20091229, 05:11  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
19·23^{2} Posts 
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 20091229 at 05:17 
20091229, 06:33  #2  
Oct 2004
Austria
100110110010_{2} Posts 
Quote:


20091229, 08:19  #3 
Nov 2008
2·3^{3}·43 Posts 
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> ] 
20091229, 16:09  #4  
Jun 2005
lehigh.edu
1024_{10} Posts 
Quote:
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 

20091230, 18:31  #5 
Oct 2006
vomit_frame_pointer
101101000_{2} Posts 
Okay: That's big, man
Code:
Found probable prime factor of 68 digits: Damn, man. I particularly love the "man" at the end of the thread title, man. 
20091231, 01:23  #6 
Oct 2006
vomit_frame_pointer
2^{3}×3^{2}×5 Posts 
Ran it myself, man
Did anyone else run this themselves, just to enjoy the feeling, man? I learned, once again, how machinedependent gmpecm can be. This was on a Windows XP laptop, using a nonetoorecent 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 GMPECM 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 20091231 at 01:24 Reason: Man. 
20091231, 16:33  #7 
Apr 2007
Spessart/Germany
246_{8} Posts 
I saw it some seconds ago, nice present for the ending decade.
Congratulations to Lazarusuk. 
20100418, 19:55  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
19×23^{2} Posts 
Nice pair!
Another p73 (for nitpickers: slightly smaller):
5888 2,1163 c318 1042816042941845750042952206680089794415014668329850393031910483526456487 . p246 Bos+Kleinjung+AKLenstra+Montgomery ECMNET 
20100418, 20:18  #9 
Oct 2006
vomit_frame_pointer
2^{3}×3^{2}×5 Posts 
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 10^711 is the largest 71digit number ever to be factored, and someone will reply with a correction.) Actually, nitpickers 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 "analretentive" supposed to be hyphenated, or not? 
20100418, 21:20  #10 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
19×23^{2} Posts 
Hehe. 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 68digits or were 2^{n}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 nitpickers: they called their targets (quote)Mersenne numbers(/quote). 
20100418, 22:34  #11  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
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 + ecmgmp, 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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