## 3019 Digit Ap6

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• Hi All I took a break from my current main search to demonstrate the practicality of using Newpgen to extend aps, when pfgw is the limiting factor as I
Message 1 of 4 , Aug 17, 2010
Hi All

I took a break from my current main search to demonstrate the practicality of using Newpgen to extend aps, when pfgw is the limiting factor as I recently suggested in

http://tech.groups.yahoo.com/group/primeform/message/10478

In this case
newpgen was used to sieve 1^e8 candidates of form
n*7001#+1 (n = 1,000,000,001-1,100,000,000)
candidates from n=1,000,000,001 to 1,056,606,126 pfgwed
(note. pfgw is still actually running, I just grabbed a copy of the pfgw.log at this point deciding I probably had enough candidates to make the following worthwhile).
128,536 prps
This yielded
9,380,118 ap3s
14,215 ap4s
23 ap5s
0 ap6s
Now for the fun bit (all of which was done in less than 24 hours)
of the 9,380,118 ap3s there were
6,245,377 chances of an ap4
Of these 1,274,166 were spanned
(term 1 with n < 1,000,000,001 and term 5 with n > 1056606126)
newpgenning the 1st terms (to only 1^e10, while I coded program to manipulate results and produce candidates for next step) reduced this to
490,487
newpgenning the matching 5th (to 1^e11) yielded
188,505, increased probability, spanned ap5s.
I then ran a pfgw script which did, basically the following
If term1 1 prp then
If term 5 prp
(test term 0 and test term 6)
This yielded (after 18 hours = 54 GHz hrs)
1,129 ap4s
13 ap5
1 ap6

cheers
Ken

(967858482 + (\$n*19401803))*7001#+1 (n=0-5) AP6 of 3019 digit
primes.

cheers
Ken
• ... Congratulations, Ken, on a nice piece of work. (How to beat the pfgw bottleneck:-) I wonder, though, is the NewPGen ing really necessary? (It must be a bit
Message 2 of 4 , Aug 17, 2010
>
> Hi All
>
> I took a break from my current main search to demonstrate the practicality of using Newpgen to extend aps, when pfgw is the limiting factor as I recently suggested in
>
> http://tech.groups.yahoo.com/group/primeform/message/10478
>
> In this case
> newpgen was used to sieve 1^e8 candidates of form
> n*7001#+1 (n = 1,000,000,001-1,100,000,000)
> candidates from n=1,000,000,001 to 1,056,606,126 pfgwed
> (note. pfgw is still actually running, I just grabbed a copy of the pfgw.log at this point deciding I probably had enough candidates to make the following worthwhile).
> 128,536 prps
> This yielded
> 9,380,118 ap3s
> 14,215 ap4s
> 23 ap5s
> 0 ap6s
> Now for the fun bit (all of which was done in less than 24 hours)
> of the 9,380,118 ap3s there were
> 6,245,377 chances of an ap4
> Of these 1,274,166 were spanned
> (term 1 with n < 1,000,000,001 and term 5 with n > 1056606126)
> newpgenning the 1st terms (to only 1^e10, while I coded program to manipulate results and produce candidates for next step) reduced this to
> 490,487
> newpgenning the matching 5th (to 1^e11) yielded
> 188,505, increased probability, spanned ap5s.
> I then ran a pfgw script which did, basically the following
> If term1 1 prp then
> If term 5 prp
> (test term 0 and test term 6)
> This yielded (after 18 hours = 54 GHz hrs)
> 1,129 ap4s
> 13 ap5
> 1 ap6
>
> cheers
> Ken
>
>
> (967858482 + (\$n*19401803))*7001#+1 (n=0-5) AP6 of 3019 digit
> primes.

Congratulations, Ken, on a nice piece of work.
(How to beat the pfgw bottleneck:-)

I wonder, though, is the NewPGen'ing really necessary?
(It must be a bit of a pain to organise.)
At this size of number, pfgw -f would fair whip through those candidates, woudn't it?

