nietpriem

Nietpriem is a term used here to denote natural numbers greater than 1 that are not prime. In standard mathematics the corresponding concept is a composite number (samengesteld getal). The term nietpriem is not widely used in literature, and this article adopts it as a nonstandard label to discuss numbers that are not prime.

Definition and basic properties: A natural number n is a nietpriem if n > 1 and n is not prime; equivalently n has a divisor d with 1 < d < n. By this definition, the number 1 is not included, since it is neither prime nor composite in standard convention. A nietpriem is therefore a number that can be factored into smaller integers greater than 1.

Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, and so on. These numbers have at least one nontrivial divisor and can be written as a product of primes in at least one way.

Relation to primes and factorization: Every nietpriem greater than 1 can be expressed as a product of prime factors; the Fundamental Theorem of Arithmetic guarantees both the existence and the uniqueness (up to order) of this factorization. There are infinitely many nietpriem, since composite numbers occur without bound as numbers grow larger, even as primes continue to appear irregularly.

See also: prime number, composite number, sieve of Eratosthenes, fundamental theorem of arithmetic.