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Bring a large pot of lightly salted water to a boil. Add linguine pasta, and cook for 8 to 10 minutes, or until al dente; drain.
In a large skillet, melt the butter over medium heat. Stir in cream, and season with pepper. Cook 6 to 8 minutes, stirring constantly.
Stir Parmesan cheese into cream sauce, stirring until thoroughly mixed. Blend in the pesto, and cook for 3 to 5 minutes, until thickened.
Stir in the shrimp, and cook until they turn pink, about 5 minutes. Serve over the hot linguine.