Chapter 179 Mersenne Prime
"Teacher He, I seem to have discovered a new Mersenne prime." Huang Tunan dropped a big bomb as soon as he came in.
"Merson prime? Really?" He Chengxuan stood up immediately.
Marin Mersenne was a unique central figure in the European scientific community in the 17th century. He kept in regular correspondence with many scientists, including Fermat, to discuss issues such as mathematics and physics.
Based on the research of Euclid, Fermat and others, he made a lot of calculations and verifications on the square of 2 (P) minus 1, and in 1644 he asserted in his book "Physical-Mathematical Feelings": Among the prime numbers ≤257, when p=2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257, 2 to the power of p minus 1 is a prime number, and the others are composite numbers.
This kind 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. From this, a famous conjecture is derived: 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, of which the first 12 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 came back from his grandfather's house before showing 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 give the banker a hard time, and 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 conform to the definition of Mersenne prime numbers." Huang Tunan reported the number.
That is to say, this 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 the 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 from the 24th to the 25th. 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.
"Let's go, I'll call Director Ping, and we'll go to the computer room to verify it together." Thinking of this, He Chengxuan could no longer sit still.
He went upstairs to find Ping Zetao, who hurriedly followed him out. The three of them hurried to the computer room and, with the help of a computer department teacher, 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 figure it out by mental arithmetic 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 method.
Huang Tunan had previously written a corresponding verification program using the linear sieve method. Now he just had to input the 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 finally 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 Suzhou Daily and ask them to come over for an interview. Lao He, after the interview, you can guide Tunan to write the paper as soon as possible and submit it to Chinese Science: 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 came very quickly. Jiangsu Normal University is not like USTC. 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 prime numbers to him, especially its influence in the field of mathematics.
Then he couldn't help but praise, "Our little genius has left the USTC junior class behind. 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 number, 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 support from the school, just ask!" The principal also thought that how many core journals can all the schools and departments in the school publish in a year? As long as Huang Tunan can publish, it is worth giving him more resources.
Huang Tunan finally heard this, and his face drooped quickly. "Originally, one or two months should have been enough, but my family has encountered some problems recently, and I am very confused. I really can't continue looking."
(End of this chapter)
Continue read on readnovelmtl.com
