News and updates, August 2005

News and updates, August 2005	2005-09-02(Fri) 01:33

Aug 31, 2005

By Wataru Sakai / GMP-ECM 6.0.1, Msieve 1.01
3·10¹⁷³-1 = 2(9)₁₇₃_<174> = 7 · 107 · 157 · 3013176114760906824959_<22> · 3438554741560059188437_<22> · C126
C126 = P38 · P40 · P49
P38 = 30644010457996651884427900089832310981_<38>
P40 = 1965123061305630337817335362597030221689_<40>
P49 = 4088876295547466384808084321913583821345407444169_<49>

Aug 26, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁴³+72·10⁷¹-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111111111911111111111111111111111111111111111111111111111111111111111111111111111_<143> = 7 · 277 · 727 · 279778297 · C128
C128 = P62 · P66
P62 = 72273103620858305018095324741944225768771546360367998482307077_<62>
P66 = 389811406670462912882304861142771874917257621758577152758207354823_<66>

Number: 11911_71
N=28172880186886902382565907756058819960301220351512976216723917393317410772426832760524239874187807805214575110233631418582982371
  ( 128 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=72273103620858305018095324741944225768771546360367998482307077 (pp62)
 r2=389811406670462912882304861142771874917257621758577152758207354823 (pp66)
Version: GGNFS-0.77.1
Total time: 101.15 hours.
Scaled time: 60.49 units (timescale=0.598).
Factorization parameters were as follows:
name: 11911_71
n: 28172880186886902382565907756058819960301220351512976216723917393317410772426832760524239874187807805214575110233631418582982371
m: 1000000000000000000000000000000000000
c4: 1
c2: 72
c0: -10
skew: 2
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [650000, 10950001)
Relations: rels:3887908, finalFF:225098
Initial matrix: 200057 x 225098 with sparse part having weight 33768894.
Pruned matrix : 196511 x 197575 with weight 28081749.
Total sieving time: 97.82 hours.
Total relation processing time: 0.84 hours.
Matrix solve time: 2.41 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,144,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 101.15 hours.
 --------- CPU info (if available) ----------

Aug 19, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁴¹-6·10⁷⁰-1)/3 = 333333333333333333333333333333333333333333333333333333333333333333333313333333333333333333333333333333333333333333333333333333333333333333333_<141> = 5679008497_<10> · C131
C131 = P38 · P94
P38 = 22054166497043884847287870515417562787_<38>
P94 = 2661433247090910549892098768566601079816496655240836213664857059852920403942119789232108468247_<94>

Number: 33133_70
N=5869569195211107875426961759189868902450654905814157180919134894073628524337341440208331727969473635625259979837873683909251832438
9
  ( 131 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=22054166497043884847287870515417562787 (pp38)
 r2=2661433247090910549892098768566601079816496655240836213664857059852920403942119789232108468247 (pp94)
Version: GGNFS-0.77.1
Total time: 45.73 hours.
Scaled time: 27.30 units (timescale=0.597).
Factorization parameters were as follows:
name: 33133_70
n:
58695691952111078754269617591898689024506549058141571809191348940736285243373414402083317279694736356252599798378736839092518324389
m: 100000000000000000000000000000000000
c4: 10
c2: -6
c0: -1
skew: 2
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [650000, 5450001)
Relations: rels:3031774, finalFF:224692
Initial matrix: 199975 x 224692 with sparse part having weight 30681510.
Pruned matrix : 196584 x 197647 with weight 25191896.
Total sieving time: 43.36 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 1.97 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,141,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 45.73 hours.
 --------- CPU info (if available) ----------

Aug 17, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
10¹⁴⁷-8·10⁷³-1 = 999999999999999999999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999999999999999999999_<147> = 268621621 · 1246336831459_<13> · 3257510230715911_<16> · C111
C111 = P43 · P69
P43 = 6918532079648681928624227305677184757812901_<43>
P69 = 132532947820656116347673308311597774490809937550021677979979509663531_<69>

