Nighter nor.
Till 1648 it is: Haldem, Hochstift Minden, Heiliges Römisches Reich
1648 till 1806 it is Haldem, Fürstentum Minden, Heiliges Römisches Reich
The later one, the Principality of Minden, was co-ruled by the Elector of Brandenburg, who in 1701 also became King of Prussia. But the region in Question till 1806 de jure was always part of the HRE (Holy Roman Empire), NOT of Prussia.
Prussia was never part of the Holy Roman Empire.