Prismetode

Prismetode is a term used in number theory to denote a family of algorithms designed for identifying prime numbers and generating prime sequences. It is not a single standardized procedure, but rather a class of methods sharing a common architecture: an initial screening stage that reduces candidates using sieve-like techniques, followed by an explicit primality test on the remaining candidates. The name blends "prime" with "metode" (method) and reflects its focus on primality-related computation.

In typical implementations, the first stage deploys a segmented sieve to strip away composites by testing divisibility against small primes over a moving window. The second stage applies a primality test that can be deterministic up to a bound or probabilistic with a controlled error rate. Some variants emphasize deterministic guarantees at the cost of speed, while others optimize for rapid prime generation in large ranges.

The approach is used for generating primes for cryptographic key material, testing conjectures about prime distribution, and pedagogical demonstrations of sieve-prime interactions. Its performance depends on the chosen tests, segment size, and hardware, but is generally competitive with standard sieve methods for large-scale prime generation when tuned properly. Limitations include the lack of a universal definition across sources and varying guarantees between implementations, which can hinder cross-compatibility and benchmarking.

See also: Sieve of Eratosthenes; Miller-Rabin primality test; AKS primality test; Elliptic curve primality proving.

References are sparse and vary by author; readers are advised to consult specific papers or software documentation describing a given prismetode variant.