Solution to Project Euler Problem 58: Spiral primes - Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. 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%?


Updated: April 11, 2021 — Training Time: 3 minutes
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Topic: Project Euler Problem 58: Spiral primes.

Difficulty: Easy.

Objective: 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 3713
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%?

Input: None.

Expected Output: 26241.

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