On 5 May 2000 Daniel Lichtblau of Wolfram Research reported at    
http://forums.wolfram.com/mathgroup/archive/2000/May/msg00088. html
that the numbers produced using to produce rando approximate machine  numbers are not completely random.  Further more at
http://forums.wolfram.com/mathgroup/archive/2004/May/msg00002. html
Andrzej Kozlowski reported that this is still a problem in Mathematica 5.0.
Daniel Lichtblau suggests that instead of using  Random[]  to  generate random real machine numbers the following should be used.  I believe  this will give a random number between 1 and 2.

Random[Integer, 2^30 - 1]/2.^30 + Random[Integer, 2^30 - 1]/2.^30

However, based on Daniel's explanation of the problem, I expect that the
following also works around the bug in Random, and runs twice as fast as the
solution above.

N[Random[Real, {0, 1}, 17]]


In the above message Daniel Lichtblau also explained how one can make
necessary changes to some of the standard packages.

Created by Mathematica  (May 16, 2004)

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