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I voted 6 because I never saw the point of separating "Indigo" and "Violet" (and ROYGBP maps nicely to three primary colors plus three secondary colors).
Then I searched around for some decent pictures of real rainbows. At first this confirmed my previous impressions; they all looked like they went from "Blue" to "Purple" then ended.
They also ran quite suddenly from "Red" to "Yellow" making "Orange" rather hard to pick out while "Green" through "Blue" were clearly not sufficiently represented in "ROYGBIV".
After reviewing several pictures of rainbows in the sky and from prisms, the best list of colors I could come up with was: Red, Orange, Yellow, Green, Teal, Cyan, Blue, Purple. The only picture that gave me an impression of separating "Purple" into "Indigo" plus "Violet" was http://people.rit.edu/andpph/photofile-c/prism-DSCN4982.jpg. Perhaps it is just that "Violet" tends to be quite faint.
Update: Then I went to look for cannonical examples of "Indigo" and "Violet" and found confirmation of my first point:
Although traditionally considered one of seven divisions of the optical spectrum, modern color scientists do not usually recognize indigo as a separate division and generally classify wavelengths shorter than about 450nm as violet.
This was immediately followed by something that was educational to me:
Indigo and violet are different from purple, which cannot be seen on the electromagnetic spectrum but can be achieved by mixing mostly blue and part red light.
Which rather reminded me of the term "monkey". Practicing biologists know that humans and (other) apes are not monkeys while non-biologists know that apes are a type of monkey (as are humans). I know that the color at the end of the rainbow is a shade of purple, despite what practicing spectrumists might believe. :)
Update: Actually, "Green" is still insufficiently represented. ... Yellow Lime Green Teal Cyan Blue ... seems more accurate. (Leprechauns++)
"Rainbows Only Yield Gold To Cannabis-Burning Potheads" - tye