The new book of prime number records:
Gespeichert in:
| Vorheriger Titel: | Ribenboim, Paulo The book of prime number records |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
1996
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 433-507) and indexes. |
| Beschreibung: | XXIV, 541 S. graph. Darst. |
| ISBN: | 0387944575 3540944575 |
Internformat
MARC
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| 100 | 1 | |a Ribenboim, Paulo |d 1928- |e Verfasser |0 (DE-588)117719404 |4 aut | |
| 245 | 1 | 0 | |a The new book of prime number records |c Paulo Ribenboim |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 1996 | |
| 300 | |a XXIV, 541 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. 433-507) and indexes. | ||
| 650 | 4 | |a Nombres premiers | |
| 650 | 7 | |a Priemgetallen |2 gtt | |
| 650 | 4 | |a Numbers, Prime | |
| 650 | 0 | 7 | |a Bibliografie |0 (DE-588)4006432-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Primzahl |0 (DE-588)4047263-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Bibliografie |0 (DE-588)4006432-3 |D s |
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Datensatz im Suchindex
| _version_ | 1804125137234034688 |
|---|---|
| adam_text | Contents
Preface ix
Guiding the Reader xv
Index of Notations xvii
Introduction 1
CHAPTER 1
How Many Prime Numbers Are There? 3
I. Euclid s Proof 3
II. Goldbach Did It Too! 4
III. Euler s Proof 6
IV. Thue s Proof 7
V. Three Forgotten Proofs 8
A. Perott s Proof 8
B. Auric s Proof 9
C. Metrod s Proof 9
VI. Washington s Proof 9
VII. Furstenberg s Proof 10
VIII. Euclidean Sequences 11
IX. Generation of Infinite Sequences of Pairwise Relatively Prime Integers 17
CHAPTER 2
How to Recognize Whether a Natural Number Is a Prime 19
I. The Sieve of Eratosthenes 20
II. Some Fundamental Theorems on Congruences 21
A. Fermat s Little Theorem and Primitive Roots Modulo a Prime 22
B. The Theorem of Wilson 25
C. The Properties of Giuga, Wolstenholme, and Mann and Shanks 28
D. The Power of a Prime Dividing a Factorial 30
E. The Chinese Remainder Theorem 33
F. Euler s Function 34
G. Sequences of Binomials 42
H. Quadratic Residues 46
III. Classical Primality Tests Based on Congruences 48
IV. Lucas Sequences 53
V. Primality Tests Based on Lucas Sequences 74
VI. Fermat Numbers 83
xi
xii Contents
VII. Mersenne Numbers 90
VIII. Pseudoprimes 103
A. Pseudoprimes in Base 2 (psp) 105
B. Pseudoprimes in Base a (psp(a)) 108
C. Euler Pseudoprimes in Base a (epsp(a)) 112
D. Strong Pseudoprimes in Base a (spsp(a)) 113
E. Somer Pseudoprimes 117
IX. Carmichael Numbers 118
X. Lucas Pseudoprimes 126
A. Fibonacci Pseudoprimes 127
B. Lucas Pseudoprimes (lpsp(P, Q)) 129
C. Euler Lucas Pseudoprimes (elpsp(P, Q)) and
Strong Lucas Pseudoprimes (slpsp(P, g)) 130
D. Somer Lucas Pseudoprimes 131
E. Carmichael Lucas Numbers 132
XI. Primality Testing and Large Primes 135
A. The Cost of Testing 136
B. More Primality Tests 139
C. Primality Certification 153
D. Fast Generation of Large Primes 156
E. Titanic Primes 157
F. Curious Primes 159
XII. Factorization and Public Key Cryptography 162
A. Factorization of Large Composite Integers 163
B. Public Key Cryptography 172
CHAPTER 3
Are There Functions Defining Prime Numbers? 179
I. Functions Satisfying Condition (a) 179
II. Functions Satisfying Condition (b) 186
HI. Functions Satisfying Condition (c) 187
IV. Prime Producing Polynomials 196
A. Surveying the Problems 196
B. Polynomials with Many Initial Prime Absolute Values 197
C. The Prime Producing Polynomials Races 203
D. Primes of the Form m2 + 1 206
CHAPTER 4
How Are the Prime Numbers Distributed? 213
I. The Growth of n(x) 214
A. History Unfolding 215
B. Sums Involving the Mobius Function 229
C. Tables of Primes 233
D. The Exact Value of 7t(x) and Comparison with x/(log x), Li(x),
and K(x) 235
E. The Nontrivial Zeros of £(s) 239
F. Zero Free Regions for £(s) and the Error Term in the
Prime Number Theorem 243
Contents xiii
G. The Growth of C(s) 245
H. Some Properties of n(x) 247
II. The nth Prime and Gaps 248
A. The nth Prime 248
B. Gaps Between Primes 250
Interlude 258
III. Twin Primes 259
Addendum on fe Tuples of Primes 265
IV. Primes in Arithmetic Progression 265
