Imagine a world where critical software is not only written by AI but also guaranteed to be correct. This isn't science fiction, but the promise of VeCoGen, a groundbreaking tool that combines the code-generation power of Large Language Models (LLMs) with the rigor of formal verification. Why is this a big deal? Because LLMs, while incredibly adept at producing code, are prone to errors, making them risky for safety-critical applications in areas like aerospace, automotive, and healthcare. VeCoGen tackles this challenge head-on. It takes formal specifications (like mathematical descriptions of what the code should do), natural language descriptions, and test cases, then uses an LLM to generate initial C code candidates. But here's the twist: VeCoGen doesn't stop there. It enters an iterative refinement loop, using feedback from a compiler and a formal verifier (tools that mathematically prove code correctness) to guide the LLM in improving its code. This process continues until a program emerges that not only compiles but also satisfies the strict formal specification, essentially guaranteeing its correctness. In tests on a set of programming challenges, VeCoGen successfully generated verified C code for a remarkable 13 out of 15 problems. This is a significant leap towards automating the creation of dependable, high-assurance software. While the research currently focuses on simpler programs without loops, the potential is vast. Future work aims to extend VeCoGen's capabilities to handle more complex code structures and integrate with real-world software development workflows. This opens doors to a future where AI not only accelerates software development but also dramatically enhances its reliability, paving the way for safer and more dependable systems in critical domains.