<?xml version="1.0" encoding="utf-8" ?>
<configuration>
  <configSections>
    <sectionGroup name="wix.bootstrapper" type="Microsoft.Tools.WindowsInstallerXml.Bootstrapper.BootstrapperSectionGroup, BootstrapperCore">
      <section name="host" type="Microsoft.Tools.WindowsInstallerXml.Bootstrapper.HostSection, BootstrapperCore" />
    </sectionGroup>
  </configSections>
  <startup useLegacyV2RuntimeActivationPolicy="true">
    <supportedRuntime version="v4.0" />
  </startup>
  <wix.bootstrapper>
    <host assemblyName="Bootstrapper.UI">
      <supportedFramework version="v4\Full" />
      <supportedFramework version="v4\Client" />
    </host>
  </wix.bootstrapper>
</configuration>

<?xml version="1.0" encoding="UTF-8"?>
<Wix xmlns="http://schemas.microsoft.com/wix/2006/wi">
    <Bundle Name="Bootstrapper" Version="!(bind.packageVersion.Msi_Installer)" Manufacturer="Justin" UpgradeCode="1b9106f0-5ba8-4857-ac0a-c1becba1fe51">
    <BootstrapperApplicationRef Id="ManagedBootstrapperApplicationHost">
        <Payload SourceFile="$(var.Bootstrapper.UI.TargetPath)" />
        <Payload SourceFile="$(var.Bootstrapper.UI.ProjectDir)BootstrapperCore.config"/>
        <Payload SourceFile="$(var.Bootstrapper.UI.TargetDir)BootstrapperCore.dll"/>
        <Payload SourceFile="$(var.Bootstrapper.UI.TargetDir)Microsoft.Deployment.WindowsInstaller.dll"/>
    </BootstrapperApplicationRef>

        <Chain>
        <PackageGroupRef Id="NetFx462Web"/>
        
        <MsiPackage Id="Msi_Installer" SourceFile="$(var.Installer.TargetPath)" EnableFeatureSelection="yes" Compressed="yes" />
        </Chain>
    </Bundle>
</Wix>

    protected override void Run()
    {
        WaitForDebugger();

        InitializePackages();

        _BootstrapDispatcher = Dispatcher.CurrentDispatcher;

        // should UI be displayed
        if (Command.Display == Display.Full || Command.Display == Display.Unknown)
        {
            Engine.Log(LogLevel.Verbose, "Launching custom UX");

            _InstallerWindowViewModel = new InstallerWindowViewModel(this);

            InstallerWindow installerWindow = new InstallerWindow
            {
                DataContext = _InstallerWindowViewModel
            };
            installerWindow.Closed += (s, e) => _BootstrapDispatcher.InvokeShutdown();
            installerWindow.Show();

            Dispatcher.Run();

            Engine.Quit(_ErrorCode);
        }
        else
        {
            DetectComplete += (sender, args) => Plan(Command.Action);
            PlanComplete += (sender, args) => Execute();
            ExecuteComplete += (sender, args) =>
            {
                Engine.Quit(args.Status);
                _BootstrapDispatcher.InvokeShutdown();
            };

            Detect();

            Dispatcher.Run();
        }
    }

    
    private void WaitForDebugger()
    {
        if (Command.GetCommandLineArgs().Contains("DEBUG"))
        {
            Engine.Log(LogLevel.Verbose, "Waiting for debugger to be attached...");

            while (!Debugger.IsAttached)
            {
                Thread.Sleep(500);
            }

