Triple derivable maps on prime algebras with involution

Let A be a unital prime *-algebra with characteristic not 2 and with a projection e? 0,1. Suppose that d:A?Q(s)(A) is a map satisfying d(xy*z+zy*x/2)=d(x)y*z+xd(y)*z+xy*d(z)+d(z)y*x+zd(y)*x+zy*d(x)/2 for all x,y,z is an element of A, where Q(s)(A) denotes the symmetric Martindale algebra of quotients of A. It is shown that d is an additive triple derivation. Moreover, there exist a?Q(s)(A) with a*=-a and an additive *-derivation d:A -> Qs(A) such that d(x)=ax+d(x) for all x is an element of A. The analogous results for prime locally matrix *-algebras, prime *-algebras with nonzero socle, factor von Neumann algebras and standard operator *-algebras on Hilbert spaces are also described.