Let G be a graph on n vertices. A bijective function f : V (G) → {1, 2,...,n} is said to be a prime labeling if for every e = xy, GCD{f (x),f (y)} = 1. A graph which permits a prime labeling is a "prime graph". On the other hand, a graph G is a prime distance graph if there is an injective function g : V(G) → Z (the set of all integers) so that for any two vertices s & t which are adjacent, the integer |g(s) - g(t)| is a prime number and g is called a prime distance labeling of G. A graph G is a prime distance graph (PDL) iff there exists a "prime distance labeling" (PDL) of G. In this paper, we obtain the prime labeling and prime distance labeling of certain classes of graphs. © 2019 Published under licence by IOP Publishing Ltd.