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Problem058.cs
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Problem058.cs
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namespace ProjectEuler.Solutions
{
using System;
using System.Collections.Generic;
using NUnit.Framework;
using ProjectEuler.Helper;
/// <summary>
/// Spiral primes.
/// Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
/// <para>37 36 35 34 33 32 31</para>
/// <para>38 17 16 15 14 13 30</para>
/// <para>39 18 5 4 3 12 29</para>
/// <para>40 19 6 1 2 11 28</para>
/// <para>41 20 7 8 9 10 27</para>
/// <para>42 21 22 23 24 25 26</para>
/// <para>43 44 45 46 47 48 49</para>
/// 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%.
/// <para>
/// 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%?
/// </para>
/// </summary>
public class Problem058 : Problem
{
public override long Solution()
{
int size = 1;
double amountPrimes = 0;
long currentNumber = 1;
double ratio;
do
{
size++;
for (int i = 0; i < 4; i++)
{
currentNumber += size;
if (Primes.IsPrimeNumber(currentNumber))
{
amountPrimes++;
}
}
size++;
double amountNumbers = size * 2 - 1;
ratio = amountPrimes / amountNumbers;
} while (ratio >= 0.10);
return size;
}
[Test]
public void TestForSolution()
{
Assert.AreEqual(26241, this.Solution());
}
}
}