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Old 2010-11-10, 14:11   #1
fivemack
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Feb 2006
Cambridge, England

143578 Posts
Default 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^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   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 2010-11-10 at 14:22
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Old 2010-11-10, 15:07   #2
R.D. Silverman
 
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Nov 2003

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Quote:
Originally Posted by fivemack View Post
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^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   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> ]
Awesome!
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Old 2010-11-10, 15:32   #3
bdodson
 
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Jun 2005
lehigh.edu

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Quote:
Originally Posted by fivemack View Post
Step 2 took 16800ms
********** Factor found in step 2: 16785703768734933461785568830025208537214399823278256352088003411
Found probable prime factor of 65 digits:

Sadly just below the top ten, but I think I've just seen an extremely improbable event. ...
What?? You mean that it's 12th on the top50? For the top10,
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.)
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Old 2010-11-10, 19:10   #4
Batalov
 
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Mar 2008
Phi(4,2^7658614+1)/2

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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!).
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Old 2010-11-10, 19:20   #5
FactorEyes
 
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Oct 2006
vomit_frame_pointer

23·32·5 Posts
Thumbs up Damn!

Quote:
Sadly just below the top ten...
I was in the middle of some M&M's and Diet Coke - this is not intended as an endorsement - and I had a coughing fit.

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 top-ten 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 2010-11-10 at 19:23 Reason: Saboteurs, francs-tireurs, and sixth-columnist Decembrists!
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Old 2010-11-10, 19:23   #6
xilman
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May 2003
Down not across

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Quote:
Originally Posted by FactorEyes View Post
I was in the middle of some M&M's and Diet Coke - this is not intended as an endorsement - and I had a coughing fit.

I have never done that "spray coffee on the keyboard" thing. Coughing is all I have to offer.

Congratulations!
C|N>K as they say.

Nice result from Tom.

Paul
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Old 2010-11-10, 19:34   #7
Andi47
 
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Oct 2004
Austria

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Quote:
Originally Posted by fivemack View Post
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
nice!
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