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Message boards : Number crunching : Start discussing new goals for 2021

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[AF>Le_Pommier] Aillas
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Message 146263 - Posted: 7 Dec 2020 | 13:25:05 UTC

Hi,

[Edit: Updated goal at the end]

2020 is near its end and it was a astonishing year for Primegrid, with a lot of new records, new applications, new staff, new....

Talking about statistics, what can we expect or wish for next year?

With LLR2 application, we almost double the computation power, say 80%.

Looking at the 2020 current results (even if Nov+Dec were already on LLR2 and Dec not finished):

+----------+-----------------------------------------------------------------------+-------+ | | MP# | | | |-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ Total | | | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | | +----------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+ | Total | 14 | 44 | 12 | 9 | 17 | 6 | 8 | 8 | 8 | 17 | 16 | 2 | 161 | +----------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+

161 + 80% = 289 MP. Rounded to 300 (+11)

Primegrid current total of MP is 566. 566 + 289 = 855 MP (rounded to 900, +45)

I suggest first goal of 300 MP for 2021. Challenging? Irrealist?

Second one, a global MP for PG about 900 MP. That implies a target of 345 MP for 2021... Ouch... That's a real challange. :)

To beat 2020 record is not a challenge for 2021. With the new application, it should be easy.

2020 - Found 2 primes in ESP, TRP, PSP or SOB projects: Found only 1. We can keep this one for 2021

We can add one for 321/27/121. The 2 that were found in 2020 were new one since 8 years or 3 years..... We can expect one more or add a challenging goal of 2.

No prime for Primorial or Factorial for years now. But they are PSA projects. Add one for challenge.

CUL/WOO project: One?

G20, we don't find one this year (yet) but already found 2, one by year. We can set a global challenge for G20/21/...: 2

To resume:

- Found 300 MP - Reach the 900 Mega Primes overall (-> 345 MP!!) - Found 2 primes in ESP, TRP, PSP or SOB projects - Found 2 primes in 27, 121 or 321 projects - Found 1 primes in Cullen or Woodall projects - Found 1 prime in Primorial or Factorial projects - Found 2 primes for G20 or higher projects

What do you think? Step too high?
Do you have other proposals?

[Live updating goals for 2021]

- Find 500 MP
- Reach the 1000 Mega Primes overall (-> 434 MP)
- Find 2 primes in TRP project
- Find 1 prime in 27, 121 or 321 projects
- Find 1 prime in Cullen or Woodall projects
- Find 1 prime in Primorial or Factorial projects
- Find 2 primes for G20 or higher projects
- Find 1 Fermat Divisor
- Find a croreprime or a hebdoprime (10 MP)
- Find 100 PPS-MEGA
- Find 100 GFN-17
- Reach 2,000,000 Workunits completed (Pending)

____________
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Message 146265 - Posted: 7 Dec 2020 | 13:48:55 UTC

- Found 300 MP
- Reach the 900 Mega Primes overall (-> 345 MP!!)
- Found 2 primes in ESP, TRP, PSP or SOB projects
- Found 2 primes in 27, 121 or 321 projects
- Found 1 primes in Cullen or Woodall projects
- Found 1 prime in Primorial or Factorial projects
- Found 2 primes for G20 or higher projects

But I think, that we maybe should have it look like this:

- Find 300 MP
- Reach the 900 Mega Primes overall (-> 345 MP!!)
- Find 2 primes in TRP project *
- Find 1 prime in 27, 121 or 321 projects **
- Find 1 prime in Cullen or Woodall projects
- Find 1 prime in Primorial or Factorial projects
- Find 2 primes for G20 or higher projects

* The reason behind this, is that we need to sieve ALL base 2 conjectures together, in the future, so to increase speed and efficiency of that sieve, we need to put a much higher focus on TRP, compared to ESP, PSP and SoB. 2 primes is not unachieveable, since TRP is the most primelikely conjecture - but it will require a 14 day challenge and some users putting their focus on TRP during TourDePrimes :)

** Lowered, due to being unattainable. 2 primes in total for these 3 low prime producing projects, simply is to optimistic. The users may prove me wrong, but 1 seems more realistical (even though it may also fail to be achieved).

- Reach 2,000,000 Workunits completed on TRP (May in itself, resolve the "Find 2 primes in TRP project" goal)

Just my thoughts :)

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Message 146267 - Posted: 7 Dec 2020 | 13:53:43 UTC

I think you might add find 1 Fermat Divisor as a goal. Improbable, but not impossible as we continue to push the DIV project with LLR2.

