The life of primes in 37 episodes - Koninck, Jean-Marie de 1948-; Doyon, Nicolas 1977- (American Mathematical Society, 2021)
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.
Includes bibliographical references and indexes
2106
Keywords: Numbers, Prime; Number theory; Number theory -- Elementary number theory {For analogues in number fields, see 11R04} -- Multiplicative structure; Euclidean algorithm; greatest common divisors; Number theory -- Elementary number theory {For analogues in number fields, see 11R04} -- Primes; Number theory -- Elementary number theory {For analogues in number fields, see 11R04} -- Factorization; primality; Number theory -- Multiplicative number theory -- Distribution of primes; Number theory -- Zeta and L-functions: analytic theory -- Nonreal zeros of zeta (s) and L(s, χ); Riemann and other hypotheses