  In this article, we study the stability of solutions to 3D stochastic
primitive equations driven by fractional noise. Since the fractional Brownian
motion is essentially different from Brownian motion, lots of stochastic
analysis tools are not available to study the exponential stability for the
stochastic systems. Therefore, apart from the standard method for the case of
Brownian motion, we develop a new method to show that 3D stochastic primitive
equations driven by fractional noise converge almost surely exponentially to
the stationary solutions. This method may be applied to other stochastic
hydrodynamic equations and other noises including Brownian motion and L\'evy
noise.
