The New Book of Prime Number Records
Autor Paulo Ribenboimen Limba Engleză Hardback – 2 feb 1996
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Specificații
ISBN-13: 9780387944579
ISBN-10: 0387944575
Pagini: 541
Ilustrații: XXIV, 541 p.
Dimensiuni: 155 x 235 x 37 mm
Greutate: 0.95 kg
Ediția:3rd ed. 1996
Editura: Springer
Colecția Springer
Locul publicării:New York, NY, United States
ISBN-10: 0387944575
Pagini: 541
Ilustrații: XXIV, 541 p.
Dimensiuni: 155 x 235 x 37 mm
Greutate: 0.95 kg
Ediția:3rd ed. 1996
Editura: Springer
Colecția Springer
Locul publicării:New York, NY, United States
Public țintă
Professional/practitionerCuprins
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.
Recenzii
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
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