Mersenne prime to the billionth digit!"

Curtis was shocked and called James Ward, whose team was responsible for the update and maintenance of prime95 and other software.

At the same time, James Ward is also an algorithm engineer for a well-known Internet company.

"James, you will never imagine what happened. The 52nd Mersenne prime, or to be more precise, the first prime number to the billionth digit, has appeared!"

Curtis said excitedly, "The users tested are from Sudong City, China, which is a very large number with a power of over 300 million."

James Ward asked in surprise, "Are you sure?"

"Of course!"

Curtis was very sure.

"Well, if I hadn't almost had a car accident while looking for the phone, I would have definitely thought I was still asleep."

"I'll go and verify it right away!"

James Ward took the numbers and found a computing center that wanted to cooperate.

After working hours, he explained the situation to the relevant personnel, who immediately arranged for verification and got the results quickly.

James Ward told Curtis the result. "I have verified it and it is indeed a prime number. The computing center is ready to release the information. I think you can also update the news."

"I can't wait any longer!"

Curtis really couldn't wait any longer. He had already written the content and even edited the text of the section, but he hadn't submitted it yet.

After receiving the confirmation message, he immediately submitted the request.

The GIMPS main site has changed. The title of the second column of the computational progress section has changed to "Major Discovery, the First Billion-Digit Prime Number!"

"GIMPS has just discovered the largest known prime number, M (3XXXXXXXX), which is an unambiguously high million-digit prime number. The calculation was done by Zhang Shuo from Sudong City, China.

Zhang Shuo is a new user of GIMPS. Before the discovery, he had only logged in twice and performed calculations for a short time.

Many GIMPS volunteers have been searching for more than 20 years and have attempted tens of thousands of calculations without any discovery.

This proves that, with a little luck, anyone can find the next Mersenne prime..."

After Curtis updated the news, he immediately sent an email to Zhang Shuo, hoping to know more about the story behind the new discovery.

There's something wrong with this.

The new prime number is an extremely large prime number with hundreds of millions of digits. The computing power required to detect it is very high, and the result cannot be obtained by simply logging in and calculating.

There is likely a team behind the new user, and perhaps the team just logs into his account and borrows GIMPS to test the hardware.

Perhaps, there are other possibilities.

Knowing more news can also help you publish more content on the website.

At this time, Dong Hao, Liu Haibin and others were very sure that they had found a new Mersenne prime number. They even did a third calculation and didn't care about the computing power costs at all.

After confirming it, Dong Hao told the school the news.

People who don't know about the discovery of Mersenne primes may think that it's just a number and nothing big, but people who know about it know that it has a great significance.

Mathematics has great significance and influence.

This is the history of the discovery of Mersenne primes.

More than a decade ago, Edson Smith, a computer scientist at UCLA, discovered a Mersenne prime with more than 1000 million digits.

This achievement was named one of the “50 Best Inventions” of the year by Time magazine, ranking 29th.

Ten years later, Jonathan Pace, a volunteer who had been a member of the GIMPS project for 14 years, found the 50th Mersenne prime known to mankind.

To commemorate this milestone discovery, a publishing house also released a book titled "The Largest Prime Number in 2017."

Only one year later, the record for the largest known prime number was broken again.

The new record was set by Patrick La Roche of Ocala, Florida, who received $100,000 and a ticket to an international mathematics conference for his discovery, with the mathematics society even reimbursing his airfare and hotel.

Now it is a new breakthrough, and it is the first billion-digit prime number.

After the GIMPS main site updated the information, hundreds of thousands of online users and more than a thousand teams immediately received the "alert of the discovery of new prime numbers."

The first to release the information internationally was a large computing center in Silicon Valley. "GIMPS discovered a new Mersenne prime, the first prime number with 100 million digits. We tested the number immediately and determined its primality."

"This is an amazing discovery, a great success of the GIMPS network, and a major milestone in Mersenne prime research!"

After that, GIMPS officials updated the information, and the GIMPS forum immediately exploded.

The forum, which usually had few posts, suddenly had a lot of discussions, and every post was talking about the news of the new Mersenne prime number.

"Billion prime numbers!"

"The power is over 300 million. It's amazing. How did you test it?"

"I found out that the person is a new user? Even if it's just a hardware test, I'm really lucky!"

"I read in the news that only one number was tested, and it feels like the chances are much lower than winning the jackpot!"

"China, Sudong City, is this the first time a Chinese person has discovered a Mersenne prime number?"

This has also been realized in China.

All the discoveries of Mersenne primes had nothing to do with the Chinese, but now with the first discovery, which is a super-large discovery of a billion-digit prime number, it has become very significant when put together.

After Sudong University learned the news, it immediately announced in a high-profile manner:

《Congratulations to our school's Professor Zhang Shuo for discovering the first billion-digit prime number! 》

The content of this release is very direct, without any lengthy introduction. It just says that Zhang Shuo used the computing power of the Computer Structure Laboratory to discover a new super-large Mersenne prime.

Simple content, with big news.

In just a few hours, the story was all over the national and international media.

"The largest prime number has been discovered, from Zhang Shuo of Soochow University!"

《What luck! A super large Mersenne prime was detected on the third login!》

"What is the probability of discovering Mersenne primes? There are over 16 million users participating, hundreds of thousands of long-term online users, and only numbers have been discovered in more than years!"

After a series of reports and discussions, many people suddenly felt something was wrong.

If an ordinary person discovered the Mersenne prime after logging in three times, it could certainly be attributed to luck.

Zhang Shuo?

He was a well-known computational mathematics genius and algorithm expert who had just completed the proof of the Jebov conjecture.

Such a scholar landed for the third time and verified a super large Mersenne number...

It happens to be a Mersenne prime?
Coincidentally?

This is no longer a coincidence!

(End of this chapter)