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Main form: prime, adjective

Related forms: primality (whether or not something is prime)

Typical use:

  • Something first, optimal, or best
  • Something smallest, indecomposable, or atomic


The term prime is typically used to denote something that cannot be decomposed into smaller pieces. Alternative words used in mathematics to describe such things are indecomposable, simple, irreducible.

It is not necessary that every object is built from prime objects, though in various specific cases, that does happen; for instance, the fundamental theorem of arithmetic states that every natural number is a product of primes in a unique way (upto ordering).

In elementary mathematics/number theory

Prime number

In knot theory

Prime knot

In field theory

Prime field

In commutative algebra

Prime ideal

Prime element

In noncommutative algebra

Prime ring

In universal algebra

Prime variety