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PRIMES is in P (2002)

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by Manindra Agrawal , Neeraj Kayal , Nitin Saxena
Venue:Ann. of Math
Citations:17 - 1 self
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BibTeX

@ARTICLE{Agrawal02primesis,
    author = {Manindra Agrawal and Neeraj Kayal and Nitin Saxena},
    title = {PRIMES is in P},
    journal = {Ann. of Math},
    year = {2002},
    volume = {2},
    pages = {781--793}
}

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Abstract

We present an unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite. 1

Citations

348 zur Gathen and - von - 1999
345 Finite Fields and their Applications - Lidl, Niederreiter - 1984
294 Introduction to Analytic Number Theory - Apostol - 1976
181 Riemann’s hypothesis and tests for primality - Miller - 1976
163 Probabilistic algorithm for testing primality - Rabin - 1980
145 The Art of Computer - Knuth - 1998
122 A fast Monte-Carlo test for primality - Solovay, Strassen - 1977
112 Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes - Hardy, Littlewood
102 On distinguishing prime numbers from composite numbers - Adleman, Pomerance, et al. - 1983
71 Every Prime has a Succinct Certificate - Pratt - 1975
67 zur Gathen and Jürgen Gerhard. Modern computer algebra - von - 2003
62 Almost all primes can be quickly certified - Goldwasser, Kilian - 1986
56 A First Course in Abstract Algebra - Fraleigh - 1989
45 Primality Testing And Abelian Varieties Over Finite Fields (Springer-Verlag - Adleman, Huang - 1992
41 On Artin’s conjecture - Murty - 1983
37 Artin’s conjecture for primitive roots - Heath-Brown - 1986
24 Primality and identity testing via Chinese remaindering - Agrawal, Biswas
17 Théorème de Brun-Titchmarsh; application au théorème de Fermat, Inventiones Mathematicae 79 - Fouvry - 1985
11 Introduction to and their applications - Lidl, Niederreiter - 1986
10 Primality Testing And Two Dimensional Abelian Varieties Over Finite Fields - Adleman, Huang - 1992
9 On Chebyshev-type inequalities for primes - Nair - 1982
9 Proving primality after Agrawal-Kayal-Saxena. http://cr.yp.to/ papers.html - Bernstein
8 The Brun-Titchmarsh theorem on average - Baker, Harman - 1995
7 On the number of primes p for which p + a has a large prime factor, Mathematika 16 - Goldfeld - 1969
6 Towards a deterministic polynomial-time test - Kayal, Saxena - 2002
5 Primality Testing - Bhattacharjee, Pandey - 2001
4 Almost all primes can be quickly certi - Goldwasser, Kilian - 1986
4 The …rst case of Fermat’s last theorem - Adleman, Heath-Brown - 1985
3 Primality Testing with Gaussian Periods, preliminary version July 20 - Lenstra, Pomerance - 2005
3 Some remarks and questions about the AKS algorithm and related conjecture - Macaj - 2002
2 Lecture notes of a conference - Atkin - 1986
2 Note on a number theory function - Carmichael - 1910
2 On the number of primes p for which p+a has a large prime factor - Goldfeld - 1969
2 Primality testing with cyclotomic rings, Unpublished, August 2002. 42 Alford, Granville and Pomerance, There are infinitely many Carmichael numbers - Lenstra - 1994
2 Leeuwen (Ed.): Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity - V - 1990
1 The Euclidian algorithm for S integers - Gupta, Murty, et al. - 1985
1 Notes on primality test and analysis of AKS. Private communication - Kalai, Sahai, et al. - 2002
1 Lecture notes of a conference, boulder (colorado - Atkin - 1986
1 A prime solution, Frontline, India’s National Magazine - RAMACHANDRAN
1 The Euclidian algorithm for S-integers, Number Theory - Gupta, Murty, et al. - 1985
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