AKS primality test [SEP] named after
AKS primality test
The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, computer scientists at the Indian Institute of Technology Kanpur, on August 6, 2002, in an article titled "PRIMES is in P". The algorithm was the first to determine whether any given number is prime or composite within polynomial time. The authors received the 2006 Gödel Prize and the
. For 64-bit inputs, the Baillie–PSW primality test is deterministic and runs many orders of magnitude faster. For larger inputs, the performance of the (also unconditionally correct) ECPP and APR tests is "far" superior to AKS. Additionally, ECPP can output a primality certificate that allows independent and rapid verification of the results, which is not possible with the AKS algorithm.
Concepts.
The AKS primality test is based upon the following theorem: Given an integer formula_1 and integer formula_2 coprime to formula_3, formula_3