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AP13s

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  • kraDen
    Hi All, The following descibe AP13s with 83 digits (9773795412+$n*81373857)*181#+1 n=0-12 (7967748420+$n*340308346)*181#+1) n=0-12 Input/output statistics:-
    Message 1 of 9 , May 19, 2010
      Hi All,

      The following descibe AP13s with 83 digits

      (9773795412+$n*81373857)*181#+1 n=0-12
      (7967748420+$n*340308346)*181#+1) n=0-12

      Input/output statistics:-
      Numbers input to NewPGen: 3*10^9 seived to 1*10^11
      Nubers input to PFGW 626824792. PRP's found by PFGW: 148388269
      AP13 search run against the PRPs in the first 4*10^6 of the numbers (exhaustively finding all AP in the 3*10^9 range)

      I know some, Mike at least, appreciate stats so
      AP07s:14260855
      AP08s:601980
      AP09s:26092
      AP10s:1215
      AP11s:58
      AP12s:2
      AP13s:0

      Additional APs through extension of ap7'3 through 12's (both forward and back)gave additional
      AP08s:773320
      AP09s:69921
      AP10s:4908
      AP11s:288
      AP12s:12
      AP13s:2

      First Ap13
      Primality testing (9773795412+0*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 191
      Calling Brillhart-Lehmer-Selfridge with factored part 35.77%
      (9773795412+0*81373857)*181#+1 is prime! (0.0047s+0.0016s)
      Primality testing (9773795412+1*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 2
      Calling Brillhart-Lehmer-Selfridge with factored part 33.58%
      (9773795412+1*81373857)*181#+1 is prime! (0.0042s+0.0017s)
      Primality testing (9773795412+2*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 197
      Running N-1 test using base 199
      Calling Brillhart-Lehmer-Selfridge with factored part 33.94%
      (9773795412+2*81373857)*181#+1 is prime! (0.0061s+0.0017s)
      Primality testing (9773795412+3*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 3
      Calling Brillhart-Lehmer-Selfridge with factored part 34.67%
      (9773795412+3*81373857)*181#+1 is prime! (0.0043s+0.0017s)
      Primality testing (9773795412+4*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 211
      Running N-1 test using base 227
      Calling Brillhart-Lehmer-Selfridge with factored part 33.58%
      (9773795412+4*81373857)*181#+1 is prime! (0.0062s+0.0018s)
      Primality testing (9773795412+5*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 7
      Calling Brillhart-Lehmer-Selfridge with factored part 34.31%
      (9773795412+5*81373857)*181#+1 is prime! (0.0047s+0.0019s)
      Primality testing (9773795412+6*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 223
      Calling Brillhart-Lehmer-Selfridge with factored part 33.58%
      (9773795412+6*81373857)*181#+1 is prime! (0.0047s+0.0017s)
      Primality testing (9773795412+7*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 11
      Calling Brillhart-Lehmer-Selfridge with factored part 35.40%
      (9773795412+7*81373857)*181#+1 is prime! (0.0046s+0.0017s)
      Primality testing (9773795412+8*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 193
      Running N-1 test using base 239
      Calling Brillhart-Lehmer-Selfridge with factored part 35.40%
      (9773795412+8*81373857)*181#+1 is prime! (0.0059s+0.0019s)
      Primality testing (9773795412+9*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 19
      Calling Brillhart-Lehmer-Selfridge with factored part 35.77%
      (9773795412+9*81373857)*181#+1 is prime! (0.0044s+0.0017s)
      Primality testing (9773795412+10*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 229
      Calling Brillhart-Lehmer-Selfridge with factored part 35.04%
      (9773795412+10*81373857)*181#+1 is prime! (0.0047s+0.0017s)
      Primality testing (9773795412+11*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 23
      Calling Brillhart-Lehmer-Selfridge with factored part 35.40%
      (9773795412+11*81373857)*181#+1 is prime! (0.0044s+0.0017s)
      Primality testing (9773795412+12*81373857)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 241
      Calling Brillhart-Lehmer-Selfridge with factored part 34.67%
      (9773795412+12*81373857)*181#+1 is prime! (0.0043s+0.0017s)

