Author:
De Koninck, J.-M. (Jean-Marie), 1948- author.
ImprintProvidence, Rhode Island : American Mathematical Society, [2021]
Descriptionxiv, 329 pages : illustrations ; 26 cm
Note: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.
Bibliography Note:Includes bibliographical references (pages 313-322) and indexes.
Note:Takes the reader on a journey through time, providing an accessible overview of the numerous prime number theory problems that mathematicians have been working on since Euclid. Topics are presented in chronological order as episodes.
Note:Recommended in Resources for College Libraries.
