# Problem 329: Prime Frog
Susan has a prime frog. Her frog is jumping around over 500 squares
numbered 1 to 500. He can only jump one square to the left or to the
right, with equal probability, and he cannot jump outside the range
\[1;500\].(if it lands at either end, it automatically jumps to the only
available square on the next move.) When he is on a square with a prime
number on it, he croaks 'P' (PRIME) with probability 2/3 or 'N' (NOT
PRIME) with probability 1/3 just before jumping to the next square. When
he is on a square with a number on it that is not a prime he croaks 'P'
with probability 1/3 or 'N' with probability 2/3 just before jumping to
the next square. Given that the frog's starting position is random with
the same probability for every square, and given that she listens to his
first 15 croaks, what is the probability that she hears the sequence
PPPPNNPPPNPPNPN? Give your answer as a fraction p/q in reduced form.