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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. 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 &qu...

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Bibliographic Details
Main Author: Ribenboim, Paulo
Format: eBook
Language:English
Published: New York, NY Springer New York 1996, 1996
Edition:3rd ed. 1996
Subjects:
Number Theory
Discrete Mathematics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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

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