Euler Problem 58
================

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%?


```python
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)
```

    26241



```python
    
```

9aafcfd8ca50c9d4ebf336e98dc3a8ade8f98d45
ipynb
Jupyter Notebook
Euler 058 - Spiral primes.ipynb
Radcliffe/project-euler
5eb0c56e2bd523f3dc5329adb2fbbaf657e7fa38
MIT
2016-05-11T18:55:35.000Z
2019-12-27T21:38:43.000Z
Euler 058 - Spiral primes.ipynb
Radcliffe/project-euler
5eb0c56e2bd523f3dc5329adb2fbbaf657e7fa38
MIT
Euler 058 - Spiral primes.ipynb
Radcliffe/project-euler
5eb0c56e2bd523f3dc5329adb2fbbaf657e7fa38
MIT
Qwen/Qwen-72B
1. YES
2. YES