Reserved for MF - Sequence 4788 - Page 29

jrk · 2009-07-21, 22:23

Quote:

Originally Posted by jrk

Code:

Using B1=43000000, B2=388112953420, polynomial Dickson(30), sigma=492002632
Step 1 took 169903ms
Step 2 took 85269ms
********** Factor found in step 2: 270389991140767419113595201012871830378223721738111
Found probable prime factor of 51 digits: 270389991140767419113595201012871830378223721738111
Probable prime cofactor 13097232778890996127721661850226147250346721968629381919532862503065919780081186230385499514937725380715199 has 107 digits

I computed the group order of the factorization:

Code:

[2 4]

[3 1]

[19 1]

[2473 1]

[17317 1]

[339331 1]

[608297 1]

[859459 1]

[1621679 1]

[4828303 1]

[4983967657 1]

So the factor could have been found with as little B1=5e6, B2=5e9.

Mini-Geek · 2009-07-22, 00:51

Quote:

Originally Posted by jrk

I computed the group order of the factorization:
...

How is this computed from the sigma? (or otherwise computed)
Here are some links related to this:
http://factordb.com/search.php?id=61049323 (the c157)
http://factordb.com/search.php?id=66234919 (the p51)
http://factordb.com/search.php?id=66581132 (the c51 you denoted by the factorization given)
http://factordb.com/search.php?id=66584546 (a p25 produced by c51-p51)

Quote:

Originally Posted by jrk

So the factor could have been found with as little B1=5e6, B2=5e9.

How much ECM was run at lengths closer to this? That would've been quite something to have found a p51 factor with B1 as low as 5e6! (which is between the B1 values for 40 and 45 digits)

jrk · 2009-07-22, 01:11

Quote:

Originally Posted by Mini-Geek

How is this computed from the sigma? (or otherwise computed)

See: this thread.

Greebley · 2009-07-22, 01:35

But isn't every elliptic curve is different so a different sigma would be a different factorization because each elliptic curve is a different size group? Thats the way I understood it.

The real point is there was a fifty digit number so you needed that size (which we chose) to find it (and we did). At 5e6 very few curves would find it.

jrk · 2009-07-22, 02:05

Quote:

Originally Posted by Greebley

But isn't every elliptic curve is different so a different sigma would be a different factorization because each elliptic curve is a different size group? Thats the way I understood it.

The real point is there was a fifty digit number so you needed that size (which we chose) to find it (and we did). At 5e6 very few curves would find it.

That's right.

bsquared · 2009-07-22, 03:15

Code:

Run 76 out of 250:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2937282173
Step 1 took 50670ms
Step 2 took 19890ms
********** Factor found in step 2: 24991157461902436638364677738700981780530893
Found probable prime factor of 44 digits: 24991157461902436638364677738700981780530893
Probable prime cofactor 770133409328510593934098647054112348863648709974876203302121061034340674324233272425893132240154136634104602673 has 111 digits

Partway through 4000 curves at 11M, this popped out.

jrk · 2009-07-22, 03:17

Good one.

Batalov · 2009-07-22, 03:17

a c134 so far

axn · 2009-07-22, 04:20

Who's this SB that is submitting all these curves??

Andi_HB · 2009-07-22, 04:28

Maybe SB = Serge Batalov?

Batalov · 2009-07-22, 04:54

correct

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2009-07-22, 01:35	#312
Greebley May 2009 Dedham Massachusetts USA 3·281 Posts	But isn't every elliptic curve is different so a different sigma would be a different factorization because each elliptic curve is a different size group? Thats the way I understood it. The real point is there was a fifty digit number so you needed that size (which we chose) to find it (and we did). At 5e6 very few curves would find it.

2009-07-22, 03:17	#315
jrk May 2008 3×5×73 Posts	Good one.

2009-07-22, 03:17	#316
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2519₁₆ Posts	a c134 so far

2009-07-22, 04:20	#317
axn Jun 2003 2·2,543 Posts	Who's this SB that is submitting all these curves??

2009-07-22, 04:28	#318
Andi_HB Mar 2007 Germany 108₁₆ Posts	Maybe SB = Serge Batalov?

2009-07-22, 04:54	#319
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22431₈ Posts	correct