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Thread: ECM for our numbers...

  1. #1
    Moderator vjs's Avatar
    Join Date
    Apr 2004
    ARS DC forum

    ECM for our numbers...

    Please correct me if I'm wrong...

    I though most of the people here use P-1 for factoring the draw back is that a number has to be smooth within B1 b2 bounds.

    If I understand correctly ECM will find all factors less than a particular number of digits depending upon B1 values and then number of curves.

    I was wondering if anyone has tried or is using ECM to factor our numbers, and time vs chances calculations.

    I think mystwalker posted 2 curves at the ~50 digit level should find all factors <20-digits. ( I realise this is a tremendous over simplification).

    I was just wondering if its worth a shot on our numbers, we could start with the assumption that no factors exist with less than 15-digits due to sieve. (Start running curves for 25 or 30 digit numbers etc.)

    If anyone wants to make a list of links etc commmand lines to run etc I'd like to make a faq or a stick for factoring.

    I know hhh made a good one this one would be included.

  2. #2
    I know hhh made a good one this one would be included.
    Huh, I think actually it is not very good; it's better than nothing, but needs to be worked over. This week I am extremely short on time, but from next Wednsday I could revise it. If the sticky can wait until then...?
    Or why not start to use the wiki, finally? It's there for this purpose, isn't it?

    I will make some suggestions later.


  3. #3
    Sieve it, baby!
    Join Date
    Nov 2002
    Potsdam, Germany
    Actually, for ECM, B1/B2 smoothness is important as well - it's only a different group order* that has to be smooth.

    As different group orders can be tested, chances are 1-exp(-1) = ~63% that a factor of the desired size will be found when a certain amount of curves with certain B1/B2 bounds have been run.

    When only 1 curve is run, chances are more or less equal to a P-1 run, but it takes a bit longer.
    Thus, I don't see a benefit in trying ECM when there's not enough computing power even for P-1...

    * I think it was group orders, but I'm not 100% sure, so don't quote me if possible...

  4. #4
    Moderator vjs's Avatar
    Join Date
    Apr 2004
    ARS DC forum
    Thanks for commenting Mystwalker,

    If one curve ecm basically takes the same time or more than a P-1.

    P-1 is obviously the best bet at present...

    From Wblipp's site

    Number of digits, the suggested B1 value
    20 digits 11K
    25 digits 50K
    30 digits 250K
    40 digits 3M
    45 digits 11M
    50 digits 43M
    60 digits 260M
    65 digits 850M

    B2 was B1x100 in the past but I'm unclear on the optimal B2 at present. (Optimal B2 depends on the n, client, memory, etc... AFAIK)

    So to continue on with my idea of two cureves at 50 b1=43000000 b2=4300000000 wow!!! That would take a while and probably quite a bit of memory.

    Just wanted to see what people think about ecm and P-1 factoring lately with our current numbers.

  5. #5
    ECM is vastly more expensive than P-1. Since P-1 is right on the borderline of improving SoB thoughput, running ECM on these big numbers would be a big step backwards in SoB throughput.

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