Since I design and build super-efficient white-LED lighting systems, this is right up my alley. (Example: I have a variable-brightness 36-LED flashlight that runs for 9-12 months on a set of 'AA' batteries.)
There currently is no LED that produces purple color off one single LED chip. However, as Johnee mentioned, two LEDs' light can mix rather nicely to produce purple. (BTW, a white LED is really a blue LED with a phosphor coating that emits other wavelengths, and these other wavelengths are what makes the output more white. The blue LED chip at the core fo the device is what gives that white light a bluish tinge.)
One LED manufacturer, Nichia Chemical Corp. (who may be the original inventor of the white LED) recently announced the creation of a purple laser diode. Such a gadget could quadruple the storage density of optical storage media, making a 20GB super-DVD possible. But, they want $2,000 PER DIODE for samples!
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