## How fast is a brute force prime gap hunt?

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• Just a quick question, what speed are people getting out of Jim s Gapper/CPAP combo? I remember seeing something like a search of 1100 billion being mentioned
Message 1 of 5 , Nov 1, 2001
Just a quick question, what speed are people getting out of Jim's Gapper/CPAP combo? I remember seeing something like a search of 1100 billion being mentioned in the last few days, but how long do such searches take? I've come up with some super-carmody-bogosity heuristic algorithmettes, and am wondering whether I should give up now, or pursue them.
I can scale CPU/MHz in my head. Anyone want to offer some figures? (And sorry, no I don't have an x86 machine I can try it on myself presently, which would appear to be the easiest way to find out.)
Phil

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• It depends on number size. :-) number 2^116 + k, k from 1 to 4,000,000,000 sieving up to 752,500,739 took 15 min, using my P450 From sieving program : **
Message 2 of 5 , Nov 1, 2001
It depends on number size. :-)

number 2^116 + k, k from 1 to 4,000,000,000
sieving up to 752,500,739 took 15 min, using my P450
From sieving program :

** There were 3563266 values removed in the last minute or so
22:04:56: 109887354 ski's left.. 750414773 is a factor of 2^116+2496270853
22:04:56: 109872444 k's left..
sieved up to prime 752500739.

File nude saved. 109872444 values stored

Then gapper :

--klip --- klip --

D:\matikka\primegaps\speedtest>gapper -g=2000 nude

+-------------------------------------------------------------------+
| Gapper v1.30 Finds consecutive prime gaps in a jfCPAP Sieve file |
| Built & designed on Sept 22-24 & Oct 27, by Jim Fougeron. |
| Free usage granted to all. Uses the GMP large math library |
+-------------------------------------------------------------------+

Gap is 2000
File nude loaded. 109872444 values left, sieved to: 752500739
Looking for gaps >= 2000 from 2^116+1 to 2^116+4000000001
4598117 prp chks, tested 2080800 gaps, k=3998697975 [4052.6 prps/s]

Time used 1135 seconds

D:\matikka\primegaps\speedtest>

--klip --- klip --

So it took 15 + 19 min to check that range. I used my P450 at home.
When I earlier mentioned some numbers I used more that one computer. Clock
time was
one day, but more than 10 cpu days.

about 170 billion k's per day using my P450.

Nuutti Kuosa

-----Original Message-----
From: Phil Carmody [mailto:fatphil@...]
Subject: [PrimeNumbers] How fast is a brute force prime gap hunt?

Just a quick question, what speed are people getting out of Jim's
Gapper/CPAP combo? I remember seeing something like a search of 1100 billion
being mentioned in the last few days, but how long do such searches take?
I've come up with some super-carmody-bogosity heuristic algorithmettes, and
am wondering whether I should give up now, or pursue them.
I can scale CPU/MHz in my head. Anyone want to offer some figures? (And
sorry, no I don't have an x86 machine I can try it on myself presently,
which would appear to be the easiest way to find out.)
Phil

Mathematics should not have to involve martyrdom;
Support Eric Weisstein, see http://mathworld.wolfram.com
Find the best deals on the web at AltaVista Shopping!
http://www.shopping.altavista.com

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

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• By the way. I have written small Excel macro that writes msdos bat files and those bat files keep my computers busy first running CPAPSieve.exe and then
Message 3 of 5 , Nov 1, 2001
By the way. I have written small Excel macro that writes msdos bat files and
those bat files keep my computers busy first running CPAPSieve.exe and then
gapper.
Here is example of these bat files :

CPAPSieve -O=output_1 -b=2 -n=198 -Mp=1600000000 -k=0000000 -K=4000006000
gapper -g=2700 output_1 >> result_p3000_1.log
del output_1
CPAPSieve -O=output_2 -b=2 -n=198 -Mp=1600000000 -k=4000000000 -K=8000006000
gapper -g=2700 output_2 >> result_p3000_1.log
del output_2

countinues up to

CPAPSieve -O=output_25 -b=2 -n=198 -Mp=1600000000 -k=96000000000 -K=10000000
6000
gapper -g=2700 output_25 >> result_p3000_1.log
del output_25

Yours,

Nuutti

-----Original Message-----
From: Nuutti Kuosa [mailto:nuutti.kuosa@...]
Subject: RE: [PrimeNumbers] How fast is a brute force prime gap hunt?

It depends on number size. :-)

number 2^116 + k, k from 1 to 4,000,000,000
sieving up to 752,500,739 took 15 min, using my P450
From sieving program :

** There were 3563266 values removed in the last minute or so
22:04:56: 109887354 ski's left.. 750414773 is a factor of 2^116+2496270853
22:04:56: 109872444 k's left..
sieved up to prime 752500739.

