PrimeGrid
Please visit donation page to help the project cover running costs for this month

Toggle Menu

Join PrimeGrid

Returning Participants

Community

Leader Boards

Results

Other

drummers-lowrise

Advanced search

Message boards : Generalized Fermat Prime Search : N=20, B=8

Author Message
Christopher Siegert
Send message
Joined: 5 Jul 09
Posts: 232
ID: 42986
Credit: 77,011,345
RAC: 0
321 LLR Amethyst: Earned 1,000,000 credits (1,041,657)Cullen LLR Amethyst: Earned 1,000,000 credits (1,366,558)PPS LLR Sapphire: Earned 20,000,000 credits (22,177,547)PSP LLR Amethyst: Earned 1,000,000 credits (1,521,444)SoB LLR Amethyst: Earned 1,000,000 credits (1,751,070)SR5 LLR Amethyst: Earned 1,000,000 credits (1,100,031)SGS LLR Amethyst: Earned 1,000,000 credits (1,014,953)TRP LLR Ruby: Earned 2,000,000 credits (3,647,371)Woodall LLR Amethyst: Earned 1,000,000 credits (1,479,507)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (41,181)PPS Sieve Sapphire: Earned 20,000,000 credits (29,702,366)TRP Sieve (suspended) Silver: Earned 100,000 credits (206,682)GFN Jade: Earned 10,000,000 credits (11,960,980)
Message 60180 - Posted: 7 Dec 2012 | 15:28:26 UTC

http://www.primegrid.com/stats_genefer.php

The minimum b value in progress has been stuck at b=8 for quite awhile.

How can this task be taking so long? Not only has it already been cleared as b=64 at the n=19 level, but it just shouldn't take very long to test, even for a CPU!

Is something wrong?

In fact 8^1048576+1 = (2^3)^1048576+1 = (2^1048576)^3+1 which has an algebraic factor. So what's the deal?

Profile Michael GoetzProject donor
Volunteer moderator
Project administrator
Avatar
Send message
Joined: 21 Jan 10
Posts: 13520
ID: 53948
Credit: 242,417,032
RAC: 338,482
The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (3,624,591)ESP LLR Turquoise: Earned 5,000,000 credits (5,021,269)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Jade: Earned 10,000,000 credits (16,688,670)PSP LLR Turquoise: Earned 5,000,000 credits (5,197,957)SoB LLR Sapphire: Earned 20,000,000 credits (34,291,181)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,423,765)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Ruby: Earned 2,000,000 credits (2,911,985)321 Sieve (suspended) Jade: Earned 10,000,000 credits (10,061,196)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (22,885,121)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Jade: Earned 10,000,000 credits (10,118,303)WW Turquoise: Earned 5,000,000 credits (6,596,000)GFN Emerald: Earned 50,000,000 credits (76,795,865)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 60181 - Posted: 7 Dec 2012 | 16:12:44 UTC - in response to Message 60180.

There's at least an 11 day deadline on these tasks. Some people run large queues and/or run other projects, both of which can cause a delay in the start of processing. Additionally, many of these are being run on CPUs which require several days of crunching.

Finally, by default, BOINC doesn't even bother returning a task when it's completed and waits until the next time it requests work.

In other words, it's not late so there can't be any expectation that it should be complete.

By the way, if memory serves, that WU actually does have two completed results but they don't match so we're waiting for a third result. I'm not at home so it's not easy for me to check.
____________
My lucky number is 75898524288+1

