Loading ...
Sorry, an error occurred while loading the content.

Re: [PrimeNumbers] Re: Largest PRP Found!?

Expand Messages
  • Cletus Emmanuel
    William, Now this makes more sense to me. Thanks 1M for the lesson. I will see what full sense I can make of this email. At the end I should be able to
    Message 1 of 14 , Dec 22, 2003
    • 0 Attachment
      William,
      Now this makes more sense to me. Thanks 1M for the lesson. I will see what full sense I can make of this email. At the end I should be able to understand Aurifeuillian factors fully.
      Thanks again...

      elevensmooth <elevensmooth@...> wrote:
      Some details were still wrong. I got the middle
      exponent of one Aurifeuillian factor wrong, and
      I selected the wrong small Aurifeuillian factor
      as a divisor of the large one. Here's yet
      another try to get this right:

      C=148330
      X=2^C+1
      N=X^4-2
      N is PRP for 2, 29, 43, 101
      (N+1) = (X^2+1)(X+1)(X-1)
      (X^2+1)/2 = (2^296659 + 2^148330 + 1)
      This is an Aurifeuillian factor of (2^593318 + 1)
      593318=11*53938
      (2^593318 + 1) has algebraic factors, including (2^53938 + 1).
      (2^53938 + 1) has Aurifeuillian factors
      (2^26969 - 2^13485 + 1) and (2^26969 + 2^13485 + 1)
      (2^26969 - 2^13485 + 1) is a factor of (X^2+1)/2

      To verify the small Aurifeuillian factor divides the
      large one without using a big number package, let
      z=2^13484. The large factor is
      (2048z^22 + 64z^11 + 1). The small factor is
      (2z^2 � 2z + 1). The polynomial factorization can be
      confirmed, for example, at this web site:

      http://icm.mcs.kent.edu/research/facdemo.html

      Sorry for the continuing string of errors.

      William
      --
      ElevenSmooth: Distributed Factoring of 2^3326400-1
      http://www.ElevenSmooth.com



      Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
      The Prime Pages : http://www.primepages.org/




      Yahoo! Groups SponsorADVERTISEMENT


      ---------------------------------
      Yahoo! Groups Links

      To visit your group on the web, go to:
      http://groups.yahoo.com/group/primenumbers/

      To unsubscribe from this group, send an email to:
      primenumbers-unsubscribe@yahoogroups.com

      Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.



      ---------------------------------
      Do you Yahoo!?
      Free Pop-Up Blocker - Get it now

      [Non-text portions of this message have been removed]
    Your message has been successfully submitted and would be delivered to recipients shortly.