Large language models (LLMs) have demonstrated strong performance on a wide range of software engineering tasks, including code generation and analysis. However, most prior work relies on cloud-based models or specialized hardware, limiting practical applicability in privacy-sensitive or resource-constrained environments. In this paper, we present a systematic empirical evaluation of two locally deployed LLMs, LLaMA 3.2 and Mistral, for real-world Python bug detection using the BugsInPy benchmark. We evaluate 349 bugs across 17 projects using a zero-shot prompting approach at the function leveResearch goal: How does prompt engineering for chain-of-thought reasoning influence LLaMA 3.2's false positive rate in bug detection tasks on the BugsInPy benchmark?Autonomous synthesis report generated by SOVEREIGN Research Kernel. Tribunal consensus score: 7.8/10.