Gratuitous factors thread - Page 17

Yeong Uk Jo · 2010-03-03, 10:49

r2/r1 is just about 1.013

Number: 29999_192
N=96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497
( 128 digits)
Divisors found:
r1=9740471141873076715269094836964843996395634689724625712596839367
r2=9870888065300008002666195086781466583752845796759751444217049391
Version:
Total time: 70.00 hours.
Scaled time: 167.45 units (timescale=2.392).
Factorization parameters were as follows:
# Murphy_E = 9.470857e-11, selected by Jeff Gilchrist
n: 96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497
Y0: -4728337515127376913733073
Y1: 113391337021723
c0: -68746208699076990334683890878800
c1: 2556257913066612300971980446
c2: -15170833482453671465739
c3: -20681738268242644
c4: 50385102936
c5: 40680
skew: 464131.78
type: gnfs
# selected mechanically
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved algebraic special-q in [4000000, 8400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: 19065947
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1260002 x 1260249
Total sieving time: 61.63 hours.
Total relation processing time: 4.29 hours.
Matrix solve time: 3.76 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
gnfs,127,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,28,28,54,54,2.5,2.5,100000
total time: 70.00 hours.
--------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b
Memory: 8046640k/8912896k available (2550k kernel code, 339524k reserved, 1291k data, 208k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5345.61 BogoMIPS (lpj=2672808)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)
Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618905)

fivemack · 2010-03-03, 13:23

aliquot sequence 1920 index 2124 splits as 2^2 . 3 . 7 . 97 . 12611 . P23 . P25 . P26 . P28 . P30

with large factors

43715010634395960945991
8257710475368317381357887
14062317576359023621153853
2136527974410831993786057559
849472442753123035317600227699

which is quite pretty and vaguely surprising.

Batalov · 2010-03-03, 19:22

Well, I've just recently noticed another similar curio:

Quote:

Originally Posted by Batalov

Nice line with p23.p24.p25.p25.p25 --

Code:

556276:6779 .  788871340341057562889230923678722189737792940800022551501177995987544153414255611539335238436104792425694403749441775012787706257880 = 2^3 * 5 * 883 * 27079631 * 91094766202869033075899 * 361000310979526340890151 * 1248561491484813471034241 * 2030361154450937185791841 * 9893694771484052066672231

(I went on to check some old .elf files; didn't find anything similar in 3 million lines.)

schickel · 2010-03-26, 04:34

Quote:

Originally Posted by Yeong Uk Jo

r2/r1 is just about 1.013

Number: 29999_192
N=96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497
( 128 digits)
Divisors found:
r1=9740471141873076715269094836964843996395634689724625712596839367
r2=9870888065300008002666195086781466583752845796759751444217049391

Darn....missed it by that much.

This is from aliquot sequence 171018:1932. r2/r1 is 1.016.

Code:

factoring 2769699872893724998777280362628763246881778451759748760598693420616396464782953 (79 digits)

prp40 factor: 1650731648154373712516554591214197107991
prp40 factor: 1677861980771030335098583193907462086783

Jens K Andersen · 2010-05-10, 00:37

RSA-180 =
400780082329750877952581339104100572526829317815807176564882178998497572771950624613470377
*
476939688738611836995535477357070857939902076027788232031989775824606225595773435668861833

A Wikipedia edit by an IP address registered in Moscow says:

"RSA-180 was factored on May 8, 2010 by S. A. Danilov and I. A. Popovyan from Moscow State University, Russia.
The factorization was found using the General Number Field Sieve algorithm implementation running on 3 Intel Core i7 PCs."

I haven't seen other mention of this. Wikipedia is not always reliable but the factorization is correct.

