Data update

Task/Ultra-useful-primes/C-sharp/ultra-useful-primes.cs

@@ -0,0 +1,82 @@
+using System.Numerics;
+using System.Security.Cryptography;
+
+internal class Program
+{
+    private static void Main(string[] args)
+    {
+        for (int i = 1; i <= 10; i++)
+        {
+            Console.WriteLine(GetUltraUsefulPrime(i));
+        }
+
+    }
+    public static int GetUltraUsefulPrime(int n)
+    {
+        int k = 1;
+
+        BigInteger num = BigInteger.Pow(2, (int)Math.Pow(2, n));
+
+        while (!IsProbablePrime(num - k, 20))
+        {
+            k += 2;
+        }
+
+        return k;
+    }
+
+    // Miller-Rabin primality from this site
+    public static bool IsProbablePrime(BigInteger source, int certainty)
+    {
+        if (source == 2 || source == 3)
+            return true;
+        if (source < 2 || source % 2 == 0)
+            return false;
+
+        BigInteger d = source - 1;
+        int s = 0;
+
+        while (d % 2 == 0)
+        {
+            d /= 2;
+            s += 1;
+        }
+
+        // There is no built-in method for generating random BigInteger values.
+        // Instead, random BigIntegers are constructed from randomly generated
+        // byte arrays of the same length as the source.
+        RandomNumberGenerator rng = RandomNumberGenerator.Create();
+        byte[] bytes = new byte[source.ToByteArray().LongLength];
+        BigInteger a;
+
+        for (int i = 0; i < certainty; i++)
+        {
+            do
+            {
+                // This may raise an exception in Mono 2.10.8 and earlier.
+                // http://bugzilla.xamarin.com/show_bug.cgi?id=2761
+                rng.GetBytes(bytes);
+                a = new BigInteger(bytes);
+            }
+            while (a < 2 || a >= source - 2);
+
+            BigInteger x = BigInteger.ModPow(a, d, source);
+            if (x == 1 || x == source - 1)
+                continue;
+
+            for (int r = 1; r < s; r++)
+            {
+                x = BigInteger.ModPow(x, 2, source);
+                if (x == 1)
+                    return false;
+                if (x == source - 1)
+                    break;
+            }
+
+            if (x != source - 1)
+                return false;
+        }
+
+        return true;
+    }
+}