#!/usr/bin/env python3

from lib import primegen
from fractions import Fraction

def is_prime(n):
    return n in primes

def Pprob(n):
    if is_prime(n):
        return Fraction(2, 3)
    return Fraction(1, 3)

def croak(n):
    return {'P' : Pprob(n),
            'N' : 1-Pprob(n)}

def jump(sqrs, let):
    r = [0] * len(sqrs)
    for i in range(1, len(sqrs)-1):
        prob = croak(i+1)[let] * \
               Fraction(1, 2) * sqrs[i]
        r[i+1] += prob
        r[i-1] += prob
    r[1] += sqrs[0] * croak(1)[let]
    r[-2] += sqrs[-1] * croak(len(sqrs))[let]
    return r

def start(n):
    return [Fraction(1, n)] * n


seq = "PPPPNNPPPNPPNPN"
N = 500

primes = set(primegen(N))
sqrs = start(N)

for letter in seq:
    sqrs = jump(sqrs, letter)

print(sum(sqrs))