Answers revealed in the comments.
GAME 1
Name three of the four most recent presidents whose presidential order number is a prime number.
GAME 2
In addition to Cheers and Becker, both of which ran for over 100 episodes, Ted Danson has appeared in at least 20 episodes of five different TV series. Name two of those five series.
hebspeaks 
Game one answers:
George W. Bush (43)
George H.W. Bush (41)
Richard Nixon (37)
Herbert Hoover (31)
GAME 2 answers:
CSI
The Good Place
Bored to Death
Damages
Ink