$RandomState

$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[$RandomState, expr] to localize the value of $RandomState during the evaluation of expr.

See The Mathematica Book: Section 3.2.3.

See also: SeedRandom.