Time complexity of Prim's algorithm is :-
$O(|e+n|(Log_{2}n))$ with the use of binary min heap.
Since $G$ is a complete graph , $e = \frac{n(n-1)}{2}$ , where n is the number of vertices
Thus complexity will be =$O(| \frac{n(n-1)}{2}+n|(Log_{2}n)) = O(n^{2}Log_{2}n)$