Prime numbers : the most mysterious figures in math

Prime numbers The most mysterious figures in math

D. G. Wells

Book - 2005

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Subjects
Numbers, Prime.
Published
Hoboken, N.J. : John Wiley & Sons [2005]
Language
English
Main Author
D. G. Wells (-)
Physical Description
xv, 272 pages
Bibliography
Includes bibliographical references (pages [253]-264) and index.
ISBN
9780471462347
  • Acknowledgments
  • Author's Note
  • Introduction
  • Entries A to Z
  • Abc conjecture
  • Abundant number
  • AKS algorithm for primality testing
  • Aliquot sequences (sociable chains)
  • Almost-primes
  • Amicable numbers
  • Amicable curiosities
  • Andrica's conjecture
  • Arithmetic progressions, of primes
  • Aurifeuillian factorization
  • Average prime
  • Bang's theorem
  • Bateman's conjecture
  • Beal's conjecture, and prize
  • Benford's law
  • Bernoulli numbers
  • Bernoulli number curiosities
  • Bertrand's postulate
  • Bonse's inequality
  • Brier numbers
  • Brocard's conjecture
  • Brun's constant
  • Buss's function
  • Carmichael numbers
  • Catalan's conjecture
  • Catalan's Mersenne conjecture
  • Champernowne's constant
  • Champion numbers
  • Chinese remainder theorem
  • Cicadas and prime periods
  • Circle, prime
  • Circular prime
  • Clay prizes, the
  • Compositorial
  • Concatenation of primes
  • Conjectures
  • Consecutive integer sequence
  • Consecutive numbers
  • Consecutive primes, sums of
  • Conway's prime-producing machine
  • Cousin primes
  • Cullen primes
  • Cunningham project
  • Cunningham chains
  • Decimals, recurring (periodic)
  • The period of 1/13
  • Cyclic numbers
  • Artin's conjecture
  • The repunit connection
  • Magic squares
  • Deficient number
  • Deletable and truncatable primes
  • Demlo numbers
  • Descriptive primes
  • Dickson's conjecture
  • Digit properties
  • Diophantus (c. AD 200; d. 284)
  • Dirichlet's theorem and primes in arithmetic series
  • Primes in polynomials
  • Distributed computing
  • Divisibility tests
  • Divisors (factors)
  • How many divisors? how big is d(n)?
  • Record number of divisors
  • Curiosities of d(n)
  • Divisors and congruences
  • The sum of divisors function
  • The size of ?(n)
  • A recursive formula
  • Divisors and partitions
  • Curiosities of ?(n)
  • Prime factors
  • Divisor curiosities
  • Economical numbers
  • Electronic Frontier Foundation
  • Elliptic curve primality proving
  • Emirp
  • Eratosthenes of Cyrene, the sieve of
  • Erdos, Paul (1913-1996)
  • His collaborators and Erdos numbers
  • Errors
  • Euclid (c. l330-270
  • Unique factorization
  • &Radic;2 is irrational
  • Euclid and the infinity of primes
  • Consecutive composite numbers
  • Primes of the form 4n +3
  • A recursive sequence
  • Euclid and the first perfect number
  • Euclidean algorithm
  • Euler, Leonhard (1707-1783)
  • Euler's convenient numbers
  • The Basel problem
  • Euler's constant
  • Euler and the reciprocals of the primes
  • Euler's totient (phi) function
  • Carmichael's totient function conjecture
  • Curiosities of ?(n)
  • Euler's quadratic
  • The Lucky Numbers of Euler
  • Factorial
  • Factors of factorials
  • Factorial primes
  • Factorial sums
  • Factorials, double, triple . .
  • Factorization, methods of
  • Factors of particular forms
  • Fermat's algorithm
  • Legendre's method
  • Congruences and factorization
  • How difficult is it to factor large numbers?
  • Quantum computation
  • Feit-Thompson conjecture
  • Fermat, Pierre de (1607-
Review by Publisher's Weekly Review

The recent spate of popular books on the Riemann hypothesis, which concerns the distribution of prime numbers and is the greatest unsolved math problem since Andrew Wiles solved Fermat?s famous last theorem 10 years ago, augurs well for this directory from British author Wells (The Penguin Dictionary of Curious and Interesting Numbers). Arranged alphabetically, the text covers such topics as gaps between primes, Mersenne primes (primes of the form 2 to the nth power minus 1), palindromic primes, record primes (the largest ?not of a special and easily tested form? as of 2003 has 10,000 digits), repunits (primes that consist exclusively of the digit 1), ?sexy? primes (primes that differ by six) and twin primes. For James Bond fans, there?s even mention of ?007? primes. Mathematicians who contributed to prime number theory, including Leonhard Euler, G.H. Hardy and A.M. Legendre, receive separate entries. While some of the math is fairly sophisticated, lay readers will find plenty that?s readily comprehensible. A bibliography and list of Web sites point the way for those wishing to explore primes in greater depth. (Aug.) Copyright 2005 Reed Business Information.

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