Note that difference: The number of GPPs will determine when a great person will be generated, and the number of sources will determine what type it will be.
Examples:
* You have the Parthenon (great artist source) and a priest specialist (great prophet source) in the city the whole time. Your chances will be 50% to get a great artist and 50% to get a great prophet. Note that it's irrelevant that the Parthenon produced only 2 GPPs while the priest produced 3 GPPs per turn; they both count as one source.
* A city has the Great Library (great scientist source), an engineer, and an artist specialist, plus the two free scientist specialists from the Great Library. So you have 5 sources (one wonder and four specialists). This will give you a 3/5 = 60% chance of getting a great scientist, a 1/5 = 20% chance of getting a great engineer, and a 1/5 = 20% chance of getting a great artist.
* You have the Pyramids (great engineer source) in a city. One turn before the city reaches the threshold to produce a great person, you hire a scientist. What happens? Well, the game remembers that for every turn but the last, the great engineer source had been the only source of GPPs, and that only on the last turn there had been a different source present. So it is a 100% chance of getting a great engineer during all turns but the last, and a 50%/50% chance for the last turn. Since it averages the odds over all the turns, you will have a 99% chance of getting a great engineer, and a 1% chance of getting a great scientist.
* Assuming normal game speed, no great person generated yet: You hire a priest specialist for 22 turns. Then you fire him, and hire two scientist specialists for 11 turns. Intuitively, one would assume that because you had 22*1=22 sources for a great prophet and 11*2=22 sources for a great scientist, this would give you a 50%/50% chance. But because the game averages over turns, the odds will be 22/33 = 67% for a great prophet and 11/33=33% for a great scientist instead, because you had 22 turns with only great prophet sources and 11 turns with only great scientist sources.
(Thanks to Roland Johansen for suggesting this!)
Once the threshold is reached and a great person is generated, the city "forgets" which types of sources there had been before and starts anew. So if you hire a scientist to produce a great scientist, and after generating that great scientist remove the scientist specialist and hire a priest instead, you will have a 100% chance of getting a great prophet as the next great person, since the city will have forgotten that there had been a great scientist source in the city during the previous cycle.
The next best GP factory is Ptah, which is currently generating 18GPP/turn. We could add a scientist here to bring it up to 24, but this would mean (nearly) stagnating the city. Excess food is limited so I propose cancelling the lumbermill (7turns remaining) to the NE and building a farm instead; also replacing the grassland cottage (not yet a hamlet) to the SW with a farm. This can then become our breeding ground for scientists.