Christopher Siegert
Send message
Joined: 5 Jul 09
Posts: 232
ID: 42986
Credit: 77,011,345
RAC: 0
321 LLR Amethyst: Earned 1,000,000 credits (1,041,657)Cullen LLR Amethyst: Earned 1,000,000 credits (1,366,558)PPS LLR Sapphire: Earned 20,000,000 credits (22,177,547)PSP LLR Amethyst: Earned 1,000,000 credits (1,521,444)SoB LLR Amethyst: Earned 1,000,000 credits (1,751,070)SR5 LLR Amethyst: Earned 1,000,000 credits (1,100,031)SGS LLR Amethyst: Earned 1,000,000 credits (1,014,953)TRP LLR Ruby: Earned 2,000,000 credits (3,647,371)Woodall LLR Amethyst: Earned 1,000,000 credits (1,479,507)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (41,181)PPS Sieve Sapphire: Earned 20,000,000 credits (29,702,366)TRP Sieve (suspended) Silver: Earned 100,000 credits (206,682)GFN Jade: Earned 10,000,000 credits (11,960,980)
Message 60200 - Posted: 7 Dec 2012 | 19:57:46 UTC

Frankly, I'm still a little disappointed that 2^3 is a b value being tested. I saw someone else post other examples of b^x that were being tested. It's just basic algebra...

Profile Michael GoetzProject donor
Volunteer moderator
Project administrator
Avatar
Send message
Joined: 21 Jan 10
Posts: 13520
ID: 53948
Credit: 242,417,032
RAC: 338,482
The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (3,624,591)ESP LLR Turquoise: Earned 5,000,000 credits (5,021,269)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Jade: Earned 10,000,000 credits (16,688,670)PSP LLR Turquoise: Earned 5,000,000 credits (5,197,957)SoB LLR Sapphire: Earned 20,000,000 credits (34,291,181)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,423,765)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Ruby: Earned 2,000,000 credits (2,911,985)321 Sieve (suspended) Jade: Earned 10,000,000 credits (10,061,196)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (22,885,121)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Jade: Earned 10,000,000 credits (10,118,303)WW Turquoise: Earned 5,000,000 credits (6,596,000)GFN Emerald: Earned 50,000,000 credits (76,795,865)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 60241 - Posted: 9 Dec 2012 | 17:12:46 UTC

After some deeper digging, the second result, from a CPU that crunched this task for 135 hours, was actually uploaded to the server two days before you asked the question.

As I mentioned above, however, the BOINC client's default behavior defers contacting the server to actually report the result as completed until either it needs to because the deadline is approaching, or it's contacting the server anyway to request more work.

In this case, the result was completed and uploaded to the server on December 5th. It has still not reported the result as completed. The deadline for doing so is late on December 10th.
____________
My lucky number is 75898524288+1

Profile JeppeSNProject donor
Avatar
Send message
Joined: 5 Apr 14
Posts: 1391
ID: 306875
Credit: 28,380,568
RAC: 342,787
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (10,164,181)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (111,958)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (6,256,000)GFN Amethyst: Earned 1,000,000 credits (1,674,106)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 81800 - Posted: 29 Dec 2014 | 1:47:25 UTC - in response to Message 60180.
Last modified: 29 Dec 2014 | 1:52:36 UTC

http://www.primegrid.com/stats_genefer.php

The minimum b value in progress has been stuck at b=8 for quite awhile.

How can this task be taking so long? Not only has it already been cleared as b=64 at the n=19 level, but it just shouldn't take very long to test, even for a CPU!

Is something wrong?

In fact 8^1048576+1 = (2^3)^1048576+1 = (2^1048576)^3+1 which has an algebraic factor. So what's the deal?


I also want to ask why we do not skip those b values which are perfect powers.

For example with 8 = 2^3 as above, where 3 is not a power of two, since:

x^3 + 1 = (x + 1) (x^2 - x + 1)


we know right away that (2^1048576)^3 + 1 is divisible by 2^1048576 + 1.

The same thing happens whenever b is a perfect power whose exponent contains an odd prime factor.

And when b is in itself a perfect square of the form b = a^{2^k}, with k>0, then this prime candidate really belongs to another GFN exponent "level". For example the test of b=16:

16^1048576+1 = GF(20, 16) = GF(21, 4) = GF(22, 2) = F(22)


belongs to the n=22 level. In the same way b=1296 should be skipped since

1296^1048576+1 = GF(20, 1296) = GF(21, 36) = GF(22, 6)


I recently noticed this phenomenon in a post in another thread.

