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Old 2010-05-28, 19:58   #1
firejuggler
 
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"Vincent"
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Default explanation on polynomial

i got a
Code:
polynomial selection complete
R0: -524241004529396631870
R1:  153210241229
A0: -9399584704303529389555531
A1:  3328070423367697250750
A2: -4382136563645405
A3: -25301949289925
A4: -99655659
A5:  6720
skew 23469.09, size 3.209650e-010, alpha -5.457662, combined = 1.441579e-009
what doest that mean exactly? -524241004529396631870X+153210241229Y-9399584704303529389555531Z+...=0?
do I have a chance to 'resolve' it by tommorrow? (core 2 duo 8300)
the firsts factors look nasty...

Last fiddled with by firejuggler on 2010-05-28 at 20:09
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Old 2010-05-28, 20:35   #2
Mini-Geek
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"Tim Sorbera"
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(I'm no expert, but here's some of the basics to help you understand the polynomial numbers:)
No, the R stands for rational, the A for algebraic, the small numbers next to them stand for the power, and the long numbers after the : are the coefficients. So e.g. the rational polynomial is something like 153210241229x-524241004529396631870, and the algebraic polynomial starts like 6720x^5-99655659x^4.
More reading:
http://en.wikipedia.org/wiki/General_number_field_sieve
http://mersennewiki.org/index.php/SN...mial_Selection

To know if you can finish it by tomorrow, I'd need to know the size of the number (it can be calculated from the polynomial, but I'm not too skilled at all that). If you got it from your Subproject 4 aliquot sequence, yes you'll probably be able to finish it within a day, especially if factmsieve.py/.pl is set to run on both cores.

Last fiddled with by Mini-Geek on 2010-05-28 at 20:38
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Old 2010-05-28, 20:37   #3
Batalov
 
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Phi(4,2^7658614+1)/2

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evaluated polynomial value is 266086184645949956978563840542316598870701152415719227516961037350589307924318351641660557747971293884125881

That's 108 digits. Probably will be done by tomorrow, unless it is a really slow machine. Next time, you may want to give people less of a puzzle if you mention the number.
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Old 2010-05-28, 20:50   #4
Mini-Geek
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Quote:
Originally Posted by Batalov View Post
evaluated polynomial value is 266086184645949956978563840542316598870701152415719227516961037350589307924318351641660557747971293884125881
How is that calculated?
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Old 2010-05-28, 20:57   #5
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Quote:
Originally Posted by Mini-Geek View Post
How is that calculated?
Shhhhh!

m=-R0/R1

f(x) = A5*x^5 + A4*x^4 + A3*x^3 + A2*x^2 + A1*x + A0

n = (R1^5)*f(m)

Last fiddled with by FactorEyes on 2010-05-28 at 20:59 Reason: Spiders!
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Old 2010-05-28, 21:17   #6
firejuggler
 
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i'm working on a sequence, 36684, which get interrupted at 36684 :871...
and continue here this one is currently the 'last' of the list.
but that still not explain how Batalov got it

Last fiddled with by firejuggler on 2010-05-28 at 21:18
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Old 2010-05-28, 21:58   #7
Batalov
 
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It is simple. factMsieve.pl fixes the polynomial for you. (It is not even msieve; it is the perl part -- see the source. Thanks, Greg. :-) )
Just prepare a t.poly file (gotta rename 'R's into 'Y's, 'A's into 'c's) and feed it to factMsieve.pl and it will complain that the "evaluated polynomial value doesn't match yada yada". Then put n: <number> in and continue if needed.

So, what usually is a simple safety net -- serves here as a solver. (e.g. if you were just done with one project, say 2,1918M and then copied and edited the poly into, say 2,1946L and forgot to flip all odd c' signs - then the script will save you from sieving a lot for the wrong {evaluated} number. Because the problem is {or rather, was} -- the sievers will sieve and not emit a single peep. Only when msieve will start filtering it will throw away all relations and you will swear, ...maybe just a little. All of the relns will be useless. This did happen to more than one person.)

Caveat: the evaluated polynomial value could be a multiple of the real number in question, but msieve will immediately chip away the small factor.

EDIT: I realized that this is rather - thanks Chris ! this is in the original factLat.pl.

Btw, the p34 factor popped out :-)
Here - 5773992468201913720319403049611491 . Stop the sievers. Good luck with the sequence!

Last fiddled with by Batalov on 2010-05-28 at 22:02 Reason: thanks to Chris Monico + the factor
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Old 2010-05-29, 02:46   #8
jasonp
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Msieve now also checks the polynomial against the input number; several times in the past, people have used the correct polynomials for the sieving but did not strip out small factors from the input number when using msieve for the postprocessing. In that case everything will work fine but the NFS square root will fail mysteriously. I put the check in after one such mistake fooled me into thinking for almost a year that there was a 1-in-a-million bug in the square root.
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