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Old 2009-12-29, 05:11   #1
Batalov
 
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Default The largest ever prime ECM factor, man

http://www.loria.fr/~zimmerma/records/p68
This is quite something.
Congratulations!

_____
*largest prime factor, of course

Last fiddled with by Batalov on 2009-12-29 at 05:17
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Old 2009-12-29, 06:33   #2
Andi47
 
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Quote:
Originally Posted by Batalov View Post
http://www.loria.fr/~zimmerma/records/p68
This is quite something.
Congratulations!

_____
*largest prime factor, of course
WOOOOHOOO!!!

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Old 2009-12-29, 08:19   #3
10metreh
 
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The group order is:

Code:
[ <2, 2>, <3, 2>, <5, 2>, <7, 2>, <11, 1>, <3529, 1>, <331819, 1>, <739751, 1>, 
<1248781, 1>, <2291803, 1>, <9209957, 1>, <67209679, 1>, <79037141, 1>, 
<723922811009, 1> ]
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Old 2009-12-29, 16:09   #4
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Quote:
Originally Posted by 10metreh View Post
The group order is:

Code:
[ <2, 2>, <3, 2>, <5, 2>, <7, 2>, <11, 1>, <3529, 1>, <331819, 1>, <739751, 1>, 
<1248781, 1>, <2291803, 1>, <9209957, 1>, <67209679, 1>, <79037141, 1>, 
<723922811009, 1> ]
p55-optimal limits, B1 = 110e6; close for the largest step1 factor
of 79e6. B2 = 7.7e11 ... wow. The step2 factor of 7.23e11 is just barely
in range. A whole bunch of large step1 factors; both limits fully used.
More than three years since my p67.

Guess I can stop apologizing for having bumped Paul's p57 out
of this year's top10. Congrats to Yoyo and BOINC. -Bruce
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Old 2009-12-30, 18:31   #5
FactorEyes
 
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Cool Okay: That's big, man

Code:
Found probable prime factor of 68 digits:
File that under "Things Which Never Happen to Me"; they almost never happen to anyone else, for that matter, so I'm not too bitter, man.

Damn, man.

I particularly love the "man" at the end of the thread title, man.
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Old 2009-12-31, 01:23   #6
FactorEyes
 
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Talking Ran it myself, man

Did anyone else run this themselves, just to enjoy the feeling, man? I learned, once again, how machine-dependent gmp-ecm can be. This was on a Windows XP laptop, using a none-too-recent version, man.

Guzzled twice the memory, and took three times as long, man.

Heh.

Code:
C:\zahlen\work>ecm -v -sigma 1998958586 -inp RecordECM.n 11e7
GMP-ECM 6.2.3 [powered by GMP 4.3.0] [ECM]
Input number is 77408690560905323438604044124883251342679827896247009602906199773873214100
553786332237393178163861313602627195323510786443486054674798080254490528322806462692451464
212829574207211148953372274886526030715252104152499523855481315533280604274379459295999774
273361676468956372168684508022110729619071 (296 digits)
Using MODMULN
Using B1=110000000, B2=900514153782, polynomial Dickson(30), sigma=1998958586
dF=199680, k=2, d=2081310, d2=13, i0=40
Expected number of curves to find a factor of n digits:
20      25      30      35      40      45      50      55      60      65
2       4       10      34      132     600     3062    17350   108466  732708
Step 1 took 5081297ms
Estimated memory usage: 1450M
Initializing tables of differences for F took 3234ms
Computing roots of F took 175109ms
Building F from its roots took 111562ms
Computing 1/F took 42609ms
Initializing table of differences for G took 3390ms
Computing roots of G took 151313ms
Building G from its roots took 96812ms
Computing roots of G took 150531ms
Building G from its roots took 98625ms
Computing G * H took 23219ms
Reducing  G * H mod F took 34562ms
Computing polyeval(F,G) took 227297ms
Computing product of all F(g_i) took 1297ms
Step 2 took 1124219ms
********** Factor found in step 2: 4259378334615022318697944343788216432489200846285048000
8134130873603
Found probable prime factor of 68 digits: 425937833461502231869794434378821643248920084628
50480008134130873603
Probable prime cofactor 181737062265218557351644978026296097813612670767642186577609884002
050297629613370452238629055461263149143063321096517438693030811430607673941784904495307464
1365372499555249805775538554420955061583147505660366237473218561112127957 has 229 digits

Last fiddled with by FactorEyes on 2009-12-31 at 01:24 Reason: Man.
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Old 2009-12-31, 16:33   #7
MatWur-S530113
 
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I saw it some seconds ago, nice present for the ending decade.
Congratulations to Lazarusuk.
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Old 2010-04-18, 19:55   #8
Batalov
 
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Default Nice pair!

Another p73 (for nitpickers: slightly smaller):
5888 2,1163- c318 1042816042941845750042952206680089794415014668329850393031910483526456487
. p246 Bos+Kleinjung+AKLenstra+Montgomery ECMNET
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Old 2010-04-18, 20:18   #9
FactorEyes
 
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Quote:
Originally Posted by Batalov View Post
Another p73 (for nitpickers: slightly smaller)
Nitpickers? On this forum?

How dare you, Sir! I deeply resent the implication!

What time do you close? What time do you go to bed? I could come back then...

(Make dumb joke that 10^71-1 is the largest 71-digit number ever to be factored, and someone will reply with a correction.)

Actually, nit-pickers should be the better term. Or has it been in usage long enough for the compound to be a sensible choice these days?

Speaking of which: Is "anal-retentive" supposed to be hyphenated, or not?
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Old 2010-04-18, 21:20   #10
Batalov
 
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He-he. Not on this forum, no, never.

But think about this (for your consolation): by your standards, some your latest factors were not ECM misses unless they were under 68-digits or were 2n-1. The PS3 code (so far) was specialized for this form* (and one is left wondering if it was special for prime n's). They may have already extended it to other forms, but our fate is to read about it in the newspapers...
__________
*) More food for nit-pickers: they called their targets (quote)Mersenne numbers(/quote).
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Old 2010-04-18, 22:34   #11
bdodson
 
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Quote:
Originally Posted by Batalov View Post
... The PS3 code (so far) was specialized for this form* (and one is left wondering if it was special for prime n's). They may have already extended it to other forms, but our fate is to read about it in the newspapers...
__________
*) More food for nit-pickers: they called their targets (quote)Mersenne numbers(/quote).
So far as I know, Serge is the single person still restricting the term to prime
exponents. (Yes, I'm expecting multiple replies to the contrary.) I think it's
part of the mersenne project; we have M_n and P_n, and the notation is
certainly not restricted to prime exponents. Meanwhile, on the _NEW_
p73 by PS3 + ecm-gmp, we're still waiting for sigma and the group order;
maybe not so close to the B1/B2 limits this time? A second one goes miles
towards showing that the first one is the result of a reproducible experiment.

-Bruce (What newspapers? We heard it first here, sounds like Raman saw
Sam's page first?)
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