Gratuitous factors thread

[hyramgraff]

I was surprised to find such a large factor with settings optimized for 30 digit factors.

GMP-ECM 6.4.4 [configured with GMP 6.1.0, --enable-asm-redc] [ECM]
Input number is 6791799153936500645432803709415674897403576115854345106509216573
02512210842714107504042514143509279143687934326862045806637465598577170030698639
39907063566032574234124386293757069836112420856904967943580197314005326553433926
69757816473416914726230827204181126950395601088979588731066439566823842928717186
75128298911533216869178867334130055945694895191331739721881 (363 digits)

Run 401 out of 430:
Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=3019497377
Step 1 took 2780ms
Step 2 took 1028ms
********** Factor found in step 2: 557172295660978462709725502307664383623870135
93731
Found probable prime factor of 50 digits: 55717229566097846270972550230766438362387013593731
Composite cofactor 1218976465059040443834739477156945548674792920302985605853429121627794
9623085784139709424457244324893107339172209402274275409256523706461433
7580941668601591059388584090906010550632184811055694891626199854079344
1844366357645987957465610950583807902371206167370270125577233154179128
6338464719210648028029318760713651 has 314 digits

[fivemack]

Input number is 76983647872843791624151541906153913917977086313839027114971383467019508946343866342583615282406460808225869127591905065014787008215584264828981273123902994205217437194952904477939999664624747162863484885320070182586711670719715251 (230 digits)
Run 11 out of 32:
Using B1=1000000000, B2=19071176724616, polynomial Dickson(30), sigma=2807183577
Step 1 took 7728506ms
Step 2 took 1153124ms
********** Factor found in step 2: 444391024295554825813920762553875384889500352609895126972409492191251
Found probable prime factor of 69 digits: 444391024295554825813920762553875384889500352609895126972409492191251
Composite cofactor 173234029636124329482413732384526787484660614027478215919523802481002152006501938783825536536976828897093688027674839882103830789172586815108211331791558012524001 has 162 digits

[hyramgraff]

Originally Posted by fivemack

Input number is
Found probable prime factor of 69 digits: 444391024295554825813920762553875384889500352609895126972409492191251

That's large enough to make it on the list of the top 50 factors: https://members.loria.fr/PZimmermann/records/top50.html

[fivemack]

Sun Jul  1 16:17:33 2018  p84 factor: 154026526536259486976791381709202414274307957213250722438177850806284297292352596891
Sun Jul  1 16:17:33 2018  p118 factor: 6944057549861420000506059176845705934485118493784592283341919973506171847370193586592773910514334148505693338642574449

Not sure this isn't the largest GNFS job using personal resources. 821 hours on 14 cores i9-7940X for the linear algebra on 44.48M density 136 matrix; about 20000 thread-days, mostly on E5-2650v1 processors, to get 978139469 relations.

[fivemack]

Originally Posted by hyramgraff

That's large enough to make it on the list of the top 50 factors: https://members.loria.fr/PZimmermann/records/top50.html

Good point! I've mailed Paul

[sean]

Originally Posted by fivemack

139!+1 done

Very impressive, shame you didn't get a slightly larger penultimate.

[chris2be8]

Here's a nice split of (21623179^17-1)/218287827114501499853622

prp51 factor: 400835974449507026429508363750399967684136291934989
prp51 factor: 564463714760965671472715787256458062957396312856251

Chris

[chris2be8]

My first job done with a septic.

(10^105-10^90-10^74-1)/107 generates a nice poly:

n: 9345794392523355140186915887849532710280373831775700934579439252336448598130841121495327102803738317757
# m = 10^17
m: 1000000000000000
c7: 10
c6: -10
c5: -1
c0: -10
type: snfs

And after a couple of hours:

p38 factor: 42430500173911639766168922724959195247
p66 factor: 220261235531454083548140762412574845378444054516121707598517853331

It would probably have been faster by GNFS since it's only a 103 digit number. But at least I can say I've done a septic.

Chris

[VBCurtis]

ECM on 13*2^962-1, a C185:

Using B1=150000000, B2=3973047228166, polynomial Dickson(30), sigma=1042721289
Step 1 took 1027041ms
Step 2 took 541536ms
********** Factor found in step 2: 2519220864327285024701856003209805861449234353205468125651304153
Found probable prime factor of 64 digits: 2519220864327285024701856003209805861449234353205468125651304153
The c122 cofactor is composite:
p64=1996676390473830958898711803711554458063469800085054040597619681
p59=18293875123847681477399988567617933809599560940077343333271

[ET_]

Originally Posted by VBCurtis

ECM on 13*2^962-1, a C185:

Using B1=150000000, B2=3973047228166, polynomial Dickson(30), sigma=1042721289
Step 1 took 1027041ms
Step 2 took 541536ms
********** Factor found in step 2: 2519220864327285024701856003209805861449234353205468125651304153
Found probable prime factor of 64 digits: 2519220864327285024701856003209805861449234353205468125651304153
The c122 cofactor is composite:
p64=1996676390473830958898711803711554458063469800085054040597619681
p59=18293875123847681477399988567617933809599560940077343333271

That's huge!

[Nooks]

The last composite divisor of (34*10^227-61)/9 factorizes nicely as p81 * p81:

52461733535023469582898980803025972072154673059207507371871956720157538\
98046977445635531886836257491304639830851690564317257362489857828241541\
1269306626660506087 == 
10827123788671956642383008247645953132666017522133372016228954601610784\
8102783919 * 
48453988851510461382956631659231929664064303447082394831858420014654224\
5073120073

Total factorization wall-clock time using the stdkmd-supplied SNFS polynomial and CADO-NFS was just shy of 3 days.