 
Summary: The Correctness of the AKS Primality Test in Coq
Fl´avio L. C. de Moura1
, Ricardo Tadeu1
1
Departamento de Ci^encia da Computac¸~ao Universidade de Bras´ilia (UnB)
Caixa Postal 4466 CEP 70910900 Bras´ilia DF Brazil
flavio@cic.unb.br, rictad@gmail.com
Abstract. In 2004, Agrawal, Kayal and Saxena published the paper "PRIMES
is in P" where they present the first polinomial algorithm that can decide in
deterministic polynomial time if a given number is prime or not. This algorithm,
known as AKS, is of relevance for both mathematical and computer science
comunities. In this work, we present our first results in order to get a complete
formalization of AKS. The formal verification is done in the Coq proof assistant.
1. Introduction
A primality test is a method for determining if a given number is prime or not. The study
of prime numbers is of great importance since the ancient Greece, when the most popular
method for computing primes, the Sieve of Eratosthenes, was created. Although it is still
in use for educational purposes, the Sieve of Eratosthenes is not used to compute large
prime numbers because it is inefficient.
In the 17th century, the work of Fermat, among others, provided a great improve