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Message 146269 - Posted: 7 Dec 2020 | 14:45:42 UTC

I will be doing WW for as long as possible whilst also bringing LLRs up to their next million levels. Interjected by challenges of course. TdP I dunno yet.

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Message 146287 - Posted: 7 Dec 2020 | 16:42:40 UTC

A 10 Mega prime is THE goal for 2021!!! SOB or GFN-21 (or better!).
In 2021, more than 1000 megaprimes will be known, there is no doubt about that: a mega is not a challenge anymore.
The first 10M was found in 2008, it is now time to get down to serious work ;o)

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Message 146302 - Posted: 7 Dec 2020 | 18:21:47 UTC - in response to Message 146287.

...
In 2021, more than 1000 megaprimes will be known, there is no doubt about that: a mega is not a challenge anymore.
...

Indeed.
Even I got one, ha.

____________
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Message 146309 - Posted: 7 Dec 2020 | 19:10:20 UTC - in response to Message 146287.

In 2021, more than 1000 megaprimes will be known, there is no doubt about that: a mega is not a challenge anymore.

Really ?
Having got the smallest megaprime I was aiming for an even smaller one in 2021 !

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Message 146311 - Posted: 7 Dec 2020 | 20:20:36 UTC

- Reach the 900 Mega Primes overall (-> 345 MP!!)

Maybe we can round this one up to 365 mega primes overall? (average of 1 mega prime / day)

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Message 146317 - Posted: 7 Dec 2020 | 21:45:44 UTC - in response to Message 146287.

A 10 Mega prime is THE goal for 2021!!! SOB or GFN-21 (or better!).
In 2021, more than 1000 megaprimes will be known, there is no doubt about that: a mega is not a challenge anymore.
The first 10M was found in 2008, it is now time to get down to serious work ;o)

We need to decide if a 10'000'000-digit prime is to be called a croreprime or a hebdoprime. /JeppeSN

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Message 146318 - Posted: 7 Dec 2020 | 22:20:33 UTC - in response to Message 146317.

A 10 Mega prime is THE goal for 2021!!! SOB or GFN-21 (or better!).
In 2021, more than 1000 megaprimes will be known, there is no doubt about that: a mega is not a challenge anymore.
The first 10M was found in 2008, it is now time to get down to serious work ;o)

We need to decide if a 10'000'000-digit prime is to be called a croreprime or a hebdoprime. /JeppeSN

You have my vote for hebdoprime. I love metric and I love obsolete terms, so this one ticks both boxes :)

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Message 146320 - Posted: 7 Dec 2020 | 22:28:12 UTC - in response to Message 146317.

We need to decide if a 10'000'000-digit prime is to be called a croreprime or a hebdoprime. /JeppeSN

In French, hebdo means weekly... a weekly prime :o(
I like crore, it's important to remember that there are different numbering systems.

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Message 146321 - Posted: 7 Dec 2020 | 22:39:14 UTC

New term "Hardcrore" ;)

or "really difficult to get, really big prime" :P
____________
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Message 146323 - Posted: 7 Dec 2020 | 23:56:31 UTC

How about 10MdP for 10 Million digit Prime?
____________

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Message 146329 - Posted: 8 Dec 2020 | 7:18:39 UTC - in response to Message 146320.

We need to decide if a 10'000'000-digit prime is to be called a croreprime or a hebdoprime. /JeppeSN

In French, hebdo means weekly... a weekly prime :o(
I like crore, it's important to remember that there are different numbering systems.

Both senses of "hebdo" are derived from a Greek word meaning seventh. A weekly magazine is a magazine that comes out every seventh day. And the number 10,000,000 (written as 1,00,00,000 in South Asia) is the seventh power of ten.
Search for croreprimes (hebdoprimes). Where are PrimeGrid's? ;-)

/JeppeSN

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Message 146330 - Posted: 8 Dec 2020 | 7:47:48 UTC - in response to Message 146329.

To reach the goal of 1000 MP overall, with current status, that means we need to find 434 new MP next year (minus December findings).
So I've rounded the overall goal to 500 new MP for next year :)
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[AF>Le_Pommier] Aillas
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Message 146331 - Posted: 8 Dec 2020 | 7:49:17 UTC - in response to Message 146265.

