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News and updates, July 2005

Jul 30, 2005

By Wataru Sakai / GMP-ECM 6.0.1
3·10¹⁸⁶-1 = 2(9)_186<187> = 1000926126622857454738657_<25> · 5038740629385387262999058978219_<31> · C132
C132 = P30 · P103
P30 = 169578631674993232722608070359_<30>
P103 = 3507729531114303162480919388024654186192017726789378826407554907313223454226891369837005953138455530667_<103>

Jul 30, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(7·10¹³⁹-18·10⁶⁹-7)/9 = 7777777777777777777777777777777777777777777777777777777777777777777775777777777777777777777777777777777777777777777777777777777777777777777_<139> = 107 · 9592227941_<10> · C127
C127 = P50 · P78
P50 = 29507116701653644529662901060986428986529525108467_<50>
P78 = 256818016930257453229026060731674332126048439991708092787438809811276850360013_<78>

Number: 77577_69 N=7577959196648368142289258349347952581746683504023822980886262846418308000216869677607333548989045910320123116523470011824530071 ( 127 digits) SNFS difficulty: 140 digits. Divisors found: r1=29507116701653644529662901060986428986529525108467 (pp50) r2=256818016930257453229026060731674332126048439991708092787438809811276850360013 (pp78) Version: GGNFS-0.77.1 Total time: 92.73 hours. Scaled time: 72.70 units (timescale=0.784). Factorization parameters were as follows: n: 7577959196648368142289258349347952581746683504023822980886262846418308000216869677607333548989045910320123116523470011824530071 m: 100000000000000000000000000000000000 c4: 7 c2: -18 c0: -70 skew: 1 type: snfs qintsize: 1500000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 11150001) Relations: rels:4171683, finalFF:254395 Initial matrix: 199731 x 254395 with sparse part having weight 39370616. Pruned matrix : 194294 x 195356 with weight 27320206. Total sieving time: 91.38 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.06 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,140,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 92.73 hours. --------- CPU info (if available) ----------

Jul 29, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
10¹⁴⁷-7·10⁷³-1 = 999999999999999999999999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999999999999999999999999_<147> = 1523 · 33359 · 163141831126890373902190714753_<30> · C111
C111 = P37 · P74
P37 = 6771196048922895791023493473450472633_<37>
P74 = 17817893241367170326405819488787733173549447168880253186019589405975907843_<74>

Number: 99299_73 N=120648448316075352508465667748310321521825875484704823624632616876735833966375958575301853071848881879601560619 ( 111 digits) Divisors found: r1=6771196048922895791023493473450472633 (pp37) r2=17817893241367170326405819488787733173549447168880253186019589405975907843 (pp74) Version: GGNFS-0.77.1 Total time: 50.84 hours. Scaled time: 30.30 units (timescale=0.596). Factorization parameters were as follows: name: 99299_73 n: 120648448316075352508465667748310321521825875484704823624632616876735833966375958575301853071848881879601560619 skew: 68786.20 # norm 5.53e+15 c5: 540 c4: -144692729 c3: 144683750682965 c2: -315598007552356899 c1: -117835315053291737704530 c0: 576691279009697362689399375 # alpha -5.75 Y1: 25102374517 Y0: -2950025664308419358918 # Murphy_E 7.98e-10 # M 41342611917903131408145342621498957256392081985933491949904044448483573025062860196910456489936128726693837630 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, 2600001) Relations: rels:7540133, finalFF:630849 Initial matrix: 460865 x 630849 with sparse part having weight 54947476. Pruned matrix : 398156 x 400524 with weight 23631619. Total sieving time: 44.42 hours. Total relation processing time: 0.60 hours. Matrix solve time: 5.36 hours. Time per square root: 0.46 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: 50.84 hours. --------- CPU info (if available) ----------

Jul 28, 2005

By Samuel Chong / GMP-ECM 6.0.1
(4·10¹⁵⁶-7)/3 = 1(3)₁₅₅1_<157> = 139 · 24919 · 252324847 · C142
C142 = P36 · P106
P36 = 436423983918762045596465851491938171_<36>
P106 = 3495623885562373118078106033211400844430238147690721820383657027903206171888118531038163898577322216417043_<106>

