Adleman–Pomerance–Rumely primality test

E199750

The Adleman–Pomerance–Rumely primality test is an early deterministic algorithm in computational number theory used to determine whether a given number is prime, notable for its theoretical importance in the development of modern primality testing methods.

All labels observed (2)

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Statements (47)

Predicate Object
instanceOf algorithm in computational number theory ⓘ
deterministic algorithm ⓘ
primality test ⓘ
assumes generalized Riemann hypothesis ⓘ
author Carl Pomerance ⓘ
Leonard Adleman ⓘ
Robert S. Rumely NERFINISHED ⓘ
basedOn generalized Riemann hypothesis ⓘ
category algorithms in algebraic number theory ⓘ
deterministic primality tests ⓘ
complexityComparedTo slower and more complicated than modern tests in practice ⓘ
computes Jacobi sums modulo n ⓘ
field computational number theory ⓘ
number theory ⓘ
hasLimitation relies on unproven hypothesis ⓘ
hasTheoreticalStatus landmark result in deterministic primality testing ⓘ
influenced development of modern primality testing ⓘ
inputType integer n > 1 ⓘ
isConditionalOn generalized Riemann hypothesis ⓘ
isDeterministic true ⓘ
isEarlyDeterministicTest true ⓘ
isPrecursorOf AKS primality test ⓘ
isProbabilistic false ⓘ
isRandomized false ⓘ
isUnconditionalPolynomialTime false ⓘ
languageOfOriginalPublication English ⓘ
namedAfter Carl Pomerance ⓘ
Leonard Adleman ⓘ
Robert S. Rumely NERFINISHED ⓘ
notableFor first practical deterministic test with polynomial-time bound under GRH ⓘ
theoretical importance in primality testing ⓘ
outputType decision prime or composite ⓘ
propertyTested primality of an integer ⓘ
publicationDecade 1980s ⓘ
purpose determine whether a given integer is prime ⓘ
relatedTo AKS primality test ⓘ
Miller primality test ⓘ
Miller–Rabin primality test ⓘ
cyclotomic fields ⓘ
timeComplexityType polynomial time under GRH ⓘ
uses Jacobi sums ⓘ
L-functions ⓘ
algebraic number theory ⓘ
character sums ⓘ
cyclotomic extensions of number fields ⓘ
properties of number fields ⓘ
yearProposed 1983 ⓘ

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Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Leonard Adleman → knownFor → Adleman–Pomerance–Rumely primality test ⓘ
Jacobi sums → appearsIn → Adleman–Pomerance–Rumely primality test ⓘ
Carl Pomerance → knownFor → Pomerance primality test ⓘ
linked to: Adleman–Pomerance–Rumely primality test