Question: Does there exist number, n, such that:

2…n has a lower percentage of prime numbers than does 2…2n?

The answer must be one of the following:

- There is a proof that there is no such number.
- There is a proof that there is such a number, but the number is not known.
- There is such a number and the number and it is_______________
- It is not known whether or not there is such a number.