Jul 26, 2005

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁵¹-2·10⁷⁵-1 = 9999999999999999999999999999999999999999999999999999999999999999999999999997999999999999999999999999999999999999999999999999999999999999999999999999999_<151> = 11 · 26293 · C146
C146 = P44 · P102
P44 = 58045103092320579472867801802574971275755973_<44>
P102 = 595664319591700023546971601179237285279082212336048740598250401382315669912840159022722808886547371381_<102>

Number: 99799_75 N=3457539683911722096790365911424748377549503324424406081120796063936823834894873505910664089647088924463130525580607351420875933103 5221956760008713 ( 146 digits) SNFS difficulty: 152 digits. Divisors found: r1=58045103092320579472867801802574971275755973 (pp44) r2=595664319591700023546971601179237285279082212336048740598250401382315669912840159022722808886547371381 (pp102) Version: GGNFS-0.77.1 Total time: 121.32 hours. Scaled time: 80.68 units (timescale=0.665). Factorization parameters were as follows: name: 99799_75 n: 345753968391172209679036591142474837754950332442440608112079606393682383489487350591066408964708892446313052558060735142087593310352 21956760008713 m: 100000000000000000000000000000000000000 c4: 1 c2: -2 c0: -10 skew: 2 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 4800001) Relations: rels:5437942, finalFF:397574 Initial matrix: 352076 x 397574 with sparse part having weight 50831921. Pruned matrix : 345772 x 347596 with weight 40312253. Total sieving time: 113.68 hours. Total relation processing time: 0.53 hours. Matrix solve time: 7.01 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: 121.32 hours. --------- CPU info (if available) ----------

Jul 24, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(7·10¹³⁹-45·10⁶⁹-7)/9 = 7777777777777777777777777777777777777777777777777777777777777777777772777777777777777777777777777777777777777777777777777777777777777777777_<139> = 53 · 761 · C135
C135 = P38 · P97
P38 = 31370267024602331790139632007760286403_<38>
P97 = 6147192152516161778791945160290758775994299914230005225313499885002983578636522012827875264702823_<97>

Number: 77277_69 N=192839059275971977729843497329179029027788108441667561990870447965134574114937589015887183640636148508114392129962506577189343162615669 ( 135 digits) SNFS difficulty: 140 digits. Divisors found: r1=31370267024602331790139632007760286403 (pp38) r2=6147192152516161778791945160290758775994299914230005225313499885002983578636522012827875264702823 (pp97) Version: GGNFS-0.77.1 Total time: 55.35 hours. Scaled time: 43.45 units (timescale=0.785). Factorization parameters were as follows: n: 192839059275971977729843497329179029027788108441667561990870447965134574114937589015887183640636148508114392129962506577189343162615669 m: 100000000000000000000000000000000000 c4: 7 c2: -45 c0: -70 skew: 1 type: snfs qintsize: 1500000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 6650001) Relations: rels:3418067, finalFF:350126 Initial matrix: 200408 x 350126 with sparse part having weight 50275219. Pruned matrix : 184489 x 185555 with weight 21546300. Total sieving time: 54.36 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.77 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,140,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 55.35 hours. --------- CPU info (if available) ----------

Jul 23, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
2·10¹⁷¹-1 = 1(9)_171<172> = 6569 · 568471 · 1534359796328829895031_<22> · 5602144536868763044479389_<25> · C116
C116 = P49 · P68
P49 = 4966249304875500322389200136777001930696447359469_<49>
P68 = 12546205073768228751789097590163050732197922850972414927607422229231_<68>

Number: 19999_171 N=62307582226426941282730497418239251189478704230641873240737131725763565707384336402366220505143817417223703576438339 ( 116 digits) Divisors found: r1=4966249304875500322389200136777001930696447359469 (pp49) r2=12546205073768228751789097590163050732197922850972414927607422229231 (pp68) Version: GGNFS-0.77.1 Total time: 79.11 hours. Scaled time: 52.61 units (timescale=0.665). Factorization parameters were as follows: name: 19999_171 n: 62307582226426941282730497418239251189478704230641873240737131725763565707384336402366220505143817417223703576438339 skew: 70354.31 # norm 9.98e+15 c5: 38640 c4: 1313355052 c3: -485208951307114 c2: -3328343126631723698 c1: 1184501065996951583035211 c0: 1182890042528989462722002970 # alpha -6.01 Y1: 3292182191399 Y0: -17438141564269073661799 # Murphy_E 4.65e-10 # M 36587589753890054593003890281994435471974230965745336332136226976327519198887792848608176262548012425841009218266819 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, 3750001) Relations: rels:7479223, finalFF:723613 Initial matrix: 631644 x 723613 with sparse part having weight 56162146. Pruned matrix : 586230 x 589452 with weight 35466708. Total sieving time: 66.72 hours. Total relation processing time: 0.90 hours. Matrix solve time: 10.85 hours. Time per square root: 0.64 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 79.11 hours. --------- CPU info (if available) ----------

