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Thread: Smallest Exponent

  1. #1

    Smallest Exponent

    Just noticed this in my factrange.txt file.

    875106614402753 | 55459*2^1882+1

    Just wondering if this is the smallest exponent (1882), or if there have been smaller.

    Happy sieving.

  2. #2
    Moderator Joe O's Avatar
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    I do hope that you submitted it!
    Yes, there have been smaller in the past, but not recently as far as I know.
    Joe O

  3. #3
    I did submit it but i was wondering why you wanted to know if i submitted it.

    Does it have any impact since are we not way above that exponent?

  4. #4
    Moderator Joe O's Avatar
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    Well there are double checks
    dropped-tests
    error-fix
    missing-test
    residue-recovery
    second-pass
    going on.
    It's just good form to record unique factors whenever possible. You never know when you might save one or more PRPs.
    Joe O

  5. #5
    I love 67607
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    Or, as they say, "Just for the record..."

  6. #6
    Sieve it, baby!
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    It's not said that factors (below the lower bound) in factrange.txt are indeed unique. Only a very small portion will be.

  7. #7
    Originally posted by Joe O
    I do hope that you submitted it!
    Yes, there have been smaller in the past, but not recently as far as I know.
    490586292728209 | 24737*2^1303+1
    I have found this one about 20 days ago. I did post about it here:
    http://www.free-dc.org/forum/showthr...5&pagenumber=4
    (about halfway down the page-following a post by VJS on another tiny factor) but nobody seemed to take any notice.
    I highly doubt it was for a unique n though...

  8. #8
    Moderator Joe O's Avatar
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    Originally posted by maddog1
    but nobody seemed to take any notice.
    I highly doubt it was for a unique n though...
    Sorry, I didn't see it, but I did say AFAIK.
    It is/was an unique factor, submitted by SMH.
    Code:
    490586292728209 24737     1303  366   49
    Maniacken's is/was an excluded factor.

    Originally posted by Mystwalker
    It's not said that factors (below the lower bound) in factrange.txt are indeed unique. Only a very small portion will be.
    Very true! But having said that, VJS and I have found 10 of them recently by mining factrange.txt files. I have a Perl program that goes through a file and identifies the factors as unique, duplicate, or excluded. This keeps us from submitting duplicate and excluded factors that do not remove k n pairs from the database.
    Joe O

  9. #9
    Sieve it, baby!
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    Originally posted by Joe O
    I have a Perl program that goes through a file and identifies the factors as unique, duplicate, or excluded. This keeps us from submitting duplicate and excluded factors that do not remove k n pairs from the database.
    Could you post it here, please?

  10. #10
    Moderator Joe O's Avatar
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    Originally posted by Mystwalker
    Could you post it here, please?
    At the moment it is part of a complex system that grew and grew and grew. I'll have to see if I can make a short and sweet 2/3 program version of it. It uses the Berkely DB and I would really like to rewrite it for MySQL
    The logic is really very simple. Check to see if it is the original sob.dat If not it is excluded. Check to see if it is in the current sob.dat, if not it is duplicate. The complexity is in maintaing a db of the current sob.dat. I could just rebuild it from Mike's new daily sob.dat, but then everything below 1M would fall out as duplicate. i process the results_duplicates_excluded_marked.txt file daily looking for new factors, and removing their k/n pairs from the current sob.dat db.
    Meanwhile, back to trying to get my ADSL connection working. Going back to dialup hurts.
    Joe O

  11. #11
    Moderator vjs's Avatar
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    Maniacken,

    I think this is the one to beat

    1904.661T | 10223*2^137

  12. #12
    thanks VJS

    ill keep sending in all factors that i get.

  13. #13
    Moderator vjs's Avatar
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    maniacken,

    Great keep them coming ... on an interesting tid-bit I didn't know... Joe_O
    pointed out to me that we have factors for all n<991 at this point.

    So some k has an n=991 which is the lowest unfactored k/n pair.

    Its actually interesting from the point that not only have we tested all k/n pairs with n>2K we actually have factors for almost all k/n pairs for n's <1K.

    So we could almost change the description of n-lower bounds, all n's less than 991 have been factored by seventeen or bust and those n's >991 and less than the lower bound have been tested by others.

  14. #14
    Moderator Joe O's Avatar
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    Originally posted by vjs

    So we could almost change the description of n-lower bounds, all n's less than 991 have been factored by seventeen or bust and those n's >991 and less than the lower bound have been tested by others.
    There are only 8 k n pairs at or below the lower bounds. They have all been P-1'd to B1=2500001 and B2=250000100
    And ECM'd to:
    B1 = 2000 B2 = 600000 40 curves (15 digit factors)
    B1 = 11000 B2 = 3300000 120 curves (20 digit factors)
    B1 = 50000 B2 = 15000000 400 curves (25 digit factors)
    and k=24737 n=991 has additionally had the following work done:
    # of Value of Expected
    Digits B1 B2 curves
    35 1000000 300000000 1800 done
    40 3000000 900000000 5100 100 done 5000 to go!


