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

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  • Bill Bouris
    forwarded... ... From: Bill Bouris To: Paul Leyland Sent: Mon, February 1, 2010 8:42:15 AM Subject: Re: {Spam?}
    Message 1 of 3 , Feb 1, 2010
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      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 so far with my outdated computer and UBasic.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 2 of 3 , Feb 1, 2010
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        --- 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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