Mike
• ... I believe NewPGen ing is definitely worthwhile On the machine I used pfgw -f 1*7001#+1 has factors: 14797 2*7001#+1 is composite: RES64: [C85147CB3425220A]
Message 3 of 4 , Aug 18, 2010
--- In primeform@yahoogroups.com, "mikeoakes2" <mikeoakes2@...> wrote:
>
>
>
> >
> > Hi All
> >
> > I took a break from my current main search to demonstrate the practicality of using Newpgen to extend aps, when pfgw is the limiting factor as I recently suggested in
> >
> > http://tech.groups.yahoo.com/group/primeform/message/10478
> >
> > In this case
> > newpgen was used to sieve 1^e8 candidates of form
> > n*7001#+1 (n = 1,000,000,001-1,100,000,000)
> > candidates from n=1,000,000,001 to 1,056,606,126 pfgwed
> > (note. pfgw is still actually running, I just grabbed a copy of the pfgw.log at this point deciding I probably had enough candidates to make the following worthwhile).
> > 128,536 prps
> > This yielded
> > 9,380,118 ap3s
> > 14,215 ap4s
> > 23 ap5s
> > 0 ap6s
> > Now for the fun bit (all of which was done in less than 24 hours)
> > of the 9,380,118 ap3s there were
> > 6,245,377 chances of an ap4
> > Of these 1,274,166 were spanned
> > (term 1 with n < 1,000,000,001 and term 5 with n > 1056606126)
> > newpgenning the 1st terms (to only 1^e10, while I coded program to manipulate results and produce candidates for next step) reduced this to
> > 490,487
> > newpgenning the matching 5th (to 1^e11) yielded
> > 188,505, increased probability, spanned ap5s.
> > I then ran a pfgw script which did, basically the following
> > If term1 1 prp then
> > If term 5 prp
> > (test term 0 and test term 6)
> > This yielded (after 18 hours = 54 GHz hrs)
> > 1,129 ap4s
> > 13 ap5
> > 1 ap6
> >
> > cheers
> > Ken
> >
> >
> > (967858482 + (\$n*19401803))*7001#+1 (n=0-5) AP6 of 3019 digit
> > primes.
>
> Congratulations, Ken, on a nice piece of work.
> (How to beat the pfgw bottleneck:-)
>
> I wonder, though, is the NewPGen'ing really necessary?

I believe NewPGen'ing is definitely worthwhile
On the machine I used
pfgw -f
1*7001#+1 has factors: 14797
2*7001#+1 is composite: RES64: [C85147CB3425220A] (0.3568s+0.1892s)
3*7001#+1 has factors: 35569
4*7001#+1 has factors: 14843
5*7001#+1 is composite: RES64: [DB5A01A8B92504CF] (0.3374s+0.1903s)
6*7001#+1 is composite: RES64: [AF04F9D4715F23A7] (0.3387s+0.1702s)
7*7001#+1 has factors: 65843
8*7001#+1 is composite: RES64: [9BAB5A625E7A3724] (0.3376s+0.1847s)
9*7001#+1 is composite: RES64: [7B1891DE1A32ED39] (0.3377s+0.1689s)
10*7001#+1 is composite: RES64: [861810998DE951E9] (0.3456s+0.1680s)

pfgw -f0
1*7001#+1 is composite: RES64: [626C500202733A8D] (0.3446s+0.0004s)
2*7001#+1 is composite: RES64: [C85147CB3425220A] (0.3492s+0.0005s)
3*7001#+1 is composite: RES64: [54080045A80CB2B3] (0.3415s+0.0005s)
4*7001#+1 is composite: RES64: [38C1AC939D039EE1] (0.3381s+0.0005s)
5*7001#+1 is composite: RES64: [DB5A01A8B92504CF] (0.3389s+0.0005s)
6*7001#+1 is composite: RES64: [AF04F9D4715F23A7] (0.3384s+0.0005s)
7*7001#+1 is composite: RES64: [E7B28A1401466FA6] (0.3359s+0.0005s)
8*7001#+1 is composite: RES64: [9BAB5A625E7A3724] (0.3368s+0.0005s)
9*7001#+1 is composite: RES64: [7B1891DE1A32ED39] (0.3383s+0.0005s)
10*7001#+1 is composite: RES64: [861810998DE951E9] (0.3373s+0.0005s)

I started with 6,245,377 ap4 chances so using
pfgw -f (which at this size will only test to around 800,000 and would find factors for a bit over a third of the numbers) so time taken
~= (6,245,377*0.17) + (4,163,584*0.34)
2,477,333 secs
28.67 days

if I only tested only the 1,274,166 "spanned" candidates then
pfgw -f so time taken
~= (1274166*0.17) + (849448*0.34)
505420 secs
5.85 days
compared to
pfgw -f0 on 188,505 candidates
~= 188,505*0.34
64091 secs
17.8 hours

> (It must be a bit of a pain to organise.)
Not really.
Just a sequence of jobs (which only take a couple of minutes to run) interspersed with 2 newpgen runs (in this case each run was only about 1 hour elapsed)

> At this size of number, pfgw -f would fair whip through those candidates, wouldn't it?
Not really (less than 3 a second)

I think it is definitely worthwhile.
I reduced what traditionally (extend all ap4s) would take a month to less than a day
(Note. Further NewPGen'ing would have been advantageous (as 38.5% of the candidates coming through each sieve whereas I suspect sieving until I had around 35% and thus only 156,000 candidates to prp would have been more efficient) but I started on it yesterday afternoon and wanted to run the pfgw script over night.

Cheers
Ken
>
> Mike
• ... Congratulations. http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. -- Jens Kruse Andersen
Message 4 of 4 , Aug 18, 2010
Ken wrote:
> (967858482 + (\$n*19401803))*7001#+1 (n=0-5) AP6 of 3019 digit

Congratulations.
http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated.

--
Jens Kruse Andersen
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