  We show that orbit equivalence relations arising from essentially free
ergodic probability measure preserving actions of Zariski dense discrete
subgroups of simple algebraic groups are strongly prime. As a consequence, we
prove the existence and the uniqueness of a prime factorization for orbit
equivalence relations arising from direct products of higher rank lattices.
This extends and strengthens Zimmer's primeness result for equivalence
relations arising from actions of lattices in simple Lie groups. The proof of
our main result relies on a combination of ergodic theory of algebraic group
actions and Popa's intertwining theory for equivalence relations.
