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Nonprime

Nonprime is a term used in number theory to refer to an integer that is not a prime number. Primes are defined as natural numbers greater than 1 that have exactly two distinct positive divisors: 1 and the number itself. By contrast, a nonprime is any integer that does not meet this criterion. In standard discussions of positive integers, the nonprimes greater than 1 are precisely the composite numbers, while the integers 1, 0, and negative numbers are not considered primes and are often described as neither prime nor composite.

Among positive integers, composite numbers have more than two positive divisors and can be factored into a

The term nonprime is less commonly used in formal contexts; mathematicians typically refer to nonprime integers

Nonprimes play a central role in topics such as divisibility, factorization, and the study of arithmetic functions.

product
of
smaller
integers
greater
than
1.
Every
composite
number
can
be
expressed
as
a
product
of
primes,
and
this
prime
factorization
is
unique
up
to
the
order
of
the
factors
(the
fundamental
theorem
of
arithmetic).
This
property
underpins
many
algorithms
for
primality
testing
and
integer
factorization.
as
composite
numbers
when
the
discussion
is
restricted
to
positive
integers
greater
than
1.
In
broader
usage,
nonprime
may
include
0
and
negative
integers,
but
these
are
not
classified
as
primes
under
the
standard
definitions.
They
form
the
complement
of
the
prime
numbers
within
the
set
of
integers
and
are
essential
for
understanding
the
structure
of
the
integers
under
multiplication.