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Old 2009-04-02, 13:22   #1
Zeta-Flux
 
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Default 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
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Old 2009-04-02, 14:16   #2
fivemack
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What's the formula for that number?
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Old 2009-04-02, 14:24   #3
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Any info on how much ECM has been done already?

Alex
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Old 2009-04-02, 15:28   #4
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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
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Old 2009-04-02, 19:21   #5
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Is it a possible SNFS target, or would you have to use GNFS on it?
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Old 2009-04-02, 19:28   #6
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Quote:
Originally Posted by philmoore View Post
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?
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Old 2009-04-02, 19:58   #7
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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.
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Old 2009-04-02, 20:12   #8
Pascal Ochem
 
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I did 3300 ECM curves with B1=11e6 and 200 with B1=43e6.
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Old 2009-04-02, 20:40   #9
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Quote:
Originally Posted by Zeta-Flux View Post
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.
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Old 2009-04-02, 20:43   #10
akruppa
 
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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
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Old 2009-04-02, 22:37   #11
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Quote:
Originally Posted by 10metreh View Post
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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