The Book of Prime Number Records / by Paulo Ribenboim
| データ種別 | 電子ブック |
|---|---|
| 版 | Second Edition |
| 出版者 | New York, NY : Springer US |
| 出版年 | 1989 |
| 本文言語 | 英語 |
| 大きさ | XXIII, 479p : online resource |
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| 内容注記 | 1. How Many Prime Numbers Are There? I. Euclid’s Proof II. Kummer’s Proof III. Polya’s Proof IV. Euler’s Proof V. Thue’s Proof VI. Two-and-a-Half Forgotten Proofs VII. Washington’s Proof VIII. Fiirstenberg’s Proof 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. Classical Primality Tests Based on Lucas Sequences VI. Fermat Numbers VII. Mersenne Numbers VIII. Pseudoprimes Addendum on the Congruence an?k ? bn?k (mod n) IX. Carmichael Numbers X. Lucas Pseudoprimes XI. Last Section on Primality Testing and Factorization! 3. Are There Functions Defining Prime Numbers? I. Functions Satisfying Condition (a) II. Functions Satisfying Condition (b) III. Functions Satisfying Condition (c) 4. How Are the Prime Numbers Distributed? I. The Growth of ?(x) II. The nth Prime and Gaps III. Twin 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 and of Carmichael Numbers 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 Values of Linear Polynomials II. Prime Values of Polynomials of Arbitrary Degree III. Some Probabilistic Estimates IV. The Density of the Set of Regular Primes Conclusion Dear Reader Citations for Some Possible Prizes for Work on the Prime Number Theorem A. General References B. Specific References 1 2 3 4 5 6 Conclusion Primes up to 10,000 Index of Names Gallimaufries Addenda to the Second Edition |
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| 一般注記 | 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 |
| 著者標目 | *Ribenboim, Paulo author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Number theory FREE:Mathematics FREE:Number Theory |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9781468405071 
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| ISBN | 9781468405071 |
| URL | http://dx.doi.org/10.1007/978-1-4684-0507-1 |
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