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Message boards : Generalized Fermat Prime Search : Guessing the future of GFN-22 and DYFL

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JeppeSN

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Message 147091 - Posted: 27 Dec 2020 | 9:55:12 UTC

Here is a tough bet: Which will happen first:

1. GFN-22 reaches the starting point (b = 846'396.7) of DYFL, likely without finding any GFN-22 primes, and the two 22-subprojects merge
2. Someone outside PrimeGrid, likely GIMPS, finds a new world record prime, and DYFL jumps to that new position (resulting in two "holes")

And when?

/JeppeSN

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Message 147093 - Posted: 27 Dec 2020 | 10:52:31 UTC - in response to Message 147091.

no.2, July 2021
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Michael Goetz
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Message 147095 - Posted: 27 Dec 2020 | 13:49:48 UTC - in response to Message 147091.

Here is a tough bet: Which will happen first:

1. GFN-22 reaches the starting point (b = 846'396.7) of DYFL, likely without finding any GFN-22 primes, and the two 22-subprojects merge
2. Someone outside PrimeGrid, likely GIMPS, finds a new world record prime, and DYFL jumps to that new position (resulting in two "holes")

And when?

/JeppeSN

Almost certainly #2 is going to happen first. GFN22's leading edge took nearly 9 years to get to where it is now at 187K, and it's over three times as far to go to get to the start of DYFL. Additionally, it will exceed both the OCL and OCL4 limits before then, so the tasks will slow down.

GIMPS has been finding new world records every few years, so unless they hit a huge dry patch in Mersenne primes, they'll probably find a new prime decades before GFN22 ends.
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Message 147096 - Posted: 27 Dec 2020 | 14:09:27 UTC

Given that a 3090 can run GFN22 in about 14 hrs, but DYFL will run in about 15.5 hrs, which sub project would you choose and which is more "likely" to have a chance of a prime, however remote?
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Message 147166 - Posted: 30 Dec 2020 | 16:35:30 UTC - in response to Message 147096.

Given that a 3090 can run GFN22 in about 14 hrs, but DYFL will run in about 15.5 hrs, which sub project would you choose and which is more "likely" to have a chance of a prime, however remote?

The lower the number, the higher the likelyhood of it being prime, so if you're only looking for A gfn22 prime, don't run DYFL.

With that said, you might as well look for a WR and have a shot at the cash reward / fame, or tone it down and look for the first GFN21 known to man instead.

GDB

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Message 147171 - Posted: 30 Dec 2020 | 18:03:16 UTC

I still think GFN22 is undersieved. I was removing a GFN22 factor every 72 seconds. That's about 1200 times faster than running GFN22.
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JeppeSN

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Message 147172 - Posted: 30 Dec 2020 | 18:25:57 UTC - in response to Message 147166.

the cash reward

I do not think you will earn a cash reward for beating the world record, here at PrimeGrid.

GIMPS got a cash prize when they found the first croreprime (10'000'000-digit prime), and might also find the first 100'000'000-digit prime in the distant future. I think GIMPS uses some of this money to give a cash reward to finders. PrimeGrid does not have that.

/JeppeSN

Frank

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Message 147282 - Posted: 2 Jan 2021 | 9:04:22 UTC - in response to Message 147171.

Sounds interesting GDB, just two questions:
1) Which sieving range (in P) were you checking? 2) And how do you have the full set of b-values that we are going to check within Primegrid?

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Message 147300 - Posted: 2 Jan 2021 | 16:03:29 UTC - in response to Message 147171.

I still think GFN22 is undersieved. I was removing a GFN22 factor every 72 seconds. That's about 1200 times faster than running GFN22.

Just because the sieve program finds a factor doesnâ€™t mean it is removing a candidate. The candidate could have already been removed earlier in the sieve. Itâ€™s also relatively moot if it is a candidate that will realistically not be primality tested anytime soon.
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GDB

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Message 147326 - Posted: 3 Jan 2021 | 15:24:37 UTC - in response to Message 147300.

I still think GFN22 is undersieved. I was removing a GFN22 factor every 72 seconds. That's about 1200 times faster than running GFN22.

Just because the sieve program finds a factor doesnâ€™t mean it is removing a candidate. The candidate could have already been removed earlier in the sieve. Itâ€™s also relatively moot if it is a candidate that will realistically not be primality tested anytime soon.

When I said that I was finding a factor every 72 seconds, I was meaning factors that ONLY removed candidates.

What's driving the lack of sieving is someone's definition of "soon". Rather than waste my GPU time running one in ten million GFN22 crapshoots, I'd prefer to use my GPUs to remove millions of candidates.

And I mean MILLIONS. With only my sieving, I could remove 2 million candidates in 5 years. 500 people running GFN22 for 5 years would only remove 500,000 candidates.
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Message 147341 - Posted: 4 Jan 2021 | 10:13:09 UTC

What is sieving speed of your GPU (P/day) ?

GDB

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Message 147344 - Posted: 4 Jan 2021 | 12:27:15 UTC - in response to Message 147341.

What is sieving speed of your GPU (P/day) ?

With my 2 1080s and 2060, I was doing 800 P per day for n=22 manual sieving.

At a removal rate of 1.5 candidates per P, I was removing 1200 candidates per day.

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Message 147353 - Posted: 4 Jan 2021 | 15:27:53 UTC - in response to Message 147344.

What is sieving speed of your GPU (P/day) ?

With my 2 1080s and 2060, I was doing 800 P per day for n=22 manual sieving.

At a removal rate of 1.5 candidates per P, I was removing 1200 candidates per day.

OK. You're sieving 800 P/day. You see that lot of factors were found.

Question #1. How many of these factors are really removing a candidate (i.e. candidate wasn't removed earlier by smaller factors)?

Yves has formulas for everything related to GFN. He also has a formula to calculate number of candidates left at given sieving depth and range. Current GFN-22 sieving depth is 1100000P and range is 2G. How many candidates will be removed between 1100000P and 1100000+800P ? Put both depths to formula and find a difference. The answer is (you have to trust my word) 6055.

Question #2. How many of these 6055 factors are useful to us?

There is a problem with candidates located too far from our current position in search. Sieving can find these factors "for free", up to 2G, but why - if we'll need, for example, 100 years to reach this range?

So we use 5 years prediction for "usable" range, based on progress for few last years. And the sad truth is that prediction (advance of 'b') for GFN-22 is only 245000!

You removed 6055 from 2G range. How may candidates are within 245K range?

6055 * 245000 / 2000000000 = 0,7417375

Multiply by two due to DC tasks. So, your whole day of sieving on 3 GPUs saved only 1,5 useful (within next 5 years) tasks.

What is duration of real tasks on these GPUs?

GDB

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Message 147361 - Posted: 4 Jan 2021 | 18:56:51 UTC - in response to Message 147353.

What is sieving speed of your GPU (P/day) ?

With my 2 1080s and 2060, I was doing 800 P per day for n=22 manual sieving.

At a removal rate of 1.5 candidates per P, I was removing 1200 candidates per day.

OK. You're sieving 800 P/day. You see that lot of factors were found.

Question #1. How many of these factors are really removing a candidate (i.e. candidate wasn't removed earlier by smaller factors)?

Yves has formulas for everything related to GFN. He also has a formula to calculate number of candidates left at given sieving depth and range. Current GFN-22 sieving depth is 1100000P and range is 2G. How many candidates will be removed between 1100000P and 1100000+800P ? Put both depths to formula and find a difference. The answer is (you have to trust my word) 6055.

Question #2. How many of these 6055 factors are useful to us?

There is a problem with candidates located too far from our current position in search. Sieving can find these factors "for free", up to 2G, but why - if we'll need, for example, 100 years to reach this range?

So we use 5 years prediction for "usable" range, based on progress for few last years. And the sad truth is that prediction (advance of 'b') for GFN-22 is only 245000!

You removed 6055 from 2G range. How may candidates are within 245K range?

6055 * 245000 / 2000000000 = 0,7417375

Multiply by two due to DC tasks. So, your whole day of sieving on 3 GPUs saved only 1,5 useful (within next 5 years) tasks.

What is duration of real tasks on these GPUs?

If you go to manual sieving, and click on "show stats", it shows stats for all GFN manual sieving. Go to GFN n=22, and click "+" to expand all GFN n=22 stats. Go all of the way to the end of n=22 stats.
User walli shows up last doing 600P jobs, and removes from the sieve about 900 candidates for each job. That's 1.5 candidates removed per P.

It also shows factors found as about 3.8. That means 1.5 candidates removed per P divided by 3.8 factors found = about 40% of factors found result in a candidate removal.
Obviously as you sieve more, the % of factors resulting in a candidate removal will slowly decrease.

As to your question #1, from actual sieve job stats near your range, 800P at 1.5 candidates removed per P = 1200 candidates removed per day, not your 6055.

As to your question #2, your usable range of 245,000 is way too small. Forget about DYFL?
DYFL is already to 925,000 for GFN22. And if a World record GIMP is found, DYFL probably will be bumped. So a much more reasonable 5 year range is 2,000,000.

So, 1200 * 2,000,000 / 2,000,000,000 = 1.2 * 2 (for DC tasks) = 2.4 useful candidates removed per day via manual sieving. Along with the equivalent of 2,400 other candidates removed from sieve.

It seems such a waste of GPU resources to me to remove 1 GFN22 candidate per day instead of 1200 via manual sieving.

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Message 147362 - Posted: 4 Jan 2021 | 21:09:39 UTC - in response to Message 147361.

