A factor of a double Mersenne number MMp has form 2*k*Mp+1. We are testing the small k.
Q: What is the rationale behind the search?
A: We deal with very big double Mersenne numbers here, starting from MM34.
A factor of a double Mersenne number MMp has the form 2*k*(2Mp)+1;
As Mp is 3 mod 4, when looking for factors of MMp of the form q=2*k*Mp+1,
we are interested only in k=0,1 (mod 4).
Q: What software is used to do these calculations?
A: At first we used a PARI script written by LaurV to eliminate all the Ks that are not 0,1 (mod 4)
and divisible by prime divisors <100M up to k<10,000.
Then we submitted all remaining Ks to a sieving program written by Ernst Mayer,
and sieved all Ks to 20G.
Actually we use George Woltman's mprime for ECM (on small MMp) and PRP (for MMp > 33) testing. George WOltman's mmff is used for MM31, MM61, MM89, MM107 and MM127.
Mark Rodenkirch provided us with gmp-doublemersenne (used for medium-sized MMp) and dmdsieve/dmdsieve-cl for K sieving under CPU and GPU.
All the software can be found on the download page.
Q: What are you considering "Complete" with regards to this deep sieving?
A: Sieving is considered "Complete" when:
Q: What does it mean to be 'tested' up to a certain value?
A: We have selected only Ks that may be considered for q=2*k*Mp+1;
"tested up to 500 T" means that q is not composite for k<500 T (500,000,000,000,000).
Q: Who is working on this project?
A: The project has been built gathering the work done from year 2000
by Tony Forbes, Phil Moore, Ernst Mayer, Will Edgington, LaurV and Luigi Morelli.
Q: Is there a reservation system set up somewhere?
A: Yes, there is a reservation system based on email.
If you want to join this search, ask me for a range.