Quote:
Originally Posted by rong123
I was actually meaning to ask what would be the first billionth Mersenne number?

You have apparently misunderstood several things and write contradictory things so it's hard to guess what you actually want to know.
There are two different definitions of a Mersenne number:
1) A number of form 2^n1 where n is a positive integer.
2) A number of form 2^n1 where n is a prime number.
Please clarify which of the two you want. It has been proven that 2^n1 cannot be prime if n is composite.
With definition 1), the billionth Mersenne number is 2^1,000,000,0001
With definition 2), the billionth Mersenne number is 2^22,801,763,4891 where 22,801,763,489 is the billionth prime.
Maybe you are actually looking for the smallest Mersenne numbers with at least 1,000,000,000 decimal digits? This has nothing to do with the billionth Mersenne number, no matter which definition is used.