Batalov · 2010-05-23, 01:57

My first p50-digit factor in two years (a.f.a.i.r. ...I had a p56 in the first day of my ECMing, but nothing but a few p49s in between; granted, I never ECMed just for ECMing)...
Input number is 276249363376530523409280639717315262381353781466043253655792070660429289799029604351245743892224245080473070069478798426088869000784041 (135 digits)
Run 1317 out of 2000:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2708170207
Step 1 took 30665ms
Step 2 took 15273ms
********** Factor found in step 2:
Found probable prime factor of 50 digits: 11503934461120817806394297433479143709264161283779
Probable prime cofactor has 86 digits

wblipp · 2010-05-31, 22:36

(41^137-1)/40

ECM to t50 was done by yoyo@home
SNFS sieving was done by RSALS
Post Processing was done by Michael Rao

This is a Brent composite that had no known factors.

P66 x P155

Code:

P66: 
161033973705341754697154184520324001898167340683045689065770231389
P155: 
13880684065684569491359317232294346200171620088300352485145905214604506443519652814063086066838446421188243573906274202230093165037609560104584786537650493

wblipp · 2010-06-23, 16:27

Another Brent Composite with no known factors

(229^103-1)/228

ECM to t50 was done by yoyo@home
SNFS sieving was done by RSALS
Post Processing was done by Jeff Gilchrist

P57 x P185

Code:

P57: 268362433332419607426712500668487479781321407137778067937
P185: 18897228431405738066692044884523569849973250950468415595822949505504061540201281773035338111521604479828346442753167705447548016373710008855028996830938575885167309088122242073769290283

Andi47 · 2010-06-23, 19:50

c103 with a 3-way split (from aliquot sequence 41916):

Code:

prp34 factor: 3351171782449542012498325222773137
prp34 factor: 7542144712915888051238977936543171
prp35 factor: 67340189601709029451666811897595767

smells a bit like an ECM miss. (this one has had 651@1e6).

Batalov · 2010-06-26, 08:26

Another day, another p50:

3,1317M c150 =
Input number is 134334378587665946471267183035011069371867992103492968128193357546608845318563925400458505568168559187151459935412018714514857987996669119402175614727 (150 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=212849622
Step 1 took 35863ms
Step 2 took 17481ms
********** Factor found in step 2:
Found probable prime factor of 50 digits: 15625305790155774800504213544664082865394459261063
Probable prime cofactor has 100 digits

wblipp · 2010-06-28, 08:28

Brent composites with no previously known factors of 12 or more digits. 211^103-1 was cracked in ECM prefactoring. 727^79-1 had

yoyo@home ECM through t50
RSALS SNFS sieving

Code:

211^103-1
P46: 2673016773059390866847396713181717347377970273
P177: 168844400309543224776452178164986374130705983357226294632545828012827726753318999768883684415379024810376371450320366427976170084341903852792493402065981811174062733171985132393


727^79-1
P83: 79100334539201141396745982114077306712457214343784359318799331632881963257976907911
P141: 200494986318800422795008525000394773223643771305790583027076117436533593190553667229530696982229261743140802717175917985282255592480093908767

2010-03-03, 10:49	#177
Yeong Uk Jo Oct 2009 Korea 4₈ Posts	A nice split r2/r1 is just about 1.013 Number: 29999_192 N=96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497 ( 128 digits) Divisors found: r1=9740471141873076715269094836964843996395634689724625712596839367 r2=9870888065300008002666195086781466583752845796759751444217049391 Version: Total time: 70.00 hours. Scaled time: 167.45 units (timescale=2.392). Factorization parameters were as follows: # Murphy_E = 9.470857e-11, selected by Jeff Gilchrist n: 96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497 Y0: -4728337515127376913733073 Y1: 113391337021723 c0: -68746208699076990334683890878800 c1: 2556257913066612300971980446 c2: -15170833482453671465739 c3: -20681738268242644 c4: 50385102936 c5: 40680 skew: 464131.78 type: gnfs # selected mechanically rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved algebraic special-q in [4000000, 8400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 19065947 Max relations in full relation-set: Initial matrix: Pruned matrix : 1260002 x 1260249 Total sieving time: 61.63 hours. Total relation processing time: 4.29 hours. Matrix solve time: 3.76 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: gnfs,127,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,28,28,54,54,2.5,2.5,100000 total time: 70.00 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046640k/8912896k available (2550k kernel code, 339524k reserved, 1291k data, 208k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 5345.61 BogoMIPS (lpj=2672808) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339) Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618905)

