In this study, we evaluated the capability of Large Language Models (LLMs), particularly OpenAI's GPT-4, in detecting software vulnerabilities, comparing their performance against traditional static code analyzers like Snyk and Fortify. Our analysis covered numerous repositories, including those from NASA and the Department of Defense. GPT-4 identified approximately four times the vulnerabilities than its counterparts. Furthermore, it provided viable fixes for each vulnerability, demonstrating a low rate of false positives. Our tests encompassed 129 code samples across eight programming languages, revealing the highest vulnerabilities in PHP and JavaScript. GPT-4's code corrections led to a 90% reduction in vulnerabilities, requiring only an 11% increase in code lines. A critical insight was LLMs' ability to self-audit, suggesting fixes for their identified vulnerabilities and underscoring their precision. Future research should explore system-level vulnerabilities and integrate multiple static code analyzers for a holistic perspective on LLMs' potential.