Does saving a file in ProPhoto colorspace increase filesize? I'd think that given that it contains more informations it would use up more diskspace, (if so, how much more?) on the other hand, the number of pixels is the same, and if the color of a pixel is "Yellow" or "slightly brigher Yellow" should use up the same amount of space.
An RGB image stores, for each pixel, an R value, a G value and a B value, which combine to define the colour of that pixel. Using 16 bits per channel (for example) allows for 281 trillion distinct colour possibilities for each pixel. This takes up the same amount of storage space regardless of the colour space of the image, whether it's sRGB, Adobe RGB, ProPhoto RGB or any other colour space.
The difference that the colour space makes is that wide-gamut colour spaces (such as ProPhoto RGB) encompass more real-world colours than narrower-gamut colour spaces; that is to say, 16-bit ProPhoto RGB images and 16-bit Adobe RGB images both have 281 trillion distinct colour values, but in the case of ProPhoto RGB, those colour values are "spread" wider to cover more real-world colours. (No colour space includes all real-world colours, but a wide-gamut colour space includes more of those colours.)
Let's say for example a pixel's (8-bit/channel) RGB value is (255, 253, 1). The difference in using one colour space over another is not in storage space, but in the fact that (255, 253, 1) will refer to a slightly different yellow in one colour space compared to the other. Or, to think of it the other way around, a wider-gamut colour space can encode a wider range of the yellows (or purples or whatever colour it might be) that are out there in the real world.