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Message boards : Generalized Fermat Prime Search : Can GFN learn any of LLR2's tricks?

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Ken_g6Project donor
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Discovered 1 mega primeFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,010,094)Cullen LLR Ruby: Earned 2,000,000 credits (2,022,806)ESP LLR Amethyst: Earned 1,000,000 credits (1,657,625)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (767,102)PPS LLR Sapphire: Earned 20,000,000 credits (24,788,060)PSP LLR Turquoise: Earned 5,000,000 credits (5,182,638)SoB LLR Turquoise: Earned 5,000,000 credits (5,923,035)SR5 LLR Ruby: Earned 2,000,000 credits (2,061,736)SGS LLR Ruby: Earned 2,000,000 credits (2,139,194)TPS LLR (retired) Bronze: Earned 10,000 credits (19,376)TRP LLR Ruby: Earned 2,000,000 credits (2,520,745)Woodall LLR Ruby: Earned 2,000,000 credits (2,021,413)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,915,071)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (8,584,236)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,461,309)PPS Sieve Emerald: Earned 50,000,000 credits (92,950,614)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Silver: Earned 100,000 credits (352,129)TRP Sieve (suspended) Gold: Earned 500,000 credits (776,202)AP 26/27 Turquoise: Earned 5,000,000 credits (5,851,049)GFN Sapphire: Earned 20,000,000 credits (35,632,932)WW Jade: Earned 10,000,000 credits (15,964,000)PSA Ruby: Earned 2,000,000 credits (4,154,617)
Message 144759 - Posted: 27 Oct 2020 | 1:15:21 UTC

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.

Michael Millerick
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Discovered 1 mega primeFound 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,023,600)Cullen LLR Ruby: Earned 2,000,000 credits (2,016,794)ESP LLR Sapphire: Earned 20,000,000 credits (20,186,009)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (3,172,603)PPS LLR Jade: Earned 10,000,000 credits (19,460,823)PSP LLR Ruby: Earned 2,000,000 credits (3,043,852)SoB LLR Ruby: Earned 2,000,000 credits (2,031,453)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Ruby: Earned 2,000,000 credits (2,035,177)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Ruby: Earned 2,000,000 credits (2,046,592)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,440,175)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,911,344)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,077,092)PPS Sieve Emerald: Earned 50,000,000 credits (50,200,870)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,034,014)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,070,774)AP 26/27 Sapphire: Earned 20,000,000 credits (20,227,947)GFN Emerald: Earned 50,000,000 credits (73,141,813)WW Emerald: Earned 50,000,000 credits (50,104,000)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 144765 - Posted: 27 Oct 2020 | 6:34:44 UTC

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.
____________

Yves Gallot
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Message 144766 - Posted: 27 Oct 2020 | 9:08:31 UTC - in response to Message 144759.

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.

Ken_g6Project donor
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Joined: 4 Jul 06
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Credit: 220,755,322
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Discovered 1 mega primeFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,010,094)Cullen LLR Ruby: Earned 2,000,000 credits (2,022,806)ESP LLR Amethyst: Earned 1,000,000 credits (1,657,625)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (767,102)PPS LLR Sapphire: Earned 20,000,000 credits (24,788,060)PSP LLR Turquoise: Earned 5,000,000 credits (5,182,638)SoB LLR Turquoise: Earned 5,000,000 credits (5,923,035)SR5 LLR Ruby: Earned 2,000,000 credits (2,061,736)SGS LLR Ruby: Earned 2,000,000 credits (2,139,194)TPS LLR (retired) Bronze: Earned 10,000 credits (19,376)TRP LLR Ruby: Earned 2,000,000 credits (2,520,745)Woodall LLR Ruby: Earned 2,000,000 credits (2,021,413)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,915,071)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (8,584,236)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,461,309)PPS Sieve Emerald: Earned 50,000,000 credits (92,950,614)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Silver: Earned 100,000 credits (352,129)TRP Sieve (suspended) Gold: Earned 500,000 credits (776,202)AP 26/27 Turquoise: Earned 5,000,000 credits (5,851,049)GFN Sapphire: Earned 20,000,000 credits (35,632,932)WW Jade: Earned 10,000,000 credits (15,964,000)PSA Ruby: Earned 2,000,000 credits (4,154,617)
Message 144775 - Posted: 27 Oct 2020 | 14:51:31 UTC - in response to Message 144766.

Very informative. Thank you! For the explanation as well as all the work!

Profile BurProject donor
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321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Ruby: Earned 2,000,000 credits (2,289,208)ESP LLR Amethyst: Earned 1,000,000 credits (1,445,099)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,180,764)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Amethyst: Earned 1,000,000 credits (1,415,335)TRP LLR Ruby: Earned 2,000,000 credits (2,089,856)Woodall LLR Ruby: Earned 2,000,000 credits (2,112,258)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Turquoise: Earned 5,000,000 credits (5,096,952)AP 26/27 Turquoise: Earned 5,000,000 credits (5,150,782)GFN Turquoise: Earned 5,000,000 credits (7,510,843)WW Double Silver: Earned 200,000,000 credits (243,096,000)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 144823 - Posted: 29 Oct 2020 | 18:58:37 UTC - in response to Message 144766.

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?
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 4,800,000

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Message boards : Generalized Fermat Prime Search : Can GFN learn any of LLR2's tricks?

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