      2nd Ap13
      Primality testing (7967748420+0*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 191
      Calling Brillhart-Lehmer-Selfridge with factored part 34.67%
      (7967748420+0*340308346)*181#+1 is prime! (0.0044s+0.0016s)
      Primality testing (7967748420+1*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 199
      Calling Brillhart-Lehmer-Selfridge with factored part 35.40%
      (7967748420+1*340308346)*181#+1 is prime! (0.0049s+0.0018s)
      Primality testing (7967748420+2*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 197
      Calling Brillhart-Lehmer-Selfridge with factored part 35.04%
      (7967748420+2*340308346)*181#+1 is prime! (0.0048s+0.0015s)
      Primality testing (7967748420+3*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 193
      Calling Brillhart-Lehmer-Selfridge with factored part 34.31%
      (7967748420+3*340308346)*181#+1 is prime! (0.0040s+0.0017s)
      Primality testing (7967748420+4*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 229
      Calling Brillhart-Lehmer-Selfridge with factored part 35.40%
      (7967748420+4*340308346)*181#+1 is prime! (0.0046s+0.0018s)
      Primality testing (7967748420+5*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 223
      Calling Brillhart-Lehmer-Selfridge with factored part 35.40%
      (7967748420+5*340308346)*181#+1 is prime! (0.0045s+0.0015s)
      Primality testing (7967748420+6*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 233
      Calling Brillhart-Lehmer-Selfridge with factored part 33.58%
      (7967748420+6*340308346)*181#+1 is prime! (0.0045s+0.0014s)
      Primality testing (7967748420+7*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 227
      Calling Brillhart-Lehmer-Selfridge with factored part 34.31%
      (7967748420+7*340308346)*181#+1 is prime! (0.0046s+0.0018s)
      Primality testing (7967748420+8*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 239
      Running N-1 test using base 241
      Calling Brillhart-Lehmer-Selfridge with factored part 35.04%
      (7967748420+8*340308346)*181#+1 is prime! (0.0058s+0.0015s)
      Primality testing (7967748420+9*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 211
      Calling Brillhart-Lehmer-Selfridge with factored part 33.94%
      (7967748420+9*340308346)*181#+1 is prime! (0.0044s+0.0014s)
      Primality testing (7967748420+10*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 197
      Calling Brillhart-Lehmer-Selfridge with factored part 33.45%
      (7967748420+10*340308346)*181#+1 is prime! (0.0044s+0.0014s)
      Primality testing (7967748420+11*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 251
      Calling Brillhart-Lehmer-Selfridge with factored part 33.82%
      (7967748420+11*340308346)*181#+1 is prime! (0.0058s+0.0015s)
      Primality testing (7967748420+12*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 233
      Calling Brillhart-Lehmer-Selfridge with factored part 34.55%
      (7967748420+12*340308346)*181#+1 is prime! (0.0047s+0.0015s)
      Primality testing (7967748420+13*340308346)*181#+1 [N-1, Brillhart-Lehmer-Selfridge]

      Cheers
      Ken
    • mikeoakes2
      ... Many congrats, Ken! But I m puzzled about how this:- ... can give this:- ... Based on my http://tech.groups.yahoo.com/group/primeform/message/7672 I would
      Message 2 of 9 , May 20, 2010
        --- In primeform@yahoogroups.com, "kraDen" <kradenken@...> wrote:
        >
        > The following descibe AP13s with 83 digits
        >
        > (9773795412+$n*81373857)*181#+1 n=0-12
        > (7967748420+$n*340308346)*181#+1) n=0-12
        >
        > Input/output statistics:-
        > Numbers input to NewPGen: 3*10^9 seived to 1*10^11
        > Nubers input to PFGW 626824792. PRP's found by PFGW: 148388269
        > AP13 search run against the PRPs in the first 4*10^6 of the numbers (exhaustively finding all AP in the 3*10^9 range)
        >
        > I know some, Mike at least, appreciate stats so
        > AP07s:14260855
        > AP08s:601980
        > AP09s:26092
        > AP10s:1215
        > AP11s:58
        > AP12s:2
        > AP13s:0
        >
        > Additional APs through extension of ap7'3 through 12's (both forward and back)gave additional
        > AP08s:773320
        > AP09s:69921
        > AP10s:4908
        > AP11s:288
        > AP12s:12
        > AP13s:2

        Many congrats, Ken!

