The set of the factorials plus one. n!+1 for all n in Z is prime for n={1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, ...} (these are the only ones known; the last is 21,507 digits long)

The first few numbers of this series, starting with n=1, are 2, 3, 7, 25, 121, 721, 5041, 40321, 362881, 3628801, 39916801 ...