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RE: [PrimeNumbers] Re: Question on power residues...

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  • 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 1 of 6 , Jun 8 9:25 AM
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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 2 of 6 , Jun 8 4:53 PM
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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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