Overview

Full Product Details

Author:   Paulo Ribenboim
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   3rd ed. 1996
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   2.150kg
ISBN:  

9780387944579

ISBN 10:   0387944575
Pages:   541
Publication Date:   02 February 1996
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

1 How Many Prime Numbers Are There?.- I. Euclid’s Proof.- II. Goldbach Did It Too!.- III. Euler’s Proof.- IV. Thue’s Proof.- V. Three Forgotten Proofs.- VI. Washington’s Proof.- VII. Fürstenberg’s Proof.- VIII. Euclidean Sequences.- IX. Generation of Infinite Sequences of Pairwise Relatively Prime Integers.- 2 How to Recognize Whether a Natural Number Is a Prime.- I. The Sieve of Eratosthenes.- II. Some Fundamental Theorems on Congruences.- III. Classical Primality Tests Based on Congruences.- IV. Lucas Sequences.- V. Primality Tests Based on Lucas Sequences.- VI. Fermat Numbers.- VII. Mersenne Numbers.- VIII. Pseudoprimes.- IX. Carmichael Numbers.- X. Lucas Pseudoprimes.- XL Primality Testing and Large Primes.- XII. Factorization and Public Key Cryptography.- 3 Are There Functions Defining Prime Numbers?.- I. Functions Satisfying Condition (a).- II. Functions Satisfying Condition (b).- III. Functions Satisfying Condition (c).- IV. Prime-Producing Polynomials.- 4 How Are the Prime Numbers Distributed?.- I. The Growth of ?(x).- II. The n th Prime and Gaps.- Interlude.- III. Twin Primes.- Addendum on k-Tuples of Primes.- IV. Primes in Arithmetic Progression.- V. Primes in Special Sequences.- VI. Goldbach’s Famous Conjecture.- VII. The Waring-Goldbach Problem.- VIII. The Distribution of Pseudoprimes, Carmichael Numbers, and Values of Euler’s Function.- 5 Which Special Kinds of Primes Have Been Considered?.- I. Regular Primes.- II. Sophie Germain Primes.- III. Wieferich Primes.- IV. Wilson Primes.- V. Repunits and Similar Numbers.- VI. Primes with Given Initial and Final Digits.- VII. Numbers k×2n±1.- VIII. Primes and Second-Order Linear Recurrence Sequences.- IX. The NSW Primes.- 6 Heuristic and Probabilistic Results about Prime Numbers.- I. Prime Valuesof Linear Polynomials.- II. Prime Values of Polynomials of Arbitrary Degree.- III. Polynomials with Many Successive Composite Values.- IV. Partitio Numerorum.- V. Some Probabilistic Estimates.- Conclusion.- The Pages That Couldn’t Wait.- Primes up to 10,000.- Index of Tables.- Index of Names.

Reviews

Third Edition P. Ribenboim The New Book of Prime Number Records ""A number-theoretical version of the Guinness Book of Records ... There is much mathematics to be found in these pages. These are records given here as well. This book is written with much wit. Experts may not find much that is new, but it is always worthwhile to view the history of a subject as a whole rather than a collection of isolated results.""--MATHEMATICAL REVIEWS

Third Edition P. Ribenboim The New Book of Prime Number Records A number-theoretical version of the Guinness Book of Records ... There is much mathematics to be found in these pages. These are records given here as well. This book is written with much wit. Experts may not find much that is new, but it is always worthwhile to view the history of a subject as a whole rather than a collection of isolated results. --MATHEMATICAL REVIEWS

"Third Edition P. Ribenboim The New Book of Prime Number Records ""A number-theoretical version of the Guinness Book of Records ... There is much mathematics to be found in these pages. These are records given here as well. This book is written with much wit. Experts may not find much that is new, but it is always worthwhile to view the history of a subject as a whole rather than a collection of isolated results.""--MATHEMATICAL REVIEWS"

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions