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 2009-04-02, 13:22 #1 Zeta-Flux     May 2003 7×13×17 Posts Odd perfect related number If people would like to run some curves on a C198 that is very useful to some computations we are running on odd perfect numbers, here it is: 734113326497375903508380883981436428492552344548308394747109592948586482115682543796022181706222408714039369623415812639904970855614632384820830270414090221896445540562946331670439914395986991208621
 2009-04-02, 14:16 #2 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 6,421 Posts What's the formula for that number?
 2009-04-02, 14:24 #3 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts Any info on how much ECM has been done already? Alex
 2009-04-02, 15:28 #4 Syd     Sep 2008 Krefeld, Germany 2·5·23 Posts Did some ECM, P+1 and P-1 on that number, so far no factor found. t40 is almost done .. http://factorization.ath.cx/search.php?id=28131033 Last fiddled with by Syd on 2009-04-02 at 16:18
 2009-04-02, 19:21 #5 philmoore     "Phil" Sep 2002 Tracktown, U.S.A. 3·373 Posts Is it a possible SNFS target, or would you have to use GNFS on it?
2009-04-02, 19:28   #6
10metreh

Nov 2008

2·33·43 Posts

Quote:
 Originally Posted by philmoore Is it a possible SNFS target, or would you have to use GNFS on it?
GNFS on a C198? Which is harder, that or M1061?

 2009-04-02, 19:58 #7 Zeta-Flux     May 2003 7·13·17 Posts The number is a factor of 753627999854532307360826893631284065754706057371051^5-1. That prime number 753627999854532307360826893631284065754706057371051 is a factor of 296032828349261431^5-1. So I don't imagine there is a nice SNFS form for the number in question.
 2009-04-02, 20:12 #8 Pascal Ochem     Apr 2006 103 Posts I did 3300 ECM curves with B1=11e6 and 200 with B1=43e6.
2009-04-02, 20:40   #9
bsquared

"Ben"
Feb 2007

DBC16 Posts

Quote:
 Originally Posted by Zeta-Flux The number is a factor of 753627999854532307360826893631284065754706057371051^5-1. That prime number 753627999854532307360826893631284065754706057371051 is a factor of 296032828349261431^5-1. So I don't imagine there is a nice SNFS form for the number in question.
Code:
n: 734113326497375903508380883981436428492552344548308394747109592948586482115682543796022181706222408714039369623415812639904970855614632384820830270414090221896445540562946331670439914395986991208621
# 753627999854532307360826893631284065754706057371051^5-1, difficulty: 203.51, skewness: 1.00, alpha: 1.45
# cost: 1.9137e+017, est. time: 91.13 GHz days (not accurate yet!)
skew: 1.000
c4: 1
c3: 1
c2: 1
c1: 1
c0: 1
Y1: -1
Y0: 753627999854532307360826893631284065754706057371051
m: 753627999854532307360826893631284065754706057371051
type: snfs
Difficulty 203 shouldn't be too bad, even with a quartic.

 2009-04-02, 20:43 #10 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts A quartic for this is somewhat annoying but far from a show-stopper. Beats GNFS for sure. Some more ECM is in order, though. Did 1041 at 44M so far, will do a few more. Edit: another 2000. Edit: another 2000. Edit: another 2000. Alex Last fiddled with by akruppa on 2009-04-04 at 21:48
2009-04-02, 22:37   #11
Random Poster

Dec 2008

17910 Posts

Quote:
 Originally Posted by 10metreh GNFS on a C198? Which is harder, that or M1061?
M1061 is a 320-digit SNFS, while 198-digit GNFS might be equivalent to something less than an SNFS 240.

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