        But I'm puzzled about how this:-
        > AP13 search run against the PRPs in the first 4*10^6 of the numbers

        can give this:-
        > AP12s:2

        Based on my
        http://tech.groups.yahoo.com/group/primeform/message/7672
        I would have expected only about (4*10^6/1.05*10^8)^2*21= 0.03 AP12's from such a small range.

        You didn't mean "the first 4*10^7" did you?

        Mike
      • kraDen
        Hi Mike, I did indeed mean 4*10^7 Sorry about that. Ken
        Message 3 of 9 , May 20, 2010
          Hi Mike,
          I did indeed mean 4*10^7
          Sorry about that.
          Ken

          --- In primeform@yahoogroups.com, "mikeoakes2" <mikeoakes2@...> wrote:
          >
          >
          >
          > --- In primeform@yahoogroups.com, "kraDen" <kradenken@> wrote:
          > >
          > > The following descibe AP13s with 83 digits
          > >
          > > (9773795412+$n*81373857)*181#+1 n=0-12
          > > (7967748420+$n*340308346)*181#+1) n=0-12
          > >
          > > Input/output statistics:-
          > > Numbers input to NewPGen: 3*10^9 seived to 1*10^11
          > > Nubers input to PFGW 626824792. PRP's found by PFGW: 148388269
          > > AP13 search run against the PRPs in the first 4*10^6 of the numbers (exhaustively finding all AP in the 3*10^9 range)
          > >
          > > I know some, Mike at least, appreciate stats so
          > > AP07s:14260855
          > > AP08s:601980
          > > AP09s:26092
          > > AP10s:1215
          > > AP11s:58
          > > AP12s:2
          > > AP13s:0
          > >
          > > Additional APs through extension of ap7'3 through 12's (both forward and back)gave additional
          > > AP08s:773320
          > > AP09s:69921
          > > AP10s:4908
          > > AP11s:288
          > > AP12s:12
          > > AP13s:2
          >
          > Many congrats, Ken!
          >
          > But I'm puzzled about how this:-
          > > AP13 search run against the PRPs in the first 4*10^6 of the numbers
          >
          > can give this:-
          > > AP12s:2
          >
          > Based on my
          > http://tech.groups.yahoo.com/group/primeform/message/7672
          > I would have expected only about (4*10^6/1.05*10^8)^2*21= 0.03 AP12's from such a small range.
          >
          > You didn't mean "the first 4*10^7" did you?
          >
          > Mike
          >
        • Jens Kruse Andersen
          ... Congratulations! http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. -- Jens Kruse Andersen
          Message 4 of 9 , May 20, 2010
            Ken wrote:
            > The following descibe AP13s with 83 digits
            >
            > (9773795412+$n*81373857)*181#+1 n=0-12
            > (7967748420+$n*340308346)*181#+1) n=0-12

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

            --
            Jens Kruse Andersen
          • djbroadhurst
            ... Interesting question (about which I have no idea): what else might be done with a database 40 million 83-digit primes? Regarding my recent study of primes
            Message 5 of 9 , May 20, 2010
              --- In primeform@yahoogroups.com,
              "kraDen" <kradenken@...> wrote:

              > I did indeed mean 4*10^7

              Interesting question (about which I have no idea):
              what else might be done with a database 40 million
              83-digit primes?

              Regarding my recent study of primes below 40 digits,
              I am now able to report (after several haphazard
              rectangular searches) that

              23889376170*265^n+1 is prime for n=0..10

              p(n)=23889376170*265^n+1;
              for(n=0,10,if(isprime(p(n)),print(p(n))))

              23889376171
              6330684685051
              1677631441538251
              444572332007636251
              117811667982023606251
              31220092015236255656251
              8273324384037607748906251
              2192430961769966053460156251
              580994204869041004166941406251
              153963464290295866104239472656251
              40800318036928404517623460253906251

              It seems to me to be rather hard to find more
              than 11 primes p[n] with p[n]-1 forming a
              geometric progression with a ratio b > 265.

              But I bet Jarek could do so, if he set his mind to it...

              David
            • ajo
              ... I was wondering if there was any possibility of finding 11 (or 12) successive n values such that p(n) is prime for a very large (or large) n value. Is
              Message 6 of 9 , May 23, 2010
                --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:

                > 23889376170*265^n+1 is prime for n=0..10
                >
                > p(n)=23889376170*265^n+1;
                > for(n=0,10,if(isprime(p(n)),print(p(n))))
                >
                > 23889376171
                > 6330684685051
                > 1677631441538251
                > 444572332007636251
                > 117811667982023606251
                > 31220092015236255656251
                > 8273324384037607748906251
                > 2192430961769966053460156251
                > 580994204869041004166941406251
                > 153963464290295866104239472656251
                > 40800318036928404517623460253906251
                >
                > It seems to me to be rather hard to find more
                > than 11 primes p[n] with p[n]-1 forming a
                > geometric progression with a ratio b > 265.
                >
                > But I bet Jarek could do so, if he set his mind to it...
                >
                > David
                >
                I was wondering if there was any possibility of finding 11 (or 12) successive n values such that p(n) is prime for a very large (or large) n value. Is there more (or less?) probability to find long prime p(n) chains with n beginning at n=0 or with n>=n0 for arbitrary n0 values?
              • ajo
                In other words: 23889376170*265^n+1 is prime for n=0..10 Is there any (good enough) probability to find another 11 prime chain with n=n0..n0+10 for a given
                Message 7 of 9 , May 23, 2010
                  In other words:
                  23889376170*265^n+1 is prime for n=0..10
                  Is there any (good enough) probability to find another 11 prime chain with n=n0..n0+10 for a given base?
                  Is there any probability that exists a 11 length (or more) prime chain k*b^n+c not discovered because n=n0..n0+10 with n0>0 ?
                • djbroadhurst
                  ... The case n = n0 = 0 is subsumed by my case, with n = 0, Suppose that k*b^n + 1 is prime in the L cases n = n0 .. n0+L-1, then K*b^n + 1 is prime in the
                  Message 8 of 9 , May 23, 2010
                    --- In primeform@yahoogroups.com,
                    "ajo" <sopadeajo2001@...> wrote:

                    > Is there more (or less?) probability to find long prime p(n)
                    > chains with n beginning at n=0 or with n>=n0 for arbitrary n0.

                    The case n >= n0 >= 0 is subsumed by my case, with n >= 0,
                    Suppose that k*b^n + 1 is prime in the L cases n = n0 .. n0+L-1,
                    then K*b^n + 1 is prime in the L cases n = 0 .. L-1
                    where K = k*b^n0.

                    Reminder: The challenge is

                    > find more than 11 primes p[n] with p[n]-1 forming a
                    > geometric progression with a ratio b > 265

                    David
                  • ajo
                    ... OK, seen it.
                    Message 9 of 9 , May 23, 2010
                      --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
                      >
                      >
                      >
                      > --- In primeform@yahoogroups.com,
                      > "ajo" <sopadeajo2001@> wrote:
                      >
                      > > Is there more (or less?) probability to find long prime p(n)
                      > > chains with n beginning at n=0 or with n>=n0 for arbitrary n0.
                      >
                      > The case n >= n0 >= 0 is subsumed by my case, with n >= 0,
                      > Suppose that k*b^n + 1 is prime in the L cases n = n0 .. n0+L-1,
                      > then K*b^n + 1 is prime in the L cases n = 0 .. L-1
                      > where K = k*b^n0.
                      >
                      > Reminder: The challenge is
                      >
                      > > find more than 11 primes p[n] with p[n]-1 forming a
                      > > geometric progression with a ratio b > 265
                      >
                      > David
                      >
                      OK, seen it.
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