Problem solving process: We need to find two prime numbers whose sum is 18. We know that 18 is an even number, so the sum of its two prime factors must also be an even number. We know that the smallest prime number is 2,2+2 = 4, which is less than 18. We need to find two prime numbers greater than 2, and their sum is 18. Common prime numbers are 3, 5, 7, 1 1, 13, 17, etc. We can find two prime numbers, 5 and 13, and their sum is exactly 18. So 18=(3)+( 15), and the two prime numbers in brackets are 3 and 15 respectively.
Prime number, also known as prime number, refers to a natural number with no other factors except 1 and itself. It only has 1 and its two positive factors, and the smallest prime number is 2, which is also the only even prime number. An important property of prime numbers is that their number is infinite. This means that no matter how big a natural number n you choose, there will always be an infinite number of prime numbers less than or equal to n.
Application fields of prime numbers:
1, Cryptography: The properties of prime numbers make it have important applications in cryptography. For example, RSA algorithm is a public key cryptosystem based on prime power operation, which can be used for data encryption and digital signature. In addition, other properties of prime numbers are also used to design secure cryptosystems.
2. Computer science: In computer science, prime numbers are used to design various algorithms and data structures. For example, in the Fast Fourier Transform (FFT) algorithm, prime numbers are used to improve the operation efficiency. In addition, prime numbers are also used to construct secure hash functions and encryption algorithms.
3. Mathematics: Prime numbers are widely used in the field of mathematics. For example, in number theory, prime numbers are used to study the distribution and theorem of prime numbers. In algebraic geometry, the properties of prime numbers are used to study the geometric properties of algebraic curves and algebraic clusters.
4. Physics: The properties of prime numbers are also used in the study of physics. For example, in quantum mechanics, the periodicity of prime numbers is used to study the properties of spin electrons and quarks. In string theory, the properties of prime numbers are also used to study the vibration modes of strings and the extra dimensions in particle physics.