We present a randomized differential testing approach to test OpenMP implementations. In contrast to previous work that manually creates dozens of verification and validation tests, our approach is able to randomly generate thousands of tests, exposing OpenMP implementations to a wide range of program behaviors. We represent the space of possible random OpenMP tests using a grammar and implement our method as an extension of the Varity program generator. By generating 1,800 OpenMP tests, we find various performance anomalies and correctness issues when we apply it to three OpenMP implementations: GCC, Clang, and Intel. We also present several case studies that analyze the anomalies and give more details about the classes of tests that our approach creates.