Year 9: Prime numbers within a range of numbers

This cheat sheet provides a quick guide to identifying prime numbers within a given range, a common task in Number problems.

What is a Prime Number?

A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are all prime numbers.

Identifying Prime Numbers within a Range

Step 1: Define the Range: Clearly identify the starting and ending numbers of the range you are considering.
Step 2: Check for Divisibility: For each number in the range, check if it's divisible by any number other than 1 and itself. Start with the smallest prime number, 2.
Step 3: Iterate: Continue checking for divisibility by prime numbers up to the square root of the number. If a number has a divisor greater than its square root, it must also have a divisor smaller than its square root.
Step 4: Identify Primes: If a number is only divisible by 1 and itself, it's a prime number.

Example: Find all prime numbers between 10 and 20

10: Divisible by 2, 5 (Not prime) 11: Divisible by 1 and 11 (Prime) 12: Divisible by 2, 3, 4, 6 (Not prime) 13: Divisible by 1 and 13 (Prime) 14: Divisible by 2, 7 (Not prime) 15: Divisible by 3, 5 (Not prime) 16: Divisible by 2, 4, 8 (Not prime) 17: Divisible by 1 and 17 (Prime) 18: Divisible by 2, 3, 6, 9 (Not prime) 19: Divisible by 1 and 19 (Prime) 20: Divisible by 2, 4, 5, 10 (Not prime)

Prime numbers within the range 10 - 20 are: 11, 13, 17, 19