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Algorithm checking for prime numbers
The AKS primality test (also known as the Agrawal–Kayal–Saxena primality test and the cyclotomic AKS test) is a deterministic primality-proving algorithm
AKS_primality_test
Algorithm for determining whether a number is prime
A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike
Primality_test
Number divisible only by 1 and itself
algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct
Prime_number
Probabilistic primality test
The Miller–Rabin primality test or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number
Miller–Rabin_primality_test
Topics referred to by the same term
a sorting network algorithm EMS Synthi AKS, an analog synthesizer AKS primality test, a deterministic primality-proving algorithm Azure Kubernetes Service
Aks
Test if a Mersenne number is prime
Lucas-Lehmer test, and is similarly fast in practice. The most efficient deterministic primality test for any n-digit number, the AKS primality test, requires
Lucas–Lehmer_primality_test
Decomposition of a number into a product
of digits of n) with the AKS primality test. In addition, there are several probabilistic algorithms that can test primality very quickly in practice
Integer_factorization
Proof that a number is prime
science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates allow the primality of a number
Primality_certificate
Indian computer scientist and mathematician
computer scientist and mathematician noted for development of the AKS primality test, along with Manindra Agrawal and Nitin Saxena. Kayal was born and
Neeraj_Kayal
Algorithmic runtime requirements for common math procedures
4171/JEMS/861. hdl:21.11116/0000-0005-717D-0. Tao, Terence (2010). "1.11 The AKS primality test". An epsilon of room, II: Pages from year three of a mathematical
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Mathematics textbook
testing whether a given number is a prime number, centered on the AKS primality test, the first method to solve this problem in polynomial time. It was
Primality Testing for Beginners
Primality_Testing_for_Beginners
Indian computer scientist (born 1966)
Shri, India's 4th highest civilian award, in 2013. He created the AKS primality test with Neeraj Kayal and Nitin Saxena, for which he and his co-authors
Manindra_Agrawal
Calendar year
number theory in 2002: Manindra Agrawal led a team in developing the AKS primality test, and Preda Mihăilescu created a proof for the 150-year-old Catalan's
2002
Indian mathematician and computer scientist
complexity. He attracted international attention for proposing the AKS Primality Test in 2002 in a joint work with Manindra Agrawal and Neeraj Kayal, for
Nitin_Saxena
Classification of algorithm
practical for numbers with merely billions or trillions of digits." The AKS primality test is galactic. It is the most theoretically sound of any known algorithm
Galactic_algorithm
Probable prime that is composite
instead of primes. On the other hand, deterministic primality tests, such as the AKS primality test, do not give false positives; because of this, there
Pseudoprime
Baillie–PSW primality test Miller–Rabin primality test Lucas–Lehmer primality test Lucas–Lehmer test for Mersenne numbers AKS primality test Pollard's p − 1
List_of_number_theory_topics
Problem of determining whether polynomials are identical
applications to Tutte matrices and also to primality testing, where PIT techniques led to the AKS primality test, the first deterministic (though impractical)
Polynomial_identity_testing
Prime pair of the form (p, 2p+1)
Pocklington's criterion can be used to prove the primality of 2p + 1 once one has proven the primality of p. Just as every term except the last one of
Safe and Sophie Germain primes
Safe_and_Sophie_Germain_primes
Indian inventions
developed by Man Mohan Suri. AKS primality test and Agrawal's conjecture– The AKS primality test is a deterministic primality-proving algorithm created and
List of Indian inventions and discoveries
List_of_Indian_inventions_and_discoveries
conjecture were true, it would decrease the runtime complexity of the AKS primality test from O ~ ( log 6 n ) {\displaystyle {\tilde {O}}{\mathord {\left(\log
Agrawal's_conjecture
Estimate of time taken for running an algorithm
doi:10.1016/0020-0190(90)90022-P. Tao, Terence (2010). "1.11 The AKS primality test". An epsilon of room, II: Pages from year three of a mathematical