Jul 22, 2005 (3rd)

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹³⁹+72·10⁶⁹-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111119111111111111111111111111111111111111111111111111111111111111111111111_<139> = 3 · 7 · 23 · 1733 · 19559 · C128
C128 = P55 · P74
P55 = 2102636820980948431411101834133362573625938170634857087_<55>
P74 = 32277573963617792933707000434735378858759799425351836764860151133226259153_<74>

Number: 11911_69 N=67868015507838747378914853125651927919516752750147719318540558200482113588765095169744389164671930658702571029994341807780667311 ( 128 digits) SNFS difficulty: 140 digits. Divisors found: r1=2102636820980948431411101834133362573625938170634857087 (pp55) r2=32277573963617792933707000434735378858759799425351836764860151133226259153 (pp74) Version: GGNFS-0.77.1 Total time: 85.37 hours. Scaled time: 67.01 units (timescale=0.785). Factorization parameters were as follows: n: 67868015507838747378914853125651927919516752750147719318540558200482113588765095169744389164671930658702571029994341807780667311 m: 100000000000000000000000000000000000 c4: 1 c2: 72 c0: -10 skew: 1 type: snfs qintsize: 10802000 Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 11202001) Relations: rels:2528812, finalFF:160615 Initial matrix: 142042 x 160615 with sparse part having weight 23462234. Pruned matrix : 140515 x 141289 with weight 19416061. Total sieving time: 84.75 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.42 hours. Time per square root: 0.04 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: 85.37 hours. --------- CPU info (if available) ----------

Jul 22, 2005 (2nd)

Jason Papadopoulos's SIQS implementation msieve 1.01 was released.
Quadratic Sieve Source Code (Jason Papadopoulos)

Jul 22, 2005

By Wataru Sakai / GMP-ECM 6.0.1
(28·10¹⁶⁵-1)/9 = 3(1)_165<166> = 3 · 1997 · 41029853253616558862159_<23> · C140
C140 = P34 · C106
P34 = 1479931381061176239842955946643233_<34>
C106 = [8552137197062135452946734939039401000390352520643770708997187105215087703113602922115601036755747663312943_<106>]
3·10¹⁸³-1 = 2(9)_183<184> = 757 · 705259 · C175
C175 = P26 · P149
P26 = 94685971491169408238495197_<26>
P149 = 59345951695499727131645089060192058135909213873136735226382733194452511684809704681156559640467203767085254024562482893630526915384657525961066917309_<149>

Jul 21, 2005 (2nd)

By Patrick Keller / GGNFS-0.77.1-050714
(31·10¹⁵⁴-13)/9 = 3(4)₁₅₃3_<155> = 3 · 19 · 1231 · 10318115811615833350849_<23> · 26353110139075738702819279411_<29> · C100
C100 = P35 · P66
P35 = 12023093835959132067018090663212227_<35>
P66 = 150154296621491793394346450363895517375583748113591057346186864293_<66>

Jul 21, 2005

By Patrick Keller / msieve
(55·10¹⁶⁹-1)/9 = 6(1)_169<170> = 1267789 · 417120271237_<12> · 3193089992685293_<16> · 23746197743073512431_<20> · 11655965793025266695761_<23> · C96
C96 = P35 · P61
P35 = 82969538107201187912861308387895899_<35>
P61 = 1575940183105005638700269656685989140264638789120620298877671_<61>

Jul 20, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(7·10¹⁸²-43)/9 = (7)₁₈₁3_<182> = 811 · 9803 · 43541 · 964128448187225411_<18> · 63518786855336021873_<20> · 6317515667788841649784757_<25> · C108
C108 = P52 · P57
P52 = 4075754667318562343182746279281284062224460215903653_<52>
P57 = 142490470262200698619444326172501867664906279915719834307_<57>

