A positive integer in the form of 2 p- 1, where p is a prime number and is usually recorded as Mp. If Mp is a prime number, it is called mersenne prime. Mersenne prime seems simple, but it is very difficult to study. It requires not only profound theories and skillful skills, but also painstaking calculations. Even the smallest M3 1=2 147483647 in the "guess" part has 10 digits. As you can imagine, its proof is very laborious. As Mei Sen speculated: "A person needs to test whether a number with 15 or 20 digits is a prime number, even if it takes a lifetime.".

So far, only 48 mersenne prime have been discovered. Because this kind of prime number is rare and fascinating, it is called "mathematical treasure". Mersenne prime has always been an important content of number theory research, and it is also one of the hot and difficult points in today's scientific exploration.

It is worth mentioning that French mathematician Lucas and American mathematician Remo made important contributions to mersenne prime's basic research. The Lucas-Remo method named after them is the most famous method to detect mersenne prime. In addition, Zhou Haizhong, a mathematician and linguist in China, gave an accurate expression of Mason's prime number distribution, which provided convenience for people to find mersenne prime. This research achievement is named "Zhou conjecture" internationally.