Primalityrelated

Primalityrelated is an adjective used to describe topics, problems, and results that concern primality—the property of a positive integer greater than 1 being divisible only by 1 and itself. In literature and discussion, the term is used informally to group ideas that hinge on whether numbers are prime, or on properties of primes and their distribution.

Its scope includes primality testing, proofs of primality, and the study of primes and prime gaps. Algorithms for testing primality range from simple sieving methods, such as the Sieve of Eratosthenes, to probabilistic tests (for example Miller-Rabin and Fermat tests) and deterministic polynomial-time methods (such as the AKS primality test). The term also covers primality certificates, primality-related complexity, and the behavior of primes in various mathematical structures.

Primalityrelated topics have applications in cryptography, where primes enable secure key generation in protocols like RSA and certain elliptic-curve systems. In pure number theory, researchers study prime distribution, arithmetic progressions, twin primes, and related conjectures. The study also includes pseudoprimes, Carmichael numbers, and methods for identifying primes within large numerical ranges.

Because primality is a foundational concept in number theory, the label primalityrelated is sometimes used in taxonomies, classifications, and educational resources to indicate relevance to primes without prescribing a single theory or method.