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For the special case of a Pr\\\"ufer domain (where $\\star$ is equal to the identity semistar operation), we show that a nonzero prime $P$ of $D$ is sharp, that is, that $D_P \\nsupseteq \\bigcap D_M$, where the intersection is taken over the maximal ideals $M$ of $D$ that do not contain $P$, if and only if two closely related spectral semistar operations on $D$ differ. 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