Prifddinas comes from prif ("chief", borrowed from Latin prīmus, "first") and dinas ("city", augmentative of din ["fortress"], and related to English down ["hill; field; tract of sandy land near the sea"]).
That is true, but it doesn't make "capital" incorrect. As a previous person said, most native English speakers would say that Cardiff is the capital of Wales - the "city" unnecessary
Is the "s" silent here? It sounds like prifddina, which doesn't look right, knowing the make-up of the word.
I'm pretty sure Welsh doesn't do silent letters.