Goldbach Conjecture

GoldbachConjecture

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace GoldbachConjecture
{
    class GoldbachConjecture
    {
        static void Main()
        {
            while (true)
            {
                Console.Write("Enter a number: ");
                int number = int.Parse(Console.ReadLine());
                IEnumerable<int> result = CalculateGC(number);
                Print(number, result);
            }
        }

        // Calculate the Goldbach Conjecture of a number using the standart Eratostene's sieve algorithm
        private static IEnumerable<int> CalculateGC(int number)
        {
            // Validate input
            if (number < 4 || number % 2 != 0)
            {
                throw new ArgumentException("The number must be a positive even integer.", "number");
            }

            // using BitArray instead of bool[] for memory usage optimization
            BitArray sieve = new BitArray(number + 1, true);
            sieve[0] = sieve[1] = false;
            int step = 2;
            List<int> primesInFirstHalf = new List<int>();
            primesInFirstHalf.Add(2);

            while (step < number)
            {
                int currentNumber = 2 * step;
                while (currentNumber < number)
                {
                    sieve[currentNumber] = false;
                    currentNumber += step;
                }

                // Calculate the next step
                int oldStep = step;
                for (int i = step + 1; i <= number; i++)
                {
                    if (sieve[i])
                    {
                        if (i <= number / 2)
                        {
                            primesInFirstHalf.Add(i);
                        }
                        step = i;
                        break;
                    }
                }

                if (step == oldStep)
                {
                    break;
                }
            }
            
            // return only these primes which pair number is also prime
            return primesInFirstHalf.Where(n => sieve[number - n]); 
        }

        private static void Print(int number, IEnumerable<int> addends)
        {
            StringBuilder output = new StringBuilder();
            output.AppendFormat("{0}", number);
            foreach (int addend in addends)
            {
                output.AppendFormat(" = {0} + {1}", addend, number - addend);
            }
            Console.WriteLine(output);
        }
    }
}