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%?
In [1]:
from sympy import isprime
corners = [3, 5, 7, 9]
squares = 5
primes = 3
delta = 8
sidelength = 3
while primes*10 >= squares:
sidelength += 2
for i in range(4):
delta += 2
corners[i] += delta
primes += isprime(corners[i])
squares += 4
print(sidelength)
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