- Reach 2,000,000 Workunits completed on TRP (May in itself, resolve the "Find 2 primes in TRP project" goal)

Just my thoughts :)

I've added it to the list, but I don't know where to get this information :)

 I think I found it. The 'Total' 'Complete' info in the TRP sub project page.
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[AF>Le_Pommier] Aillas
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Message 146362 - Posted: 8 Dec 2020 | 15:51:23 UTC - in response to Message 146335.

- Find 100 PPS-MEGA
- Find 100 GFN-17
____________
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Message 146375 - Posted: 8 Dec 2020 | 18:04:34 UTC - in response to Message 146263.

All good goals, I especially root for those three:

- Find 1 prime in Cullen or Woodall projects
- Find 1 prime in Primorial or Factorial projects
- Find 1 Fermat Divisor

Only 9000 WUs left in Factorial prime search until 279999! +-1 and last prime was around 208000!, so I'm pessimistic anything will turn up before the project stops. Would be nice to have the largest factorial back to PG though.

Cullen is overdue though. Largest known one is from 11.5 years ago with n ~ 6 million, now we've reached 20 million. Almost 14 million composite numbers in a row...

And Fermat divisors are just a very nice thing to me. Fermat would probably never have imagined that 400 years later people would use machines to compute divisors of Fermat numbers.
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

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Message 146391 - Posted: 8 Dec 2020 | 19:07:51 UTC - in response to Message 146375.

Only 9000 WUs left in Factorial prime search until 279999! +-1 and last prime was around 208000!, so I'm pessimistic anything will turn up before the project stops. Would be nice to have the largest factorial back to PG though.

For factorial/primorial I believe that they were sieved to much higher n than what is loaded into the server.

Since these are not BOINC projects, the question will be whether or not PRPNet can handle large numbers of users trying to get work at the same time. I think it will be okay as long as there are not more than a few connections per second, but since it is PRPNet and not BOINC, I would not expect as much participation.

I suspect that neither of these projects is sieved deeply enough. mfsieve and psieve now have AVX code (up to 2^52) which was a nice performance boost. No AVX2 code yet (as I don't have an AVX2 cpu to test on). I think that mfsievecl (with OpenCL support) will be faster than mfsieve (with AVX), but I haven't compared the speed.

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Message 146403 - Posted: 8 Dec 2020 | 21:13:51 UTC

Goals for 2021:

-Break DO servers in the middle of a challenge (again).
-Find a CUL / Woo Prime.
-Find the first GFN-21 prime.
-Bring back GFN Manual Sieve, this time as Boinc Project.
-Have the second user achieve the Shut Up! badge :)

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Message 146405 - Posted: 8 Dec 2020 | 21:20:13 UTC

Only one, the rest better cancel: push SoB forward up to sieve files run-out.
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Message 146407 - Posted: 8 Dec 2020 | 22:50:31 UTC

Goal for 2021

-Find the first GFN-21 prime.

Also was goal for 2018, 2019 and 2020, but its gotta happen sometime ;)
Over 30% the way there so .....any day now Ã°Å¸â„¢Æ’
____________
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Message 146412 - Posted: 9 Dec 2020 | 0:14:29 UTC

I think some of the posted goals will require some extended Challenges to get enough work done to get to the goals, otherwise too many people will haphazardly crunch for something they like or what fits their own needs at the time.

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Message 146413 - Posted: 9 Dec 2020 | 0:21:18 UTC

Complete search for Wieferich search to 2^64. This will require updated software.

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Message 146443 - Posted: 9 Dec 2020 | 15:00:14 UTC - in response to Message 146403.

-Bring back GFN Manual Sieve, this time as Boinc Project.

Well then it's not manual anymore... :P
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Proth "SoB": 44243*2^440969+1

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Message 146444 - Posted: 9 Dec 2020 | 15:05:13 UTC - in response to Message 146443.

-Bring back GFN Manual Sieve, this time as Boinc Project.

Well then it's not manual anymore... :P

Also, any discussion of GFN sieving (or LLR sieving) needs to be done in the context of fast proof checking and the fact that at some point we'll no longer be running GFN double check tasks. That cuts the optimal sieving point in half, and therefore cuts not only the Genefer time in half, but the sieving time in half too.

Bottom line is if we didn't need sieving before, we certainly don't now.
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Message 146454 - Posted: 9 Dec 2020 | 19:07:16 UTC - in response to Message 146444.

-Bring back GFN Manual Sieve, this time as Boinc Project.

Well then it's not manual anymore... :P

Also, any discussion of GFN sieving (or LLR sieving) needs to be done in the context of fast proof checking and the fact that at some point we'll no longer be running GFN double check tasks. That cuts the optimal sieving point in half, and therefore cuts not only the Genefer time in half, but the sieving time in half too.

