This paper presents the concept of Industry 6.0, introducing the world's first fully automated production system that autonomously handles the entire product design and manufacturing process based on user-provided natural language descriptions. By leveraging generative AI, the system automates critical aspects of production, including product blueprint design, component manufacturing, logistics, and assembly. A heterogeneous swarm of robots, each equipped with individual AI through integration with Large Language Models (LLMs), orchestrates the production process. The robotic system includes manipulator arms, delivery drones, and 3D printers capable of generating assembly blueprints. The system was evaluated using commercial and open-source LLMs, functioning through APIs and local deployment. A user study demonstrated that the system reduces the average production time to 119.10 minutes, significantly outperforming a team of expert human developers, who averaged 528.64 minutes (an improvement factor of 4.4). Furthermore, in the product blueprinting stage, the system surpassed human CAD operators by an unprecedented factor of 47, completing the task in 0.5 minutes compared to 23.5 minutes. This breakthrough represents a major leap towards fully autonomous manufacturing.