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Re: {Spam?} [PrimeNumbers] the 357 rule

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  • Paul Leyland
    Aargh! I misunderstood the example and posted complete claptrap. My apologies. To make amends: all Fermat numbers pass the 2-PRP test. Many composite
    Message 1 of 3 , Feb 1, 2010
      Aargh! I misunderstood the example and posted complete claptrap. My
      apologies.

      To make amends: all Fermat numbers pass the 2-PRP test. Many composite
      Fermat numbers N are known and all are divisible only by integers larger
      that 7. In every case, N is a power of 2, by definition, and so not
      divisible by 3, 5, 7.

      Your conjecture is still false.


      Paul


      On Mon, 2010-02-01 at 14:34 +0000, Paul Leyland wrote:
      > If you used your elderly computer to search for known results rather
      > than for computations you would have discovered
      > http://www.research.att.com/~njas/sequences/A055550 and, in particular,
      > the entry 264239
      >
      > 264239 = 139 * 1901
      > 264238 = 2 * 13 * 10163
      >
      >
      > Paul
      >
      >
      > On Mon, 2010-02-01 at 06:18 -0800, Bill Bouris wrote:
      > >
      > > Group,
      > > I believe that if 'N' passes the 2-PRP test that either 3, 5, or 7
      > > divides 'N-1', one or
      > > all of them, or 'N' will be divisible by 3, 5, or 7 and be composite.
      > > I could only go
      > > so far with my outdated computer and UBasic. Can anyone find a
      > > counter-example ???
      > > Bill
      > >
      > >
      > >
      > >
      > >
    • Bill Bouris
      forwarded... ... From: Bill Bouris To: Paul Leyland Sent: Mon, February 1, 2010 8:42:15 AM Subject: Re: {Spam?}
      Message 2 of 3 , Feb 1, 2010
        forwarded...



        ----- Forwarded Message ----
        From: Bill Bouris <leavemsg1@...>
        To: Paul Leyland <paul@...>
        Sent: Mon, February 1, 2010 8:42:15 AM
        Subject: Re: {Spam?} [PrimeNumbers] the 357 rule

        not a complete craptrap... I was going to say that if it were false, that a simple
        3-PRP would expose those numbers that did not have that property.



        ----- Original Message ----
        From: Paul Leyland <paul@...>
        To: Bill Bouris <leavemsg1@...>
        Cc: pgroup <primenumbers@yahoogroups.com>
        Sent: Mon, February 1, 2010 8:39:10 AM
        Subject: Re: {Spam?} [PrimeNumbers] the 357 rule

        Aargh!  I misunderstood the example and posted complete claptrap.  My
        apologies.

        To make amends: all Fermat numbers pass the 2-PRP test.  Many composite
        Fermat numbers N are known and all are divisible only by integers larger
        that 7.  In every case, N is a power of 2, by definition, and so not
        divisible by 3, 5, 7.

        Your conjecture is still false.


        Paul


        On Mon, 2010-02-01 at 14:34 +0000, Paul Leyland wrote:
        > If you used your elderly computer to search for known results rather
        > than for computations you would have discovered
        > http://www.research.att.com/~njas/sequences/A055550 and, in particular,
        > the entry 264239
        >
        > 264239 = 139 * 1901
        > 264238 = 2 * 13 * 10163
        >
        >
        > Paul
        >
        >
        > On Mon, 2010-02-01 at 06:18 -0800, Bill Bouris wrote:
        > > 
        > > Group,
        > > I believe that if 'N' passes the 2-PRP test that either 3, 5, or 7
        > > divides 'N-1', one or
        > > all of them, or 'N' will be divisible by 3, 5, or 7 and be composite.
        > > I could only go
        > > so far with my outdated computer and UBasic. Can anyone find a
        > > counter-example ???
        > > Bill
        > >
        > >
        > >
        > >
        > >
      • djbroadhurst
        ... n = 1097343303233 is not prime n is 2-PRP n is 3-PRP n is coprime to 3*5*7 n-1 is coprime to 3*5*7 There are 95 such counterexamples in
        Message 3 of 3 , Feb 1, 2010
          --- In primenumbers@yahoogroups.com,
          Bill Bouris <leavemsg1@...> wrote:

          > I was going to say that if it were false
          > that a simple 3-PRP would expose those
          > numbers that did not have that property

          n = 1097343303233 is not prime
          n is 2-PRP
          n is 3-PRP
          n is coprime to 3*5*7
          n-1 is coprime to 3*5*7

          There are 95 such counterexamples in
          http://physics.open.ac.uk/~dbroadhu/cert/crxptrxp.gp
          the largest being n = 972137210279970593

          David
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