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Nonprime numbers

Nonprime numbers are integers that are not prime numbers, i.e. zero (0), units (e.g. one (1), minus one (–1)), composite numbers and the associates of prime numbers (negated primes). Some nonprime numbers are –2563, 1, 48 and 1729. With the modern exclusion of 1 (now considered a unit, i.e. an invertible element) from the set of prime numbers, a term is necessary to distinguish composite numbers (of which 1 is not one of) and numbers that are not prime (a set that 1 does belong to).

In set theory terms, the set of nonprimes ${\displaystyle \scriptstyle \mathbb {P} ^{\prime }\,}$ is the complement of the set of primes ${\displaystyle \scriptstyle \mathbb {P} \,}$ in ${\displaystyle \scriptstyle \mathbb {Z} \,}$.

Positive nonprime numbers

Positive nonprime numbers: the unit 1 and the primes.

A018252 The nonprime numbers (the unit 1 together with the composite numbers, A002808.)

{1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, ...}

Nonnegative nonprime numbers

Nonnegative nonprime numbers: 0, the unit 1 and the primes.

A141468 Zero together with the nonprime numbers A018252.

{0, 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, ...}