Bottom line is if we didn't need sieving before, we certainly don't now.

I was under the impression that GFN23 was nowhere near close to optimal, if we ever got to need it for DYFL, and was only really closed as a result of manual sieve being closed in general.

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Message 146455 - Posted: 9 Dec 2020 | 19:30:40 UTC - in response to Message 146454.

-Bring back GFN Manual Sieve, this time as Boinc Project.

Well then it's not manual anymore... :P

Also, any discussion of GFN sieving (or LLR sieving) needs to be done in the context of fast proof checking and the fact that at some point we'll no longer be running GFN double check tasks. That cuts the optimal sieving point in half, and therefore cuts not only the Genefer time in half, but the sieving time in half too.

Bottom line is if we didn't need sieving before, we certainly don't now.

I was under the impression that GFN23 was nowhere near close to optimal, if we ever got to need it for DYFL, and was only really closed as a result of manual sieve being closed in general.

We've hardly done any GFN 23 sieving, but to get started, you don't need to be "optimal". The way sieving works, you find most of the factors you're ever going to find in the first week or even the first hour of sieving.

So while it may not be optimal, it's definitely usable.

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Message 146490 - Posted: 10 Dec 2020 | 18:02:19 UTC - in response to Message 146391.

For factorial/primorial I believe that they were sieved to much higher n than what is loaded into the server.

I always assumed that was the sieve depth, all the better if not.

Since these are not BOINC projects, the question will be whether or not PRPNet can handle large numbers of users trying to get work at the same time. I think it will be okay as long as there are not more than a few connections per second, but since it is PRPNet and not BOINC, I would not expect as much participation.

I don't think many users know or care about these goals. And if it involves setting up PRPnet, even less will want to participate. Factorials are around 10^1 300 000 now, which makes the prime probability of one of them approximately 1:280 000. Not taking into account that the probability is ever decreasing with increasing n, another one should appear before we reach n = 300 000 (as we check both + and -). At the current rate this means a couple of years though...

I suspect that neither of these projects is sieved deeply enough. mfsieve and psieve now have AVX code (up to 2^52) which was a nice performance boost. No AVX2 code yet (as I don't have an AVX2 cpu to test on). I think that mfsievecl (with OpenCL support) will be faster than mfsieve (with AVX), but I haven't compared the speed.

The "up to 2^52" means prime factors up to limit can be used? And do you know up to which n and which p the factorials/primorials have been sieved? I think I asked that before, but have a hazy recollection of nobody knowing for sure.

I would like to try if mfsievecl works well beyond current ranges. Do you have win64 binaries? On the other hand, maybe it should stay at PSA, so the WW subproject gets all the GPU power... ;)
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

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Message 146510 - Posted: 11 Dec 2020 | 0:31:23 UTC - in response to Message 146490.

You can find the mtsieve source and all Windows binaries using the framework here: https://sourceforge.net/projects/mtsieve/

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Message 146555 - Posted: 11 Dec 2020 | 18:26:51 UTC - in response to Message 146510.

I was searching for mfsieve, didn't know it was part of mtsieve, thanks.

The prime limit of 2^52 is probably the reason why sieving came to an end.

Sorry for OT...
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

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Message 146564 - Posted: 11 Dec 2020 | 22:46:48 UTC - in response to Message 146555.

I was searching for mfsieve, didn't know it was part of mtsieve, thanks.

The prime limit of 2^52 is probably the reason why sieving came to an end.

Sorry for OT...

It shouldn't be too hard to support up to 2^62, although AVX code cannot be used between 2^52 and 2^62.

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Message 146565 - Posted: 11 Dec 2020 | 22:50:12 UTC - in response to Message 146564.

I was searching for mfsieve, didn't know it was part of mtsieve, thanks.

The prime limit of 2^52 is probably the reason why sieving came to an end.

Sorry for OT...

It shouldn't be too hard to support up to 2^62, although AVX code cannot be used between 2^52 and 2^62.

This has me quite curious.

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Message 146590 - Posted: 12 Dec 2020 | 10:01:54 UTC - in response to Message 146565.

It shouldn't be too hard to support up to 2^62, although AVX code cannot be used between 2^52 and 2^62.

This has me quite curious.

