  In this work we consider a stochastic version of the Primitive Equations
(PEs) of the ocean and the atmosphere and establish the existence and
uniqueness of pathwise, strong solutions. The analysis employs novel techniques
in contrast to previous works in order to handle a general class of nonlinear
noise structures and to allow for physically relevant boundary conditions. The
proof relies on Cauchy estimates, stopping time arguments and anisotropic
estimates.
