In mathematics, a double Mersenne number is a Mersenne number of the form:
MMp = 22p-1 - 1where Mp is a Mersenne number.
A double Mersenne number that is prime is called a double Mersenne prime.
Since a Mersenne prime Mp can be prime only for prime p, a double Mersenne prime can be prime only for prime Mp, i.e., Mp a Mersenne prime.
The first values of p for which Mp is prime are p = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127.
Of these, MMp is known to be prime for p = 2, 3, 5, 7; for p = 13, 17, 19, and 31, explicit factors have been found showing that the corresponding double Mersenne numbers are not prime.
Thus, the smallest candidate for the next double Mersenne prime is MM61, or 22305843009213693951 - 1. Being approximately 1.695x10694127911065419641, this number is far too large for any currently known primality test.
It is not known whether the double Mersenne numbers MM61, MM89, MM107, MM127 are prime or composite, and, just as with other Mersenne numbers, it is interesting to resolve this question one way or another.
There is no hope of testing those numbers for primality; however, if MMp is composite (and it very probably is), it might have a factor which is small enough to be discoverable.
This project is a coordinated search for such a factor.
If you have a PC equipped with a nVidia graphic card having computing capabilities ≥ 2.0, and are interested in helping to find a factor of a double Mersenne number:
First go to the download section, choose George Woltman's program 'mmff' and perform a simple test to see that the software works on your computer.
Then e-mail me for a range to test.
A big thank you to Marco Licio Fabi, who donated a beautiful new logo to the project!