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Fwd: Factorization of 2,797+

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  • Phil Carmody
    Can I recommend the following factoring project to those who are sitting on idle PCs? http://www.nfsnet.org/ (note, ones that are starved for memory are alas
    Message 1 of 1 , Jul 18, 2006
      Can I recommend the following factoring project to those
      who are sitting on idle PCs? http://www.nfsnet.org/
      (note, ones that are starved for memory are alas probably
      not suitable, see the project FAQ). It's part of the
      longest-running distributed computing task there is -
      the Cunningham Project http://www.cerias.purdue.edu/homes/ssw/cun/ .

      I enclose their latest announcement, which is very positive
      in that they've had success with new techniques, but the final
      paragraph is alas the negative one which caused me to write
      this - they've had to relinquish some of their crunching
      machines recently.


      --- Richard Wackerbarth wrote:
      > To: NFSNET <nfsnet-announce@...>
      > Subject: Factorization of 2,797+
      > As an experiment to test the feasibility of performing gnfs
      > factorizations, we used the NFSNet infrastructure to perform a gnfs
      > solution to determine the remaining factors of 2,797+.
      > We collected 78.6M relations during this past Spring using a very
      > limited subset of the volunteer sievers.
      > Sievers at Lehigh University (Bruce Dodson 40%), Universiteit Gent
      > (Jeroen Demeyer 46%) and my personal sievers (13%).
      > We limited the participation because we were unsure how the extremely
      > long sieving lines would affect the sievers. We intentionally chose
      > machines that were controlled by a limited number of participants and
      > generally ran the siever at all times (at least in the background).
      > At the same time, the other NFSNet participants were sieving on other
      > projects.
      > Other than the elapsed calendar time for the sieving of these
      > projects, I do not feel that this splitting of resources has reduced
      > our combined progress in supplying additional factorizations.
      > I handled the post-processing on my dual G5 desktop system, reducing
      > the relations to a matrix with 4.19M rows.
      > This matrix was solved using the CWI implementation of Block Lanczos.
      > With some additional guidance from Paul Leyland, finally, on the 4th
      > dependency, I found the solution:
      > Factorization completed after 32284.53 seconds, at Mon Jul 3
      > 21:29:58 2006
      > Original number had 150 digits:
      > 808327788723521825530207728143259941867725165285280602423994411926146120
      > 344539039289407533152438819052946060624026017056923683548235948384716482
      > 729353
      > Probable prime factor 1 has 60 digits:
      > 721081346319803014103048601140804555897014469307122160867977
      > Probable prime factor 2 has 91 digits:
      > 112099389735846057840449050218413577174385806530863598272111947388567753
      > 5372544659994092289
      > For The NFSNet Sieving Group,
      > Richard Wackerbarth
      > PS: Since we finished the sieving mentioned above, other researchers
      > have been utilizing much of the available time on the Universiteit
      > Gent machine. This has significantly slowed our progress on the
      > sieving for 3,479+. If you have some machines that could help out,
      > your assistance would be appreciated.

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