# 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 10_{2}.
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, 10_{2} (2) can become 11_{2} (3) which
can become 111_{2} (7) which in turn can become 101_{2} (5).
The goal is to obtain some
Mersenne prime number of the form 2^{p} - 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.

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