Priemheid

Priemheid is a Dutch noun referring to the property of being prime. The term is formed from priem (prime) and -heid indicating a property. In contemporary Dutch, the preferred term for this concept is primaliteit; priemheid exists mainly in older texts or as a language-learning illustration of word formation.

Definition: In number theory, priemheid applies to integers greater than 1 that have exactly two distinct positive divisors: 1 and the number itself. Such numbers are called primes; those with more than two divisors are composite. The concept generalizes to other algebraic structures: an element is prime if it cannot be factored in a way that uses non-unit divisors; in a ring, a prime element divides a product only if it divides one factor.

Examples: 2, 3, 5 are primes; 4, 6, 9 are composite.

Significance: Primes are fundamental in number theory; Euclid proved there are infinitely many primes; every integer factors uniquely into primes (the Fundamental Theorem of Arithmetic). Primes underpin cryptography; primality testing algorithms include deterministic methods for small inputs and probabilistic methods (for example Miller-Rabin); the AKS primality test provides a deterministic polynomial-time method.

See also: primaliteit, prime number, primality, prime element, prime factorization.