So the request is: Could we please skip the b values (4, 8, 16, 32, 36, 64, 100, 128, 144, 196, 216, 256, 324, 400, 484, 512, 576, 676, 784, 900, 1000, 1024, 1156, 1296, 1444, 1600, etc.) which are perfect powers?

/JeppeSN

JimBProject donor
Honorary cruncher
Send message
Joined: 4 Aug 11
Posts: 916
ID: 107307
Credit: 974,494,172
RAC: 911
Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,691,081)Cullen LLR Turquoise: Earned 5,000,000 credits (5,031,868)ESP LLR Turquoise: Earned 5,000,000 credits (5,064,082)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,038,750)PPS LLR Turquoise: Earned 5,000,000 credits (5,000,220)PSP LLR Turquoise: Earned 5,000,000 credits (7,674,374)SoB LLR Sapphire: Earned 20,000,000 credits (42,604,648)SR5 LLR Jade: Earned 10,000,000 credits (11,829,173)SGS LLR Ruby: Earned 2,000,000 credits (2,410,847)TRP LLR Ruby: Earned 2,000,000 credits (2,291,092)Woodall LLR Turquoise: Earned 5,000,000 credits (5,046,412)321 Sieve (suspended) Jade: Earned 10,000,000 credits (10,057,614)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,002,919)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,005,451)PPS Sieve Emerald: Earned 50,000,000 credits (52,042,965)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,341,676)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,070,804)AP 26/27 Jade: Earned 10,000,000 credits (10,742,251)GFN Emerald: Earned 50,000,000 credits (50,000,251)PSA Double Gold: Earned 500,000,000 credits (728,547,693)
Message 81801 - Posted: 29 Dec 2014 | 4:02:48 UTC

We do eliminate some candidates in the way you're talking about. Hundreds of them. Right now I'm a little too sleep-deprived to figure all this out and I'm trying to fix things that have a far more significant effect on our site than running a few extra tests.

I believe a lot of this stuff wasn't put into effect on 524288 because those tests were so fast. Now that we're getting beyond the b-limit of what GPUs can handle, we may want to revisit it at some point in the future. We do not, however, consider it a large problem, and most likely not an effective way to spend the limited resources available to us. A few extra tests is a small drop in a very large bucket.

axn
Volunteer developer
Send message
Joined: 29 Dec 07
Posts: 285
ID: 16874
Credit: 28,027,106
RAC: 0
321 LLR Gold: Earned 500,000 credits (656,177)Cullen LLR Silver: Earned 100,000 credits (457,297)ESP LLR Silver: Earned 100,000 credits (437,502)PPS LLR Amethyst: Earned 1,000,000 credits (1,256,334)SoB LLR Amethyst: Earned 1,000,000 credits (1,246,109)SR5 LLR Ruby: Earned 2,000,000 credits (2,193,129)SGS LLR Silver: Earned 100,000 credits (101,658)Woodall LLR Silver: Earned 100,000 credits (292,129)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (32,498)PPS Sieve Jade: Earned 10,000,000 credits (15,515,229)AP 26/27 Amethyst: Earned 1,000,000 credits (1,491,867)GFN Ruby: Earned 2,000,000 credits (4,245,870)PSA Silver: Earned 100,000 credits (101,309)
Message 81804 - Posted: 29 Dec 2014 | 4:32:31 UTC - in response to Message 81800.

In the same way b=1296 should be skipped since

1296^1048576+1 = GF(20, 1296) = GF(21, 36) = GF(22, 6)



So, you want to avoid testing the same number using a smaller FFT and use a larger FFT instead?! Testing GF(22, 6) takes 4 times as much time as testing GF(20, 1296).

Profile JeppeSNProject donor
Avatar
Send message
Joined: 5 Apr 14
Posts: 1391
ID: 306875
Credit: 28,380,568
RAC: 342,787
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (10,164,181)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (111,958)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (6,256,000)GFN Amethyst: Earned 1,000,000 credits (1,674,106)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 81809 - Posted: 29 Dec 2014 | 11:39:58 UTC - in response to Message 81801.

