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3019 Digit Ap6

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  • kraDen
    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
    • mikeoakes2
      ... 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
        --- 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?
        (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
      • kraDen
        ... 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:
          >
          >
          >
          > --- 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?

          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
        • Jens Kruse Andersen
          ... 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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