A. There Are Infinitely Many! 265
B. The Smallest Prime in an Arithmetic Progression 277
C. Strings of Primes in Arithmetic Progression 284
V. Primes in Special Sequences 288
VI. Goldbach s Famous Conjecture 291
VII. The Waring Goldbach Problem 299
A. Waring s Problem 300
B. The Waring Goldbach Problem 310
VIII. The Distribution of Pseudoprimes, Carmichael Numbers,
and Values of Euler s Function 311
A. Distribution of Pseudoprimes 311
B. Distribution of Carmichael Numbers 314
C. Distribution of Lucas Pseudoprimes 317
D. Distribution of Elliptic Pseudoprimes 318
E. Distribution of Values of Euler s Function 319
CHAPTER 5
Which Special Kinds of Primes Have Been Considered? 323
I. Regular Primes 323
II. Sophie Germain Primes 329
HI. Wieferich Primes 333
IV. Wilson Primes 346
V. Repunits and Similar Numbers 350
VI. Primes with Given Initial and Final Digits 355
VII. Numbers k x 2 + 1 355
VIII. Primes and Second Order Linear Recurrence Sequences 361
IX. The NSW Primes 367
CHAPTER 6
Heuristic and Probabilistic Results about Prime Numbers 371
I. Prime Values of Linear Polynomials 372
II. Prime Values of Polynomials of Arbitrary Degree 386
HI. Polynomials with Many Successive Composite Values 400
IV. Partitio Numerorum 403
V. Some Probabilistic Estimates 411
A. Distribution of Mersenne Primes 411
B. The log log Philosophy 413
VI. The Density of the Set of Regular Primes 414
xiv Contents
Conclusion 427
Bibliography 433
The Pages That Couldn t Wait 509
Primes up to 10,000 513
Index of Tables 517
Index of Names 519
Subject Index 535
|
| 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 | BV010658050 |
| callnumber-first | Q - Science |
| callnumber-label | QA246 |
| callnumber-raw | QA246.R47 1996 |
| callnumber-search | QA246.R47 1996 |
| callnumber-sort | QA 3246 R47 41996 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)31971477 (DE-599)BVBBV010658050 |
| dewey-full | 512/.7220 512/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.72 20 512/.72 |
| dewey-search | 512/.72 20 512/.72 |
| dewey-sort | 3512 272 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-09T17:56:46Z |
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| isbn | 0387944575 3540944575 |
| language | English |
| lccn | 95005441 |
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| physical | XXIV, 541 S. graph. Darst. |
| publishDate | 1996 |
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| spelling | Ribenboim, Paulo 1928- Verfasser (DE-588)117719404 aut The new book of prime number records Paulo Ribenboim 3. ed. New York, NY [u.a.] Springer 1996 XXIV, 541 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 433-507) and indexes. Nombres premiers Priemgetallen gtt Numbers, Prime Bibliografie (DE-588)4006432-3 gnd rswk-swf Primzahl (DE-588)4047263-2 gnd rswk-swf Primzahl (DE-588)4047263-2 s Bibliografie (DE-588)4006432-3 s 1\p DE-604 2. Aufl. (1989) u.d.T. Ribenboim, Paulo The book of prime number records text/html http://www.loc.gov/catdir/enhancements/fy0814/95005441-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007114368&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ribenboim, Paulo 1928- The new book of prime number records Nombres premiers Priemgetallen gtt Numbers, Prime Bibliografie (DE-588)4006432-3 gnd Primzahl (DE-588)4047263-2 gnd |
| subject_GND | (DE-588)4006432-3 (DE-588)4047263-2 |
| title | The new book of prime number records |
| title_auth | The new book of prime number records |
| title_exact_search | The new book of prime number records |
| title_full | The new book of prime number records Paulo Ribenboim |
| title_fullStr | The new book of prime number records Paulo Ribenboim |
| title_full_unstemmed | The new book of prime number records Paulo Ribenboim |
| title_old | Ribenboim, Paulo The book of prime number records |
| title_short | The new book of prime number records |
| title_sort | the new book of prime number records |
| topic | Nombres premiers Priemgetallen gtt Numbers, Prime Bibliografie (DE-588)4006432-3 gnd Primzahl (DE-588)4047263-2 gnd |
| topic_facet | Nombres premiers Priemgetallen Numbers, Prime Bibliografie Primzahl |
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