On-device inference offers privacy, offline use, and instant response, but consumer hardware restricts large language models (LLMs) to low throughput and capability. To overcome this challenge, we present prima.cpp, a distributed on-device inference system that runs 30-70B LLMs on consumer home clusters with mixed CPUs/GPUs, insufficient RAM/VRAM, slow disks, Wi-Fi links, and heterogeneous OSs. We introduce pipelined-ring parallelism (PRP) to overlap disk I/O with compute and communication, and address the prefetch-release conflict in mmap-based offloading. We further propose Halda, a heterogeneity-aware scheduler that co-optimizes per-device CPU/GPU workloads and device selection under RAM/VRAM constraints. On four consumer home devices, a 70B model reaches 674 ms/token TPOT with <6% memory pressure, and a 32B model with speculative decoding achieves 26 tokens/s. Compared with llama.cpp, exo, and dllama, our proposed prima.cpp achieves 5-17x lower TPOT, supports fine-grained model sizes from 8B to 70B, ensures broader cross-OS and quantization compatibility, and remains OOM-free, while also being Wi-Fi tolerant, privacy-preserving, and hardware-independent. The code is available at https://gitee.com/zonghang-li/prima.cpp.