Task: Mersenne primes
C#: using System;
using System.Numerics;

namespace MersennePrimes {
    class Program {
        static BigInteger Sqrt(BigInteger x) {
            if (x < 0) throw new ArgumentException("Negative argument.");
            if (x < 2) return x;
            BigInteger y = x / 2;
            while (y > x / y) {
                y = ((x / y) + y) / 2;
            }
            return y;
        }

        static bool IsPrime(BigInteger bi) {
            if (bi < 2) return false;
            if (bi % 2 == 0) return bi == 2;
            if (bi % 3 == 0) return bi == 3;
            if (bi % 5 == 0) return bi == 5;
            if (bi % 7 == 0) return bi == 7;
            if (bi % 11 == 0) return bi == 11;
            if (bi % 13 == 0) return bi == 13;
            if (bi % 17 == 0) return bi == 17;
            if (bi % 19 == 0) return bi == 19;

            BigInteger limit = Sqrt(bi);
            BigInteger test = 23;
            while (test < limit) {
                if (bi % test == 0) return false;
                test += 2;
                if (bi % test == 0) return false;
                test += 4;
            }

            return true;
        }

        static void Main(string[] args) {
            const int MAX = 9;

            int pow = 2;
            int count = 0;

            while (true) {
                if (IsPrime(pow)) {
                    BigInteger p = BigInteger.Pow(2, pow) - 1;
                    if (IsPrime(p)) {
                        Console.WriteLine("2 ^ {0} - 1", pow);
                        if (++count >= MAX) {
                            break;
                        }
                    }
                }
                pow++;
            }
        }
    }
}

VB: Imports System.Numerics

Module Module1

    Function Sqrt(x As BigInteger) As BigInteger
        If x < 0 Then
            Throw New ArgumentException("Negative argument.")
        End If
        If x < 2 Then
            Return x
        End If
        Dim y = x / 2
        While y > (x / y)
            y = ((x / y) + y) / 2
        End While
        Return y
    End Function

    Function IsPrime(bi As BigInteger) As Boolean
        If bi < 2 Then
            Return False
        End If
        If bi Mod 2 = 0 Then
            Return bi = 2
        End If
        If bi Mod 3 = 0 Then
            Return bi = 3
        End If
        If bi Mod 5 = 0 Then
            Return bi = 5
        End If
        If bi Mod 7 = 0 Then
            Return bi = 7
        End If
        If bi Mod 11 = 0 Then
            Return bi = 11
        End If
        If bi Mod 13 = 0 Then
            Return bi = 13
        End If
        If bi Mod 17 = 0 Then
            Return bi = 17
        End If
        If bi Mod 19 = 0 Then
            Return bi = 19
        End If

        Dim limit = Sqrt(bi)
        Dim test As BigInteger = 23
        While test < limit
            If bi Mod test = 0 Then
                Return False
            End If
            test += 2
            If bi Mod test = 0 Then
                Return False
            End If
            test += 4
        End While

        Return True
    End Function

    Sub Main()
        Const MAX = 9

        Dim pow = 2
        Dim count = 0

        While True
            If IsPrime(pow) Then
                Dim p = BigInteger.Pow(2, pow) - 1
                If IsPrime(p) Then
                    Console.WriteLine("2 ^ {0} - 1", pow)
                    count += 1
                    If count >= MAX Then
                        Exit While
                    End If
                End If
            End If
            pow += 1
        End While
    End Sub

End Module