- 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 - --- In primeform@yahoogroups.com, "kraDen" <kradenken@...> wrote:
>

Congratulations, Ken, on a nice piece of work.

> 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.

(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 - --- In primeform@yahoogroups.com, "mikeoakes2" <mikeoakes2@...> wrote:
>

I believe NewPGen'ing is definitely worthwhile

>

>

> --- In primeform@yahoogroups.com, "kraDen" <kradenken@> 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?

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 - 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