Training the Heavens

Chapter 179 Mersenne Primes
"Teacher He, I seem to have discovered a new Mersenne prime." Huang Tunan dropped a big bomb as soon as he came in.

"Mersenne prime? Really?" He Chengxuan stood up immediately.

Marin Mersenne was a unique central figure in the European scientific community in the 17th century. He often maintained correspondence with many scientists, including Fermat, to discuss issues such as mathematics and physics.

在欧几里得、费马等人有关研究的基础上对2的（P）次减1方型的数作了大量的计算、验证，并于1644年在他的《物理数学随感》一书中断言：在≤257的素数中，当p=2、3、5、7、13、17、19、31、67、127、257时，2的p次方减1是素数，其它都是合数。

This type of number is called a Mersenne number, which is a type of number in the form of 2 to the power of P minus 1, where the exponent p is a prime number. If a Mersenne number is a prime number, it is called a Mersenne prime number. This gave rise to a famous conjecture: whether there are an infinite number of Mersenne primes.

Later mathematicians began to verify the numbers proposed by Mersenne and look for new Mersenne primes. They found that there were many errors in the numbers proposed by Mersenne. Only 3, 7, 31, and 127 were true Mersenne primes, and the others were not.

They then discovered some more Mersenne primes. By the time Huang Tunan traveled through time, mathematicians had discovered a total of 52 Mersenne primes, the first 12 of which were found by hand calculation, and the last 40 were all found by computers.

Up to now, mathematicians have found a total of 24 Mersenne primes. If the number found by Huang Tunan is confirmed, it will be the 25th Mersenne prime.

The Mersenne prime problem is also an important topic in the field of number theory. With this achievement, Huang Tunan was able to publish an article in a top domestic journal, and this article was much easier to write than the Goldbach conjecture.

After all, it is just finding a new prime number, which does not involve too advanced mathematical knowledge. If a college student who has just entered college is lucky, he may discover it.

In fact, this new Mersenne prime was discovered by two American high school students using computers a few months later. Huang Tunan referred to their method and found this number in advance with the help of computers at Pujiang College.

He had originally planned to wait until he returned from his grandfather's house to show the number to He Chengxuan, but now that his family had encountered problems, he took it out in advance. He planned to use this opportunity to teach the banker a lesson. Just beating Zhendong and Zhenbei would not be enough.

"Teacher He, the number I found, P=21701, is a 6533-digit number. It has been verified by a computer. Both 21701 and the final number are prime numbers, which fully meet the definition of Mersenne prime numbers." Huang Tunan reported the number.

This means the number is 2 to the power of 21701 minus 1. The final calculated result is 6533 digits long, which is difficult to verify by hand. So He Chengxuan immediately asked, "Can you repeat the verification process on a computer?"

"No problem, and I have a hunch that the 26th Mersenne prime may not be far from this number. Maybe it's even closer than the distance between the 24th and 25th numbers. Give me some more time, give me some time to calculate, and I should be able to find this number." Huang Tunan took the opportunity to lay the groundwork.

"If the test is successful, you have made an amazing achievement." He Chengxuan sighed. He did think that Huang Tunan might make some achievements in the field of mathematics, but he didn't expect it to come so soon.

Finding a new Mersenne prime may be more about luck, but once it is found, it is found. This achievement is undeniable. Not only can it be published in top domestic journals, but it is also worthy of being known to mathematicians all over the world. The Department of Mathematics at Jiangsu Normal University has not achieved similar results for many years.

"Come on, I'll call Director Ping, and we'll go to the computer lab to verify it." Thinking of this, He Chengxuan couldn't sit still any longer. He went upstairs to find Ping Zetao, who quickly followed him out. The three of them hurried to the computer lab, and with the help of a computer science teacher, they began to verify whether 2 to the power of 21701 minus 1 was a prime number.

There was no need to verify 21701. It was only a five-digit number, and they could calculate it mentally on the way. This number was indeed a prime number.

There are four ways to use a computer to verify whether a number is prime: brute force enumeration, trial division, sieve of Ehrlich, and linear sieve. They used the most efficient linear sieve.

Huang Tunan had previously written a corresponding verification program using the linear sieve method. Now he just needed to input this number. After a period of calculation, the computer gave the final result. 2 to the power of 21701 minus 1 is indeed a prime number.

"You really found it!" Ping Zetao was very excited. The Department of Mathematics at Jiangsu Normal University had made important achievements just one semester after resuming enrollment. This was definitely something worth celebrating.

Moreover, the college entrance examination has not started yet. If this good news is published in the newspaper at this time, the name of Jiangsu Normal University will spread throughout the country, and it is very likely to attract some high-scoring students to apply, which will also be of great benefit to the school.

"Hurry up and call the Suzhou Daily and have them come over for an interview. Lao He, after the interview, you should instruct Tunan to write the paper as quickly as possible and submit it to Science China: Mathematics. Give him a big boost!"

"Science China: Mathematics" is a comprehensive academic journal of mathematics sponsored by the Chinese Academy of Sciences. It is also the most influential mathematics journal in China today. Huang Tunan's first paper is going to be published in a core journal, which is a dazzling debut.

"I'll go right away!" He Chengxuan jogged happily and went outside to find a phone to contact reporters, but he did not forget to inform the school leaders. This matter was definitely worth celebrating for the whole school.

The principal arrived very quickly. Jiangsu Normal University is not like the University of Science and Technology of China. Any breakthrough that can be published in domestic core journals will attract the attention of the principal. He listened with a smile as Ping Zetao popularized the basic knowledge of Mersenne primes to him, especially its influence in the field of mathematics.

Then he couldn't help but praise, "Our little genius has surpassed the USTC Junior Class by a mile. They haven't published such an important paper yet, right?"

"Indeed not! And according to Tunan, he is very likely to find a new Mersenne prime, and then he can write a paper!" Two core journals a year, even Ping Zetao himself dare not think of such a thing.

"Oh? How long will it take to find one? If you need any support from the school, just let me know!" The principal also wondered how many core journals all the schools and departments combined could publish in a year. As long as Huang Tunan could publish, it would be worth giving him more resources.

Huang Tunan finally heard these words, and his face quickly drooped. "Originally, one or two months should have been enough, but some things happened at home recently, and I'm very confused. I really can't continue looking."

(End of this chapter)