            Debugger.Break();
        }
    }

    private readonly XNamespace ManifestName = "http://schemas.microsoft.com/wix/2010/BootstrapperApplicationData";
…
    private void InitializePackages()
    {
        const string DataFilePathName = "BootstrapperApplicationData.xml";
        const string ApplicationDataNamespace = "BootstrapperApplicationData";
        const string MbaPrereqNamespace = "WixMbaPrereqInformation";
        const string PackageNamespace = "WixPackageProperties";
        const string FeatureNamespace = "WixPackageFeatureInfo";

        var workingDir = Path.GetDirectoryName(GetType().Assembly.Location);
        var dataFilePath = Path.Combine(workingDir, DataFilePathName);
        XElement applicationData = null;

        try
        {
            using (var reader = new StreamReader(dataFilePath))
            {
                var xml = reader.ReadToEnd();
                var xDoc = XDocument.Parse(xml);
                applicationData = xDoc.Element(ManifestName + ApplicationDataNamespace);
            }
        }
        catch (Exception ex)
        {
            Engine.Log(LogLevel.Error, $"Unable to parse {DataFilePathName}.\nReason: {ex.Message}");
        }

        var mbaPrereqs = applicationData.Descendants(ManifestName + MbaPrereqNamespace)
                                        .Select(x => new MbaPrereqPackage(x));
        // exclude prereq packages
        Packages = applicationData.Descendants(ManifestName + PackageNamespace)
                                      .Select(x => new BundlePackage(x))
                                      .Where(pkg => !mbaPrereqs.Any(preReq => preReq.PackageId == pkg.Id))
                                      .ToArray();

        // get features and associate with their package
        var featureNodes = applicationData.Descendants(ManifestName + FeatureNamespace);
        foreach (var featureNode in featureNodes)
        {
            var feature = new PackageFeature(featureNode);
            var parentPkg = Packages.First(pkg => pkg.Id == feature.PackageId);
            parentPkg.Features.Add(feature);
            feature.Package = parentPkg;
        }
    }

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

1634 = 1⁴ + 6⁴ + 3⁴ + 4⁴
8208 = 8⁴ + 2⁴ + 0⁴ + 8⁴
9474 = 9⁴ + 4⁴ + 7⁴ + 4⁴

As 1 = 1⁴ is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

using System;
using System.Diagnostics;

namespace Project_Euler_30
{
    internal class Program
    {
        // 5x9^5 has 6 digits, so the upper bound should be 6x9^6
        private const int UpperBound = 59049 * 6;

        private static readonly int[] powersCache = new int[] { 0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049 };

        private static void Main(string[] args)
        {
            Stopwatch sw = Stopwatch.StartNew();
            int result = 0;

            // start the loop at 243 since that is the lower bound (3^5) of a possible sum
            for(int i = powersCache[3]; i <= UpperBound; i++)
            {
                int sum = 0;
                int workingNumber = i;

                while(workingNumber > 0)
                {
                    int digit = workingNumber % 10;
                    workingNumber /= 10;

                    sum += powersCache[digit];

                    if(sum > i)
                    {
                        // passed the number, stop checking
                        break;
                    }
                }

                if(sum == i)
                {
                    result += i;
                }
            }
            sw.Stop();

            Console.WriteLine($"Sum of results: {result}");
            Console.WriteLine($"Took {sw.ElapsedMilliseconds}ms");
        }
    }
}

Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

2²=4, 2³=8, 2⁴=16, 2⁵=32
3²=9, 3³=27, 3⁴=81, 3⁵=243
4²=16, 4³=64, 4⁴=256, 4⁵=1024
5²=25, 5³=125, 5⁴=625, 5⁵=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

using System;
using System.Collections.Generic;
using System.Diagnostics;

namespace Project_Euler_29
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            Stopwatch sw = Stopwatch.StartNew();
            HashSet<double> results = new HashSet<double>();

            for (int a = 2; a <= 100; a++)
            {
                for (int b = 2; b <= 100; b++)
                {
                    results.Add(Math.Pow(a, b));
                }
            }

            sw.Stop();

            Console.WriteLine($"Number of distinct powers: {results.Count}");
            Console.WriteLine($"Took {sw.ElapsedMilliseconds}ms");
        }
    }
}

