20090402, 13:22  #1 
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 
20090402, 14:16  #2 
(loop (#_fork))
Feb 2006
Cambridge, England
6441_{10} Posts 
What's the formula for that number?

20090402, 14:24  #3 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Any info on how much ECM has been done already?
Alex 
20090402, 15:28  #4 
Sep 2008
Krefeld, Germany
2×5×23 Posts 
Did some ECM, P+1 and P1 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 20090402 at 16:18 
20090402, 19:21  #5 
"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?

20090402, 19:28  #6 
Nov 2008
100100010010_{2} Posts 

20090402, 19:58  #7 
May 2003
7·13·17 Posts 
The number is a factor of 753627999854532307360826893631284065754706057371051^51.
That prime number 753627999854532307360826893631284065754706057371051 is a factor of 296032828349261431^51. So I don't imagine there is a nice SNFS form for the number in question. 
20090402, 20:12  #8 
Apr 2006
103 Posts 
I did 3300 ECM curves with B1=11e6 and 200 with B1=43e6.

20090402, 20:40  #9  
"Ben"
Feb 2007
2·1,789 Posts 
Quote:
Code:
n: 734113326497375903508380883981436428492552344548308394747109592948586482115682543796022181706222408714039369623415812639904970855614632384820830270414090221896445540562946331670439914395986991208621 # 753627999854532307360826893631284065754706057371051^51, 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 

20090402, 20:43  #10 
"Nancy"
Aug 2002
Alexandria
100110100011_{2} Posts 
A quartic for this is somewhat annoying but far from a showstopper. 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 20090404 at 21:48 
20090402, 22:37  #11 
Dec 2008
179 Posts 

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