Any positive integer (≠1) can be expressed as a product of primes. This expression is unique except for the order in which the primes occur.

Thus, any positive integer n(≠1) can be written uniquely as:

pα‎11, pα‎22,…, pα‎rr,

where p₁, p₂,…, p_r are primes, satisfying p₁<p₂<⋯<p_r, and α‎₁, α‎₂,…, α‎_r are positive integers. This is the prime decomposition of n, for example 360=2³×3²×5. Note this decomposition would not be unique if 1 were considered a prime number. Prime factorization of large integers is computationally difficult and so commonly used in cryptography. See unique factorization domain.