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# What Is the Diamond on the Mountain of Mathematics?

BY Kelly 21 Dec,2020 Diamond Mathematics Mersenne prime

A Mersenne prime is a prime number of the form 2^P-1. The first Mersenne primes are 3, 7, and 31 corresponding to P = 2, 3, and 5 respectively. 2300 years ago, ancient Greek mathematician Euclid was able to prove that the number of primes is infinite by using reduction to absurdity, who thought some of which could be written in the form of 2^P-1. Such prime numbers, with their unique properties and boundless charm, have long fascinated professional mathematicians and amateurs to explore it. Marin Mersenne, a French polymath in the 17th century, is best known today among mathematicians for Mersenne prime numbers.

This particular form of prime was named “Mersenne Prime” in memory of Mersenne, who was knowledgeable, talented, enthusiastic and the first one to conduct the systematic and in-depth study of primes in 2^P-1 format. So far, only 51 Mersenne primes have been discovered, which are rare and charming, reputed as “the diamond on the mountain of mathematics”. Mersenne primes have always been an important part of number theory research, but also one of the hot spots of scientific research.

Those of format 2^P-1 seem simple, but are difficult to explore. When the exponent P is large, it requires not only advanced theory, skillful technique, but also arduous calculation. In 1772, Swiss-born mathematician Leohard Euler, who was known as “the hero of mathematics”, proved by mental arithmetic that 2^31-1 (2147483647) was the eighth Mersenne prime even when he was blind. The 10-digit prime was the largest known prime at that time.