Number: 77773_182 N=580756199219581309176798751506149414432555926561180701540672917837877847873829728066568125486993571436023471 ( 108 digits) Divisors found: r1=4075754667318562343182746279281284062224460215903653 (pp52) r2=142490470262200698619444326172501867664906279915719834307 (pp57) Version: GGNFS-0.77.1 Total time: 25.80 hours. Scaled time: 15.38 units (timescale=0.596). Factorization parameters were as follows: name: 77773_182 n: 580756199219581309176798751506149414432555926561180701540672917837877847873829728066568125486993571436023471 skew: 37739.91 # norm 1.93e+15 c5: 7380 c4: 1656265443 c3: -45444609960584 c2: -510192825638705008 c1: 40308296871262418615274 c0: -240458323485339314699172120 # alpha -6.37 Y1: 42407195303 Y0: -601431435567597392371 # Murphy_E 1.18e-09 # M 270318479892486145518999499963405043139584006942110790385476246090737366897252067273220988440866932939604189 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2600001) Relations: rels:4657789, finalFF:475385 Initial matrix: 365521 x 475385 with sparse part having weight 39940865. Pruned matrix : 328652 x 330543 with weight 19349984. Polynomial selection time: 0.50 hours. Total sieving time: 21.53 hours. Total relation processing time: 0.39 hours. Matrix solve time: 3.04 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 25.80 hours. --------- CPU info (if available) ----------

Jul 19, 2005 (3rd)

By Samuel Chong / GMP-ECM 6.0.1, GGNFS-0.77.1-050706, GGNFS-0.77.1
(4·10¹⁵¹-7)/3 = 1(3)₁₅₀1_<152> = 11 · C151
C151 = P34 · P117
P34 = 2654556875419822081359149595230891_<34>
P117 = 456619040015676200361886468778998703135419004800522660645707221302698105894404427756432042889553089487767871029499531_<117>
(4·10¹⁵²-7)/3 = 1(3)₁₅₁1_<153> = 4710903416984659_<16> · C137
C137 = P33 · P104
P33 = 284380384951060053674387900671561_<33>
P104 = 99525621536122188377243271405135370562885542102702768696714945192631799716649369603171814530522932702969_<104>
(4·10¹⁵³-7)/3 = 1(3)₁₅₂1_<154> = 11 · 53 · 2530547 · 83672528054113_<14> · 54946641131623793491_<20> · C111
C111 = P37 · P74
P37 = 7443975329698353653369348809552558177_<37>
P74 = 26407470826627688333874212135138982379401990967198526622236551592059175341_<74>
(64·10¹⁵¹-1)/9 = 7(1)_151<152> = 293 · 45025957 · 726274511 · 1305759391_<10> · C124
C124 = P45 · P80
P45 = 168926696146768039588385780025811918524845557_<45>
P80 = 33646867900134114396506115605045020905798675373641624350409023079910457482818323_<80>

Number: 71111_151 N=5683854230056398741879882474777030568379236876305051951381289709413124448281187852368728736937435648737392529868114664740911 ( 124 digits) SNFS difficulty: 152 digits. Divisors found: r1=168926696146768039588385780025811918524845557 (pp45) r2=33646867900134114396506115605045020905798675373641624350409023079910457482818323 (pp80) Version: GGNFS-0.77.1-050706 Total time: 26.68 hours. Scaled time: 29.14 units (timescale=1.092). Factorization parameters were as follows: name: 71111_151 n: 5683854230056398741879882474777030568379236876305051951381289709413124448281187852368728736937435648737392529868114664740911 m: 2000000000000000000000000000000 c5: 20 c0: -1 type: snfs skew: 0.9 lss: 1 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 50000 # q0: 3000000 # qintsize: 1000 # total yield: 10652, 0.00956 sec/rel Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1200000, 1850001) Primes: RFBsize:176302, AFBsize:175838, largePrimes:8141148 encountered Relations: rels:8678748, finalFF:727638 Max relations in full relation-set: 20 Initial matrix: 352206 x 727638 with sparse part having weight 66095382. Pruned matrix : 239046 x 240871 with weight 27394237. Total sieving time: 23.87 hours. Total relation processing time: 0.28 hours. Matrix solve time: 2.42 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 26.68 hours. --------- CPU info (if available) ---------- dual Athlon MP 2600+ (2.0GHz Bartons), 3GB RAM total actual time: 16h04m13.062s

(14·10¹⁶⁷-41)/9 = 1(5)₁₆₆1_<168> = 11 · C167
C167 = P70 · P97
P70 = 1551762673453065953013392460694176562588480360498237956375794389510177_<70>
P97 = 9113129464537192620276698738976018093378747212696395351751862940975801863458685343597372761347933_<97>

