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 (1)

Label Occurrences
Adleman–Pomerance–Rumely primality test canonical 1

How this entity was disambiguated

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 primality test
surface form: 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

How these facts were elicited

Referenced by (1)

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

Leonard Adleman knownFor Adleman–Pomerance–Rumely primality test