A lot of confusion in this thread, hopefully I don’t add to it.
To generate a Great Person (GP), you need to generate enough Great Person Points (GPP) in one city to fill that city’s GPP ‘bucket’. At normal speed, the GPP bucket initially holds 100 GPP. Each time you fill it and generate a GP, the bucket empties and the capacity goes up in all cities – from 100 GPP to 200, then 300 for the third one and so on (the progression increases after you generate your 10th GP)
From the Civ4 wiki:
Great Person Threshold
1 2 3 4 5 6 7 8 9 10 11 12 13
Quick 67 134 200 267 334 400 467 534 600 667 800 934 1067
Normal 100 200 300 400 500 600 700 800 900 1000 1200 1400 1600
Epic 150 300 450 600 750 900 1050 1200 1350 1500 1800 2100 2400
Mara. 300 600 900 1200 1500 1800 2100 2400 2700 3000 3600 4200 4800
GPP are generated in 3 ways – from specialists (each specialist generates 3GPP per turn, of whatever type the specialist is – Scientist, Merchant, Artist, Engineer, Priest, Spy), from Wonders (World Wonders generate 2 GPP per turn and National Wonders generate 1 GPP per turn, of a particular type – again, Scientist, Merchant, Artist, Engineer, Priest, Spy), and from Shrines (1 Prophet GPP/turn). The amount of base GPP generated per turn can be modified by things like city buildings (Forum), Wonders (Parthenon, National Epic), Civics (Pacifism) and Golden Ages.
The type of GP you get when the bucket is full is determined by the percentage of GPP of each type in the bucket. So for example, Stonehenge generates two Priest GPP per turn. Assuming you don’t run any specialists and don’t have any other Wonders in the Stonehenge city, in 50 turns, the city with Stonehenge in it will produce a Great Person, and that Great Person will have a 100% chance of being a Great Prophet. Now, assume instead that the Stonehenge city builds a Library 25 turns after Stonehenge is completed, and runs 2 Scientist specialists thereafter. Each Scientist generates 3GPP. So now the city will generate 8GPP/turn, 6 Scientist and 2 Prophet. And the GPP bucket progresses like this:
Turn 25 – 50 Priest GPP
Turn 26 – 52 Priest, 6 Scientist (58 GPP total)
Turn 27 – 54 Priest, 12 Scientist (66 total)
Turn 28 – 56 Priest, 18 Scientist (74 total)
Turn 29 – 58 Priest, 24 Scientist (82 total)
Turn 30 – 60 Priest, 30 Scientist (90 total)
Turn 31 – 62 Priest, 36 Scientist (98 total)
On turn 32, the city will generate a Great Person. There’s about a 63% chance it will be a Great Prophet, and about a 37% chance that it will be a Great Scientist*. What determines the GP’s type is the amount of points in the pool, not how many points of each type that the city generated that turn. The bucket empties, and the excess GPP (6 GPP) go into the empty bucket. Now that bucket needs 200 GPP for the next GP, less the 6 it got on turn 32.
Things to remember:
1. The GPP bucket is filled city-by-city, but when the bucket size increases, it increases for all cities. So if City 1 generates a Great Prophet, the next GP will require 200 GPP, whether it’s generated in City 1 or any other city.
2. Great Generals are generated by combat (or Fascism) and don’t impact your GPP pool.
3. “Free” Great People (like the free Great Artist at Music, or the Great Scientist at Physics) don’t affect your GPP bucket. A free GP doesn’t affect how many GPP you need for your next one.
4. “Free” specialists (like the 2 free Scientists you get from the Great Library, or the free specialist you get from Mercantilism or Statue of Liberty) generate GPP (3 each). Settled Great People do not generate GPP.
5. Citizen specialists don’t generate GPP. If you are entitled to a free specialist in every city, a city with no open specialist slots (which are unlocked by building things like Libraries, Temples, or Forges, or by the Caste System civic) will only be able to run a Citizen specialist.
It gets complicated if you have 2 or more cities generating GPP. Consider this example: I finish building Great Lighthouse in City 1, and a Library in City 2 on the same turn (for purposes of this example, I don’t have any wonders or specialists in other cities). City 1 will generate a Great Merchant in 50 turns (2 GPP/turn x 50 turns). City 2 will generate a Great Scientist in 17 turns (6 GPP/turn x 17 turns). 17 turns later, I have my Great Scientist. But now, the ‘bucket’ needs 200 GPP to fill it. And City 1 has just 34 GPP. It’ll now take 83 more turns for City 1 to get that Great Merchant, not 33. Meanwhile, City 2 is still putting out 6 Scientist GPP per turn. It has 2 overflow from when it filled the last bucket, so it needs 198 more GPP. So in 33 more turns, I’ll get another Great Scientist. Now City 1 has 100 GPP (34+(2x33)), but it now needs 300 GPP to fill its bucket and generate a Great Merchant. City 2’s bucket is empty, but it is still generating 6GPP per turn, so in 50 turns (6x50), it’ll generate yet another Great Scientist. You can probably see where this is going – City 2 will generate a lot of Great Scientists before City 1, chugging along at 2 Merchant GPP/turn, ever generates a Great Merchant. This is why a lot of players tend to focus their GPP production on 1 city, or possibly 2. You get the most out of your GPP if they are concentrated in in city – two GPP-focused cities won’t produce twice as many GP as one city will. So you’ll often put Great Library, National Epic, etc, in a city with a big food surplus, and run as many specialists as you can, there. If you have a state religion, you’ll want to spread it to your GP city so you can benefit from Pacifism’s +100% modifier to GPP. Etc.
TL;DR - you don’t get this kind of depth in Civ5
*I don’t know how the points on turn 32 are distributed. The city needs 2 GPP to fill the bucket. Does it add 1.5 Scientist points and 0.5 Priests points? Or does it add 2 GPP of one type? Does the overflow work the same way? Is there any rounding involved? If anyone knows, please chime in.