Algorithms for primes

This talk will consist of a series of light mini-talks inspired by Atkin's papers on recognizing primes (1982, 'On a primality test of Solovay and Strassen'; 1995, 'Intelligent primality test offer'), proving primes to be prime (1993, 'Elliptic curves and primality proving'), factoring integers into primes (1993, 'Finding suitable curves for the elliptic curve method of factorization'), and enumerating primes (2004, 'Prime sieves using binary quadratic forms').