What do the following numbers have in common?
3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727.
Each one is a prime number, evenly divisible only by itself and 1. Each one can also be written in the form a power of 2, less 1: 2p – 1, where p is itself a prime number.