Year 9: Prime numbers

This cheat sheet provides a quick reference for understanding prime numbers. Prime numbers are fundamental to number theory and cryptography.

What is a Prime Number?

A prime number is a whole number greater than 1 that has exactly two distinct positive divisors: 1 and itself.

Key Properties

• All prime numbers greater than 1 are, by definition, prime.
• 1 is *not* a prime number. It only has one divisor: itself.
• 2 is the smallest and only even prime number.
• Prime numbers are also known as prime integers.

Examples

• 2 - Divisible by 1 and 2
• 3 - Divisible by 1 and 3
• 5 - Divisible by 1 and 5
• 7 - Divisible by 1 and 7
• 11 - Divisible by 1 and 11

How to Check if a Number is Prime

1. Divide the number by all integers from 2 up to the square root of the number.
2. If any of these divisions results in a whole number, then the number is *not* prime.
3. If none of the divisions result in a whole number, then the number is prime.

Famous Prime Numbers

The sequence of prime numbers continues infinitely. Some well-known examples include: 3, 5, 7, 11, 13, 17, 19, 23, 29...