The Book of Prime Number Records

The Book of Prime Number Records by Paulo Ribenboim.

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 anot...

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Bibliographic Details
Main Author: Ribenboim, Paulo (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1989.
Edition:2nd ed. 1989.
Series:Springer eBook Collection.
Subjects:
Number theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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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