The growing scarcity of spectrum resources, wideband spectrum sensing is required to process a prohibitive volume of data at a high sampling rate. For some applications, spectrum estimation only requires second-order statistics. In this case, a fast power spectrum sensing solution is proposed based on the generalized coprime sampling. By exploring the sensing vector inherent structure, the autocorrelation sequence of inputs can be reconstructed from sub-Nyquist samples by only utilizing the parallel Fourier transform and simple multiplication operations. Thus, it takes less time than the state-of-the-art methods while maintaining the same performance, and it achieves higher performance than the existing methods within the same execution time, without the need for pre-estimating the number of inputs. Furthermore, the influence of the model mismatch has only a minor impact on the estimation performance, which allows for more efficient use of the spectrum resource in a distributed swarm scenario. Simulation results demonstrate the low complexity in sampling and computation, making it a more practical solution for real-time and distributed wideband spectrum sensing applications.