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FilledSmallSquare$ProcessID gives the ID assigned to the Mathematica kernel process by the operating system under which it is run.

FilledSmallSquare On operating systems where no process ID is assigned, $ProcessID is None.

FilledSmallSquare See The Mathematica Book: Section 2.13.5.

FilledSmallSquare See also: $ParentProcessID, $UserName, Environment, $SessionID.