Crazy Librarian's Arithmetic Sequence of Primes
Pyth, 49 bytes

Like the Python3 and other Pyth answer, the runtime for finding 100 numbers is prohibitive. (test suite gives 10)

?}z"1379".f&amp;!tPZ!|FmtPvjzc`Z]dhl`Z*TT3"Empty Set"


Try it online