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http://en.wikipedia.org/wiki/Visible_spectrum would give 6 colors,
http://en.wikipedia.org/wiki/Rainbow would give 7 colors ...
Place your bets!
In the rgb theory the prisma could also have 6768-1 colors, refered to http://upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Spectre.svg/744px-Spectre.svg.png
I've just been counting the colors in the visible spectre image below, 6768 colors including the black waveline... but I think I'm just pulling the line a bit too much now ;)
Personally I think infinity-1, with 7 distinct visible differences.
In reply to Wikipedia gives interesting results of the spectrum