Abstract: The current document is directed to methods and systems that generate sequences of random numbers. Unlike many currently available random-number generators that continuously measures a physical apparatus or other signal source, the currently disclosed methods and systems employ nondeterministic phenomena that are computationally initiated and computationally accessed within a computer system. The nondeterministic phenomena are often a produced by multiple simultaneously executing, asynchronous threads or other computational entities, with the unpredictability arising from multiple different types and sources of nondeterministic behavior within the computer system. Unlike pseudorandom-number generators, statistics and metrics computed from sequences of random numbers produced by the currently disclosed random-number generators have values close to those expected for a random-selection process.