58.py

from gmpy2 import is_prime
from math import sqrt
"""
65 64 63 62 61 60 59 58 57
66 37 36 35 34 33 32 31 56
67 38 17 16 15 14 13 30 55
68 39 18  5  4  3 12 29 54
69 40 19  6  1  2 11 28 53
70 41 20  7  8  9 10 27 52
71 42 21 22 23 24 25 26 51
72 43 44 45 46 47 48 49 50
73 74 75 76 77 78 79 80 81

key observation: bottom right diagonals are odd squares 

We'll use the notation 
d1 d2
d3 d4
to denote diagonals 1,2,3, and 4.

d4 = some odd 'n' squared
d3 = d4 - (sqrt(d4) - 1)
d2 = d4 - 2 * (sqrt(d4) - 1)
d1 = d4 - 3 * (sqrt(d4) - 1)

At this point the code writes itself.
"""

def get_percent_prime(l):
    return sum(map(is_prime, l)) / len(l)

def get_diags(d4):
    l = [d4]
    l += [int(d4 - n * (sqrt(d4) - 1)) for n in range(1,4)]
    return l

def main():
    arr = [1] + get_diags(9)
    idx = 5
    p = get_percent_prime(arr)
    # while p > 1/10:
    for i in range(10):
        print(p)
        arr += get_diags(idx**2)
        idx += 2
    print(idx)

if __name__ == "__main__":
    main()