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Message boards :
Generalized Fermat Prime Search :
Can GFN learn any of LLR2's tricks?
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Ken_g6 Volunteer developer
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This one might belong in the FAQ if it can't.
Can the current GFN programs be modified to do the things LLR2 can do? Specifically:
Can a GFN program do Gerbicz checking?
Can a GFN program save a bunch of data to do fast double-checks later?
Is the answer different for CPU vs. GPU?
Just curious. It would sure be nice not to have to race to be the first to report a GFN GPU result, though.
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I remember reading the answers to some of this in the Discord, but couldn't find them later when I wanted to read the messages again. I'm looking forward to seeing the answers again.
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Yves GallotVolunteer developer
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Can the current GFN programs be modified to do the things LLR2 can do? Specifically:
Can a GFN program do Gerbicz checking?
Yes and the implementation was tested.
The new program is slower: with Proth numbers, Gerbicz checking is as fast as 'no checking' because of the base 2. If c = ak then c2n can be computed with a sequence of squares but the computation of 2bN requires also some multiplications with Gerbicz check. Without Gerbicz check, the exponentiation can be computed with a left-to-right binary algorithm and no full multiplication is necessary just some duplicates (what genefer is doing).
Gerbicz check is already implemented in genefer20. This program was used to test the range b in [2; 2G] for n = 10 and 11: https://www.primegrid.com/forum_thread.php?id=9046&nowrap=true#144155. But today this program is dedicated to "small" GFNs and tests a vector of GFNs, which is faster than a single test on GPU.
genefer20 will be extended to large n and a single test for PrimeGrid ranges. The new program will be slower but because one WU will be one test and one validation rather than two tests, the whole test will be faster.
Can a GFN program save a bunch of data to do fast double-checks later?
Yes, Pavel's algorithm is an extension of Gerbicz checking that can be implemented in any program. A good approach is to write a PrimeGrid library for the test of large prime numbers. This API will encapsulate BOINC, Gerbicz and Pavel's methods and maybe other top level functions. Then LLR2 can be written with GWNUM, genefer20 with its CPU/GPU transforms and Proth20 with its GPU implementation and all of them be linked to this library. Therefore, files and inputs/outputs with PrimeGrid server are unified (and LLR2 can validate genefer20 or Proth20 can validate LLR2, ...).
Is the answer different for CPU vs. GPU?
No, CPU and GPU are two different low-level implementations but the main program is identical.
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Ken_g6Volunteer developer
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Very informative. Thank you! For the explanation as well as all the work! | |
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 BurVolunteer tester
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Maybe I'm a bit slow, but does that mean that Gerbicz checking is so slow with GFN that in total it's slower than doing a DC task, i.e. twice as slow?
If not, can we expect GFN tasks with certificate-style DC'ing?
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000 | |
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Message boards :
Generalized Fermat Prime Search :
Can GFN learn any of LLR2's tricks? |
