  We continue algebraization of the set of ultrafilters on a metric spaces
initiated in [6]. In particular, we define and study metric counterparts of
prime, strongly prime and right cancellable ultrafilters from the
Stone-$\check{C}$ech compactification of a discrete group as a right
topological semigroup [3]. Our approach is based on the concept of parallelity
introduced in the context of balleans in [4].
