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MM61

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  • Di Maria Giovanni
    Hi How can i perform this expression: (2^(2^61-1)-1) mod 223 with GMP library? What s the C function sequence? Thank you Giovanni
    Message 1 of 13 , Oct 2, 2009
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      Hi
      How can i perform this expression:

      (2^(2^61-1)-1) mod 223

      with GMP library?
      What's the C function sequence?
      Thank you
      Giovanni
    • maximilian_hasler
      ... in PARI, use Mod(2,223)^(2^61 % eulerphi(223) -1) - 1 %146 = Mod(14, 223) i.e. MM61 = 14 (mod 223) Since 223 is prime, the exponent can be reduced mod
      Message 2 of 13 , Oct 2, 2009
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        --- In primenumbers@yahoogroups.com, "Di Maria Giovanni" <calimero22@...> wrote:
        >
        > Hi
        > How can i perform this expression:
        >
        > (2^(2^61-1)-1) mod 223
        >
        > with GMP library?
        > What's the C function sequence?


        in PARI, use

        Mod(2,223)^(2^61 % eulerphi(223) -1) - 1
        %146 = Mod(14, 223)

        i.e. MM61 = 14 (mod 223)

        Since 223 is prime, the exponent can be reduced mod phi(223).
        Here I did it using %, but it would be better to do it via Mod(),
        to avoid computation of the big number:

        Mod(2,223)^lift(Mod(2,eulerphi(223))^61-1) - 1


        Maximilian
      • djbroadhurst
        ... According to Landon Curt Noll and Tony Forbes, MM61 is not divisible by any prime less than 43180130614086110782608760243
        Message 3 of 13 , Oct 2, 2009
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          --- In primenumbers@yahoogroups.com,
          "maximilian_hasler" <maximilian.hasler@...> wrote:

          > i.e. MM61 = 14 (mod 223)

          According to Landon Curt Noll and Tony Forbes,
          MM61 is not divisible by any prime less than
          43180130614086110782608760243

          http://www.garlic.com/~wedgingt/MMPstats.txt

          David
        • Norman Luhn
          More also here: http://anthony.d.forbes.googlepages.com/mm61prog.htm Norman
          Message 4 of 13 , Oct 2, 2009
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          • mgrogue@wi.rr.com
            ... Geoff Reynolds and I wrote a program that is faster than Tony s, but he has not responded to our inquiries to see if he is interested in our code. --Mark
            Message 5 of 13 , Oct 2, 2009
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              ---- Norman Luhn <nluhn@...> wrote:
              > More also here:
              >
              > http://anthony.d.forbes.googlepages.com/mm61prog.htm

              Geoff Reynolds and I wrote a program that is faster than Tony's, but he has not responded to our inquiries to see if he is interested in our code.

              --Mark
            • j_chrtn
              Hi, BTW, does someone here know if there s (still) an active project to find a factor of MM127 (i.e. C5); and if so, what s the current status for this number?
              Message 6 of 13 , Oct 5, 2009
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                Hi,

                BTW, does someone here know if there's (still) an active project to find a factor of MM127 (i.e. C5); and if so, what's the current status for this number?

                http://www.garlic.com/~wedgingt/MMPstats.txt page seems a bit outdated.

                Jean-Louis





                --- In primenumbers@yahoogroups.com, <mgrogue@...> wrote:
                >
                >
                > ---- Norman Luhn <nluhn@...> wrote:
                > > More also here:
                > >
                > > http://anthony.d.forbes.googlepages.com/mm61prog.htm
                >
                > Geoff Reynolds and I wrote a program that is faster than Tony's, but he has not responded to our inquiries to see if he is interested in our code.
                >
                > --Mark
                >
              • Bernardo Boncompagni
                Andrew Steward maintains an amazing list of all known legal generalized repunit primes at http://www.primes.viner-steward.org/andy/titans.html . In Chris
                Message 7 of 13 , Oct 5, 2009
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                  Andrew Steward maintains an amazing list of all known legal generalized
                  repunit primes at http://www.primes.viner-steward.org/andy/titans.html .

                  In Chris Caldwell's sense, a legal generalized repunit prime is a prime
                  number of the form (b^p-1)/(b-1) such that 3<=b<=5p, b<>10, p prime.

                  Unfortunately, as far as I know, a list of pseudoprimes to fill the gaps
                  in Andy's list is not available, so I started collecting them to help
                  Andrew's site grow.

                  You can find the list at phi.redgolpe.com .

                  Bernardo Boncompagni

                  ________________________________________________

                  "When the missionaries arrived, the Africans had
                  the land and the missionaries had the bible.
                  They taught how to pray with our eyes closed.
                  When we opened them, they had the land and we
                  had the bible"
                  Jomo Kenyatta

                  VisualTaxa - Taxonomy in a visual way
                  http://visualtaxa.redgolpe.com
                  ________________________________________________
                • djbroadhurst
                  ... If you mean Caldwell-legal probable GRU primes, then Andy has no gaps below 16679 digits: http://www.primes.viner-steward.org/andy/titans.html ... Those
                  Message 8 of 13 , Oct 5, 2009
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                    --- In primenumbers@yahoogroups.com,
                    Bernardo Boncompagni <RedGolpe@...> wrote:

                    > a list of pseudoprimes to fill the gaps

                    If you mean Caldwell-legal probable GRU primes,
                    then Andy has no gaps below 16679 digits:

                    http://www.primes.viner-steward.org/andy/titans.html
                    > All legal examples with fewer than 16679 digits
                    > have been found. 3452 await proof.

