There's a technical answer too.
Are three primaries really necessary for a full range of color?
Since 1810, it has been accepted that colors must be represented in a connected line, rather than by the linear spectrum alone. The spectral colors are connected through a mixed color, magenta, as previously discussed. This forces the 'color line' into a closed loop.
The color wheel shown above, is the CIE chromaticity diagram, a way of organizing the range of possible colors acording to calculated parameters. The gamut, or 2 dimensional range, of colors possible for any set of primary colors are inside a triangle inscribed within the CIE diagram. The chosen primary colors are the verticies of the triangle. Here is a page from the fantastic York University website that explains the CIE diagram in more detail.
In fact, it is possible to convert between any two chosen sets of primary colors using just a bit of matrix arithmetic. For example,
||||G||||| = |||||17.5||-1.07||-3.7||||| X |||||C||M||Y||||
Will convert cyan, magenta and yellow triplets to RGB values on my Powerbook's screen. Expanding this, any number of primaries can be converted to any other number of other primaries, by choosing the appropriate conversion matrix. The entire spectrum of a color can be encoded into three or more primary colors. More primary colors will result in a larger range of color, but two additive primaries are not enough to define more than a tiny portion of colors along a straight line.
Next: mutants with superpowers and colorblindness and I experiment on myself. (continued...)