Verfügbarkeit: Prime numbers

Prime numbers: an unpredictable series

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Bibliographische Detailangaben
1. Verfasser:	Gracián, Enrique (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	London RBA 2012
Schriftenreihe:	Everything is mathematical
Schlagworte:	Primzahl
Online-Zugang:	Inhaltsverzeichnis Klappentext
Beschreibung:	143 S. Ill., graph. Darst.

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Preface .................................... Chapter l.At the Dawn of Arithmetic ............................................................................. 9 Nothing more natural than a natural number ................................................................... 9 What is a prime number? .............................................................................................................. 12 The fundamental theorem of arithmetic ............................................................................... 14 Prime numbers: invention or discovery? ............................................................................... 16 Eratosthenes s sieve ............................................................................................................................. 20 How many prime numbers are there? .................................................................................... 22 Chapter 2. Prime Numbers: The Elusive Rule .......................................................... 25 Genius in context ................................................................................................................................. 25 Information hub .................................................................................................................................... 27 Alexandria .......................................................................................................................................... 27 Large gaps ................................................................................................................................................... 30 A sense of rhythm ................................................................................................................................. 33 Twin primes .............................................................................................................................................. 35 Magic and mathematics .................................................................................................................... 38 Chapter 3. New Paradigms ........................................................................................................ 41 Marin Mersenne .................................................................................................................................... 41 Mersenne numbers ...................................................................................................................... 42 Pierre de Fermat .................................................................................................................................... 44 Fermaťs little theorem ............................................................................................................... 45 Fermat numbers ............................................................................................................................. 48 Leonhard Euler ....................................................................................................................................... 49 Functions ............................................................................................................................................ 50 Infinite sums ..................................................................................................................................... 53 The Goldbach conjecture ............................................................................................................... 58 Chapter 4. Logarithms and Prime Numbers ............................................................... 61 John Napier ............................................................................................................................................. 61 Logarithms ......................................................................................................................................... 64 es» ich Gauss ierstones tir* Sides of a Coin action are Prime Numbers F°f in cryptography .............. <ffc*s:- numbers .......................... if a number is prime? CONTENTS Johann Carl Friedrich Gauss ......................................................................................................... 68 The first conjecture .................................................................................................................... 69 Chapter 5. Cornerstones .............................................................................................................. 79 Magic sums ............................................................................................................................................... 79 Gauss s clock ............................................................................................................................................. 82 Identities .............................................................................................................................................. 84 Imaginary numbers ............................................................................................................................. 86 An extra dimension ............................................................................................................................. 92 Chapter 6. Two Sides of a Coin ............................................................................................. 101 Bernhard Riemann .............................................................................................................................. 101 The zeta function .......................................................................................................................... 102 Mathematical thought ........................................................................................................................ 106 Srinivasa Ramanujan .......................................................................................................................... 110 Chapter 7. What are Prime Numbers For? .................................................................. 119 Prime numbers in cryptography ................................................................................................. 119 The age of computing ....................................................................................................................... 122 Ρ versus NP .............................................................................................................................................. 124 Generating prime numbers ............................................................................................................ 127 How do we know if a number is prime? .............................................................................. 131 Pseudoprimes ........................................................................................................................................... 132 Certification methods ........................................................................................................................ 133 The story continues .......................................................................................................................... 134 Appendix ................................................................................................................................................... 137 Bibliography ............................................................................................................................................ 139 Index ............................................................................................................................................................. 141 Prime Numbers An unpredictable series Most numbers behave according to simple, clear rules. However, prime numbers are a real anomaly: they appear wherever they want to, without prior warning, in an apparently chaotic fashion and without following any pattern. And the worst of it is that they cannot be ignored - they are essential to arithmetic and, to a certain extent, all mathematics.
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spelling	Gracián, Enrique Verfasser aut Prime numbers an unpredictable series Enrique Gracián London RBA 2012 143 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Primzahl (DE-588)4047263-2 gnd rswk-swf Primzahl (DE-588)4047263-2 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431204&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431204&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext
spellingShingle	Gracián, Enrique Prime numbers an unpredictable series Primzahl (DE-588)4047263-2 gnd
subject_GND	(DE-588)4047263-2
title	Prime numbers an unpredictable series
title_auth	Prime numbers an unpredictable series
title_exact_search	Prime numbers an unpredictable series
title_full	Prime numbers an unpredictable series Enrique Gracián
title_fullStr	Prime numbers an unpredictable series Enrique Gracián
title_full_unstemmed	Prime numbers an unpredictable series Enrique Gracián
title_short	Prime numbers
title_sort	prime numbers an unpredictable series
title_sub	an unpredictable series
topic	Primzahl (DE-588)4047263-2 gnd
topic_facet	Primzahl
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431204&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431204&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
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