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Well, you have a point - with the difficulty level settings with bitcoin, the first and many more bits have to be zero, so they can't be prime numbers. I haven't studied the mathematics of these tokens so well that I can describe exactly what the characteristics of these numbers is, but I do know that you can't just throw any number out with the requisite zeroes, the number itself contains proof that the work was done in some way.

The number is practically random, what is unique about it is that putting it along with the header of the last block through the hash algorithm results in another number with the prerequisite zeros.