The definition of prime number can be traced back to the ancient Greek mathematician Euclid, who gave the definition of prime number in the Elements of Geometry. Since Euclid, prime number has been considered as one of the most basic concepts in mathematics.
Prime numbers are widely used in mathematics and science. They not only play an important role in cryptography, computer science, number theory and other fields, but also play a certain role in physical science. Therefore, the research and application of prime numbers have always been concerned and valued by mathematicians and scientists.
The definition of a prime number can be mathematically expressed as follows: if a natural number n is greater than 1 and there are no other factors except 1 and itself, then n is a prime number. For example, 2, 3, 5 and 7 are all prime numbers, while 4, 6 and 8 are not prime numbers, because they have other factors besides 1 and themselves. The distribution of prime numbers also has certain rules.
In natural sequences, prime numbers appear less and less. For example, among natural numbers less than 100, there are 25 prime numbers; Among the natural numbers less than 1000, the prime number is only 2 18. Although there are fewer and fewer prime numbers, mathematicians are still looking for more prime numbers because they are widely used in mathematics and science.
Application fields of prime numbers:
1, cryptography: prime numbers play a vital role in cryptography. Because prime numbers are unique and irreversible, they are used to encrypt and decrypt information. For example, RSA algorithm is a public key cryptosystem based on prime numbers, which is widely used in e-commerce, network security and other fields.
2. Computer science: Prime numbers are also widely used in computer science. First of all, prime numbers are used to detect whether a number is a prime number, which is a common algorithm in computer science. Secondly, prime numbers are used to generate random numbers. For example, the method of generating random numbers by using prime numbers is widely used in computer programming.
3. Number theory: prime numbers have important applications in number theory. Prime numbers are used to study the properties and distribution of integers. For example, the prime number theorem is a basic theorem in number theory, which describes the distribution of prime numbers. In addition, prime numbers are also used to study prime factorization and congruence equations.
4. Physical science: Prime numbers also have certain applications in physical science. For example, in quantum mechanics, prime numbers are used to describe the quantum states of particle states because they are discrete. In addition, prime numbers are also used to describe the energy level structure of atoms and molecules.