AKS primality test
E734843
deterministic algorithm
landmark result in computational complexity theory
number theory algorithm
polynomial-time algorithm
primality test
The AKS primality test is a landmark deterministic polynomial-time algorithm that can conclusively determine whether a number is prime without relying on unproven assumptions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| AKS primality test canonical | 6 |
| Agrawal–Kayal–Saxena primality test | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8448934 — 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.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: AKS primality test Context triple: [Adleman–Pomerance–Rumely primality test, isPrecursorOf, AKS primality test]
-
A.
Selfridge–Conway primality test
The Selfridge–Conway primality test is a probabilistic algorithm in number theory used to determine whether a given integer is prime.
-
B.
Adleman–Pomerance–Rumely primality test
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.
-
C.
Fermat primality test
The Fermat primality test is a probabilistic algorithm that checks whether a number is prime by verifying congruences derived from Fermat's little theorem.
-
D.
Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
-
E.
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.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: AKS primality test Target entity description: The AKS primality test is a landmark deterministic polynomial-time algorithm that can conclusively determine whether a number is prime without relying on unproven assumptions.
-
A.
Selfridge–Conway primality test
The Selfridge–Conway primality test is a probabilistic algorithm in number theory used to determine whether a given integer is prime.
-
B.
Adleman–Pomerance–Rumely primality test
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.
-
C.
Fermat primality test
The Fermat primality test is a probabilistic algorithm that checks whether a number is prime by verifying congruences derived from Fermat's little theorem.
-
D.
Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
-
E.
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.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
deterministic algorithm
ⓘ
landmark result in computational complexity theory ⓘ number theory algorithm ⓘ polynomial-time algorithm ⓘ primality test ⓘ |
| basedOn |
congruence (x - 1)^n ≡ x^n - 1 mod (x^r - 1, n)
ⓘ
polynomial identity testing ⓘ properties of binomial expansion ⓘ |
| comparedTo |
Miller primality test
ⓘ
Miller–Rabin primality test ⓘ Solovay–Strassen primality test ⓘ |
| countryOfOrigin | India ⓘ |
| developedAt | Indian Institute of Technology Kanpur ⓘ |
| differenceFrom |
probabilistic primality tests
ⓘ
tests relying on unproven hypotheses ⓘ |
| doesNotRelyOn |
extended Riemann hypothesis
ⓘ
linked to:
generalized Riemann hypothesis
generalized Riemann hypothesis ⓘ unproven hypotheses such as the Riemann hypothesis ⓘ |
| field |
algorithmic number theory
ⓘ
computational complexity theory ⓘ
linked to:
Complexity Theory
computational number theory ⓘ |
| fullName |
Agrawal–Kayal–Saxena primality test
ⓘ
linked to:
AKS primality test
|
| guarantees | zero error probability in primality decision ⓘ |
| hasAcronym | AKS ⓘ |
| improvedTimeComplexity | O((log n)^{7.5}) ⓘ |
| influenceOn |
complexity-theoretic study of P versus NP-related questions
ⓘ
design of later deterministic primality tests ⓘ research in deterministic algorithms for number theory ⓘ |
| input | natural number n ⓘ |
| languageOfOriginalPaper | English ⓘ |
| namedAfter |
Manindra Agrawal
ⓘ
Neeraj Kayal ⓘ Nitin Saxena ⓘ |
| originalTimeComplexity | O((log n)^{12}) ⓘ |
| output | decision whether n is prime ⓘ |
| practicality | slower than probabilistic tests for typical input sizes ⓘ |
| property |
deterministic
ⓘ
runs in polynomial time ⓘ unconditional ⓘ |
| publishedIn | Annals of Mathematics ⓘ |
| resultType | decision algorithm ⓘ |
| significance |
first general-purpose deterministic polynomial-time primality test
ⓘ
major breakthrough in theoretical computer science ⓘ resolved long-standing open problem of whether primality can be tested in polynomial time deterministically ⓘ |
| solvesProblem | primality testing ⓘ |
| timeComplexity | polynomial in log n ⓘ |
| usesConcept |
Euler’s theorem generalizations
ⓘ
cyclotomic-like polynomials modulo n ⓘ order of elements modulo n ⓘ |
| yearProposed | 2002 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: AKS primality test Description of subject: The AKS primality test is a landmark deterministic polynomial-time algorithm that can conclusively determine whether a number is prime without relying on unproven assumptions.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: AKS primality test