A prime number is a natural number greater than 1 that can only be divided by itself and 1 without remainders. In other words, a prime number is a positive integer greater than 1 with exactly two factors, 1 and the number itself. For example, the first five prime numbers are 2, 3, 5, 7, and 11. Numbers that have more than two factors are called composite numbers. For instance, 15 is not a prime number because it can be divided by 5, 3, 1, and itself. Prime numbers are often seen as "building blocks" by mathematicians in number theory, and the fundamental theorem of arithmetic states that a composite number can be expressed as the product of prime numbers. Some key points about prime numbers include:

• A prime number is a whole number greater than 1 with only two factors: 1 and itself.
• Prime numbers are often used in cryptography.
• The number 1 is neither prime nor composite.
• The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

To check whether a given number is prime or not, you can simply check if it can be written in the form $6n + 1$ or $6n - 1$ .