Bizarre Behavior in the Prime Numbers

Stan Wagon

The distribution of the prime numbers is generally well behaved: an accurate rule of thumb is that, near x, the chance of a number being prime is 1/log_e x. But there are several situations where such probabilistic interpretations or other numerical evidence can be very misleading. I will discuss such anomalies, and other surprising facts about the primes, such as the Hardy-Littlewood Conjecture that no interval [x, x+y] has more primes in it than the corresponding interval of the same length starting at 2.