Local Differential Privacy (LDP) enables privacy-preserving range queries, yet existing LDP methods face inherent structural limitations that lead to significant noise accumulation, especially in high-dimensional scenarios. To address this, we propose Prefix-sum Adaptive Hierarchical Partitioning (PriTree), a novel framework that synergistically integrates prefix-sum techniques with adaptive tree structures. PriTree employs dynamic threshold-based hierarchical partitioning of prefix-sum boundaries, where partitioning granularity is automatically optimized by evaluating frequency differences between adjacent prefix sums, which can enhance query accuracy. Theoretically, we establish a computational model for dynamic threshold determination that systematically controls partitioning density, effectively mitigating noise accumulation from excessive segmentation. Our solution demonstrates remarkable scalability, with extensibility to \(\lambda \) -D scenarios through integration of multiple 1-D and 2-D PriTree structures. Comprehensive experiments validate PriTree’s superiority in both low and high-dimensional settings.