① From the concepts of prime numbers and composite numbers, we can know that 1 is neither a prime number nor a composite number among natural numbers other than 0. Historically, 1 was included in the prime number, but later, for the sake of fundamental theorem of arithmetic, 1 was finally excluded from the prime number by mathematicians. In primary school, students learn prime numbers and composite numbers, laying the foundation for finding the greatest common factor, the least common multiple, divisor and total score in future study.
② In number theory, prime numbers play an important role and have always attracted many mathematicians to explore. 2500 years ago, the ancient Greek mathematician Euclid proved that the number of prime numbers is infinite, and proposed that a few prime numbers can be written as "2 to the nth power minus1"-where n is also a prime number.
③ Application of prime numbers.
Prime numbers have recently been used in cryptography. The so-called public key is to add a prime number to the information to be transmitted when encoding, and then transmit it to the receiver after encoding. After receiving this message, if anyone does not have the key possessed by the receiver, it is meaningless to get the information even if it takes too long in the process of decryption (actually, the process of finding prime numbers).
Furthermore, in the design of automobile gearbox gears, it is best to design the number of teeth of two adjacent gears as prime numbers, so as to increase the least common multiple of the times when two identical teeth meet and mesh, which can enhance durability and reduce failures.
In addition, in the relationship between the biological growth cycle of pests and the number of pesticide use, prime number pesticide use effect has also been proved to be the best. Experiments show that it is the most reasonable to use pesticides many times: they are all used in the climax of pest reproduction, and it is difficult for pests to produce drug resistance.