Time_complexity
Prime integer calculated using a primality-proving algorithm
probabilistic primality test. In principle, every prime number can be proved to be prime in polynomial time by using the AKS primality test. Other methods
Provable_prime
Computational complexity class
subsequently been shown to have a polynomial time algorithm, the AKS primality test. In some cases, quasi-polynomial time bounds can be proven to be optimal
Quasi-polynomial_time
Conjecture on zeros of the zeta function
Kayal and Nitin Saxena proved this result unconditionally using the AKS primality test. Odlyzko (1990) discussed how the generalized Riemann hypothesis can
Riemann_hypothesis
Unsolved problem in computer science
also happens to be in P, a fact demonstrated by the invention of the AKS primality test. There are many equivalent ways of describing NP-completeness. Let
P_versus_NP_problem
Notation describing limiting behavior in computational number theory
} The existence of the AKS primality test, which runs in polynomial time, means that the time complexity for primality testing is known to be at most
L-notation
arbitrarily large primes (2013), and the modularity theorem (2001). The AKS primality test was published in 2002, which is the first algorithm that can determine
History_of_mathematics
Quantum algorithm for integer factorization
with the Newton method and checking each integer result for primality (AKS primality test). Ekerå, Martin (June 2021). "On completely factoring any integer
Shor's_algorithm
Complexity class
which the verifier can confirm to be valid by multiplication and the AKS primality test. It is presently not known whether there is a polynomial-time algorithm
Co-NP
processing, mathematical linguistics Nitin Saxena – AKS Primality test for polynomial time primality testing, computational complexity theory Jonathan Schaeffer
List_of_computer_scientists
eigenvalues of symmetric eigenvalue problems by Andrew Knyazev 2002 – AKS primality test developed by Manindra Agrawal, Neeraj Kayal and Nitin Saxena 2002
Timeline_of_algorithms
Award for advancements in discrete mathematics
polynomial. 2006: Manindra Agrawal, Neeraj Kayal and Nitin Saxena, for the AKS primality test. Mark Jerrum, Alistair Sinclair and Eric Vigoda, for approximating
Fulkerson_Prize
Mathematical conjecture about zeros of L-functions
test is guaranteed to run in polynomial time. In 2002, Manindra Agrawal, Neeraj Kayal and Nitin Saxena proved unconditionally that the AKS primality test
Generalized Riemann hypothesis
Generalized_Riemann_hypothesis
development of AKS primality test Nitin Saxena 2002 Computer scientist and mathematician noted for development of AKS primality test Pradyut Ghosh 1998
List_of_IIT_Kanpur_people
Overview of and topical guide to algorithms
Euclidean algorithm Sieve of Eratosthenes Integer factorization Primality test AKS primality test Modular exponentiation Fast Fourier transform Karatsuba algorithm
Outline_of_algorithms
Computer science award
algorithms 1999 2006 Manindra Agrawal, Neeraj Kayal, Nitin Saxena for the AKS primality test 2004 2007 Alexander Razborov, Steven Rudich for natural proofs 1997
Gödel_Prize
Primality tests: determining whether a given number is prime AKS primality test Baillie–PSW primality test Fermat primality test Lucas primality test
List_of_algorithms
Prasad Maharashtra Number theory 2003 Manindra Agrawal Uttar Pradesh AKS primality test 2003 Vasudevan Srinivas Karnataka Algebraic geometry 2004 Sujatha
List of Shanti Swarup Bhatnagar Prize recipients
List_of_Shanti_Swarup_Bhatnagar_Prize_recipients
time algorithm to determine whether a given number is prime (the AKS primality test). 2002 – Preda Mihăilescu proves Catalan's conjecture. 2003 – Grigori
Timeline_of_mathematics
Tool used in probabilistic polynomial identity testing
10^{350}\approx 2^{1024}} ) becomes very important and efficient primality testing algorithms are required. Let G = ( V , E ) {\displaystyle G=(V,E)}
Schwartz–Zippel_lemma
test (QFT) is a probabilistic primality test to determine whether a number is a probable prime. It is named after Ferdinand Georg Frobenius. The test
Quadratic_Frobenius_test
Integer factorization algorithm
inverse. R. Crandall and J. Papadopoulos, On the implementation of AKS-class primality tests, available at [1] A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse
Rational_sieve
AKS PRIMALITY-TEST
AKS PRIMALITY-TEST
Boy/Male
Russian
Great.
