Theorem C asserts that the set of integers with a given coefficient stopping time k is a set of arithmetic progressions , which has the immediate consequence that has the asymptotic density

which is given by

Furthermore Theorem C asserts that the set

differs from by a finite set, so that also has an asymptotic density which is the same as that of . Consequently, Theorem C implies the first part of Theorem A, that the set of all integers with stopping time at most k have an asymptotic density given by



Now the formula (2.16) can be used to prove the second part of Theorem A, and in fact to prove the stronger result that approaches 1 at an exponential rate as .