Number: 15551_167 N=14141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141 ( 167 digits) SNFS difficulty: 168 digits. Divisors found: r1=1551762673453065953013392460694176562588480360498237956375794389510177 (pp70) r2=9113129464537192620276698738976018093378747212696395351751862940975801863458685343597372761347933 (pp97) Version: GGNFS-0.77.1 Total time: 97.14 hours. Scaled time: 106.07 units (timescale=1.092). Factorization parameters were as follows: name: 15551_167 n: 14141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141 deg: 5 m: 1000000000000000000000000000000000 c5: 1400 c0: -41 skew: 0.75 type: snfs lss: 1 rlim: 5500000 alim: 5500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.6 alambda: 2.6 # q0: 8000000 # qintsize: 1000 # total yield: 5585, 0.02661 sec/rel Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2750000, 4650001) Primes: RFBsize:380800, AFBsize:379898, largePrimes:10060309 encountered Relations: rels:10612927, finalFF:857796 Max relations in full relation-set: 20 Initial matrix: 760765 x 857796 with sparse part having weight 65863381. Pruned matrix : 725154 x 729021 with weight 48141392. Total sieving time: 79.66 hours. Total relation processing time: 0.39 hours. Matrix solve time: 16.77 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.6,2.6,100000 total time: 97.14 hours. --------- CPU info (if available) ---------- dual Athlon MP 2600+ (2.0GHz Bartons), 3GB RAM total actual time: 57h10m9.750s

Jul 19, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(4·10¹⁵⁵-31)/9 = (4)₁₅₄1_<155> = 4969 · 1161384764379587557_<19> · 782494652727784355839_<21> · C112
C112 = P53 P53 = 32446837159203339193884150697151992926501317981434793_<53>
P60 = 303332268525905712949350851846704001699989866755046360134251_<60>

Number: 44441_155 N=9842172721991802980016493108579024883977588247997182207655686748197703648161747117498644119268354472329082395043 ( 112 digits) Divisors found: r1=32446837159203339193884150697151992926501317981434793 (pp53) r2=303332268525905712949350851846704001699989866755046360134251 (pp60) Version: GGNFS-0.77.1 Total time: 57.17 hours. Scaled time: 34.19 units (timescale=0.598). Factorization parameters were as follows: name: 44441_155 n: 9842172721991802980016493108579024883977588247997182207655686748197703648161747117498644119268354472329082395043 skew: 49671.47 # norm 8.35e+15 c5: 12960 c4: 4476295394 c3: -299143304227205 c2: -8043965794808848098 c1: 220316302410226109388396 c0: 804656506548070477807120440 # alpha -6.26 Y1: 250338497129 Y0: -3767863863528840852709 # Murphy_E 6.93e-10 # M 7565174254746187767176314659151201359252327605151860423427946056328323373590570349809585549819597165985588730847 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, 2850001) Relations: rels:7724215, finalFF:718164 Initial matrix: 500042 x 718164 with sparse part having weight 63219417. Pruned matrix : 416794 x 419358 with weight 24674328. Polynomial selection time: 0.52 hours. Total sieving time: 49.85 hours. Total relation processing time: 0.61 hours. Matrix solve time: 5.70 hours. Time per square root: 0.49 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: 57.17 hours. --------- CPU info (if available) ----------

Jul 19, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹³⁹+54·10⁶⁹-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111117111111111111111111111111111111111111111111111111111111111111111111111_<139> = 3361 · C135
C135 = P62 · P73
P62 = 52070496553369761790102847965951773055481163109715236258179551_<62>
P73 = 6348882051363135965307216999905078239101419073148489032611069392180478201_<73>

Number: 11711_69 N=330589440973255314225263645079176171113094647756950642996462692981587953320770934576349631392773314820324638831035736718569208899467751 ( 135 digits) SNFS difficulty: 140 digits. Divisors found: r1=52070496553369761790102847965951773055481163109715236258179551 (pp62) r2=6348882051363135965307216999905078239101419073148489032611069392180478201 (pp73) Version: GGNFS-0.77.1 Total time: 95.27 hours. Scaled time: 74.79 units (timescale=0.785). Factorization parameters were as follows: n: 330589440973255314225263645079176171113094647756950642996462692981587953320770934576349631392773314820324638831035736718569208899467751 m: 100000000000000000000000000000000000 c4: 1 c2: 54 c0: -10 skew: 1 type: snfs qintsize: 1000000 Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 12400001) Relations: rels:2666570, finalFF:167117 Initial matrix: 142442 x 167117 with sparse part having weight 24961771. Pruned matrix : 140358 x 141134 with weight 19591177. Total sieving time: 94.65 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.42 hours. Time per square root: 0.04 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: 95.27 hours. --------- CPU info (if available) ----------

