Édouard Lucas and primality testing:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1998
|
| Series: | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 525 S. Ill. |
| ISBN: | 0471148520 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Table of symbols ix
Preface xiii
1 Preliminaries 1
1.1 Results from elementary number theory 1
1.2 Algorithms and complexity 7
1.3 Continued fractions 12
1.4 Some arithmetic functions 16
1.5 Results concerning binomial congruences 18
Notes for Chapter 1 24
2 The Beginnings 27
2.1 Antiquity 27
2.2 From the Middle Ages to Mersenne 30
2.3 Fermat and Euler 35
2.4 Lagrange, Legendre, and Gauss 40
2.5 The early tablemakers 44
Notes for Chapter 2 47
3 Lucas Early Work 53
3.1 Lucas earliest primality tests 53
3.2 Lucas and MU7 58
Notes for Chapter 3 65
4 The Lucas Functions 69
4.1 Definition of the Lucas functions 69
4.2 Identity properties of the Lucas functions 73
4.3 Arithmetic properties 83
4.4 Computation of the Lucas functions 90
Notes for Chapter 4 93
v
vi CONTENTS
5 Lucas Tests 97
5.1 Lucas early tests for Mersenne primes 97
5.2 The Fermat numbers 99
5.3 Landry and F6 102
5.4 Lucas and necessity 107
5.5 Lucas extended tests 114
Notes for Chapter 5 117
6 Later Developments 121
6.1 The work of Proth and Pocklington 121
6.2 Early factoring methods 125
6.3 Cole s example 132
6.4 The Fermat numbers 133
Notes for Chapter 6 138
7 Early Devices 141
7.1 The beginnings of mechanization 141
7.2 Mechanisms for testing Mersenne numbers 145
7.3 The number sieve 156
Notes for Chapter 7 169
8 Kraitchik and Lehmer 173
8.1 Kraitchik 173
8.2 D.H. Lehmer 180
8.3 Some special numbers 189
8.4 The Lehmer functions 196
8.5 Some tables 199
Notes for Chapter 8 201
9 Finite Fields 205
9.1 Groups and rings 205
9.2 Polynomials and fields 210
9.3 Finite fields 219
9.4 Some polynomial congruences 223
Notes for Chapter 9 230
10 Lucas Functions Generalized 231
10.1 A generalization of the Lucas functions 231
10.2 Some identity properties 236
10.3 Some arithmetic properties 240
10.4 Some results on Cn 248
10.5 Primality tests 252
CONTENTS vii
Notes for Chapter 10 255
11 Special Tests for Primality 257
11.1 Gauss and Jacobi sums 257
11.2 A primality test 267
11.3 Some special cases 272
Notes for Chapter 11 282
12 The Influence of the Computer 285
12.1 Some observations 285
12.2 Some primality tests 290
12.3 Some further tests 297
12.4 A result of Lenstra and i?io3i 306
Notes for Chapter 12 313
13 Results from the Computer 317
13.1 The Cunningham project 317
13.2 Primes of the form k2n + 1 321
13.3 Fast multiplication 326
13.4 Fermat and Mersenne numbers 332
Notes for Chapter 13 338
14 Primality Proofs 343
14.1 Factoring and primality tests 343
14.2 The complexity of primality testing 346
14.3 Certificates of primality 351
14.4 Introduction to elliptic curves 357
14.5 Very short certificates of primality 361
Notes for Chapter 14 367
15 Probabilistic Primality Tests 371
15.1 Pseudoprimes and Carmichael numbers 371
15.2 Stronger pseudoprimes 376
15.3 Cryptography 385
15.4 Probabilistic methods 392
Notes for Chapter 15 398
16 Recent Sieve Devices 405
16.1 Modern sieve devices 405
16.2 Pseudosquares and primality testing 412
16.3 The search for pseudosquares 417
16.4 Application to testing primality 423
viii CONTENTS
Notes for Chapter 16 428
17 Primality Proving Today 431
17.1 The APR test 431
17.2 The Jacobi sums test 435
17.3 Primality testing with elliptic curves 444
17.4 The Lucas connection 450
17.5 Conclusion 462
Notes for Chapter 17 464
Bibliography 469
Index 515
|
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| institution | BVB |
| isbn | 0471148520 |
| language | English |
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| physical | XVIII, 525 S. Ill. |
| publishDate | 1998 |
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| publisher | Wiley |
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| series | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts |
| series2 | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts |
| spelling | Williams, Hugh C. 1943- Verfasser (DE-588)124230415 aut Édouard Lucas and primality testing Hugh C. Williams New York [u.a.] Wiley 1998 XVIII, 525 S. Ill. txt rdacontent n rdamedia nc rdacarrier Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts 22 Lucas, Edouard <1842-1891> Lucas, Édouard 1842-1891 (DE-588)1063212561 gnd rswk-swf Numbers, Prime Primzahltheorie (DE-588)4175715-4 gnd rswk-swf Lucas, Édouard 1842-1891 (DE-588)1063212561 p Primzahltheorie (DE-588)4175715-4 s DE-604 Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts 22 (DE-604)BV012067942 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008320346&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Williams, Hugh C. 1943- Édouard Lucas and primality testing Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts Lucas, Edouard <1842-1891> Lucas, Édouard 1842-1891 (DE-588)1063212561 gnd Numbers, Prime Primzahltheorie (DE-588)4175715-4 gnd |
| subject_GND | (DE-588)1063212561 (DE-588)4175715-4 |
| title | Édouard Lucas and primality testing |
| title_auth | Édouard Lucas and primality testing |
| title_exact_search | Édouard Lucas and primality testing |
| title_full | Édouard Lucas and primality testing Hugh C. Williams |
| title_fullStr | Édouard Lucas and primality testing Hugh C. Williams |
| title_full_unstemmed | Édouard Lucas and primality testing Hugh C. Williams |
| title_short | Édouard Lucas and primality testing |
| title_sort | edouard lucas and primality testing |
| topic | Lucas, Edouard <1842-1891> Lucas, Édouard 1842-1891 (DE-588)1063212561 gnd Numbers, Prime Primzahltheorie (DE-588)4175715-4 gnd |
| topic_facet | Lucas, Edouard <1842-1891> Lucas, Édouard 1842-1891 Numbers, Prime Primzahltheorie |
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