Euler-Problems/problem58.py at master · respectus/Euler-Problems · GitHub

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"""
Spiral Primes
Project Euler Problem #58
by Muaz Siddiqui

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 euler_helpers import timeit, is_prime

@timeit
def answer():
    prime = 0
    diagonals = [1]
    ratio = 0.62
    side = 3
    while True:
        square = side**2
        next1 = square - (side-1)
        next2 = square - (side-1)*2
        next3 = square - (side-1)*3
        if is_prime(next1):
            prime += 1
        if is_prime(next2):
            prime += 1
        if is_prime(next3):
            prime += 1
        diagonals.extend([square, next1, next2, next3])
        ratio = prime / len(diagonals)
        if ratio < 0.1:
            break
        side += 2
    return side