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We show that the Stanley's Conjecture holds for an intersection of fourmonomial prime ideals of a polynomial algebra $S$ over a field and for anarbitrary intersection of monomial prime ideals $(P_i)_{i\in [s]}$ of $S$ suchthat $P_i\not\subset \Sigma_{1=j\not =i}^s P_j$ for all $i\in [s]$.

Stanley conjecture on intersections of four monomial prime ideals