Task: Factors of a Mersenne number





Java: import java.math.BigInteger;

class MersenneFactorCheck
{

  private final static BigInteger TWO = BigInteger.valueOf(2);
  
  public static boolean isPrime(long n)
  {
    if (n == 2)
      return true;
    if ((n < 2) || ((n & 1) == 0))
      return false;
    long maxFactor = (long)Math.sqrt((double)n);
    for (long possibleFactor = 3; possibleFactor <= maxFactor; possibleFactor += 2)
      if ((n % possibleFactor) == 0)
        return false;
    return true;
  }
  
  public static BigInteger findFactorMersenneNumber(int primeP)
  {
    if (primeP <= 0)
      throw new IllegalArgumentException();
    BigInteger bigP = BigInteger.valueOf(primeP);
    BigInteger m = BigInteger.ONE.shiftLeft(primeP).subtract(BigInteger.ONE);
    
    BigInteger maxFactor = BigInteger.ONE.shiftLeft((primeP + 1) >>> 1);
    BigInteger twoP = BigInteger.valueOf(primeP << 1);
    BigInteger possibleFactor = BigInteger.ONE;
    int possibleFactorBits12 = 0;
    int twoPBits12 = primeP & 3;
    
    while ((possibleFactor = possibleFactor.add(twoP)).compareTo(maxFactor) <= 0)
    {
      possibleFactorBits12 = (possibleFactorBits12 + twoPBits12) & 3;
      
      if ((possibleFactorBits12 == 0) || (possibleFactorBits12 == 3))
        if (TWO.modPow(bigP, possibleFactor).equals(BigInteger.ONE))
          return possibleFactor;
    }
    return null;
  }
  
  public static void checkMersenneNumber(int p)
  {
    if (!isPrime(p))
    {
      System.out.println("M" + p + " is not prime");
      return;
    }
    BigInteger factor = findFactorMersenneNumber(p);
    if (factor == null)
      System.out.println("M" + p + " is prime");
    else
      System.out.println("M" + p + " is not prime, has factor " + factor);
    return;
  }

  public static void main(String[] args)
  {
    for (int p = 1; p <= 50; p++)
      checkMersenneNumber(p);
    checkMersenneNumber(929);
    return;
  }
  
}







Ada: with Ada.Text_IO;

with Is_Prime;

procedure Mersenne is
   function Is_Set (Number : Natural; Bit : Positive) return Boolean is
   begin
      return Number / 2 ** (Bit - 1) mod 2 = 1;
   end Is_Set;

   function Get_Max_Bit (Number : Natural) return Natural is
      Test : Natural := 0;
   begin
      while 2 ** Test <= Number loop
         Test := Test + 1;
      end loop;
      return Test;
   end Get_Max_Bit;

   function Modular_Power (Base, Exponent, Modulus : Positive) return Natural is
      Maximum_Bit : constant Natural := Get_Max_Bit (Exponent);
      Square      : Natural := 1;
   begin
      for Bit in reverse 1 .. Maximum_Bit loop
         Square := Square ** 2;
         if Is_Set (Exponent, Bit) then
            Square := Square * Base;
         end if;
         Square := Square mod Modulus;
      end loop;
      return Square;
   end Modular_Power;

   Not_A_Prime_Exponent : exception;

   function Get_Factor (Exponent : Positive) return Natural is
      Factor : Positive;
   begin
      if not Is_Prime (Exponent) then
         raise Not_A_Prime_Exponent;
      end if;
      for K in 1 .. 16384 / Exponent loop
         Factor := 2 * K * Exponent + 1;
         if Factor mod 8 = 1 or else Factor mod 8 = 7 then
            if Is_Prime (Factor) and then Modular_Power (2, Exponent, Factor) = 1 then
               return Factor;
            end if;
         end if;
      end loop;
      return 0;
   end Get_Factor;

   To_Test : constant Positive := 929;
   Factor  : Natural;
begin
   Ada.Text_IO.Put ("2 **" & Integer'Image (To_Test) & " - 1 ");
   begin
      Factor := Get_Factor (To_Test);
      if Factor = 0 then
         Ada.Text_IO.Put_Line ("is prime.");
      else
         Ada.Text_IO.Put_Line ("has factor" & Integer'Image (Factor));
      end if;
   exception
      when Not_A_Prime_Exponent =>
         Ada.Text_IO.Put_Line ("is not a Mersenne number");
   end;
end Mersenne;