data/problems/58.yml
---
:id: 58
:name: Spiral primes
:url: https://projecteuler.net/problem=58
:content: "Starting with 1 and spiralling anticlockwise in the following way, a square
spiral with side length 7 is formed.\n\n**37** 36 35 34 33 32 **31** \n38 **17**
16 15 14 **13** 30 \n39 18 **5** 4 **3** 12 29 \n40 19 6
1 2 11 28 \n41 20 **7** 8 9 10 27 \n42 21 22 23
24 25 26 \n**43** 44 45 46 47 48 49\n\nIt 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%.\n\nIf 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%?\n\n"