File nude saved. 109872444 values stored

Then gapper :

--klip --- klip --

D:\matikka\primegaps\speedtest>gapper -g=2000 nude

+-------------------------------------------------------------------+
| Gapper v1.30 Finds consecutive prime gaps in a jfCPAP Sieve file |
| Built & designed on Sept 22-24 & Oct 27, by Jim Fougeron. |
| Free usage granted to all. Uses the GMP large math library |
+-------------------------------------------------------------------+

Gap is 2000
File nude loaded. 109872444 values left, sieved to: 752500739
Looking for gaps >= 2000 from 2^116+1 to 2^116+4000000001
4598117 prp chks, tested 2080800 gaps, k=3998697975 [4052.6 prps/s]

Time used 1135 seconds

D:\matikka\primegaps\speedtest>

--klip --- klip --

So it took 15 + 19 min to check that range. I used my P450 at home.
When I earlier mentioned some numbers I used more that one computer. Clock
time was
one day, but more than 10 cpu days.

about 170 billion k's per day using my P450.

Nuutti Kuosa

-----Original Message-----
From: Phil Carmody [mailto:fatphil@...]
Subject: [PrimeNumbers] How fast is a brute force prime gap hunt?

Just a quick question, what speed are people getting out of Jim's
Gapper/CPAP combo? I remember seeing something like a search of 1100 billion
being mentioned in the last few days, but how long do such searches take?
I've come up with some super-carmody-bogosity heuristic algorithmettes, and
am wondering whether I should give up now, or pursue them.
I can scale CPU/MHz in my head. Anyone want to offer some figures? (And
sorry, no I don't have an x86 machine I can try it on myself presently,
which would appear to be the easiest way to find out.)
Phil

Mathematics should not have to involve martyrdom;
Support Eric Weisstein, see http://mathworld.wolfram.com
Find the best deals on the web at AltaVista Shopping!
http://www.shopping.altavista.com

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
• ... It also depends heavily on the memory in the PC. More memory, and CPAPSieve will process larger ranges, and you can possibly push the sieve a little
Message 4 of 5 , Nov 1, 2001
--- In primenumbers@y..., "Nuutti Kuosa" <nuutti.kuosa@i...> wrote:
> It depends on number size. :-)

It also depends heavily on the memory in the PC. More memory, and
CPAPSieve will process larger ranges, and you can possibly push the
sieve a little higher (10-100x), thus gapper will have to check
fewer numbers on average to find prp's. It certainly takes some
"fine tuning" to determine what the best sized range to work with, and
what the best level is to sieve to, to minimize the time taken to
process a range. You are currently running at 510 to 520 seconds per
billion range (as listed 4 billion in 34 minutes)

> number 2^116 + k, k from 1 to 4,000,000,000
> sieving up to 752,500,739 took 15 min, using my P450
> From sieving program :
>
> ** There were 3563266 values removed in the last minute or so
> 22:04:56: 109887354 ski's left.. 750414773 is a factor of
2^116+2496270853
> 22:04:56: 109872444 k's left..
> sieved up to prime 752500739.
>
> File nude saved. 109872444 values stored
>
> Then gapper :
>
> --klip --- klip --
>
> D:\matikka\primegaps\speedtest>gapper -g=2000 nude
>
> +-------------------------------------------------------------------
+
> | Gapper v1.30 Finds consecutive prime gaps in a jfCPAP Sieve file
|
> | Built & designed on Sept 22-24 & Oct 27, by Jim Fougeron.
|
> | Free usage granted to all. Uses the GMP large math library
|
> +-------------------------------------------------------------------
+
>
> Gap is 2000
> File nude loaded. 109872444 values left, sieved to: 752500739
> Looking for gaps >= 2000 from 2^116+1 to 2^116+4000000001
> 4598117 prp chks, tested 2080800 gaps, k=3998697975 [4052.6 prps/s]
>
> Time used 1135 seconds
>
> D:\matikka\primegaps\speedtest>
>
> --klip --- klip --
>
> So it took 15 + 19 min to check that range.

There is probably at least another minute added in for the file I/O.
Even with the compression in the saved files, writing the 75mb file
then re-reading it in (along with testing each and every bit to write
the file, and then resetting them upon re-reading) takes some time.
I would say probably 35s to save and 25s to read for this size (on a
P450) is probably close to reality.

>I used my P450 at home.
> When I earlier mentioned some numbers I used more that one
computer. Clock
> time was
> one day, but more than 10 cpu days.
>
> about 170 billion k's per day using my P450.
>
> Nuutti Kuosa
>
> -----Original Message-----
> From: Phil Carmody [mailto:fatphil@a...]
> Sent: 1. marraskuuta 2001 21:23
> Subject: [PrimeNumbers] How fast is a brute force prime gap hunt?
>
>
> Just a quick question, what speed are people getting out of Jim's
> Gapper/CPAP combo? I remember seeing something like a search of
1100 billion
> being mentioned in the last few days, but how long do such searches
take?
> I've come up with some super-carmody-bogosity heuristic
algorithmettes, and
> am wondering whether I should give up now, or pursue them.
> I can scale CPU/MHz in my head. Anyone want to offer some figures?
(And
> sorry, no I don't have an x86 machine I can try it on myself
presently,
> which would appear to be the easiest way to find out.)
> Phil
>
> Mathematics should not have to involve martyrdom;
> Support Eric Weisstein, see http://mathworld.wolfram.com
> Find the best deals on the web at AltaVista Shopping!
> http://www.shopping.altavista.com
>
> Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
> The Prime Pages : http://www.primepages.org
>
>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
• When selecting how high to sieve I have tried to balance these numbers (from my earlier posting) : ... I have calculated ratio 109872444 values left / 4598117
Message 5 of 5 , Nov 1, 2001
When selecting how high to sieve I have tried to balance
these numbers (from my earlier posting) :
sieve :
> ** There were 3563266 values removed in the last minute or so

