The Book of Prime Number Records

The Book of Prime Number Records

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A. J. Coleman and H. W. Ellis and to acknowledge their long-lasting interest in ...

Author: Paulo Ribenboim

Publisher: Springer

ISBN: UOM:39015017288872

Category: Mathematics

Page: 586

View: 196

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A. J. Coleman and H. W. Ellis and to acknowledge their long-lasting interest in the quality of teaching undergraduate students. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book oj Records, reminded me very gently that the most "innumerate" people of the world are of a certain tribe in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes Morris, I'm from Brazil, but my book will contain numbers different from 'one.' " He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name), and consists of about 16 million digits of the number 11. "I assure you Morris, that in spite of the beauty of the apparent randomness of the decimal digits of 11, I'll be sure that my text will also include some words." Acknowledgment. The manuscript of this book was prepared on the word processor by Linda Nuttall. I wish to express my appreciation for the great care, speed, and competence of her work. Paulo Ribenboim CONTENTS Preface vii Guiding the Reader xiii Index of Notations xv Introduction Chapter 1. How Many Prime Numbers Are There? 3 I. Euclid's Proof 3 II.
Categories: Mathematics

The New Book of Prime Number Records

The New Book of Prime Number Records

The new book of prime number records/Paulo Ribenboim.–3rd ed. p. cm. Rev. ed. of: The book of prime number records. 2nd ed. c.1989. Includes bibliographical references and index. ISBN 978-1-4612-6892-5 ISBN 978-1-4612-0759-7 (eBook) DOI ...

Author: Paulo Ribenboim

Publisher: Springer Science & Business Media

ISBN: 9781461207597

Category: Mathematics

Page: 541

View: 253

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.
Categories: Mathematics

The Book of Prime Number Records

The Book of Prime Number Records

There are also several new records in the text, which were attained since this book appeared one year ago, including a new Mersenne number. On the other hand, no space could be made to describe the very recent primality testing methods ...

Author: Paulo Ribenboim

Publisher: Springer Science & Business Media

ISBN: 9781468405071

Category: Mathematics

Page: 479

View: 387

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquim series established to honor Professors A. J. Coleman and H. W. Ellis and to acknow ledge their long lasting interest in the quality of teaching under graduate students. In another colloquim lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guilllless Book oj Records, remainded me very gently that the most "innumerate" people of the world are of a certain tribe in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes Morris, I'm from Brazil, but my book will contain numbers different from 'one.' " He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name), and consists of about 16 million digits of the number 11. "I assure you Morris, that in spite of the beauty of the apparent randomness of the decimal digits of 11, I'll be sure that my text will include also some words." Acknowledgment. The manuscript of this book was prepared on the word processor by Linda Nuttall. I wish to express my appreciation for the great care, speed, and competence of her work.
Categories: Mathematics

The New Book of Prime Number Records

The New Book of Prime Number Records

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes.

Author: Paulo Ribenboim

Publisher: Springer

ISBN: 1461268923

Category: Mathematics

Page: 541

View: 495

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.
Categories: Mathematics

Secret History

Secret History

Ribenboim, Paulo, The Little Book of Bigger Primes, second edition, Springer, New York, 2004. This is a condensed version of The New Book of Prime Number Records. Robinson, Sara, “Researchers Develop Fast Deterministic Algorithm for ...

Author: Craig Bauer

Publisher: CRC Press

ISBN: 9781351668491

Category: Computers

Page: 775

View: 244

The first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks, it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook, the mathematics can be prioritized, with a book both students and instructors will enjoy reading. Secret History: The Story of Cryptology, Second Edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here. The first edition of this book contained chapters devoted to the cracking of German and Japanese systems during World War II. Now the other side of this cipher war is also told, that is, how the United States was able to come up with systems that were never broken. The text is in two parts. Part I presents classic cryptology from ancient times through World War II. Part II examines modern computer cryptology. With numerous real-world examples and extensive references, the author skillfully balances the history with mathematical details, providing readers with a sound foundation in this dynamic field. FEATURES Presents a chronological development of key concepts Includes the Vigenère cipher, the one-time pad, transposition ciphers, Jefferson’s wheel cipher, Playfair cipher, ADFGX, matrix encryption, Enigma, Purple, and other classic methods Looks at the work of Claude Shannon, the origin of the National Security Agency, elliptic curve cryptography, the Data Encryption Standard, the Advanced Encryption Standard, public-key cryptography, and many other topics New chapters detail SIGABA and SIGSALY, successful systems used during World War II for text and speech, respectively Includes quantum cryptography and the impact of quantum computers
Categories: Computers

Elementary Number Theory in Nine Chapters

Elementary Number Theory in Nine Chapters

Dirichlet , P.G.L. , Vorlesung über Zahlentheorie , F. Vieweg , Braunschweig , 1894 , reprinted Chelsea , New York , 1968 . ... Ribenboim , P. , The Book of Prime Number Records , 2nd ed . , Springer - Verlag , New York , 1989 .

Author: James J. Tattersall

Publisher: Cambridge University Press

ISBN: 0521585317

Category: Mathematics

Page: 420

View: 796

This book serves as a one-semester introductory course in number theory. Throughout the book, Tattersall adopts a historical perspective and gives emphasis to some of the subject's applied aspects, highlighting the field of cryptography. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises has been included. The reader should have "pencil in hand" and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.
Categories: Mathematics

The Development of Prime Number Theory

The Development of Prime Number Theory

Ramachandra,K.,Sankaranarayanan, A. (1993): On some theorems of Littlewood and Selberg,I. J. Number Th., 44, 281–291. MR 94f:11081. ... 95j:11004. Ribenboim,P. (1996): The New Book of Prime Number Records. Springer, 416 References.

Author: Wladyslaw Narkiewicz

Publisher: Springer Science & Business Media

ISBN: 9783662131572

Category: Mathematics

Page: 449

View: 330

1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
Categories: Mathematics

17 Lectures on Fermat Numbers

17 Lectures on Fermat Numbers

From Number Theory to Geometry Michal Krizek, Florian Luca, Lawrence Somer. 25 (1971), 944-945, Math. Comp. 26 (1972), 814. ... Ribenboim, P., Prime number records (a new chapter for the Guinness book of records) (Russian), Uspekhi Mat.

Author: Michal Krizek

Publisher: Springer Science & Business Media

ISBN: 9780387218502

Category: Mathematics

Page: 257

View: 824

The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.
Categories: Mathematics

CRC Concise Encyclopedia of Mathematics

CRC Concise Encyclopedia of Mathematics

New York: Springer-Verlag, p. 94, 1994. Pomerance, C.; Selfridge, J. L.; and Wagstaff, S. S. Jr. "The Pseudoprimes to 25 ⋅ 109./ " Math. Comput. 35, 1003Á/1026, 1980. Ribenboim, P. The Book of Prime Number Records, 2nd ed.

Author: Eric W. Weisstein

Publisher: CRC Press

ISBN: 9781420035223

Category: Mathematics

Page: 3252

View: 804

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Categories: Mathematics

From Great Discoveries in Number Theory to Applications

From Great Discoveries in Number Theory to Applications

Princeton University Press, New Jersey (1957), (1966) (1970) 316. ... Prentice-Hall Inc, Englewood Cliffs, New Jersey (1989) 317. ... Springer, New York (1979) 321. Ribenboim, P.: The Book of Prime Number Records. Springer, New ...

Author: Michal Křížek

Publisher: Springer Nature

ISBN: 9783030838997

Category: Mathematics

Page: 337

View: 714

This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
Categories: Mathematics