Assuming you have a religion, before the industrial era you have the option to use your faith to generate great prophets (as a chance after your faith exceeds a threshold value). I've noticed this threshold varies from say 400 to as high as 800 or more. Does the pre-industrial great prophet faith threshold increase with other great people being generated (so if I generate several great artists does that make it more expensive to generate great prophets?) or is it based on some other factor such as era or the previous number of great prophets generated?
It is based exclusively on the game speed and on the number of great prophets generated. Other Great People do not affect the cost of great prophets. The price of a great prophet on normal speed begins at 200, then 300, and then increases in the Fibonacci sequence resulting in 500, 800, 1300...