  A refinement of Shor's Algorithm for determining order is introduced, which
determines a divisor of the order after any one run of a quantum computer with
almost absolute certainty. The information garnered from each run is
accumulated to determine the order, and for any k greater than 1, there is a
guaranteed minimum positive probability that the order will be determined after
at most k runs. The probability of determination of the order after at most k
runs exponentially approaches a value negligibly less than one, so that the
accumulated information determines the order with almost absolute certainty.
The probability of determining the order after at most two runs is more than
60%, and the probability of determining the order after at most four runs is
more than 90%.
