Finding Mersenne numbers using Lucas-Lehmer iteration

Question

I am currently writing a C++ program to find Mersenne prime numbers, utilizing the ttmath api on MS Win8.1. I have written the Lucas-Lehmer algorithm, but whatever value I try I always get a no-Mersenne-number message. Can somebody point out the error in my Lucas-Lehmer algorithm?

void LLIteration::calculate()
{
    ttmath::UInt<100> num = 2;
    ttmath::UInt<100> s = 4;
    (num.Pow(this->exp));
    num = num-1;

    for(int i = 3; i < exp; ++i){
        s = (s*s-2) % num;
        std::cout << s << std::endl;
    }

    if(s == 0){
        std::cout << "Found Mersenne prime, 2^" << exp << " = " << num << std::endl;
    } else {
        std::cout << "no prime 2^" << exp << " = " << num << std::endl;
    }
}

Like I said, I always get the no prime message, and I cannot figure out why. Exp is an int representing the power to raise 2 to, and the rest is pretty straightforward.

Thanks in advance!

Answer 1

Look up the article on Wikipedia.

If you follow the article exactly, the loop should be

for (int i = 1; i <= exp - 2; ++i)

That's exp - 2 iterations of the loop. Yours only iterates exp - 3 times.