problem_058.py

# coding: utf-8


'''
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 26
43 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%?
'''

from helpers import is_prime


def main():
    _len = 1
    nb_primes = 0
    ratio = 1
    nb_diag_number = 1
    while ratio > 0.1 or _len < 9:
        _len += 2
        _len2 = _len ** 2
        if is_prime(_len2):
            nb_primes += 1
        if is_prime(_len2 - (_len - 1)):
            nb_primes += 1
        if is_prime(_len2 - 2 * (_len - 1)):
            nb_primes += 1
        if is_prime(_len2 - 3 * (_len - 1)):
            nb_primes += 1
        nb_diag_number += 4
        ratio = nb_primes / nb_diag_number
    return _len


if __name__ == '__main__':
    print(main())
    # 26241 in 25ms