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The life of primes in 37 episodes /

Bibliographic Details
Main Authors: De Koninck, J.-M. (Jean-Marie), 1948- (Author), Doyon, Nicolas, 1977- (Author)
Corporate Author: ProQuest (Firm)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2021]
Subjects:
Numbers, Prime.
Number theory.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • An infinite family
  • The search for large primes
  • The great insight of Legendre and Gauss
  • Euler, the visionary
  • Dirichlet's theorem
  • The Bertrand postulate and the Chebyshev theorem
  • Riemann shows the way
  • Connecting the zeta function to the prime counting function
  • The intriguing Riemann Hypothesis
  • Mertens' theorems
  • Counting the number of primes, from Meissel to today
  • Hadamard and de la Vall'ee Poussin stun the world
  • An elementary proof of the prime number theorem
  • Sieve methods
  • Prime clusters
  • Primes in arithmetic progression
  • Small and large gaps between consecutive primes
  • Irregularities in the distribution of primes
  • Exceptional sets of primes
  • The birth of probabilistic number theory
  • The multiplicative structure of integers
  • Generalized prime number systems
  • Establishing if a given integer is prime or not
  • The Lucas and P'epin primality tests
  • Those annoying Carmichael numbers
  • The Lucas-Lehmer primality test for Mersenne numbers
  • The probabilistic Miller-Rabin primality test
  • The deterministic AKS primality test
  • The Fermat factorisation algorithm
  • From the Germat factorisation algorithm to the quadratic sieve
  • The Pollard p
  • 1 factorisation algorithm
  • The Pollard Rho factorisation algorithm
  • Two factorisation methods based on modern algebra
  • Algebraic factorisation
  • Measuring and comparing the speed of various algorithms
  • Cryptography, from Julius Caesar to the RSA cryptosystem
  • The present and future life of primes.