2010-03-03, 13:23	#178
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2³×11×73 Posts	Five factors between 23 and 30 digits aliquot sequence 1920 index 2124 splits as 2^2 . 3 . 7 . 97 . 12611 . P23 . P25 . P26 . P28 . P30 with large factors 43715010634395960945991 8257710475368317381357887 14062317576359023621153853 2136527974410831993786057559 849472442753123035317600227699 which is quite pretty and vaguely surprising.

2010-05-10, 00:37	#181
Jens K Andersen Feb 2006 Denmark 2×5×23 Posts	RSA-180 factored RSA-180 = 400780082329750877952581339104100572526829317815807176564882178998497572771950624613470377 * 476939688738611836995535477357070857939902076027788232031989775824606225595773435668861833 A Wikipedia edit by an IP address registered in Moscow says: "RSA-180 was factored on May 8, 2010 by S. A. Danilov and I. A. Popovyan from Moscow State University, Russia. The factorization was found using the General Number Field Sieve algorithm implementation running on 3 Intel Core i7 PCs." I haven't seen other mention of this. Wikipedia is not always reliable but the factorization is correct.

2010-05-31, 22:36	#183
wblipp "William" May 2003 New Haven 2×7×13² Posts	(41^137-1)/40 ECM to t50 was done by yoyo@home SNFS sieving was done by RSALS Post Processing was done by Michael Rao This is a Brent composite that had no known factors. P66 x P155 Code: P66: 161033973705341754697154184520324001898167340683045689065770231389 P155: 13880684065684569491359317232294346200171620088300352485145905214604506443519652814063086066838446421188243573906274202230093165037609560104584786537650493

2010-06-23, 16:27	#184
wblipp "William" May 2003 New Haven 2·7·13² Posts	Another Brent Composite with no known factors (229^103-1)/228 ECM to t50 was done by yoyo@home SNFS sieving was done by RSALS Post Processing was done by Jeff Gilchrist P57 x P185 Code: P57: 268362433332419607426712500668487479781321407137778067937 P185: 18897228431405738066692044884523569849973250950468415595822949505504061540201281773035338111521604479828346442753167705447548016373710008855028996830938575885167309088122242073769290283

2010-05-23, 01:57	#182
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	My first p50-digit factor in two years (a.f.a.i.r. ...I had a p56 in the first day of my ECMing, but nothing but a few p49s in between; granted, I never ECMed just for ECMing)... Input number is 276249363376530523409280639717315262381353781466043253655792070660429289799029604351245743892224245080473070069478798426088869000784041 (135 digits) Run 1317 out of 2000: Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2708170207 Step 1 took 30665ms Step 2 took 15273ms ********** Factor found in step 2: Found probable prime factor of 50 digits: 11503934461120817806394297433479143709264161283779 Probable prime cofactor has 86 digits

2010-06-23, 19:50	#185
Andi47 Oct 2004 Austria 100110110010₂ Posts	c103 with a 3-way split (from aliquot sequence 41916): Code: prp34 factor: 3351171782449542012498325222773137 prp34 factor: 7542144712915888051238977936543171 prp35 factor: 67340189601709029451666811897595767 smells a bit like an ECM miss. (this one has had 651@1e6).

2010-06-26, 08:26	#186
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2519₁₆ Posts	Another day, another p50: 3,1317M c150 = Input number is 134334378587665946471267183035011069371867992103492968128193357546608845318563925400458505568168559187151459935412018714514857987996669119402175614727 (150 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=212849622 Step 1 took 35863ms Step 2 took 17481ms ********** Factor found in step 2: Found probable prime factor of 50 digits: 15625305790155774800504213544664082865394459261063 Probable prime cofactor has 100 digits

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