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Re: Question on power residues...

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  • richard_heylen
    ... As I implied, any strong base 2 psuedoprime will do. So from http://www.research.att.com/cgi- bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001262
    Message 1 of 6 , Jun 8, 2004
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      --- In primenumbers@yahoogroups.com, David Cleaver <wraithx@m...>
      wrote:
      >
      > Yeah, it looks like this method will not work
      > when the numbers is of the form ((2^prime) - 1).
      > However, this may be the only class of numbers
      > that this method is unnable to factor. If you
      > can think of any other numbers that might have
      > this property, or if you know of any numbers that
      > can never be factored by the pollard-rho algorithm,
      > please let me know. Thanks for your input so far.

      As I implied, any strong base 2 psuedoprime will do.
      So from

      http://www.research.att.com/cgi-
      bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001262

      2047,3277,4033,4681,8321,15841,29341,42799,49141,52633,
      65281,74665,80581,85489,88357,90751,104653,130561,196093,
      220729,233017,252601,253241,256999,271951,280601,314821,
      357761,390937,458989,476971,486737

      Richard Heylen
    • Milton Brown
      Residues for the Powers of Prime numbers are discussed in detail in Elementary Number Theory by Jones and Jones with a separate section on page 135. You
      Message 2 of 6 , Jun 8, 2004
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        Residues for the Powers of Prime numbers are discussed
        in detail in "Elementary Number Theory" by Jones and Jones
        with a separate section on page 135.

        You should look there, instead of suggesting that some new
        theory is being developed here.

        Milton L. Brown
        miltbrown at earthlink.net
        miltbrown@...


        > [Original Message]
        > From: richard_heylen <rick.heylen@...>
        > To: <primenumbers@yahoogroups.com>
        > Date: 6/8/2004 5:24:23 AM
        > Subject: [PrimeNumbers] Re: Question on power residues...
        >
        > --- In primenumbers@yahoogroups.com, David Cleaver <wraithx@m...>
        > wrote:
        > >
        > > Yeah, it looks like this method will not work
        > > when the numbers is of the form ((2^prime) - 1).
        > > However, this may be the only class of numbers
        > > that this method is unnable to factor. If you
        > > can think of any other numbers that might have
        > > this property, or if you know of any numbers that
        > > can never be factored by the pollard-rho algorithm,
        > > please let me know. Thanks for your input so far.
        >
        > As I implied, any strong base 2 psuedoprime will do.
        > So from
        >
        > http://www.research.att.com/cgi-
        > bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001262
        >
        > 2047,3277,4033,4681,8321,15841,29341,42799,49141,52633,
        > 65281,74665,80581,85489,88357,90751,104653,130561,196093,
        > 220729,233017,252601,253241,256999,271951,280601,314821,
        > 357761,390937,458989,476971,486737
        >
        > Richard Heylen
        >
        >
        >
        >
        >
        > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
        > The Prime Pages : http://www.primepages.org/
        >
        >
        > Yahoo! Groups Links
        >
        >
        >
        >
      • pbtoau
        Milton, Your first paragraph is very helpful. Your second paragraph has an unfortunate condescending tone. I know people are frequently thinking they have
        Message 3 of 6 , Jun 8, 2004
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          Milton,

          Your first paragraph is very helpful. Your second paragraph has an
          unfortunate condescending tone. I know people are frequently
          thinking they have discovered something new that is 400 years old.
          It is great to point them to the earlier work, but I do not want
          people to be afraid to post to the list because they might be subtly
          ridiculed.

          Best regards,

          David

          --- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
          wrote:
          >
          > Residues for the Powers of Prime numbers are discussed
          > in detail in "Elementary Number Theory" by Jones and Jones
          > with a separate section on page 135.
          >
          > You should look there, instead of suggesting that some new
          > theory is being developed here.
          >
          > Milton L. Brown
          > miltbrown at earthlink.net
          > miltbrown@e...
          >
          >
          > > [Original Message]
          > > From: richard_heylen <rick.heylen@m...>
          > > To: <primenumbers@yahoogroups.com>
          > > Date: 6/8/2004 5:24:23 AM
          > > Subject: [PrimeNumbers] Re: Question on power residues...
          > >
          > > --- In primenumbers@yahoogroups.com, David Cleaver <wraithx@m...>
          > > wrote:
          > > >
          > > > Yeah, it looks like this method will not work
          > > > when the numbers is of the form ((2^prime) - 1).
          > > > However, this may be the only class of numbers
          > > > that this method is unnable to factor. If you
          > > > can think of any other numbers that might have
          > > > this property, or if you know of any numbers that
          > > > can never be factored by the pollard-rho algorithm,
          > > > please let me know. Thanks for your input so far.
          > >
          > > As I implied, any strong base 2 psuedoprime will do.
          > > So from
          > >
          > > http://www.research.att.com/cgi-
          > > bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001262
          > >
          > > 2047,3277,4033,4681,8321,15841,29341,42799,49141,52633,
          > > 65281,74665,80581,85489,88357,90751,104653,130561,196093,
          > > 220729,233017,252601,253241,256999,271951,280601,314821,
          > > 357761,390937,458989,476971,486737
          > >
          > > Richard Heylen
          > >
          > >
          > >
          > >
          > >
          > > Unsubscribe by an email to: primenumbers-
          unsubscribe@yahoogroups.com
          > > The Prime Pages : http://www.primepages.org/
          > >
          > >
          > > Yahoo! Groups Links
          > >
          > >
          > >
          > >
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