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.
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
NERFINISHED
ⓘ
Miller–Rabin primality test ⓘ Solovay–Strassen primality test NERFINISHED ⓘ |
| countryOfOrigin | India ⓘ |
| developedAt | Indian Institute of Technology Kanpur NERFINISHED ⓘ |
| differenceFrom |
probabilistic primality tests
ⓘ
tests relying on unproven hypotheses ⓘ |
| doesNotRelyOn |
extended Riemann hypothesis
NERFINISHED
ⓘ
generalized Riemann hypothesis NERFINISHED ⓘ unproven hypotheses such as the Riemann hypothesis ⓘ |
| field |
algorithmic number theory
ⓘ
computational complexity theory NERFINISHED ⓘ computational number theory ⓘ |
| fullName | Agrawal–Kayal–Saxena primality test NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
Neeraj Kayal NERFINISHED ⓘ Nitin Saxena NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| 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 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.