The little book of bigger primes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2004
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 356 S. |
| ISBN: | 0387201696 |
Internformat
MARC
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| 245 | 1 | 0 | |a The little book of bigger primes |c Paulo Ribenboim |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2004 | |
| 300 | |a XXIII, 356 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Primzahl | |
| 650 | 4 | |a Numbers, Prime | |
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Datensatz im Suchindex
| _version_ | 1804130303583715328 |
|---|---|
| adam_text | Contents
Preface vii
Acknowledgements ix
Guiding the Reader xv
Index of Notations xvii
Introduction 1
1 How Many Prime Numbers Are There? 3
I Euclid s Proof 3
II Goldbach Did It Too! 6
III Euler s Proof 8
IV Thue s Proof 9
V Three Forgotten Proofs 10
A Perott s Proof 10
B Auric s Proof 11
C Metrod s Proof 11
VI Washington s Proof 11
VII Furstenberg s Proof 12
2 How to Recognize Whether a Natural Number is a
Prime 15
I The Sieve of Eratosthenes 16
xii Contents
II Some Fundamental Theorems on Congruences 17
A Fermat s Little Theorem and Primitive Roots
Modulo a Prime 17
B The Theorem of Wilson 21
C The Properties of Giuga and of Wolstenholme . 21
D The Power of a Prime Dividing a Factorial . . 24
E The Chinese Remainder Theorem 26
F Euler s Function 28
G Sequences of Binomials 33
H Quadratic Residues 37
III Classical Primality Tests Based on Congruences .... 39
IV Lucas Sequences 44
V Primality Tests Based on Lucas Sequences 63
VI Fermat Numbers 70
VII Mersenne Numbers 75
VIII Pseudoprimes 88
A Pseudoprimes in Base 2 (psp) 88
B Pseudoprimes in Base a (psp(a)) 92
C Euler Pseudoprimes in Base a (epsp(a)) .... 95
D Strong Pseudoprimes in Base a (spsp(a)) ... 96
IX Carmichael Numbers 100
X Lucas Pseudoprimes 103
A Fibonacci Pseudoprimes 104
B Lucas Pseudoprimes (lpsp(P, Q)) 106
C Euler Lucas Pseudoprimes (elpsp(P, Q)) and
Strong Lucas Pseudoprimes (slpsp(P, Q)) . . . 106
D Carmichael Lucas Numbers 108
XI Primality Testing and Factorization 109
A The Cost of Testing 110
B More Primality Tests Ill
C Titanic and Curious Primes 119
D Factorization 122
E Public Key Cryptography 126
3 Are There Functions Denning Prime Numbers? 131
I Functions Satisfying Condition (a) 131
II Functions Satisfying Condition (b) 137
III Prime Producing Polynomials 138
A Prime Values of Linear Polynomials 139
Contents xiii
B On Quadratic Fields 140
C Prime Producing Quadratic Polynomials . . . .144
D The Prime Values and Prime Factors Races . . 148
IV Functions Satisfying Condition (c) 151
4 How Are the Prime Numbers Distributed? 157
I The Function tt(x) 158
A History Unfolding 159
B Sums Involving the Mobius Function 172
C Tables of Primes 173
D The Exact Value of ir(x) and Comparison with
x/logx, Li(x), and R(x) 174
E The Nontrivial Zeros of ((s) 177
F Zero Free Regions for ((s) and the Error Term
in the Prime Number Theorem 180
G Some Properties of ir(x) 181
H The Distribution of Values of Euler s Function 183
II The nth Prime and Gaps Between Primes 184
A The nth Prime 185
B Gaps Between Primes 186
III Twin Primes 192
IV Prime fc Tuplets 197
V Primes in Arithmetic Progression 204
A There Are Infinitely Many! 204
B The Smallest Prime in an Arithmetic
Progression 207
C Strings of Primes in Arithmetic Progression . . 209
VI Goldbach s Famous Conjecture 211
VII The Distribution of Pseudoprimes and of Carmichael
Numbers 216
A Distribution of Pseudoprimes 216
B Distribution of Carmichael Numbers 218
C Distribution of Lucas Pseudoprimes 220
5 Which Special Kinds of Primes Have Been
Considered? 223
I Regular Primes 223
II Sophie Germain Primes 227
III Wieferich Primes 230
IV Wilson Primes 234
xiv Contents
V Repunits 235
VI Numbers fcx6 ±l 237
VII Primes and Second Order Linear Recurrence
Sequences 243
6 Heuristic and Probabilistic Results About Prime
Numbers 249
I Prime Values of Linear Polynomials 250
II Prime Values of Polynomials of Arbitrary Degree . . . 253
III Polynomials with Many Successive Composite Values . 261
IV Partitio Numerorum 263
Appendix 1 269
Appendix 2 275
Conclusion 279
Bibliography 281
Web Site Sources 325
Primes up to 10,000 327
Index of Tables 331
Index of Records 333
Index of Names 335
Subject Index 349
|
| any_adam_object | 1 |
| author | Ribenboim, Paulo 1928- |
| author_GND | (DE-588)117719404 |
| author_facet | Ribenboim, Paulo 1928- |
| author_role | aut |
| author_sort | Ribenboim, Paulo 1928- |
| author_variant | p r pr |
| building | Verbundindex |
| bvnumber | BV017514618 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA246 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)249676842 (DE-599)BVBBV017514618 |
| dewey-full | 512.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.723 |
| dewey-search | 512.723 |
| dewey-sort | 3512.723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV017514618 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:18:53Z |
| institution | BVB |
| isbn | 0387201696 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010547888 |
| oclc_num | 249676842 |
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| owner_facet | DE-20 DE-355 DE-BY-UBR DE-824 DE-384 DE-11 |
| physical | XXIII, 356 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| spelling | Ribenboim, Paulo 1928- Verfasser (DE-588)117719404 aut The little book of bigger primes Paulo Ribenboim 2. ed. New York [u.a.] Springer 2004 XXIII, 356 S. txt rdacontent n rdamedia nc rdacarrier Primzahl Numbers, Prime Primzahl (DE-588)4047263-2 gnd rswk-swf Primzahl (DE-588)4047263-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010547888&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ribenboim, Paulo 1928- The little book of bigger primes Primzahl Numbers, Prime Primzahl (DE-588)4047263-2 gnd |
| subject_GND | (DE-588)4047263-2 |
| title | The little book of bigger primes |
| title_auth | The little book of bigger primes |
| title_exact_search | The little book of bigger primes |
| title_full | The little book of bigger primes Paulo Ribenboim |
| title_fullStr | The little book of bigger primes Paulo Ribenboim |
| title_full_unstemmed | The little book of bigger primes Paulo Ribenboim |
| title_short | The little book of bigger primes |
| title_sort | the little book of bigger primes |
| topic | Primzahl Numbers, Prime Primzahl (DE-588)4047263-2 gnd |
| topic_facet | Primzahl Numbers, Prime |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010547888&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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