Prime Numbers

A number p \in \mathbb{N}^{+} is a prime number, if it has exactly two positive divisors (1 and p). These numbers are the building blocks of all \mathbb{N}, since every natural number n<1 can be written as the product of prime numbers.

10 is the product of 2 and 5. A lot of asymmetric methods in cryptography are base around prime numbers. \mathbb{P} is the set of all prime numbers. All prime numbers, except 2, are odd numbers.

The prime factor p of n \in \mathbb{n} , n>1 is defined as p \in \mathbb{P}: p | n.

Fundamental Theorem of Arithmetic

The fundamental theorem of arithmetic asserts that every number n \in \mathbb{N}, n>1 can be written as the product one or more p \in \mathbb{P}.

Furthermore n can be deconstructed in it's prime factors in a process called prime factorization. Numbers that are no prime numbers are also referred to as composite numbers.

Definition: Every n \in \mathbb{N}, n>1 can be written as the product of one or more prime numbers, i.e. n = \prod_{i=1}^k p_i with p_{i} \in \mathbb{P}. Every prime factor is uniquely defined through this product up to the order of the factors.

Related Topics:

• Prime Number Distribution
• Prime Factorization
• Fermats Primality Test
• Miller Rabin