The prime numbers do obey some simple patterns—for instance, all primes but 2 are odd numbers. The great achievement of the Green-Tao theorem is its use of subtle and novel methods of harmonic analysis (very much indebted to the work of 2002 Fields Medalist Timothy Gowers) to show that these simple patterns are essentially the only structure the primes possess. Beyond these basic structures, the primes look random—they are, in a sense, all noise and no music.