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$RandomState gives a representation of the internal state of the pseudorandom generator used by Random.
The value of $RandomState changes every time Random is called.
You can use s
$RandomState to explicitly save the value of $RandomState, and $RandomState
s to restore.
The value of $RandomState is always a long integer chosen from a certain large set of possibilities. You can assign $RandomState only to values in this set.
You can use Block[
] to localize the value of $RandomState during the evaluation of expr.
See the Mathematica book: Section 3.2.3.
See also: SeedRandom.