There is no limit that I know if. They just keep getting harder to produce. example ( you receive your great person after accumulating 50 great person points, then 100, 200 etc. then actual numbers might be wrong but you get the point).
And the number of points you need is set for your entire empire its not city specific. For example: You need 50 great people points to get a Great Person. City A has accumulated 48 @ 1 per turn and City B has 49 @ 1 per turn. On your next turn City B will produce a Great Person and the Level is bumped up to say 100. So City A will now be at 49 of 100 and City B will be at 0/100.
not to mention that some Wonders give you free great people.
And some techs too, like Music, give you a free GP. When this happens, the "cost" is bumped to the next level. So that if you have a city at 290/300 (+5/turn), then discover music, that city would then be 295/400.
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