How can an OpenGL visualization run for weeks? For an art project, I need to make an OpenGL visualization run for at least 4 weeks. Is this possible? I can pretty much choose the rest of the hardware and software.
Opengl doesn't care how long it has been running. 

However there are a few other challenges with long running applications in general:


memory leaks, both normal ones and opengl resources. 
lack of precision after incrementing a float to a big number. After 4 weeks your millisecond counter will be at 2.4 billion which is well beyond the point where integers cannot be expressed exactly in a single precision floating point number. Make sure that those numbers are wrapped down to a smaller value explicitly.