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
This entity first appeared as the object of triple T1778774 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: Adleman–Pomerance–Rumely primality test Context triple: [Leonard Adleman, knownFor, Adleman–Pomerance–Rumely primality test]
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A.
Blum–Blum–Shub pseudorandom number generator
The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
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B.
Berlekamp’s algorithm for factoring polynomials over finite fields
Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
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C.
Blum–Micali pseudorandom number generator
The Blum–Micali pseudorandom number generator is a foundational cryptographic algorithm that produces provably secure pseudorandom bits based on number-theoretic hardness assumptions.
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D.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
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E.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Adleman–Pomerance–Rumely primality test Target entity description: 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.
-
A.
Blum–Blum–Shub pseudorandom number generator
The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
-
B.
Berlekamp’s algorithm for factoring polynomials over finite fields
Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
-
C.
Blum–Micali pseudorandom number generator
The Blum–Micali pseudorandom number generator is a foundational cryptographic algorithm that produces provably secure pseudorandom bits based on number-theoretic hardness assumptions.
-
D.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
-
E.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
- F. None of above. chosen
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
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Subject: Adleman–Pomerance–Rumely primality test Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.