How to create a random number generator that is completely random.

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I'm trying to write an autonomous music composition program that makes use of many random number generators in order to make seemingly random melodies but I have no clue how to formulate a rigorous formula or algorithm to create actual random numbers. Any help would be greatly appreciated.

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You can't. It is impossible. There are however good libraries out there for pseudo-random number generation.

Here's a list of generators: http://en.wikipedia.org/wiki/List_of_pseudorandom_number_generators

Is there a particular programming language you are using?

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There is no algorithm to generate truly random numbers. An algorithm follows rules (by definition), so its output can't be random.