Old buildings all the sudden generate more culture?

I remember seeing in one of my games that a culture-producing building was listed in the city screen as generating more culture than it should have, I think it was 3 instead of 2 or something like that. And I remember reading about how if a building reaches a certain age, it generates more culture. Is anyone familiar with this mechanic that can explain the length requirements for this additional culture on your building?

 

I believe all culture buildings produce double culture once they are 1000 years old.

It appears you actually asked this same question 5 years ago!
https://forums.civfanatics.com/threads/why-my-library-says-4-culture.538514/

 

All except the academy.

 

Yeah there are a handful of exceptions.

 

Palace. Anything else?

 

SH monument instead of handmade monument. (if conquer city that has SH but some old cities would have monument already, they would still get 2x culture or not? )