When rendering large images, it's important to understand how your scene will perform.

Since many things in RenderMan are resolution dependent, like dicing and mipmapping, you will find your scene will take more memory to render at larger resolutions. You may also find the memory needed to store the image framebuffer will be large as well. But there are ways to ameliorate some of this memory grab and still comfortably render your image.

To begin, your image format should be OpenEXR as it allows for better management through the EXR driver in RenderMan.