The Prime Number Maze

The maze you are about to enter is one determined completely by the distribution of the prime numbers. The rules are simple. Start with the smallest prime number 2, whose binary representation is 102. You can change one binary digit at a time, to form a new prime number. You may also add the digit 1 to the beginning of the binary number to form larger primes. For example, 102 (2) can become 112 (3) which can become 1112 (7) which in turn can become 1012 (5). The goal is to obtain some Mersenne prime number of the form 2p - 1. The larger the number, the harder the maze. There are some interesting questions that arise while working this maze. Here are some questions and answers discovered so far:

Can you get to Room 11?
In theory, does this maze go on forever?
Is there a totally isolated room?
Can one get to Room 35759?
Unsolved problems.
More games by Dr. Paulsen.
This site was voted cool math site of the week on 7-17-00 by KaBoL--"Knot of Braid of Links" sponcered by the Canadian Math Society.