    These are the 8 kn pairs I mentioned:
    Testing k=24737 n=991.
    Testing k=21181 n=1148.
    Testing k=19249 n=1166.
    Testing k=10223 n=1181.
    Testing k=27653 n=1257.
    Testing k=33661 n=1320.
    Testing k=67607 n=2051.
    Testing k=4847 n=2247.


    So the only one below the lower bounds is 24737*2^991+1. All the others have been PRP'd. I think that this one is below the lower limit for PRPing.
    Joe O

  15. #15
    Moderator vjs's Avatar
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    Humm, Joe is this important,

    [Tue April 01 12:45:59 1892] residue: 0000000000000000
    [Tue April 01 12:45:59 2010] completed proth test(k=24737, n=991): result 2






    No Really none of them are prime,


    [Thu Dec 16 16:01:17 2004] residue: 519B29073C609658
    [Thu Dec 16 16:01:17 2004] completed proth test(k=24737, n=991): result 3

    [Thu Dec 16 19:26:19 2004] residue: 1CB61408F443927D
    [Thu Dec 16 19:26:19 2004] completed proth test(k=21181, n=1148): result 3

    [Thu Dec 16 19:26:56 2004] residue: C106AB9E88F05EBD
    [Thu Dec 16 19:26:56 2004] completed proth test(k=19249, n=1166): result 3

    [Thu Dec 16 19:27:29 2004] residue: 49B738C745710FC2
    [Thu Dec 16 19:27:29 2004] completed proth test(k=10223, n=1181): result 3

    [Thu Dec 16 19:28:17 2004] residue: 0E44FB49C99D3595
    [Thu Dec 16 19:28:17 2004] completed proth test(k=27653, n=1257): result 3

    [Thu Dec 16 19:28:44 2004] residue: 42E3AFB6325D24E2
    [Thu Dec 16 19:28:44 2004] completed proth test(k=33661, n=1320): result 3

    [Thu Dec 16 19:29:10 2004] residue: 4FD14A95008330AB
    [Thu Dec 16 19:29:10 2004] completed proth test(k=67607, n=2051): result 3

    [Thu Dec 16 19:29:44 2004] residue: C288BD2E3D4B0BAB
    [Thu Dec 16 19:29:44 2004] completed proth test(k=4847, n=2247): result 3
    [Thu Dec 16 19:29:44 2004] connecting to server
    [Thu Dec 16 19:29:45 2004] couldn't report to server [can't connect], retry in 1200 secs [error: 0]

    No I didn't submit them, but I guess it means that we tested all k/n's <1.2m now

  16. #16
    Unholy Undead Death's Avatar
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    huh huh

    great vjs! smart solution. looks like it takes less than a minute to you to add values to registry and run sb client =))

    I've asked sometime ago can we retest all k\n pair's n<2000 or something (that's where sob takes a flag from other researchers) with regular clients and how long it takes. but they say that there's no need to do this.
    I suppose it can be done just for fun, as it takes only a few hours to complete.

    well if somebody just add 11*2000=22000 such short test's to global queue, they all returns back in a hour I suppose.
    wbr, Me. Dead J. Dona \


  17. #17
    Moderator Joe O's Avatar
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    Death,
    The reason "They say there is no need to do this" is because it has been done. They should say "There is no need to do this, again." VJS just did it again for this batch. Louie et al did it a while back. All numbers have been tested by S|B. S|B initially started off where other researchers had been, but has since backfilled and checked all their work.

    Perhaps, if someone has the time the description of "n Lower Bound" should be changed to:
    n Lower Bound: The value of n at which we started testing this multiplier. It was assumed that all n less than this lower bound had been previously tested by other members of the Sierpinski search community. All numbers below this point have now been retested by us.
    This might prevent this question from coming up again.
    Joe O

  18. #18
    Moderator vjs's Avatar
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    Death the reason I did it was to prove a point, yes those test have probably been done again, again, and again, several times over.

    Did anyone else catch the april fools 1892 reference in the log file resulting in a prime???

  19. #19

    Re: huh huh

    Originally posted by Death
    I've asked sometime ago can we retest all k\n pair's n<2000 or something (that's where sob takes a flag from other researchers) with regular clients and how long it takes. but they say that there's no need to do this.
    I suppose it can be done just for fun, as it takes only a few hours to complete.

    well if somebody just add 11*2000=22000 such short test's to global queue, they all returns back in a hour I suppose. [/B]
    You'd better use (win)pfgw with a small script to test all these numbers. Most of them have small factors so it shouldn't take long..

    Just tried K=4847 and without sieving/factoring it takes only a few seconds on my P4 to test all N<2000

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