This paper presents significant advancements in the efficient evaluation of the exact exchange (EXX) contribution for hybrid density functional theory (DFT) simulations, particularly for large-scale systems beyond 10,000 atoms. The authors, from various institutions, focus on optimizing the resolution-of-identity-based real-space implementation of EXX in the all-electron code FHI-aims, targeting high-performance CPU clusters. Key improvements include refined Message Passing Interface (MPI) parallelization layers and the use of MPI-3 standard shared memory arrays, which significantly enhance memory efficiency, performance, and scalability. The optimized implementation is benchmarked for a wide range of chemical systems, including hybrid organic-inorganic perovskites, organic crystals, and ice crystals with up to 30,576 atoms. The results demonstrate that the new method achieves almost perfect linear scaling with system size, making hybrid DFT calculations feasible for very large, complex systems on typical high-performance computing resources. This work not only improves the accuracy of hybrid DFT but also extends its applicability to a broader range of scientific and engineering applications.This paper presents significant advancements in the efficient evaluation of the exact exchange (EXX) contribution for hybrid density functional theory (DFT) simulations, particularly for large-scale systems beyond 10,000 atoms. The authors, from various institutions, focus on optimizing the resolution-of-identity-based real-space implementation of EXX in the all-electron code FHI-aims, targeting high-performance CPU clusters. Key improvements include refined Message Passing Interface (MPI) parallelization layers and the use of MPI-3 standard shared memory arrays, which significantly enhance memory efficiency, performance, and scalability. The optimized implementation is benchmarked for a wide range of chemical systems, including hybrid organic-inorganic perovskites, organic crystals, and ice crystals with up to 30,576 atoms. The results demonstrate that the new method achieves almost perfect linear scaling with system size, making hybrid DFT calculations feasible for very large, complex systems on typical high-performance computing resources. This work not only improves the accuracy of hybrid DFT but also extends its applicability to a broader range of scientific and engineering applications.