# python 3.x – Ratio of primes in square diagonals | Problem 58 Project Euler

I solved problem 58 in Project Euler and I am happy with my solution. However, are there any areas where I can improve my code here as I am learning how to write good python code.

Prompt:

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%?

``````#! /usr/bin/env python

from funcs import isPrime

# Corner values of a square of size s have values:
# s^2 - 3s + 3, s^2 - 2s + 2, s^2 - s + 1, s^2

def corner_values(n):
"""
returns a tuple of all 4 corners of an nxn square

>>> corner_values(3)
(3, 5, 7, 9)
"""
return (n ** 2 - 3 * n + 3, n ** 2 - 2 * n + 2, n ** 2 - n + 1, n ** 2)

def main():
ratio, side_length = 1, 1
primes, total = 0, 0
while ratio >= 0.1:
side_length += 2
for n in corner_values(side_length):
if isPrime(n):
primes += 1
total += 1
else:
total += 1
ratio = primes / total
return side_length - 2

if __name__ == "__main__":
print(main())
``````