Tools

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

namespace Euler // Warning! Golfed code ahead.
{
    class Tools
    {
        // Checks whether a number is a prime number
        public static bool IsPrime(BigInteger i)
        {
            BigInteger x, y = 0;
            for (x = 2; x < i; x++)
            {
                if (i % x == 0)
                {
                    y++;
                }
            }
            return y==0;
        }
        // Returns the nearest integer below the number
        public static BigInteger Ceiling(BigInteger i)
        {
            return i = BigInteger.Parse(i.ToString("0.#"));
        }
        // Checks whether a number is the square root
        public static bool IsSqrt(BigInteger i, BigInteger r)
        {
            BigInteger x, y;
            x = r * r;
            y = (r + 1) * (r + 1);
            return (i >= x && i < y);
        }
        // Returns the perfect square root of a number (round down)
        public static BigInteger GetPerfectSqrt(BigInteger i)
        {
            if (i == 0) return i;
            BigInteger x, r;
            if (i > 0)
            {
                x = Ceiling((BigInteger)BigInteger.Log(i, 2));
                r = BigInteger.One << (Convert.ToInt32(x) / 2);
                while (!IsSqrt(i, r))
                {
                    r += i / r;
                    r /= 2;
                }
                return r;
            }
            throw new ArithmeticException("Input was not a posetive integer");
        }
        // Return the number of factors of a number
        public static BigInteger GetFactorCount(BigInteger i)
        {
            BigInteger x, y, a = 0;
            y = GetPerfectSqrt(i);
            for (x = 1; x < y; x++)
            {
                if (y % i == 0)
                {
                    a += 2;
                }
            }
            if (y*y==i)
            {
                a++;
            }
            return a;
        }
        // Return all factors of a number
        public static BigInteger[] GetFactors(BigInteger i)
        {
            BigInteger x, y, z = 0;
            List<BigInteger> a = new List<BigInteger>();
            y = GetPerfectSqrt(i);
            for (x = 1; x < y; x++)
            {
                if (y % i == 0)
                {
                    z += 2;
                    a.Add(z);
                }
            }
            return a.ToArray();
        }
        // Return all prime factors of a number
        public static BigInteger[][] GetPrimeFactors(BigInteger i)
        {
            BigInteger x, y;
            List<BigInteger[]> a = new List<BigInteger[]>();
            for (x = 2; i > 1; x++)
            {
                if (i%x == 0)
                {
                    y = 0;
                    while (i%x==0)
                    {
                        i /= x;
                        y++;
                    }
                    BigInteger[] z = {x,y};
                    a.Add(z);
                }
            }
            return a.ToArray();
        }
    }
}