We do eliminate some candidates in the way you're talking about. Hundreds of them. Right now I'm a little too sleep-deprived to figure all this out and I'm trying to fix things that have a far more significant effect on our site than running a few extra tests.

I believe a lot of this stuff wasn't put into effect on 524288 because those tests were so fast. Now that we're getting beyond the b-limit of what GPUs can handle, we may want to revisit it at some point in the future. We do not, however, consider it a large problem, and most likely not an effective way to spend the limited resources available to us. A few extra tests is a small drop in a very large bucket.


OK, it could be interesting to hear what b values we do eliminate.

Of course checking if b is a perfect power, b=a^k, or not is extremely fast, much easier than e.g. sieving for small factors of GF(n, b).

/JeppeSN

Profile JeppeSNProject donor
Avatar
Send message
Joined: 5 Apr 14
Posts: 1391
ID: 306875
Credit: 28,380,568
RAC: 342,787
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (10,164,181)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (111,958)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (6,256,000)GFN Amethyst: Earned 1,000,000 credits (1,674,106)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 81810 - Posted: 29 Dec 2014 | 11:54:50 UTC - in response to Message 81804.
Last modified: 29 Dec 2014 | 11:59:30 UTC

In the same way b=1296 should be skipped since

1296^1048576+1 = GF(20, 1296) = GF(21, 36) = GF(22, 6)



So, you want to avoid testing the same number using a smaller FFT and use a larger FFT instead?! Testing GF(22, 6) takes 4 times as much time as testing GF(20, 1296).


My first thought is if GF(22, 6) is already tested, no matter how fast testing GF(20, 1296) would be, it would be useless to do it since both are just different ways of writing the same number.

And you do realize that any number GF(22, a) can be seen as belonging to any of the smaller n series, since:

GF(22, a) = GF(21, a^2) = GF(20, a^4) = GF(19, a^8) = ... = GF(1, a^2097152) = GF(0, a^4194304)


In particular if GF(20, ·) is always faster to check than GF(22, ·), then for every number we can use the identity GF(22, a) = GF(20, a^4) to gain this advantage. However, the much larger base value a^4 must somehow spoil this plan, at least for "usually" large a values, otherwise checking generalized Fermat numbers would be "too easy".

In practice, the number GF(n, a^2) has almost always been checked earlier, historically, in the form with much smaller base, that is GF(n+1, a). So we should exclude bases b=a^2.

/JeppeSN

axn
Volunteer developer
Send message
Joined: 29 Dec 07
Posts: 285
ID: 16874
Credit: 28,027,106
RAC: 0
321 LLR Gold: Earned 500,000 credits (656,177)Cullen LLR Silver: Earned 100,000 credits (457,297)ESP LLR Silver: Earned 100,000 credits (437,502)PPS LLR Amethyst: Earned 1,000,000 credits (1,256,334)SoB LLR Amethyst: Earned 1,000,000 credits (1,246,109)SR5 LLR Ruby: Earned 2,000,000 credits (2,193,129)SGS LLR Silver: Earned 100,000 credits (101,658)Woodall LLR Silver: Earned 100,000 credits (292,129)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (32,498)PPS Sieve Jade: Earned 10,000,000 credits (15,515,229)AP 26/27 Amethyst: Earned 1,000,000 credits (1,491,867)GFN Ruby: Earned 2,000,000 credits (4,245,870)PSA Silver: Earned 100,000 credits (101,309)
Message 81852 - Posted: 30 Dec 2014 | 5:03:11 UTC

Found this thread: http://www.primegrid.com/forum_thread.php?id=4644

Profile JeppeSNProject donor
Avatar
Send message
Joined: 5 Apr 14
Posts: 1391
ID: 306875
Credit: 28,380,568
RAC: 342,787
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (10,164,181)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (111,958)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (6,256,000)GFN Amethyst: Earned 1,000,000 credits (1,674,106)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 81865 - Posted: 30 Dec 2014 | 15:05:29 UTC - in response to Message 81852.
Last modified: 30 Dec 2014 | 15:07:32 UTC

Found this thread: http://www.primegrid.com/forum_thread.php?id=4644


Interesting. So we have removed some perfect-power b in the past.