Jul 18, 2005

By Yousuke Koide / GMP-ECM
10⁴⁵¹+1 = 1(0)₄₅₀1_<452> = 11² · 23 · 4093 · 8779 · 298693693 · 2670502781396266997_<19> · 3404193829806058997303_<22> · C392
C392 = P47 · P345
P47 = 69606016705406484991000471515023784726122029891_<47>
P345 = 529078180447156123547139381902466803953567690179466499154820732870017143631924842993162213960820334158132869761951163618188569020448797613562208575078943929357425069002353812387723435521818619393646414711466802657777328740814397284244180152385678587483481542586127970096191455772802766113324200333714391155370081222019852283144907740894279174797_<345>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 17, 2005 (2nd)

By Yousuke Koide / GMP-ECM
10⁸²⁸+1 = 1(0)₈₂₇1_<829> = 73 · 137 · 1657 · 2393 · 3169 · 98641 · 99990001 · 1469409649_<10> · 1984699441_<10> · 86239064881_<11> · 22361420916001_<14> · 57623262784777_<14> · 3199044596370769_<16> · 41168686909062457_<17> · 38115215074391056784287931569_<29> · 27043868269833638345091057330221113_<35> · 4178437150016715837818641871709193476807772628503969494400330129962348520684914375257_<85> · 1077654773020602154835873595438016994801570811542710006429679112760889048401772560028378495799359646781326368530020399986158679489264953_<136> · C430
C430 = P37 · C394
P37 = 2992954220671053473210428102132664473_<37>
C394 = [1360717814909119921394530999562515854330400817823129559295246729918328868659492638364491602140084679017403336326713513331777843416209155739993092648873579171737893966036107119009147272385928719343037262812896722599476556303173082788292432326861971850185783476265348480677118480040774295197381632659845653482773775700890523528939777229724723081943292355590171722406264805747359379920883716708721_<394>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 17, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(7·10¹³⁷+18·10⁶⁸-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777977777777777777777777777777777777777777777777777777777777777777777777_<137> = 10506477473_<11> · C127
C127 = P50 · P78
P50 = 51057648425002667453045636059406307164844188663419_<50>
P78 = 144989845932924771329522847083309110544324949053020515127168660970901874753571_<78>

Number: 77977_68 N=7402840578838575860122417432586996779617782537245038242683507420087529633042194957341034768882883586588905236381862442487319249 ( 127 digits) SNFS difficulty: 137 digits. Divisors found: r1=51057648425002667453045636059406307164844188663419 (pp50) r2=144989845932924771329522847083309110544324949053020515127168660970901874753571 (pp78) Version: GGNFS-0.77.1 Total time: 122.47 hours. Scaled time: 116.23 units (timescale=0.949). Factorization parameters were as follows: name: 77977_68 n: 7402840578838575860122417432586996779617782537245038242683507420087529633042194957341034768882883586588905236381862442487319249 m: 10000000000000000000000000000000000 c4: 70 c2: 18 c0: -7 skew: 1 type: snfs qintsize: 1000000 Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 14400001) Relations: rels:3014398, finalFF:164178 Initial matrix: 142052 x 164178 with sparse part having weight 26085903. Pruned matrix : 140755 x 141529 with weight 21127433. Total sieving time: 121.87 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.29 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,137,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 122.47 hours. --------- CPU info (if available) ----------

Jul 16, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(4·10¹⁶⁶+41)/9 = (4)₁₆₅9_<166> = 3 · 1259 · 8881923858737_<13> · 40401364458263_<14> · 51065495646920997327834599_<26> · C110
C110 = P36 · P75
P36 = 252853655896565745602501592959710301_<36>
P75 = 253963105929661508765623961233148369053911499956655824042019151346308187173_<75>

