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483Re: A Record Prime Factor by Pollard's "p-1" method

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  • Phil Carmody
    Mar 5, 2001
      On Sun, 04 March 2001, Andy Steward wrote:
      [On the NMBRTHRY mailing list]
      > Early on 3rd March 2001, my own Ubasic "p-1" code found the following
      > factor of 922^47-1:
      > p39=188879386195169498836498369376071664143
      > p-1=
      > I therefore claim the world record factor found by this method (unless
      > any of you know better).

      Well done, Andy.
      Is UBasic as fast for this kind of job as C would be with one of the standard bignum packages. Or a dedicated number-theoretic package, such as pari or LiDIA?

      I was looking on the prime pages, for some info on the p-1 factoring method, and I noticed that there is no "Factoring into primes" section on the prime pages. My favourite search engine quickly pointed me in the direction of Wolfram/Eric Weisstein's Mathworld, several dead links, and some source code in an unknown language... So perhaps we could put our heads together to create the kernel of a new prime pages page of factoring methods? As far as my memory serves me (traditionally very poorly), it would be nice to get information on the following.
      - Trial division
      - Pollard p-1
      - Pollard p+1
      - Continued Fractions
      - Pollard Rho
      - NFS
      - ECM
      Note - I haven't got a clue what any of the above are (apart from one), I'm just parroting.

      I do have Knuth, so I am prepared to put my reading spec's on to learn a few of the above, but that still leaves half of them for others.

      Any takers?


      Mathematics should not have to involve martyrdom;
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