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

using System;
using System.Diagnostics;
using System.Linq;

namespace ProjectEuler_28
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            const int squareSize = 1001;

            Stopwatch sw = Stopwatch.StartNew();

            int half = (int)Math.Ceiling(squareSize / 2D) - 1;
            int[] topRight = new int[half];
            int[] topLeft = new int[half];
            int[] bottomLeft = new int[half];
            int[] bottomRight = new int[half];

            int idx = 0;
            for (int i = squareSize; i > 1;)
            {
                topRight[idx] = i * i;
                topLeft[idx] = topRight[idx] - i + 1;
                bottomLeft[idx] = topLeft[idx] - i + 1;
                bottomRight[idx] = bottomLeft[idx] - i + 1;

                i = (int)Math.Floor(Math.Sqrt(bottomRight[idx]));

                idx++;
            }

            sw.Stop();

            Console.WriteLine($"Sum of diagonols: {topRight.Sum() + topLeft.Sum() + bottomLeft.Sum() + bottomRight.Sum() + 1} in {sw.ElapsedTicks} ticks");
        }
    }
}

Euler discovered the remarkable quadratic formula:

n² + n + 41

It turns out that the formula will produce 40 primes for the consecutive integer values 0 ≤ n ≤ 39. However, when n = 40, 40² + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible by 41.

The incredible formula n² - 79n + 1601 was discovered, which produces 80 primes for the consecutive values 0 ≤ n ≤ 79. The product of the coefficients, −79 and 1601, is −126479.

Considering quadratics of the form:

n² + an + b, where |a| < 1000 and |b| ≤ 1000

where |n| is the modulus/absolute value of n
e.g. |11| = 11 and |-4| = 4

Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.

using Common.Math;
using System;
using System.Diagnostics;
using System.Linq;

namespace ProjectEuler_27
{
    internal class Program
    {
        private static int[] primeCache = Eratosthenes.GetPrimes(1000).ToArray();

        private static bool IsPrime(int num)
        {
            if (num > primeCache.Last())
            {
                primeCache = Eratosthenes.GetPrimes(primeCache.Last() * 2);
            }

            // array.contains checks every value, these are in order from smallest to largest
            // so creating our own contains is more efficient.
            int i = 0;
            while (i < primeCache.Length && primeCache[i] < num)
            {
                i++;
            }

            return primeCache[i] == num;
        }

        private static void Main(string[] args)
        {
            Stopwatch sw = Stopwatch.StartNew();
            ResultHelper result = new ResultHelper();

            // 'b' must be prime because when n=0 we get 0^2 + a(0) + b which is just 'b'
            // since 0 is inclusive and all results must be prime, we can narrow down 'b' to just prime numbers
            int[] bPossibles = primeCache;

            // we can also narrow down 'a' possiblities because all primes except for 2 are odd
            // so if n=1 we get 1^2 + a(1) + b = 1 + a + b
            // since an odd added to an odd is always even, we know that for all cases except 2 'a' must be odd
            // in the case of 2 'a' must be even
            for (int a = -999; a < 1000; a += 2)
            {
                for (int bIdx = 0; bIdx < bPossibles.Length; bIdx++)
                {
                    // handle the case of b=2
                    int workingA = bPossibles[bIdx] == 2 ? a - 1 : a;

                    int n = 0;
                    while (IsPrime(Math.Abs(n * n + workingA * n + bPossibles[bIdx])))
                    {
                        n++;
                    }

                    if (result.Count < n)
                    {
                        result = new ResultHelper
                        {
                            A = a,
                            B = bPossibles[bIdx],
                            Count = n
                        };
                    }
                }
            }

            sw.Stop();

            Console.WriteLine($"{result.Count} primes found in {sw.ElapsedMilliseconds}ms when a={result.A} and b={result.B} with a product of {result.A * result.B}.");
        }

        private struct ResultHelper
        {
            public int A;
            public int B;
            public int Count;
        }
    }
}