Number Theory
Explore the fascinating properties and relationships of integers and number systems
Topics
Prime Numbers
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Properties of Prime Numbers
Fundamental Theorem of Arithmetic
Every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors.
Infinitude of Primes
There are infinitely many prime numbers, as proven by Euclid around 300 BCE.
Sieve of Eratosthenes
An ancient algorithm for finding all prime numbers up to a specified limit by iteratively marking the multiples of each prime, starting with 2.
Prime Numbers up to 100:
2357111317192329313741434753596167717379838997