"""

http://projecteuler.net/index.php?section=problems&id=58

"""

from lib import spiraldiagonals

from lib import euler

"""

this is pretty easy - we can generate the diagonals indefinitely from the

formula we came up with in q28 and simply check the prime ratio

it's a bit slow, probably the prime check, but still less than a minute

"""

primes = []

ds = [1]

for i, diagonals in enumerate(spiraldiagonals.diagonals()):

for d in diagonals:

ds += [d]

if euler.is_prime(d): primes += [d]

ratio = float(len(primes)) / len(ds)

if ratio <= 0.1:

print (i+1)*2 + 1 # this is the spiral width

break