As to your question #1, from actual sieve job stats near your range, 800P at 1.5 candidates removed per P = 1200 candidates removed per day, not your 6055.

Manual sieving stats are rescaled to 400M sieving range. Sieving was started on 400M range and lately resieved to 2G, but Jim decided to keep all graph and stats in "old style" to simplify coding.

1200 candidates removed in 400M range are equal to 6000 candidates removed in 2G range. Your numbers matches my numbers exactly.

As to your question #2, your usable range of 245,000 is way too small.

As any prediction, it may be wrong, but it's based on facts about our throughput on each GFN project.

I recalculated predictions using current data.

2019-10-20, GFN-22 leading edge was 159180.
2021-01-04, GFN-22 leading edge is 188590

For more then a year. 'b' was advanced only by 29410 !

The prediction model is exponential, it considers that throughput in every year will be faster by 30% then previous one. After applying the formula, we'll get that in next 5 years leading edge of GFN-22 will be advanced by 285,5K - it's a bit better then our previous estimation of 245K, but not much. Expected leading edge in 2026 will be 474K. (This is mostly an answer for first post in this thread - GFN-22 is still on a looong way to meet DYFL).

DYFL is already to 925,000 for GFN22. And if a World record GIMP is found, DYFL probably will be bumped. So a much more reasonable 5 year range is 2,000,000.

Well... You're partially correct here.

You're absolutely wrong about "bumping". It's not working this way. It does not matter how far we bump starting point. We can start from anywhere, it'll not change number of usable candidates. What matter is how many candidates we test per year (and how far 'b' advances "naturally", by removing tested candidates).

You're right about... that we really forgot about DYFL! Candidates tested by DYFL were not included in our calculation of "usable ranges", although these two numbers should be summed up.

A prediction on DYFL is much better then on GFN-22. It may be advanced by 404K in 5 years. Summing this usable range with 285,5K from main search and rescaling number of factors to this sum, we'll have much better results - your system removes 2,09 usable candidates per day.

Now I'm asking once again: what are runtimes of real GFN-22/DYFL tasks on your GPUs? When I'll know runtimes, I can calculate how efficient sieve will be and how far it should go to stay efficient in your setup.

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Message 147367 - Posted: 4 Jan 2021 | 23:06:20 UTC - in response to Message 147362.

Now I'm asking once again: what are runtimes of real GFN-22/DYFL tasks on your GPUs? When I'll know runtimes, I can calculate how efficient sieve will be and how far it should go to stay efficient in your setup.

The last line of his latest post may mean that the Genefer runtime is about a day. /JeppeSN

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Message 147368 - Posted: 4 Jan 2021 | 23:24:28 UTC

To get specific current timing for each GPU, I'll need to run small manual GFN22 sieve on each. Do you want the time for a GFN22 and/or DYFL for each card?
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Message 147370 - Posted: 4 Jan 2021 | 23:27:25 UTC - in response to Message 147367.

Now I'm asking once again: what are runtimes of real GFN-22/DYFL tasks on your GPUs? When I'll know runtimes, I can calculate how efficient sieve will be and how far it should go to stay efficient in your setup.

The last line of his latest post may mean that the Genefer runtime is about a day. /JeppeSN

Need to know *which* GFN you're talking about. DYFL uses a slower transform than GFN-22, so it takes about 25% longer to run.
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Message 147371 - Posted: 4 Jan 2021 | 23:38:31 UTC - in response to Message 147370.

Now I'm asking once again: what are runtimes of real GFN-22/DYFL tasks on your GPUs? When I'll know runtimes, I can calculate how efficient sieve will be and how far it should go to stay efficient in your setup.

The last line of his latest post may mean that the Genefer runtime is about a day. /JeppeSN

Need to know *which* GFN you're talking about. DYFL uses a slower transform than GFN-22, so it takes about 25% longer to run.

So, my question is do I run GFN-22 and/or DYFL for each card?
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Message 147378 - Posted: 5 Jan 2021 | 11:57:52 UTC - in response to Message 147371.

So, my question is do I run GFN-22 and/or DYFL for each card?

Yes please. As Mike noticed, both GFN-22 and DYFL must be tested because they're using different transforms.

If you're familiar with command line, it may be simpler to run tests manually, using, for example, candidates from current leading edges:

188626^4194304+1
925078^4194304+1

No need to run full test - after 2-3 minutes, Genefer will print "estimated time for ...". Write down the time, you can abort test at this point. I found one DYFL task in your results, Genefer' estimate was 54 hours and real runtime was 55 hours. Such precision will be enough.

If you're not familiar with command line, you can run tasks in Boinc and abort them after 5 minutes. We will see estimated runtime in stderr output of your tasks.

Message boards : Generalized Fermat Prime Search : Guessing the future of GFN-22 and DYFL