Generating Prime Numbers

[Back] Many public key algorithms depend on prime number, which are difficult to factorize when multiplied together. This program creates the ones from:

Code used

       string primeList = "";

        static ulong RecursiveModulo(ulong uBase, ulong uPower, ulong uDivisor)
        {
            ulong uAux;

            if (uPower == 0) return 1;

            //a^2c mod n = (ac mod n)2 mod n
            else if (uPower % 2 == 0)
            {
                uAux = RecursiveModulo(uBase, uPower / 2, uDivisor);
                return (uAux * uAux) % uDivisor;
            }
            //ac+1 mod n = (ac mod n) · a mod n
            else return (RecursiveModulo(uBase, uPower - 1, uDivisor) * uBase) % uDivisor;
        }


        public static bool TestPrime(ulong uNumber, uint uIterations)
        {
            Random Rnd = new Random();
            ulong uAux;
            for (ulong i = 0; i < uIterations; ++i)
            {
                uAux = (ulong)(Rnd.Next()) % uNumber;
                if (uAux == 0) uAux = uNumber - 1;
                if (RecursiveModulo(uAux, uNumber - 1, uNumber) != 1)
                {
                    return false;
                }
            }
            return true;

        }


        bool findprimes = true;
        public void goPrimes(int val)
        {

            int j = -1;
            DateTime startTime = DateTime.Now;

            //      for (uint i = 2; i < Math.Pow(2, 32); i++)
            for (uint i = 2; i < val; i++)
            {
                if (i == 2) primes = String.Format("\r\nPrime numbers 1 to {0}:\r\n", val);
                if (findprimes == false) { return; }
                if (TestPrime(i, 2) == true && findprimes == true)
                {
                    j++;
                    if (j % 6 == 0) primes += "\r\n";
                    primes += Convert.ToString(i) + "\t";




                }
                
            }
            TimeSpan elapsed = DateTime.Now - startTime;

            string nicePrettyString = elapsed.ToString();
            primes += String.Format("\r\n\r\nTime taken is {0}\r\n", nicePrettyString);
        }