The book of prime number records:
Gespeichert in:
| Späterer Titel: | Ribenboim, Paulo The new book of prime number records |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
1989
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [355] - 455 |
| Beschreibung: | XXIII, 479 S. graph. Darst. |
| ISBN: | 0387970428 3540970428 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV002510327 | ||
| 003 | DE-604 | ||
| 005 | 20141219 | ||
| 007 | t | ||
| 008 | 900129s1989 d||| |||| 00||| eng d | ||
| 010 | |a 89021675 | ||
| 020 | |a 0387970428 |9 0-387-97042-8 | ||
| 020 | |a 3540970428 |9 3-540-97042-8 | ||
| 035 | |a (OCoLC)20217086 | ||
| 035 | |a (DE-599)BVBBV002510327 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-739 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA246 | |
| 050 | 0 | |a QA246 .R47 1989 | |
| 082 | 0 | |a 512/.72 |2 20 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a MAT 100f |2 stub | ||
| 100 | 1 | |a Ribenboim, Paulo |d 1928- |e Verfasser |0 (DE-588)117719404 |4 aut | |
| 245 | 1 | 0 | |a The book of prime number records |c Paulo Ribenboim |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 1989 | |
| 300 | |a XXIII, 479 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. [355] - 455 | ||
| 650 | 4 | |a Nombres premiers | |
| 650 | 7 | |a Nombres premiers |2 ram | |
| 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 |
| 689 | 0 | 0 | |a Primzahl |0 (DE-588)4047263-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Primzahl |0 (DE-588)4047263-2 |D s |
| 689 | 1 | 1 | |a Bibliografie |0 (DE-588)4006432-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 785 | 0 | 0 | |i 3. Aufl. (1996) u.d.T. |a Ribenboim, Paulo |t The new book of prime number records |w (DE-604)BV010658050 |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001616554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001616554 | ||
Datensatz im Suchindex
| _version_ | 1804116915745980416 |
|---|---|
| adam_text | TABLE OF CONTENTS
Preface to the First Edition vii
Preface to the Second Edition viii
Guiding the Reader xiii
Index of Notations xv
Introduction 1
Chapter 1. How Many Prime Numbers Are There? 3
I. Euclid s Proof 3
II. Kummer s Proof 4
III. Polya s Proof 5
IV. Euler s Proof 7
V. Thue s Proof 8
VI. Two and a Half Forgotten Proofs 8
A. Perott s Proof 9
B. Auric s Proof 9
C. Metrod s Proof 10
VII. Washington s Proof 10
VIII. Fiirstenberg s Proof 11
Chapter 2. How to Recognize Whether a Natural
Number Is a Prime? 13
I. The Sieve of Eratosthenes 14
II. Some Fundamental Theorems on Congruences 15
A. Fermat s Little Theorem and Primitive Roots
.; Modulo a Prime 16
j B. The Theorem of Wilson 19
1
x Contents
C. The Properties of Giuga, Wolstenholme and Mann
Shanks 20
D. The Power of a Prime Dividing a Factorial 22
E. The Chinese Remainder Theorem 24
F. Euler s Function 25
G. Sequences of Binomials 31
H. Quadratic Residues 34
III. Classical Primality Tests Based on Congruences 36
IV. Lucas Sequences 41
Addendum on Lehmer Numbers 61
V. Classical Primality Tests Based on Lucas Sequences 61
VI. Fermat Numbers 71
VII. Mersenne Numbers 75
Addendum on Perfect Numbers 81
VIII. Pseudoprimes 86
A. Pseudoprimes in Base 2 (psp) 86
B. Pseudoprimes in Base a (psp(a)) 89
B. Euler Pseudoprimes in Base a (epsp(a)) 92
D. Strong Pseudoprimes in Base a (spsp(a)) 94
Addendum on the Congruence an k = 6n k (mod n) 97
IX. Carmichael Numbers 98
Addendum on Knodel Numbers 100
X. Lucas Pseudoprimes 101
A. Fibonacci Pseudoprimes 102
B. Lucas Pseudoprimes (ipsp(i Q)) 104
C. Euler Lucas Pseudoprimes (eipsp(/ , Q)) and Strong
Lucas Pseudoprimes (sJpsp(P, Q)) 105
D. Carmichael Lucas Numbers 107
XI. Last Section on Primality Testing and Factorization! 107
A. The Cost of Testing 109
B. Recent Primality Tests 113
C. Monte Carlo Methods 116
D. Titanic Primes 120
E. Factorization 121
F. Public Key Cryptography 123
Chapter 3. Arc There Functions Defining Prime Numbers? 129
I. Functions Satisfying Condition (a) 129
II. Functions Satisfying Condition (b) 135
III. Functions Satisfying Condition (c) 144
Chapter 4. How Are the Prime Numbers Distributed? 153
I. The Growth of n(x) 154
A. History Unfolding 155
Euler 155
Legendre 159
Gauss 160
Contents xi
Tschebycheff 160
Riemann 161
de la Vallee Poussin and Hadamard 164
Erdos and Selberg 167
B. Sums Involving the Mobius Function 168
C. The Distribution of Values of Euler s Function 172
D. Tables of Primes 175
E. The Exact Value of n(x) and Comparison with
x/(log x), Li(x), and R(x) 178
F. The Nontrivial Zeroes of 5(5) 180
G. Zero Free Regions for £(s) and the Error Term
in the Prime Number Theorem 184
H. The Growth of £(s) 186
II. The nth Prime and Gaps 188
A. Some Properties of n(x) 188
B. The nth Prime 190
C. Gaps between Primes 191
D. The Possible Gaps between Primes 196
E. Interlude 197
III. Twin Primes 199
Addendum on Polignac s Conjecture 204
IV. Primes in Arithmetic Progression 205
A. There Are Infinitely Many! 205
B. The Smallest Prime in an Arithmetic Progression 217
C. Strings of Primes in Arithmetic Progression 223
V. Primes in Special Sequences 226
VI. Goldbach s Famous Conjecture 229
VII. The Waring Goldbach Problem 236
A. Waring s Problem 236
B. The Waring Goldbach Problem 247
VIII. The Distribution of Pseudoprimes and of
Carmichael Numbers 248
A. Distribution of Pseudoprimes 248
B. Distribution of Carmichael Numbers 252
C. Distribution of Lucas Pseudoprimes 253
Chapter 5. Which Special Kinds of Primes Have Been
Considered? 255
I. Regular Primes 255
II. Sophie Germain Primes 261
III. Wieferich Primes 263
IV. Wilson Primes 277
V. Repunits and Similar Numbers 277
VI. Primes with Given Initial and Final Digits 280
VII. Numbers i x 2 i I 280
Addendum on Cullen Numbers 283
xii Table of Contents
VIII. Primes and Second Order Linear Recurrence
Sequences 283
IX. The NSW Primes 288
Chapter 6. Heuristic and Probabilistic Results About
Prime Numbers 291
I. Prime Values of Linear Polynomials 292
