Is religious conversion broken?

[apollon]

- One of my starting provinces was 39% my religion.
- I stationed my two priests there and left them there for the rest of the game.
- I built shrines, temples, graveyards.
- I'm currently at turn 90.
- There are no heretics. The province only borders provinces that are under my control.
Result: The province is still 39% my religion.

Is there anything I can do to convert these infidels?

[apollon]

It's not broken after all, just very slow.