Male
Finnish
 Short form of Finnish Aukusti, AKU means "venerable." Compare with another form of Aku.
Surname or Lastname
North German (Frisian)
North German (Frisian) : patronymic of the Old Frisian personal name Ake, a variant of Ag(g)o (see Agena).English : variant of Akers.
Female
Japanese
(1-秋, 2-明, 3-晶) Japanese unisex name AKI means: 1) "autumn" 2) "bright" 3) "sparkle." Compare with strictly masculine Aki.
Boy/Male
Hindu, Indian, Punjabi, Sikh
High Like Sky; All Pervading; As Great as Sky
Boy/Male
Muslim
Name of a tree.
Male
Japanese
(1-秋, 2-明, 3-晶) Japanese unisex name AKI means: 1) "autumn" 2) "bright" 3) "sparkle." Compare with another form of Aki.
Boy/Male
Indian
Hope
Girl/Female
Indian
Soul, Gods blessing, A mosque
Surname or Lastname
English
English : variant spelling of Oakes.Americanized form of Jewish Ochs.
Surname or Lastname
Swedish and Norwegian
Swedish and Norwegian : from ask ‘ash tree’, applied either as a habitational name from a place named with this word or as an ornamental name.English : habitational name from a place in North Yorkshire named Aske, from Old English as æsc ‘ash tree’, later replaced by the Old Norse cognate askr.
Girl/Female
Latin
Firstborn.
Boy/Male
Muslim
Hope
Girl/Female
Indian
Glass
Boy/Male
Norse
From the ash tree.
Girl/Female
Muslim
Glass
Girl/Female
Maori
Affectionate.
Boy/Male
Indian
Reflection; Gnawing Reflection
Surname or Lastname
English
English : topographic name for someone living by a prominent oak tree, from Middle English ake ‘oak’, or a habitational name from the village of Aike, near Lockington, East Yorkshire, which is named with Old English Äc ‘oak’, dative Äce ‘(place at) the oak tree’.
Boy/Male
Indian
Divider
AKS PRIMALITY-TEST
AKS PRIMALITY-TEST
Boy/Male
Arabic, Muslim
Little
Boy/Male
Hindu, Indian, Traditional
Lord of the Lords
Boy/Male
British, English
From the Damp Meadow
Boy/Male
Indian, Sanskrit
Competent
Surname or Lastname
English
English : occupational name for a plowman, from Old French estivur (Latin stivarius).
Boy/Male
Arabic, Australian, Muslim
The Son of Hazrat Haroon
Girl/Female
Muslim
Cotton
Male
Russian
Variant spelling of Russian Sevastian, SEVASTYAN means "from Sebaste."
Male
French
Variant spelling of French Alphonse, ALFONSE means "noble and ready."
Boy/Male
Indian, Punjabi, Sikh
Love for Simplicity
AKS PRIMALITY-TEST
AKS PRIMALITY-TEST
AKS PRIMALITY-TEST
AKS PRIMALITY-TEST
AKS PRIMALITY-TEST
v. i.
To request or petition; -- usually followed by for; as, to ask for bread.
n.
Rivalry; competition.
adv.
At first; primarily.
adv.
In a primary manner; in the first place; in the first place; in the first intention; originally.
v. t.
To invite; as, to ask one to an entertainment.
n.
Animal existence or nature.
v. t.
To require, demand, claim, or expect, whether by way of remuneration or return, or as a matter of necessity; as, what price do you ask?
n.
The quality or state of being primal.
n.
Probability.
adv.
As.
n.
Equality, as of right or rank.
n.
Quality of being first; primitiveness.
adv.
Primarily.
adv.
Primarily; not derivatively.
adv.
In a principal manner; primarily; above all; chiefly; mainly.
ads.
In the direction of the breadth.
adv.
Primarily; originally; essentially; radically; at the foundation; in origin or constituents.
n.
Animality.
n.
Three united; state of being three.
ads.
Breadthwise.