On this day 437 years ago, on September 8, 1588 (July 18, 1588 lunar calendar), French theologian, mathematician, and music theorist Marin Mersenne was born. Marin Mersenne (September 8, 1588 - September 1, 1648), French theologian, mathematician, and music theorist. Mason entered the monastery in 1611 and became a priest of the French Catholic Minemaeans. In 1626, he established his monastery in Paris as a meeting place for scientists and a center for the exchange of information, called the "Mason Academy". He maintained regular correspondence with the greatest mathematicians of his generation and was good friends with Fermat, the prince of amateur mathematics. Mason edited the works of several Greek mathematicians and discussed the topics in them, especially the Mason primes, which he discussed in his Cogitataphysico - mathe-matica (1644). His book Harmonieuniverselle (Harmony in the Universe) is a valuable historical document of contemporary musical instruments. Mason died in Paris on September 1, 1648. In June 1640, Fermat wrote to Mason: "In my difficult study of number theory, I have discovered three very important properties. I believe they will form the basis for future solutions to the problem of prime numbers." This letter discusses numbers in the form of 2 ^ P-1 (where p is a prime number). As early as 300 BC, the ancient Greek mathematician Euclid pioneered the study of 2 ^ P-1. When he discussed the perfect number in the ninth chapter of the famous work "Elements of Geometry", he pointed out: If 2 ^ P-1 is a prime number, then (2 ^ p-1) 2 ^ (p-1) is a perfect number. Mason made a lot of calculations and verification work on 2 ^ P-1 on the basis of the relevant research of Euclid, Fermat and others, and in 1644 he asserted in his book "Physical Mathematical Random": For p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257, 2P-1 is a prime number; and for all other numbers less than 257, 2 ^ P-1 is a composite number. The first seven numbers (i.e. 2, 3, 5, 7, 13, 17, and 19) belong to the confirmed part, which he obtained by sorting out the work of his predecessors; the last four numbers (i.e. 31, 67, 127, and 257) belong to the speculated part. However, people still believe in its assertion, and even the great mathematicians Leibniz and Goldbach agree that it is correct. Although Mason's assertion contains several errors (more on this later), his work has greatly stimulated the enthusiasm for the study of prime numbers of type 2 ^ P-1, which has been freed from its status as a vassal of "perfect numbers". It can be said that Mason's work is a turning point and milestone in the study of prime numbers. Due to Mason's profound knowledge, talent, enthusiasm, and the earliest systematic and in-depth study of numbers of type 2 ^ P-1, in memory of him, the mathematical community calls this number "Mason number"; and it is remembered as Mp (where M is the initials of Mason's name), that is, Mp = 2 ^ P-1. If the Mason number is a prime number, it is called "Mersenne prime number" (that is, 2 ^ P-1 prime number). The Mason prime number seems simple, but it is very difficult to study. It requires not only advanced theory and skilled skills, but also arduous calculations. Even the smallest M^31=2^31-1=2147483647 in the "guess" section has 10 digits. It is conceivable that its proof is very difficult. As Mason speculated: "A person, using the general method of verification, wants to test whether a 15-digit or 20-digit number is prime, even a lifetime is not enough." Yes, boring, long, monotonous, and rigid calculations will consume a person's whole life energy, who wants to let the sails of life always bump in the dark! How people want to know the basis and method of Mason's guess, but he was too old to leave a record, and died four years later; people's hope is lost in the passage of time along with Mason's life. It seems that the "guess" of the great man can only be solved by the later great man. The law of twelve averages In the West, the first person to propose the law of twelve averages was Marlan Mason, who proposed it in 1636. Twelve equal is to divide an octave into 12 equal intervals, each interval is specified as a semitone, and the two semitones are a whole tone. The greatest advantage of the twelve average is that no matter how you transpose or transpose, you can get an equal musical effect. But this is relative, because the twelve average is to divide an octave into 12 equal parts, so the vibration ratio between each semitone is an infinite decimal number, so no matter which chord is played, it is impossible to get a truly harmonious musical effect, but the magnitude of the twelve average effect is quite small, which is still a very good interval system by comparison. The reason why MIDI can't replace the live performance effect no matter how advanced it is is is because when the live player plays, the player will judge the degree of interval harmony by his own ears, which is usually close to pure rhythm, but it cannot be done in the computer. The fundamental reason is that there are fundamental differences in the interval definition system, but the difference is not too big. Comments are knowledgeable and talented, and have made great achievements and indelible contributions in mathematics and other fields.