Number: 99199_73
N=916933451107614207977491393274790653521017522562624288275315249667852377151353868032210260082035715381961013431
  ( 111 digits)
Divisors found:
 r1=6918532079648681928624227305677184757812901 (pp43)
 r2=132532947820656116347673308311597774490809937550021677979979509663531 (pp69)
Version: GGNFS-0.77.1
Total time: 46.39 hours.
Scaled time: 30.90 units (timescale=0.666).
Factorization parameters were as follows:
name: 99199_73
n: 916933451107614207977491393274790653521017522562624288275315249667852377151353868032210260082035715381961013431
skew: 92018.84
# norm 2.29e+15
c5: 2580
c4: -164595030
c3: -93487085999328
c2: 891120778083026509
c1: 250431877736007509209512
c0: -2277452151238083520167368440
# alpha -5.69
Y1: 2577594437
Y0: -3237006910593019894047
# Murphy_E 8.15e-10
# M 755602497340319720753600300174863421702075262789471555617565943466725266074363016624019553016563101108387204505
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 2500001)
Relations: rels:7840940, finalFF:767722
Initial matrix: 460794 x 767722 with sparse part having weight 68953522.
Pruned matrix : 350229 x 352596 with weight 20384629.
Total sieving time: 41.69 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 3.69 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 46.39 hours.
 --------- CPU info (if available) ----------

Aug 15, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(7·10¹⁴⁵-18·10⁷²-7)/9 = 7777777777777777777777777777777777777777777777777777777777777777777777775777777777777777777777777777777777777777777777777777777777777777777777777_<145> = 31337 · 10207927 · 4373145025202319447727_<22> · C112
C112 = P35 · P77
P35 = 92866052707040947788116402231861249_<35>
P77 = 59870059706292377489750144616722782975145763789830724139519840298455819562801_<77>

Number: 77577_72
N=5559896120258236414034846893348395205002429377172857370701234440446468916392707974193072114223436257151673798449
  ( 112 digits)
Divisors found:
 r1=92866052707040947788116402231861249 (pp35)
 r2=59870059706292377489750144616722782975145763789830724139519840298455819562801 (pp77)
Version: GGNFS-0.77.1
Total time: 53.43 hours.
Scaled time: 35.59 units (timescale=0.666).
Factorization parameters were as follows:
name: 77577_72
n: 5559896120258236414034846893348395205002429377172857370701234440446468916392707974193072114223436257151673798449
skew: 57568.01
# norm 9.18e+15
c5: 12360
c4: 4125169214
c3: -83810437096847
c2: -2565486382885458031
c1: 175872415273834200941691
c0: -3283473328532952956915197019
# alpha -6.18
Y1: 424712788957
Y0: -3393173080646087123664
# Murphy_E 6.70e-10
# M 5048155764753586441569837315618718831685323041662770967849248395447341958506427926356149893035522071106858837755
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2750001)
Relations: rels:7252580, finalFF:581163
Initial matrix: 499706 x 581163 with sparse part having weight 46847319.
Pruned matrix : 462887 x 465449 with weight 28851319.
Total sieving time: 45.39 hours.
Total relation processing time: 0.61 hours.
Matrix solve time: 6.92 hours.
Time per square root: 0.52 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 53.43 hours.
 --------- CPU info (if available) ----------

Aug 13, 2005

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁵¹-4·10⁷⁵-1 = 9999999999999999999999999999999999999999999999999999999999999999999999999995999999999999999999999999999999999999999999999999999999999999999999999999999_<151> = 13 · 1399 · 16302156079139241779389_<23> · C125
C125 = P45 · P81
P45 = 140684559337675769430249526788079461538589821_<45>
P81 = 239743837024742116073004013726167157177219146951323324165616082687053255604169333_<81>

Number: 99599_75
N=33728256065749401321947519978188403445131969827166842882306756094510580657741804858054977739871277830956367256686320914159393
  ( 125 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=140684559337675769430249526788079461538589821 (pp45)
 r2=239743837024742116073004013726167157177219146951323324165616082687053255604169333 (pp81)
Version: GGNFS-0.77.1
Total time: 96.94 hours.
Scaled time: 57.87 units (timescale=0.597).
Factorization parameters were as follows:
name: 99599_75
n: 33728256065749401321947519978188403445131969827166842882306756094510580657741804858054977739871277830956367256686320914159393
m: 100000000000000000000000000000000000000
c4: 1
c2: -4
c0: -10
skew: 2
type: snfs

Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 
)
Relations: rels:5108890, finalFF:395238
Initial matrix: 352394 x 395238 with sparse part having weight 44599917.
Pruned matrix : 345737 x 347562 with weight 34987824.
Total sieving time: 89.92 hours.
Total relation processing time: 0.55 hours.
Matrix solve time: 6.37 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,152,4,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 96.94 hours.
 --------- CPU info (if available) ----------

Aug 9, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
10¹³⁹-8·10⁶⁹-1 = 9999999999999999999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999999999999999999_<139> = 163 · 1062432269_<10> · C128
C128 = P48 · P81
P48 = 302855476516074177647629415714756028303921414367_<48>
P81 = 190667078116784852082971325091397033054587376040953643790001855636676885107219351_<81>

