This work presents the results of the exact computation of (180) 3 = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark's 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3 rd-order sensitivities are significantly larger than their corresponding 1 stand 2 nd-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3 rd-order relative sensitivity is the mixed sensitivity How to cite this paper: Fang, R.X. and Cacuci, D.G.