This study systematically analyzes the vulnerability of 36 large language models (LLMs) to various prompt injection attacks, a technique that leverages carefully crafted prompts to elicit malicious LLM behavior. Across 144 prompt injection tests, we observed a strong correlation between model parameters and vulnerability, with statistical analyses, such as logistic regression and random forest feature analysis, indicating that parameter size and architecture significantly influence susceptibility. Results revealed that 56 percent of tests led to successful prompt injections, emphasizing widespread vulnerability across various parameter sizes, with clustering analysis identifying distinct vulnerability profiles associated with specific model configurations. Additionally, our analysis uncovered correlations between certain prompt injection techniques, suggesting potential overlaps in vulnerabilities. These findings underscore the urgent need for robust, multi-layered defenses in LLMs deployed across critical infrastructure and sensitive industries. Successful prompt injection attacks could result in severe consequences, including data breaches, unauthorized access, or misinformation. Future research should explore multilingual and multi-step defenses alongside adaptive mitigation strategies to strengthen LLM security in diverse, real-world environments.