Double Mersennes Prime Search

Project deep sieving - Frequently Asked Questions

A factor of a double Mersenne number MMp has form 2*k*Mp+1. We are testing the small k.
All k < 10,000 have been tested up to 20G except for MM34 ad MM35 where k < 500,000.

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: 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.

Q: What are you considering "Complete" with regards to this deep sieving?
A: Sieving of K is considered "Complete" when:

  • a factor of q=2*k*Mp+1 is found via sieving of K;
  • q is found composite via modular testing;

   Please note that, for high K and MMp>45, a q prime could be a record size prime of a non-Mersenne number!

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 10T" means that q is not composite for k<10T.

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, download Ernst Mayer's siever and ask me for a range.

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