Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic says that every integer greater than $1$ can be written as a product of prime numbers in essentially one way: the order of the factors may change, but the prime factors and their multiplicities do not.

This theorem makes primes the unique multiplicative building blocks of the positive integers. It is part of the background that makes Euler's product for the zeta function so powerful.

See also: prime number, prime factorisation, Euler product..