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The Prime Page

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The Prime Page

Study Guide

Key Definition

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. For example, $5$ is a prime number, but $6$ is not because $2 \times 3 = 6$.

Important Notes

Prime numbers are greater than $1$.
Composite numbers can be expressed as the product of prime numbers.
There are infinitely many prime numbers.
The distribution of prime numbers does not follow a simple pattern, but their overall density is described by the Prime Number Theorem.
Prime numbers are crucial in cryptography.

Mathematical Notation

$\times$ represents multiplication

$\div$ represents division

$+$ represents addition

$-$ represents subtraction

$|$ represents divisibility

$≡$ represents congruence (modular arithmetic)

$√$ represents square root

Remember to use proper notation when solving problems

Why It Works

Prime numbers are the building blocks of natural numbers because any integer greater than 1 is either a prime or can be broken down into a product of prime numbers in exactly one way (up to order).

Remember

To check if a number is prime, try dividing it by prime numbers up to its square root. This works because if n = ab and a > √n, then b < √n, so any non-prime factor must appear by √n.

Quick Reference

Prime Number Examples:$2, 3, 5, 7, 11, 13, 17, 19$

Composite Number Example:$4 = 2 \times 2$

Understanding The Prime Page

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Prime numbers are numbers greater than $1$ that can only be divided by $1$ and themselves.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is a prime number? $6, 11, 15, 21$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have a lock with a 3-digit code. Each digit is a prime number less than $10$. What is one possible code?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the sum of all prime numbers less than $20$.

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following numbers is a prime number? $77, 97, 91, 87$

Recap

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Review key concepts and takeaways