Reserved for MF - Sequence 4788

[Andi47]

Originally Posted by jrk

I started a poly search for the c146. In about 24 hours I'll post a result.

How much ECM did this one have? I guess we should do at least t45 (7500@11e6) before doing GNFS?

[schickel]

Originally Posted by Andi47

How much ECM did this one have? I guess we should do at least t45 (7500@11e6) before doing GNFS?

I did some higher level curves. I'm not sure what the conversion ration is....

[Andi47]

Originally Posted by schickel

I did some higher level curves. I'm not sure what the conversion ration is....

According to my calculations based on the curves which have been reported to the DB, t45 is ~57% done.

[jrk]

Originally Posted by Andi47

How much ECM did this one have? I guess we should do at least t45 (7500@11e6) before doing GNFS?

Since we can search for polys on a GPU now but not ECM or sieving, it doesn't hurt to do poly searching early in parallel.

My best poly so far is 9.198e-12. I will do some testing to find the right parameters and post it later.

[jrk]

This is the best from today but I will do another day of searching.

n: 34128802065277683324940497060114456028128085387534241677541889565653711918779403288707008461679255695847408643283266931540024693124361473714544539
# norm 3.792523e-14 alpha -7.832101 e 9.198e-12
skew: 3154674.50
c0:  6160701223310457747430798454115232525
c1: -5353471580850156751287280021324
c2: -5703088353790837679214303
c3:  44415752942820154
c4:  1079694510848
c5:  53760
Y0: -14472016831258149683092208646
Y1:  27360769963746067
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
alambda: 2.6
rlambda: 2.6
alim: 20000000
rlim: 20000000

[jrk]

I had a 9.589e-12 poly but it test-sieved slower than the 9.198e-12 one.

[henryzz]

Originally Posted by jrk

I had a 9.589e-12 poly but it test-sieved slower than the 9.198e-12 one.

probably something to do with the 9.198e-12 having quite a good alpha
from memory someone said a while back that higher alpha means a higher chance of smaller factors and lower norms means the numbers to be factored are smaller
the e value attempts to get the mix right but doesnt always

[10metreh]

Originally Posted by henryzz

probably something to do with the 9.198e-12 having quite a good alpha
from memory someone said a while back that higher alpha means a higher chance of smaller factors and lower norms means the numbers to be factored are smaller
the e value attempts to get the mix right but doesnt always

With degree 4, the poly with the highest e value is very often suboptimal in fact.

[henryzz]

Originally Posted by 10metreh

With degree 4, the poly with the highest e value is very often suboptimal in fact.

how do you find the optimal polynomial then?
look for the highest alpha or the smallest norms?

[Andi47]

...I found this factor by ECM:

Run 226 out of 2000:
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1163832276
Step 1 took 774079ms
Step 2 took 165421ms
********** Factor found in step 2: 1590362231581241185334390845152913218796531
Found probable prime factor of 43 digits: 1590362231581241185334390845152913218796531
Probable prime cofactor 21459766452919733123897504849837291094001756254327858522371153821180836119029805033757220337331923926969 has 104 digits

and...

2470.   116139550403454963217308225651624963448867441989096972645425812805257941827791127060931251649177260779207291173182882743273752673953845861192804201869628446785478569115056 = 2^4 * 3^2 * 7 * 115217807939935479382250223860739051040543097211405726830779576195692402606935641925527035366247282519054852354348097959596976859081196290865877184394472665461784294757
2471.   255322662394897022311066496075397737105843503420475090657007540849654364176969382506967910371603978062225552817235385078466900719723930980558783840618151426663313997184736 = 2^5 * 311 * 5867 * 1736734882092577 * c148

The 3 is gone!!

[jrk]

Using B1=43000000, B2=388112953420, polynomial Dickson(30), sigma=1033163144
Step 1 took 138254ms
Step 2 took 77893ms
********** Factor found in step 2: 314401460320696602393783174941
Found probable prime factor of 30 digits: 314401460320696602393783174941
Probable prime cofactor 8008382854566027043204017961675695251441834519040939952694150641178698834997735974059700130106717640670945550858659647 has 118 digits