Understanding Prime and Composite Numbers

In number theory, a prime number is a positive integer that is divisible only by itself and 1. For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13.

A composite number, on the other hand, is a positive integer that is divisible by at least one other number besides itself and 1. For example, the first few composite numbers are 4, 6, 8, 9, and 10.

To determine whether a given number is prime or composite, we can use various primality tests, such as the Fermat primality test, the Miller-Rabin primality test, and the AKS primality test. These tests are based on different mathematical properties of prime numbers and have varying degrees of accuracy and efficiency.

In summary, primality refers to the property of being divisible only by itself and 1, and a prime number is a positive integer that has this property. Composite numbers are positive integers that are divisible by at least one other number besides themselves and 1.