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Primality testing for beginners

Author: Lasse Rempe-Gillen; Rebecca Waldecker
Publisher: Providence, Rhode Island : American Mathematical Society, [2014]
Series: Student mathematical library, v. 70.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or  Read more...

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Document Type: Book
All Authors / Contributors: Lasse Rempe-Gillen; Rebecca Waldecker
ISBN: 9780821898833 0821898833
OCLC Number: 855858285
Notes: Translation of: Primzahltests für Einsteiger : Zahlentheorie - Algorithmik - Kryptographie.
Description: xii, 244 pages ; 22 cm.
Contents: ch. 1 Natural numbers and primes --
1.1. The natural numbers --
1.2. Divisibility and primes --
1.3. Prime factor decomposition --
1.4. The Euclidean algorithm --
1.5. The Sieve of Eratosthenes --
1.6. There are infinitely many primes --
Further reading --
ch. 2 Algorithms and complexity --
2.1. Algorithms --
2.2. Decidable and undecidable problems --
2.3.Complexity of algorithms and the class P --
2.4. The class NP --
2.5. Randomized algorithms --
Further reading --
ch. 3 Foundations of number theory --
3.1. Modular arithmetic --
3.2. Fermat's Little Theorem --
3.3.A first primality test --
3.4. Polynomials --
3.5. Polynomials and modular arithmetic --
Further reading --
ch. 4 Prime numbers and cryptography --
4.1. Cryptography --
4.2. RSA --
4.3. Distribution of primes --
4.4. Proof of the weak prime number theorem --
4.5. Randomized primality tests --
Further reading --
ch. 5 The starting point: Fermat for polynomials --
5.1.A generalization of Fermat's Theorem --
5.2. The idea of the AKS algorithm --
5.3. The Agrawal-Biswas test --
ch. 6 The theorem of Agrawal, Kayal, and Saxena --
6.1. Statement of the theorem --
6.2. The idea of the proof --
6.3. The number of polynomials in P --
6.4. Cyclotomic polynomials --
ch. 7 The algorithm --
7.1. How quickly does the order of n modulo r grow? --
7.2. The algorithm of Agrawal, Kayal, and Saxena --
7.3. Further comments --
Further reading --
Further reading.
Series Title: Student mathematical library, v. 70.
Other Titles: Primzahltests für Einsteiger.
Responsibility: Lasse Rempe-Gillen, Rebecca Waldecker.

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"The authors can be congratulated on making an important recent result accessible to a very wide audience." - Ch. Baxa, Monatsh Math

 
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