Number: 99199_69
N=57744568798986415510773932976505073180299887158946907306679422930356375851224384106461875755450059382111512647059891598431815817
  ( 128 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=302855476516074177647629415714756028303921414367 (pp48)
 r2=190667078116784852082971325091397033054587376040953643790001855636676885107219351 (pp81)
Version: GGNFS-0.77.1
Total time: 208.65 hours.
Scaled time: 163.79 units (timescale=0.785).
Factorization parameters were as follows:
n: 57744568798986415510773932976505073180299887158946907306679422930356375851224384106461875755450059382111512647059891598431815817 
m: 100000000000000000000000000000000000
c4: 1 
c2: -8
c0: -10
skew: 1
type: snfs
qintsize: 1500000
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [400000, 28900001)
Relations: rels:3968017, finalFF:182233
Initial matrix: 142444 x 182233 with sparse part having weight 29662836.
Pruned matrix : 140031 x 140807 with weight 20887958.
Total sieving time: 207.86 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,140,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 208.65 hours.
 --------- CPU info (if available) ----------

Aug 8, 2005

By Sinkiti Sibata / GGNFS-0.77.1
10¹³⁹-4·10⁶⁹-1 = 9999999999999999999999999999999999999999999999999999999999999999999995999999999999999999999999999999999999999999999999999999999999999999999_<139> = 13 · 3371 · 4459361 · C128
C128 = P34 · P94
P34 = 9093166788015632376354737529539617_<34>
P94 = 5627430068621602347797796257575031305382650518686424260015430403586239623261886314643346512049_<94>

Number: 99599_69
N=51171160201870485513080405198795010591453381095677096444927440835929973402710848191919926612329176065107845063847929701713345233
  ( 128 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=9093166788015632376354737529539617 (pp34)
 r2=5627430068621602347797796257575031305382650518686424260015430403586239623261886314643346512049 (pp94)
Version: GGNFS-0.77.1
Total time: 72.45 hours.
Scaled time: 43.32 units (timescale=0.598).
Factorization parameters were as follows:
name: 99599_69
n: 51171160201870485513080405198795010591453381095677096444927440835929973402710848191919926612329176065107845063847929701713345233
m: 100000000000000000000000000000000000
c4: 1
c2: -4
c0: -10
skew: 2
type: snfs

Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [400000, 9475001)
Relations: rels:2395349, finalFF:162523
Initial matrix: 142408 x 162523 with sparse part having weight 23836958.
Pruned matrix : 140648 x 141424 with weight 19421252.
Total sieving time: 70.56 hours.
Total relation processing time: 0.89 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,140,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 72.45 hours.
 --------- CPU info (if available) ----------

Aug 5, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
10¹⁴¹-4·10⁷⁰-1 = 999999999999999999999999999999999999999999999999999999999999999999999959999999999999999999999999999999999999999999999999999999999999999999999_<141> = 166609 · 168892705626840317_<18> · C119
C119 = P38 · P81
P38 = 69601747779002689794628246744089845171_<38>
P81 = 510587882640423485418476391438744702348606597088037480834827701746902682358566873_<81>

Number: 99599_70
N=35537809026553781358388852153474695439648624939407069519743470077963216916534262677747826085919217510685375636019620283
  ( 119 digits)
Divisors found:
 r1=69601747779002689794628246744089845171 (pp38)
 r2=510587882640423485418476391438744702348606597088037480834827701746902682358566873 (pp81)
Version: GGNFS-0.77.1
Total time: 161.09 hours.
Scaled time: 96.01 units (timescale=0.596).
Factorization parameters were as follows:
name: 99599_70
n: 35537809026553781358388852153474695439648624939407069519743470077963216916534262677747826085919217510685375636019620283
skew: 189526.16
# norm 6.13e+16
c5: 1920
c4: 1859260232
c3: 940958798448133
c2: -45971932498535203527
c1: -9004151374362697326116263
c0: 77743814714520445390033373470
# alpha -5.98
Y1: 1364027900503
Y0: -113103714933809449396359
# Murphy_E 2.87e-10
# M 12071100189367619106537480873581774950505039136236748682596382857408903799569354795385588773392413321309616487608958455
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 5610001)
Relations: rels:8011734, finalFF:732220
Initial matrix: 631506 x 732220 with sparse part having weight 74395567.
Pruned matrix : 593341 x 596562 with weight 50427406.
Total sieving time: 142.27 hours.
Total relation processing time: 1.46 hours.
Matrix solve time: 16.55 hours.
Time per square root: 0.80 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 161.09 hours.
 --------- CPU info (if available) ----------