Theory of Positive Integers

An exploration of the properties, relationships, and applications of positive integers in various mathematical contexts.

Basic Concepts

Prime Numbers and Composite Numbers

Prime Numbers

A prime number is a positive integer greater than 1 that has exactly two divisors: 1 and itself. For example, 7 is prime because only 1 and 7 divide it exactly.

Composite Numbers

Composite numbers have more than two divisors. For example, 12 is composite because it can be divided by 1, 2, 3, 4, 6, and 12.

Why Are They Important?

Primes are the "atoms" of the number world. Every positive integer can be broken down into prime factors. This is called the Fundamental Theorem of Arithmetic.

Quick List

  • Primes: 2, 3, 5, 7, 11, 13...
  • Composites: 4, 6, 8, 9, 10...

Real-World Use

Primes play a big role in computer security and codes!

Examples

  • 13 is a prime number; it can only be divided by 1 and 13.

  • 18 is composite; it can be divided by 1, 2, 3, 6, 9, and 18.

In a Nutshell

Prime numbers have only two divisors, while composite numbers have more.