Prime Numbers

Prime Numbers#

Welcome to the Prime Numbers section! Here, you will find detailed explanations and examples on various topics related to prime numbers, including their properties, how to find coprime numbers, prime factorisation, the greatest common divisor (GCD), and the least common multiple (LCM).

Access the handy maths symbol cheat sheet to help with covering these topics here: Cheat Sheet

Introduction to Prime Numbers#

Prime numbers are natural numbers greater than \(1\) that have no positive divisors other than \(1\) and themselves. In simpler terms, a prime number is a number that cannot be formed by multiplying two smaller natural numbers.

For Example:#

  • \(2\) is a prime number because its only divisors are \(1\) and \(2\).

  • \(3\) is a prime number because its only divisors are \(1\) and \(3\).

  • \(4\) is not a prime number because it can be divided by \(1\), \(2\), and \(4\).

Properties of Prime Numbers#

  • The number \(2\) is the only even prime number: All other even numbers can be divided by \(2\), so they cannot be prime.

  • Every prime number greater than \(2\) is odd: This is because even numbers greater than \(2\) can always be divided by \(2\).

  • There are infinitely many prime numbers: This was proven by the ancient Greek mathematician Euclid.

Topics Covered#

  1. Finding Prime Numbers: Techniques and algorithms to identify prime numbers.

  2. Coprime Numbers: Understanding and finding numbers that share no common divisors other than \(1\).

  3. Prime Factorisation: Breaking down numbers into their prime components.

  4. Greatest Common Divisor (GCD) and Least Common Multiple (LCM): Methods to find the largest common divisor of two or more numbers and to find the smallest common multiple of two or more numbers.

Why Study Prime Numbers?#

Prime numbers play a crucial role in various fields of mathematics and computer science, particularly in number theory and cryptography. They are the building blocks of the integers, and understanding their properties can help solve a wide range of mathematical problems.

Interesting Fact

Did you know? The largest known prime number (as of 2024) has over 24 million digits! It was discovered using distributed computing projects where volunteers donate their computer’s processing power to search for new prime numbers.

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