II. Prime Values of Polynomials of Arbitrary Degree 307
III. Some Probabilistic Estimates 321
A. Partitio Numerorum 321
B. Polynomials with Many Successive
Composite Values 329
C. Distribution of Mersenne Primes 332
D. The log log Philosophy 333
IV. The Density of the Set of Regular Primes 334
Conclusion 347
Dear Reader 347
Citations for Some Possible Prizes for Work on
the Prime Number Theorem 349
Bibliography 355
A. General References 355
B. Specific References 357
Chapter 1 357
Chapter 2 361
Chapter 3 390
Chapter 4 398
Chapter 5 439
Chapter 6 449
Conclusion 455
Primes up to 10,000 456
Index of Names 461
Gallimaufries 471
Subject Index 473
Addenda to the Second Edition 477
|
| 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 | BV002510327 |
| callnumber-first | Q - Science |
| callnumber-label | QA246 |
| callnumber-raw | QA246 QA246 .R47 1989 |
| callnumber-search | QA246 QA246 .R47 1989 |
| callnumber-sort | QA 3246 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| classification_tum | MAT 100f |
| ctrlnum | (OCoLC)20217086 (DE-599)BVBBV002510327 |
| dewey-full | 512/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.72 |
| dewey-search | 512/.72 |
| dewey-sort | 3512 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01855nam a2200505 c 4500</leader><controlfield tag="001">BV002510327</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20141219 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">900129s1989 d||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">89021675</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387970428</subfield><subfield code="9">0-387-97042-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540970428</subfield><subfield code="9">3-540-97042-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)20217086</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002510327</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA246</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA246 .R47 1989</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.72</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 100f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ribenboim, Paulo</subfield><subfield code="d">1928-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)117719404</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The book of prime number records</subfield><subfield code="c">Paulo Ribenboim</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXIII, 479 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. [355] - 455</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nombres premiers</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Nombres premiers</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Numbers, Prime</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Bibliografie</subfield><subfield code="0">(DE-588)4006432-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Primzahl</subfield><subfield code="0">(DE-588)4047263-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Primzahl</subfield><subfield code="0">(DE-588)4047263-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Primzahl</subfield><subfield code="0">(DE-588)4047263-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Bibliografie</subfield><subfield code="0">(DE-588)4006432-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="785" ind1="0" ind2="0"><subfield code="i">3. Aufl. (1996) u.d.T.</subfield><subfield code="a">Ribenboim, Paulo</subfield><subfield code="t">The new book of prime number records</subfield><subfield code="w">(DE-604)BV010658050</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001616554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001616554</subfield></datafield></record></collection> |
| id | DE-604.BV002510327 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:46:06Z |
| institution | BVB |
| isbn | 0387970428 3540970428 |
| language | English |
| lccn | 89021675 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001616554 |
| oclc_num | 20217086 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-739 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-739 DE-634 DE-83 DE-11 DE-188 |
| physical | XXIII, 479 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Springer |
| record_format | marc |
| spelling | Ribenboim, Paulo 1928- Verfasser (DE-588)117719404 aut The book of prime number records Paulo Ribenboim 2. ed. New York, NY [u.a.] Springer 1989 XXIII, 479 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [355] - 455 Nombres premiers Nombres premiers ram Numbers, Prime Bibliografie (DE-588)4006432-3 gnd rswk-swf Primzahl (DE-588)4047263-2 gnd rswk-swf Primzahl (DE-588)4047263-2 s DE-604 Bibliografie (DE-588)4006432-3 s 3. Aufl. (1996) u.d.T. Ribenboim, Paulo The new book of prime number records (DE-604)BV010658050 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001616554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ribenboim, Paulo 1928- The book of prime number records Nombres premiers Nombres premiers ram 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 book of prime number records |
| title_auth | The book of prime number records |
| title_exact_search | The book of prime number records |
| title_full | The book of prime number records Paulo Ribenboim |
| title_fullStr | The book of prime number records Paulo Ribenboim |
| title_full_unstemmed | The book of prime number records Paulo Ribenboim |
| title_new | Ribenboim, Paulo The new book of prime number records |
| title_short | The book of prime number records |
| title_sort | the book of prime number records |
| topic | Nombres premiers Nombres premiers ram Numbers, Prime Bibliografie (DE-588)4006432-3 gnd Primzahl (DE-588)4047263-2 gnd |
| topic_facet | Nombres premiers Numbers, Prime Bibliografie Primzahl |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001616554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ribenboimpaulo thebookofprimenumberrecords |