For example, is a Cunningham number because it is equal to .
For any fixed base , the exponents for which or is prime are in general very scarce.
This is due to the fact that is always divisible by , and thus it can be prime only if . Moreover is always divisible by , thus a necessary condition for to be prime is that is prime as well.
On the other side, is always divisible by 2 if is odd, and by , if is odd. If is even because it is of the form with odd, then is divisible by , hence the only candidates left for primality are of the form with even.
In general, the factorization of Cunningham numbers with small bases (and large exponents) has been and is a popular topic in (computational) number theory.