"""

Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
37 36 35 34 33 32 31
38 17 16 15 14 13 30
39 18  5  4  3 12 29
40 19  6  1  2 11 28
41 20  7  8  9 10 27
42 21 22 23 24 25 2643 44 45 46 47 48 49
It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.
If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?

"""

import itertools as it


from sympy import isprime


# bottom-right diags are never prime, since they are always square numbers

nprimes = 0
for i in it.count(1, 2):
    diags = range(i**2 + i + 1, (i + 2)**2, i + 1)
    nprimes += sum(isprime(n) for n in diags)
    nrows = i + 2
    ndiags = 2 * nrows - 1
    percent = 100 * nprimes / ndiags

    if percent < 10.0:
        print(nrows)
        break