I don't know if anyone has a clear picture of what b values were skipped, and what were not. Can one see a list of all work units belonging to n=20 and n=22 somewhere? For the PRPNet subprojects (n=15,16,18,19) I can see a list of work units in progress (but I cannot see the work units finished or those yet unassigned).

If for n=22 we did not skip perfect-square b, we have shown that GF(24, 10) = GF(22, 10000) and GF(24, 12) = GF(22, 20736) are composite. If that is the case, someone should inform Wilfrid Keller or whoever updates prothsearch.com, for the b=10 Summary and the b=12 Summary claim that the cases GF(24, 10) and GF(24, 12) are Character unknown. Should be: Composite but no factor known. Unless we found factors during our sieving, of course!

/JeppeSN

Profile Michael GoetzProject donor
Volunteer moderator
Project administrator
Avatar
Send message
Joined: 21 Jan 10
Posts: 13520
ID: 53948
Credit: 242,417,032
RAC: 338,482
The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (3,624,591)ESP LLR Turquoise: Earned 5,000,000 credits (5,021,269)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Jade: Earned 10,000,000 credits (16,688,670)PSP LLR Turquoise: Earned 5,000,000 credits (5,197,957)SoB LLR Sapphire: Earned 20,000,000 credits (34,291,181)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,423,765)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Ruby: Earned 2,000,000 credits (2,911,985)321 Sieve (suspended) Jade: Earned 10,000,000 credits (10,061,196)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (22,885,121)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Jade: Earned 10,000,000 credits (10,118,303)WW Turquoise: Earned 5,000,000 credits (6,596,000)GFN Emerald: Earned 50,000,000 credits (76,795,865)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 81873 - Posted: 30 Dec 2014 | 19:23:30 UTC - in response to Message 81865.
Last modified: 30 Dec 2014 | 19:23:46 UTC

I don't know if anyone has a clear picture of what b values were skipped, and what were not. Can one see a list of all work units belonging to n=20 and n=22 somewhere? For the PRPNet subprojects (n=15,16,18,19) I can see a list of work units in progress (but I cannot see the work units finished or those yet unassigned).


As a general rule, we have not made the results of primality tests generally available -- meaning, you can't just go to the website and download them. There's a few not-so-obvious reasons for that.

The results are not secret nor proprietary, so we are happy to make them available to anyone who wants the information. However, to my knowledge, nobody has ever expressed an interest in this data before, and without some sort of request or use case, we're only guessing about what information would be useful.

So if you want this kind of data, just ask, and let us know what you want it for so we can put something together that suits your needs. Understand, however, that not all of the results are online, so I might not be able to give you what you need. Also, some data that people might want might not be available at all.
____________
My lucky number is 75898524288+1

Profile JeppeSNProject donor
Avatar
Send message
Joined: 5 Apr 14
Posts: 1391
ID: 306875
Credit: 28,380,568
RAC: 342,787
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (10,164,181)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (111,958)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (6,256,000)GFN Amethyst: Earned 1,000,000 credits (1,674,106)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 81890 - Posted: 31 Dec 2014 | 0:13:15 UTC - in response to Message 81873.

Michael Goetz, this is just out of curiosity.

I wanted to check if we skip impossible b values such as b=a^3, b=a^5, b=a^6, etc. Both in the PRPNet GFN subprojects and in the BOINC GFN subprojects.

I wanted to also check if we skip b values of the form b=a^{2^j} (with a not itself a perfect power) which may be prime, but which will in many cases be redundant because they were checked earlier in a "larger" subproject. In the forum post i linked above I saw that we did assign the PRPNet task 910116^524288+1 to someone even if 910116^524288+1 = 954^1048576+1 which means that we already knew the result. GF(19, 910116) = GF(20, 954).

