20101110, 14:11  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
14357_{8} Posts 
Unexpected jackpot
While running 5000@1e7 on 41589736558029544246565083974491624657173986172871770832111564777905257022360877402491398634730464093984676839103191549884835448808426403814480553982267 (factor of term 3033 of aliquot sequence 3678), what should I see but
Run 842 out of 1250: Using B1=10000000, B2=35132741290, polynomial Dickson(12), sigma=2806272118 Step 1 took 37700ms Step 2 took 16800ms ********** Factor found in step 2: 16785703768734933461785568830025208537214399823278256352088003411 Found probable prime factor of 65 digits: 16785703768734933461785568830025208537214399823278256352088003411 Probable prime cofactor 2477687985623493724345242897456632374207345125703301521609644949212001889191707885317497 has 88 digits Report your potential champion to Richard Brent <champs@rpbrent.com> (see http://wwwmaths.anu.edu.au/~brent/ftp/champs.txt) Sadly just below the top ten, but I think I've just seen an extremely improbable event. Even more absurdly, this could have been found with B1=1E6 (though a larger than normal B2): Code:
FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^25); x := u^3; b := 4*x*v; a := (vu)^3*(3*u+v); A := a/b2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p := 16785703768734933461785568830025208537214399823278256352088003411; s := 2806272118; FindGroupOrder2(p, s); Code:
[ <2, 3>, <3, 2>, <19, 1>, <881, 1>, <967, 1>, <2017, 1>, <34147, 1>, <51637, 1>, <109793, 1>, <131759, 1>, <152111, 1>, <347969, 1>, <895457, 1>, <968113, 1>, <6101051807, 1> ] Last fiddled with by fivemack on 20101110 at 14:22 
20101110, 15:07  #2  
Nov 2003
2^{2}·5·373 Posts 
Quote:


20101110, 15:32  #3  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
it's 6th and almost certain to remain in the top10 for 2010 (with less than two months to go). _Very_ nice. Bruce Ah, you mean Brent's list. Then you'll have to settle for the ECMNET list. Please email your result to PaulZ. (Neither the top10 nor the top50 are restricted to Cunninghams.) 

20101110, 19:10  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9334_{10} Posts 
That's a very neat hit for B1=1e7 ...and a shocker with B1=1e6 !
Congratulations! (And I thought I was lucky with a tight fit just under the B1=2e7 (a p63), Sheesh!). 
20101110, 19:20  #5  
Oct 2006
vomit_frame_pointer
2^{3}·3^{2}·5 Posts 
Damn!
Quote:
I have never done that "spray coffee on the keyboard" thing. Coughing is all I have to offer. Congratulations! EDIT: Ahh! I see that you meant topten all time ECM finds. (Things are getting so nutso that I believed a P65 was not enough to make the top ten for 2010.) Last fiddled with by FactorEyes on 20101110 at 19:23 Reason: Saboteurs, francstireurs, and sixthcolumnist Decembrists! 

20101110, 19:23  #6  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10598_{10} Posts 
Quote:
Nice result from Tom. Paul 

20101110, 19:34  #7  
Oct 2004
Austria
4662_{8} Posts 
Quote:


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