                    Those PRPs sit in his private files, while ECM tries
                    to factorize cyclotomic cofactors of N-1, for a proof.

                    David
                  • Bernardo Boncompagni
                    ... I know. Since his files are private I m just trying to speed up the process of primality proving by publishing at least a small portion of those PRP s. A
                    Message 9 of 13 , Oct 5, 2009
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                      djbroadhurst dice:

                      > If you mean Caldwell-legal probable GRU primes,
                      > then Andy has no gaps below 16679 digits:

                      > Those PRPs sit in his private files

                      I know. Since his files are private I'm just trying to speed up the
                      process of primality proving by publishing at least a small portion of
                      those PRP's. A quantity of them are below 3,500 digits and could be
                      easily proven with PRIMO without terrible efforts. And tbh, I don't like
                      the idea of "private files" in the first place.

                      Bernardo Boncompagni

                      ________________________________________________

                      "When the missionaries arrived, the Africans had
                      the land and the missionaries had the bible.
                      They taught how to pray with our eyes closed.
                      When we opened them, they had the land and we
                      had the bible"
                      Jomo Kenyatta

                      VisualTaxa - Taxonomy in a visual way
                      http://visualtaxa.redgolpe.com
                      ________________________________________________
                    • djbroadhurst
                      ... Here s a PRP for your collection: http://www.primenumbers.net/prptop/searchform.php?form=%3F180181%3F ... Solution:
                      Message 10 of 13 , Oct 6, 2009
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                        --- In primenumbers@yahoogroups.com,
                        Bernardo Boncompagni <RedGolpe@...> wrote:

                        > Since his files are private I'm just trying to speed up the
                        > process of primality proving by publishing at least a small
                        > portion of those PRP's.

                        Here's a PRP for your collection:
                        http://www.primenumbers.net/prptop/searchform.php?form=%3F180181%3F

                        Incidentally, Andy's site provides what is neeed here:

                        > Puzzle 89: For a base with 89 > b > 2, find a gigantic
                        > base-b superpseudoprime with precisely 26 composite divisors.

                        Solution: 206007889*425389507*662130751*2517984907*(15^8741-1)/14
                        is a gigantic base-15 pseudoprime with precisely
                        26 composite divisors, all of which are 15-PRP.

                        David
                      • Bernardo Boncompagni
                        ... Added :) I was aware of Henry Lifchitz s site but didn t think about checking it for generalized repunits. Unfortunately now that I did I couldn t find any
                        Message 11 of 13 , Oct 7, 2009
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                          djbroadhurst dice:

                          > Here's a PRP for your collection:

                          Added :) I was aware of Henry Lifchitz's site but didn't think about
                          checking it for generalized repunits. Unfortunately now that I did I
                          couldn't find any more than the one you mentioned.

                          Bernardo Boncompagni

                          ________________________________________________

                          "When the missionaries arrived, the Africans had
                          the land and the missionaries had the bible.
                          They taught how to pray with our eyes closed.
                          When we opened them, they had the land and we
                          had the bible"
                          Jomo Kenyatta

                          VisualTaxa - Taxonomy in a visual way
                          http://visualtaxa.redgolpe.com
                          ________________________________________________
                        • tjw99
                          ... http://www.primenumbers.net/prptop/searchform.php?form=%28b^n-1%29%2Fa&action=Search That will catch some Mersenne cofactors as well, but will turn up no
                          Message 12 of 13 , Oct 7, 2009
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                            --- In primenumbers@yahoogroups.com, Bernardo Boncompagni <RedGolpe@...> wrote:
                            >
                            > djbroadhurst dice:
                            >
                            > > Here's a PRP for your collection:
                            >
                            > Added :) I was aware of Henry Lifchitz's site but didn't think about
                            > checking it for generalized repunits. Unfortunately now that I did I
                            > couldn't find any more than the one you mentioned.

                            http://www.primenumbers.net/prptop/searchform.php?form=%28b^n-1%29%2Fa&action=Search

                            That will catch some Mersenne cofactors as well, but will turn up no shortage of PrP GRUs.

                            Tom
                          • Bernardo Boncompagni
                            ... Nice one. I actually searched only for ?Phi? . Bernardo Boncompagni ________________________________________________ When the missionaries arrived, the
                            Message 13 of 13 , Oct 8, 2009
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                              tjw99 dice:

                              > That will catch some Mersenne cofactors as well, but will turn up no
                              > shortage of PrP GRUs.

                              Nice one. I actually searched only for "?Phi?".

                              Bernardo Boncompagni

                              ________________________________________________

                              "When the missionaries arrived, the Africans had
                              the land and the missionaries had the bible.
                              They taught how to pray with our eyes closed.
                              When we opened them, they had the land and we
                              had the bible"
                              Jomo Kenyatta

                              VisualTaxa - Taxonomy in a visual way
                              http://visualtaxa.redgolpe.com
                              ________________________________________________
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