This particular pairing is popular to the more historical fans because of the many years of war and alliances between Norway and Prussia. However, in the anime, they are never shown together, creating a gap between history and anime.
The most popular headcanon for this pairing is the Prussian/German invasion of WWII. But, not much is known about their relationship during the time and before that.
Something people notice is that Prussia is very similar to Denmark personality-wise. They both love beer, they are both loud and both are full of themselves which is another thing that most likely brings the pairing together.