Prime Patterns

Primes look random up close, yet follow a beautiful law from far away. Explore how many primes there are below a number, why gaps between them can be as long as you like, and the great open problems, from Goldbach's conjecture to the Riemann hypothesis. Then hunt for patterns in Ulam's prime spiral, discover which primes are sums of two squares, and learn how computers certify 300-digit primes in a blink.