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Abstract In this paper, we prove that for certain class of initial data, the corresponding solutions to the 3-D viscous primitive equations blow up in finite time. Specifically, we find a special solution to simplify the 3-D systems, assuming that the pressure function p ( x , y , t ) $p(x,y,t)$ is a concave function. We also consider the equations on the line x = 0 $x=0$ , y = 0 $y=0$ .