AVX2 instruction set has no 64-bit multiplication. Four 64-bit integers can be added or subtracted but the multiplication is 32x32 => 64.
For this reason, basic 64-bit integer instructions are faster. If four primes are tested simultaneouly, the latency of the MUL operation (3-4 cycles) can be hidden and the throughput is 1 cycle.
The best algorithm for sieving is Montgomery modular multiplication. The modular multiplication of two numbers for any p < 2^64 is calculated with 3 multiplications, 1 subtraction and 1 conditional addition. The theoretical speed limit of the modular multiplication of two 64-bit integers is 3 cycles because the subtraction and conditional addition can be executed in parallel on another unit of the core. It's difficult to achieve because of the small number of registers of x64 but with hyperthreading, we are close to the limit.

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Message 146597 - Posted: 12 Dec 2020 | 12:31:54 UTC - in response to Message 146590.

Is it related to the fact that the double-precision floating-point format uses 52 bits (out of 64) for its mantissa component? /JeppeSN

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Message 146598 - Posted: 12 Dec 2020 | 13:24:07 UTC - in response to Message 146597.

Is it related to the fact that the double-precision floating-point format uses 52 bits (out of 64) for its mantissa component? /JeppeSN

Yes. x mod p = x - p * [x/p]. With FP64, p_inv = 1.0/p can be precomputed and x mod p = x - p * [x * p_inv]. This is a FP implementation of Barrett reduction.
AVX instruction set can test four primes simultaneouly.

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Message 146600 - Posted: 12 Dec 2020 | 14:16:54 UTC

I can modify the main loop (which is in asm) to use extended floating point, (which is x86 only) to support sieving p up to 2^62.

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Message 146607 - Posted: 12 Dec 2020 | 17:48:28 UTC - in response to Message 146600.

I can modify the main loop (which is in asm) to use extended floating point, (which is x86 only) to support sieving p up to 2^62.

Actually I do have extended floating point code, but am not using it, probably because mmx is faster, but the mmx code is only used for p < maxn.

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Message 146616 - Posted: 13 Dec 2020 | 2:44:30 UTC - in response to Message 146455.

We've hardly done any GFN 23 sieving, but to get started, you don't need to be "optimal". The way sieving works, you find most of the factors you're ever going to find in the first week or even the first hour of sieving.

So while it may not be optimal, it's definitely usable.

S out of curoisity is there a GFN-24 thru GFN-100 etc set of numbers to crunch at some point in the future? I'm not asking for a time frame just IF there are possible prime numbers that fit into those categories too.

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Message 146621 - Posted: 13 Dec 2020 | 9:00:17 UTC - in response to Message 146616.

S out of curoisity is there a GFN-24 thru GFN-100 etc set of numbers to crunch at some point in the future? I'm not asking for a time frame just IF there are possible prime numbers that fit into those categories too.

Technically speaking, these GFN exponents can be sieved. But the size of the remaining candidates grows quickly and the primality test of these numbers can't yet be computed in a reasonable amount of time.
Because of rapid advances in hardware technology, it's unnecessary to sieve a range that will be tested in 10 or 20 years' time.
GFN-22 > 25M digits GFN-23 > 50M digits GFN-24 > 100M digits GFN-25 > 250M digits GFN-26 > 500M digits GFN-27 > 1000M digits

Bur
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Message 146628 - Posted: 13 Dec 2020 | 17:17:36 UTC - in response to Message 146600.

I can modify the main loop (which is in asm) to use extended floating point, (which is x86 only) to support sieving p up to 2^62.
That sounds good. We'd have to find out though, how big the current pools is. Does it end where PRPnet currently says it does, ot is there a reserve of unprepared candidates.

Especially if fact/primorials will ever be moved to PG more sieving would be required.

Since this is really off-topic, I opened a new thread: PSA forum
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Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

mikey

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Message 147240 - Posted: 1 Jan 2021 | 11:29:07 UTC - in response to Message 146621.

S out of curoisity is there a GFN-24 thru GFN-100 etc set of numbers to crunch at some point in the future? I'm not asking for a time frame just IF there are possible prime numbers that fit into those categories too.

Technically speaking, these GFN exponents can be sieved. But the size of the remaining candidates grows quickly and the primality test of these numbers can't yet be computed in a reasonable amount of time.
Because of rapid advances in hardware technology, it's unnecessary to sieve a range that will be tested in 10 or 20 years' time.
GFN-22 > 25M digits GFN-23 > 50M digits GFN-24 > 100M digits GFN-25 > 250M digits GFN-26 > 500M digits GFN-27 > 1000M digits

Thank you

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