Find the smallest positive integer fitting the following description:

i. All its digits, except two, are sixes.

ii. It is prime.

Why is this puzzle D2?

Number 3 can be expressed as the sum of one or more positive integers in 4 distinct ways:

**
3; 2 + 1; 1 + 2; 1 + 1 + 1 **

Number 4 can be expressed as the sum of one or more positive integers in 8 distinct ways:

** 4; 3 + 1; 1+3; 2 + 2; 2 + 1 + 1; 1+2+1; 1+1+2; 1+1+1+1 **

Prove : any positive integer **n **can be so expressed in** 2**^{n - 1 }ways.