and gapper:
>File nude loaded. 109872444 values left, sieved to: 752500739
> Looking for gaps >= 2000 from 2^116+1 to 2^116+4000000001
> 4598117 prp chks, tested 2080800 gaps, k=3998697975 [4052.6 prps/s]

I have calculated ratio 109872444 values left / 4598117 prp chks = 23,90
and multipled prps/s and this ratio = 23,90 * 4053 =96868 effective prps / s
= 5,812,080 effective prps /min

so I sieved little too high (may be one minute). But right sieving amount
depends on size of memory.

Yours,

Nuutti

-----Original Message-----
From: jfoug@... [mailto:jfoug@...]
Subject: [PrimeNumbers] Re: How fast is a brute force prime gap hunt?

--- In primenumbers@y..., "Nuutti Kuosa" <nuutti.kuosa@i...> wrote:
> It depends on number size. :-)

It also depends heavily on the memory in the PC. More memory, and
CPAPSieve will process larger ranges, and you can possibly push the
sieve a little higher (10-100x), thus gapper will have to check
fewer numbers on average to find prp's. It certainly takes some
"fine tuning" to determine what the best sized range to work with, and
what the best level is to sieve to, to minimize the time taken to
process a range. You are currently running at 510 to 520 seconds per
billion range (as listed 4 billion in 34 minutes)

> number 2^116 + k, k from 1 to 4,000,000,000
> sieving up to 752,500,739 took 15 min, using my P450
> From sieving program :
>
> ** There were 3563266 values removed in the last minute or so
> 22:04:56: 109887354 ski's left.. 750414773 is a factor of
2^116+2496270853
> 22:04:56: 109872444 k's left..
> sieved up to prime 752500739.
>
> File nude saved. 109872444 values stored
>
> Then gapper :
>
> --klip --- klip --
>
> D:\matikka\primegaps\speedtest>gapper -g=2000 nude
>
> +-------------------------------------------------------------------
+
> | Gapper v1.30 Finds consecutive prime gaps in a jfCPAP Sieve file
|
> | Built & designed on Sept 22-24 & Oct 27, by Jim Fougeron.
|
> | Free usage granted to all. Uses the GMP large math library
|
> +-------------------------------------------------------------------
+
>
> Gap is 2000
> File nude loaded. 109872444 values left, sieved to: 752500739
> Looking for gaps >= 2000 from 2^116+1 to 2^116+4000000001
> 4598117 prp chks, tested 2080800 gaps, k=3998697975 [4052.6 prps/s]
>
> Time used 1135 seconds
>
> D:\matikka\primegaps\speedtest>
>
> --klip --- klip --
>
> So it took 15 + 19 min to check that range.

There is probably at least another minute added in for the file I/O.
Even with the compression in the saved files, writing the 75mb file
then re-reading it in (along with testing each and every bit to write
the file, and then resetting them upon re-reading) takes some time.
I would say probably 35s to save and 25s to read for this size (on a
P450) is probably close to reality.

>I used my P450 at home.
> When I earlier mentioned some numbers I used more that one
computer. Clock
> time was
> one day, but more than 10 cpu days.
>
> about 170 billion k's per day using my P450.
>
> Nuutti Kuosa
>
> -----Original Message-----
> From: Phil Carmody [mailto:fatphil@a...]
> Sent: 1. marraskuuta 2001 21:23
> Subject: [PrimeNumbers] How fast is a brute force prime gap hunt?
>
>
> Just a quick question, what speed are people getting out of Jim's
> Gapper/CPAP combo? I remember seeing something like a search of
1100 billion
> being mentioned in the last few days, but how long do such searches
take?
> I've come up with some super-carmody-bogosity heuristic
algorithmettes, and
> am wondering whether I should give up now, or pursue them.
> I can scale CPU/MHz in my head. Anyone want to offer some figures?
(And
> sorry, no I don't have an x86 machine I can try it on myself
presently,
> which would appear to be the easiest way to find out.)
> Phil
>
> Mathematics should not have to involve martyrdom;
> Support Eric Weisstein, see http://mathworld.wolfram.com
> Find the best deals on the web at AltaVista Shopping!
> http://www.shopping.altavista.com
>
> Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
> The Prime Pages : http://www.primepages.org
>
>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

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