Are today's Prussians descendents of the old Prussians?
Prussia was the name of the kingdom established in 1701 by the Hohenzollern dynasty, the Electors of Brandenburg. As they weren't allowed to establish new kingdom within the Holy Roman Empire they named the new kingdom after a territory outside the Empire, Prussia, and were crowned in its capital, Koenigsberg (now called Kaliningrad).
'Old Prussia' corresponded roughly to what was East Prussia from 1815-1945. Before the area was colonized by Germans, the population spoke a Baltic language - Prussian. The Kingdom of Prussia established in 1701 covered a large area and only a minority of its inhabitants were descended from former speakers of Prussian.
In 1945 East Prussia was divided between the Soviet Union and Poland and German population was expelled.
Because of the long-standing assocoation of the Kingdom of Prussia with military aggression, in 1947 the Allies declared Prussia dissolved. Since then Prussia had ceased to exist, though some people are still sentimentally attached to it.