CSharpCode

Code:

public class GoldbachsConjecture
{
    public IEnumerable<int[]> TwoPrimeCalculation(int number)
    {
        if (number < 3 || number%2 != 0) return null;
        IList<int[]> results = new List<int[]>();

        for (int i = 1; i <= number/2; i++)
        {
            if (!IsPrimeNumber(i) || !IsPrimeNumber(number - i)) continue;
                
            int[] result = new int[2];
            result[0] = i;
            result[1] = number - i;
            results.Add(result);
        }

        return results;
    }

    public IEnumerable<int[]> ThreePrimeCalculation(int number)
    {
        if (number < 6 || number % 2 == 0) return null;
        IList<int[]> results = new List<int[]>();

        for (int i = 1; i <= number / 2; i++)
        {
            if (!IsPrimeNumber(i)) continue;
            int remain = number - i;
            int startValue = i;

            while (true)
            {
                bool breakWhile = true;

                for (int j = startValue; j <= remain / 2; j++)
                {
                    if (!IsPrimeNumber(j) || !IsPrimeNumber(remain - j)) continue;
                        
                    int[] result = new int[3];
                    result[0] = i;
                    result[1] = j;
                    result[2] = remain - j;
                    results.Add(result);

                    breakWhile = false;
                    startValue = j + 1;
                    break;
                }
                if (breakWhile) break;
            }
        }

        return results;
    }

    private bool IsPrimeNumber(int number)
    {
        if (number == 1) return false;
        for (int i = 2; i <= Math.Sqrt(number); i++)
        {
            if (number % i == 0) return false;
        }
        return true;
    }
}

Test:

[TestFixture]
public class GoldbachsConjectureTests
{
    [TestCase(4, "2,2" )]
    [TestCase(6, "3,3")]
    [TestCase(8, "3,5")]
    [TestCase(12, "5,7")]
    public void TwoPrimeCalculationSimple(int value, string expected)
    {
        // arrange
        GoldbachsConjecture gc = new GoldbachsConjecture();

        // act
        string actual = PrintResult(gc.TwoPrimeCalculation(value));
            
        // assert
        Assert.AreEqual(expected, actual);
    }

    [TestCase(10, "3,7 | 5,5")]
    [TestCase(14, "3,11 | 7,7")]
    [TestCase(16, "3,13 | 5,11")]
    [TestCase(22, "3,19 | 5,17 | 11,11")]
    [TestCase(34, "3,31 | 5,29 | 11,23 | 17,17")]
    [TestCase(48, "5,43 | 7,41 | 11,37 | 17,31 | 19,29")]
    public void TwoPrimeCalculationMultiple(int value, string expected)
    {
        // arrange
        GoldbachsConjecture gc = new GoldbachsConjecture();

        // act
        string actual = PrintResult(gc.TwoPrimeCalculation(value));

        // assert
        Assert.AreEqual(expected, actual);
    }

    [TestCase(-1, "")]
    [TestCase(0, "")]
    [TestCase(1, "")]
    [TestCase(2, "")]
    [TestCase(3, "")]
    [TestCase(5, "")]
    [TestCase(9, "")]
    public void ErrorHandling(int value, string expected)
    {
        // arrange
        GoldbachsConjecture gc = new GoldbachsConjecture();

        // act
        string actual = PrintResult(gc.TwoPrimeCalculation(value));

        // assert
        Assert.AreEqual(expected, actual);
    }

    [TestCase(7, "2,2,3")]
    public void ThreePrimeCalculationSimple(int value, string expected)
    {
        // arrange
        GoldbachsConjecture gc = new GoldbachsConjecture();

        // act
        string actual = PrintResult(gc.ThreePrimeCalculation(value));

        // assert
        Assert.AreEqual(expected, actual);
    }

    [TestCase(9, "2,2,5 | 3,3,3")]
    [TestCase(11, "2,2,7 | 3,3,5")]
    [TestCase(13, "3,3,7 | 3,5,5")]
    [TestCase(15, "2,2,11 | 3,5,7 | 5,5,5")]
    [TestCase(17, "2,2,13 | 3,3,11 | 3,7,7 | 5,5,7")]
    public void ThreePrimeCalculationMultiple(int value, string expected)
    {
        // arrange
        GoldbachsConjecture gc = new GoldbachsConjecture();

        // act
        string actual = PrintResult(gc.ThreePrimeCalculation(value));

        // assert
        Assert.AreEqual(expected, actual);
    }

    public string PrintResult(IEnumerable<int[]> results)
    {
        string print = string.Empty;
        if (results == null || !results.Any()) return print;

        foreach (int[] result in results)
        {
            foreach (int num in result)
            {
                print += num + ",";
            }

            print = print.Substring(0, print.Length - 1) + " | ";
        }

        print = print.Substring(0, print.Length - 3);
        return print;
    }
}