What Is the Diamond on the Mountain of Mathematics?

Now anyone who goes to the GIMPS homepage and downloads a free program called "Prime95" can immediately join the GIMPS project to search for Mersenne primes. At present, there are nearly 230,000 online users from more than 190 countries and regions in the world participating in GIMPS project, and more than 2.15 million core central processing units (CPU) have been used to network to find Mersenne primes. In addition, participants in BOINC, the world's largest Grid computing platform, can also join the GIMPS project. It can be seen that the search for Mersenne primes is a super hit, which is rarely seen in the history of both mathematics and science.

Not long ago, Patrick Laroche, an Internet expert and math enthusiast from Florida, USA, successfully discovered the 51st Mersenne prime — 2^82589933-1, by using GIMPS. With 24,862,048 digits, it is the largest prime ever discovered. If this Mersenne prime is printed in regular size, it will be over 100 km in length!

It is particularly worth mentioning that French mathematician Édouard Lucas and American mathematician Derek Lehmer both made significant contributions to the way of testing the primality of Mersenne primes. The Lucas-Lehmer primality test serves as the best method of testing if a number of this form is prime. Zhou Haizhong, a Chinese mathematician and linguist, gives the exact expression of the distribution of Mersenne primes, which has been named “Zhou’s Conjecture” internationally.

Mersenne prime is of great theoretical importance and rich practical value in modern times. Its exploration has promoted the research of number theory -- The Queen of Mathematics, advanced the development of computing technology, cryptography technology, programming technology and the application of Fast Fourier Transform. By the way, over the past 100 years, almost all of the "largest primes" discovered are Mersenne primes. 

Besides, Mersenne prime is often used to test whether the computer's hardware operation is correct. Lately, a German GIMPS project participant found that when the Intel Skylake processor was executing Prime95 to search for Mersenne prime, the bug that can trigger system crash appeared while the exponent P is equal to 14,942,209. Experts think this bug can lead to applications that freeze up or even crash. Intel has acknowledged the bug and fixed it.

Because the research of Mersenne prime needs the support of various disciplines and technologies, many scientists believe that the research results of Mersenne prime, to some extent, reflect the scientific and technological level of a country. Marcus Sautoy, President of the British Society for Mathematics and author of The Music of the Primes, even believes that Mersenne prime exploration can challenge the limits of human science and technology and wisdom, and its results are one of the important symbols of a country's scientific and technological innovation ability. It can be believed that Mersenne prime with infinite charm will attract more and more explorers, and there will be more and more research achievements in the future.