In the field of mathematics, prime numbers and composite numbers are fundamental and important concepts. They form the cornerstone of the digital world and play a key role in the nature and decomposition of integers. This article will delve into the definitions, properties, and applications of prime and composite numbers.
A prime number is a number that is not divisible by any natural number other than 1 and itself in a natural number greater than 1. Specifically, if a number has only two positive factors, i.e., 1 and itself, then it is prime.
Prime numbers have some unique properties:
The number of prime numbers is infinite, and their set is; Prime numbers have no other factors than 1; Any integer greater than 1 can be uniquely factored into the product of prime numbers, which is the unique decomposition theorem. 
A composite number is a number that has other positive factors besides 1 and itself. In other words, a composite number is a number that can be broken down into the product of more than two prime numbers.
Composite numbers also have their own unique properties:
The factor of a composite number has other positive factors besides 1 and itself; The number of composite numbers is finite, and only a finite number of infinite natural numbers are composite numbers. 
Prime numbers and composite numbers are inseparable, and there is an important connection between them:
Prime numbers are the basic unit of composite numbers, and any composite number can be decomposed into the product of prime numbers; Prime factor decomposition is an effective way to study the properties of composite numbers, and by decomposing composite numbers into prime factors, this number can be better understood and analyzed. To better understand prime and composite numbers, let's deepen our understanding with some examples:
5 is a prime number because it is only divisible by 1 and 5; 13 is a prime number because it is only divisible by 1 and 13. 
6 is a composite number because it is divisible by 2 and 3; 15 is a composite number because it is divisible by 3 and 5. Prime and composite numbers have a wide range of applications in cryptography, factorization, and other fields. For example, the RSA encryption algorithm is based on the difficulty of decomposing large prime numbers.
As the basic concepts of mathematics, prime numbers and composite numbers run through the entire mathematical system. By understanding their definitions, properties, and interrelationships, we can better grasp the structure and laws of integers, and lay a solid foundation for subsequent mathematical learning.