I also wanted to see if GF(22, 10000) = 10000^{2^22}+1 and GF(22, 20736) = 20736^{2^22}+1 have been checked or skipped, as I said above, these are GF(24, 10) and GF(24, 12), respectively.

When, for a given subproject, the b values get big, the perfect powers appear relatively rarely, so it is not a massive optimization to skip them, but it would still be interesting to see if we skip or not.

For each b, let f(b) be the maximal exponent i possible when writing b on the form b=a^i, then f is tabulated here (OEIS A052409). The case f(b)=1 is the normal one. When f(b)>1, we either have f(b) is a power of two (primality possible, but might be checked already in another subproject) or f(b) contains an odd prime factor (GFN(n, b) then has an algebraic divisor and is composite).

/JeppeSN

Profile Michael GoetzProject donor
Volunteer moderator
Project administrator
Avatar
Send message
Joined: 21 Jan 10
Posts: 13520
ID: 53948
Credit: 242,417,032
RAC: 338,482
The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (3,624,591)ESP LLR Turquoise: Earned 5,000,000 credits (5,021,269)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Jade: Earned 10,000,000 credits (16,688,670)PSP LLR Turquoise: Earned 5,000,000 credits (5,197,957)SoB LLR Sapphire: Earned 20,000,000 credits (34,291,181)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (3,423,765)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Ruby: Earned 2,000,000 credits (2,911,985)321 Sieve (suspended) Jade: Earned 10,000,000 credits (10,061,196)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (22,885,121)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Jade: Earned 10,000,000 credits (10,118,303)WW Turquoise: Earned 5,000,000 credits (6,596,000)GFN Emerald: Earned 50,000,000 credits (76,795,865)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 81892 - Posted: 31 Dec 2014 | 0:37:13 UTC - in response to Message 81890.

I wanted to check if we skip impossible b values ...


Short answer: we try to.

However, we don't try with the same compulsiveness that someone searching on their own would do. Small scale searching and large scale distributed computing have significant differences.

If I'm searching on my own, my biggest constraint is almost always going to be the amount of hardware I own, can buy, or can rent. My own time is virtually unlimited. As such, it's paramount to squeeze every last drop of computing out of what I've got and not waste any of it.

On a big distributed project, it's very different. I've got essentially unlimited computing power at my fingertips. If we need to push some calculation for whatever reason, all we have to do is ask and plenty of people will come and help. Being a little less efficient -- either by doing more double checking, or, as in this case, running a few unnecessary tests -- has a very small effect on the overall computation.

On the other hand, the time we might need to spend to eliminate every last redundant test is time we could spend doing something else, which might enable lots more computing to be done, as opposed to computing more efficiently. When I'm doing my own searching, increasing efficiency is the only way to do more searching, so it's natural for people, like yourself, with a background in prime searching, to focus on efficiency. But from my perspective, we usually get more bang for the buck by trying to get more total computing done than to increase efficiency.

It's not that efficiency isn't important, because it is. It's just not nearly as important as is the total computing effort.

That's why we spend far more time on trying to reduce the number of errors people have and widening the range of hardware that can be used. That's going to benefit us more than spending time thinking about eliminating a handful of tests.

That being said, those tests kind of fall into the "low hanging fruit" category, so we do have a program that eliminates the ones that have been mentioned. But it's not likely to be worth the time to repeatedly rehash this discussion trying to find a few more tests that can be skipped. As such this will probably be my last comment on this topic, since we seem to repeating the same statements over and over.
____________
My lucky number is 75898524288+1

Message boards : Generalized Fermat Prime Search : N=20, B=8

[Return to PrimeGrid main page]
DNS Powered by DNSEXIT.COM
Copyright © 2005 - 2021 Rytis Slatkevičius (contact) and PrimeGrid community. Server load 1.13, 0.92, 1.05
Generated 17 Jan 2021 | 7:46:19 UTC