Primitive cohomology, example request

Question

$X$ is a compact Kähler manifold or smooth projective variety. is there an example that a primitive class $0\neq [\omega]$ of $H^{p+q}(X, \mathbb{C})$ is wedge product of other two primitive classes: $[\omega_1]\in H^p(X, \mathbb{C})$ and $[\omega_2]\in H^q(X, \mathbb{C})$, where $p,q$ are not zero?