Number: 44449_166 N=64215499797161706827556621033272257352479923928817161623830377582115563446339781572769051365696464966564169073 ( 110 digits) Divisors found: r1=252853655896565745602501592959710301 (pp36) r2=253963105929661508765623961233148369053911499956655824042019151346308187173 (pp75) Version: GGNFS-0.77.1 Total time: 41.77 hours. Scaled time: 27.86 units (timescale=0.667). Factorization parameters were as follows: name: 44449_166 n: 64215499797161706827556621033272257352479923928817161623830377582115563446339781572769051365696464966564169073 skew: 51100.86 # norm 2.02e+15 c5: 16380 c4: 697501395 c3: -110197902058147 c2: -1221084352388025982 c1: 133445717291689851669595 c0: 306001293022180624140253150 # alpha -6.00 Y1: 86760301183 Y0: -1314210551609021917161 # Murphy_E 9.54e-10 # M 1101232051600298967678521977257133459155584196269097313965937274557513455965430142008081627143156241433344184 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, 2400001) Relations: rels:7822421, finalFF:783387 Initial matrix: 460487 x 783387 with sparse part having weight 69725892. Pruned matrix : 340230 x 342596 with weight 19674972. Total sieving time: 37.50 hours. Total relation processing time: 0.63 hours. Matrix solve time: 3.29 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 41.77 hours. --------- CPU info (if available) ----------

Jul 14, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(22·10¹⁵⁵-1)/3 = 7(3)_155<156> = 66463 · 294067 · 10793869098912920411_<20> · 84564878541774027181_<20> · C107
C107 = P46 · P61
P46 = 8394639465107877835800536533522911091629400829_<46>
P61 = 4896727872734246461613189779121106863103962201653671255815107_<61>

Number: 73333_155 N=41106265050348651209109426079823610418401505792705524390769516294978128829630033410243134554955236416523703 ( 107 digits) Divisors found: r1=8394639465107877835800536533522911091629400829 (pp46) r2=4896727872734246461613189779121106863103962201653671255815107 (pp61) Version: GGNFS-0.77.1 Total time: 24.93 hours. Scaled time: 14.91 units (timescale=0.598). Factorization parameters were as follows: name: 73333_155 n: 41106265050348651209109426079823610418401505792705524390769516294978128829630033410243134554955236416523703 skew: 15824.46 # norm 1.24e+15 c5: 30960 c4: 2295784782 c3: -7907675997233 c2: 318189896619804173 c1: -1630944452349060114983 c0: -10672555180726442152409139 # alpha -5.94 Y1: 212316019289 Y0: -265837515430114422086 # Murphy_E 1.34e-09 # M 11587786637167125728995468002773571506908754310662218139944668555444326562087581892928045032656288300419183 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2600001) Relations: rels:4641823, finalFF:461556 Initial matrix: 366018 x 461556 with sparse part having weight 40158039. Pruned matrix : 334009 x 335903 with weight 21203944. Total sieving time: 21.05 hours. Total relation processing time: 0.37 hours. Matrix solve time: 3.18 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 24.93 hours. --------- CPU info (if available) ----------

Jul 13, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(28·10¹⁵⁷-1)/9 = 3(1)_157<158> = 311 · 487 · 480670490093480346271_<21> · 6438097168233354220222049_<25> · C107
C107 = P49 · P59
P49 = 2963884335817527111335736587670265958585892914749_<49>
P59 = 22395457197128163961438045327803254457295208979708748555213_<59>

Number: 31111_157 N=66377544780040065582029086378904075006514291269444715000330262029447448632398896725246594427162887128536537 ( 107 digits) Divisors found: r1=2963884335817527111335736587670265958585892914749 (pp49) r2=22395457197128163961438045327803254457295208979708748555213 (pp59) Version: GGNFS-0.77.1 Total time: 21.35 hours. Scaled time: 12.72 units (timescale=0.596). Factorization parameters were as follows: name: 31111_157 n: 66377544780040065582029086378904075006514291269444715000330262029447448632398896725246594427162887128536537 skew: 38410.06 # norm 1.14e+15 c5: 17400 c4: 8935325 c3: -44831202975396 c2: 516808779302800968 c1: 1325186689434675137624 c0: -206609403013721160074402976 # alpha -6.35 Y1: 29364425377 Y0: -328317765419041739371 # Murphy_E 1.38e-09 # M 17489802452575438360601809893882234647113953374254161428124547585323647853048195622704181285091601406412204 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2300001) Relations: rels:4383088, finalFF:412079 Initial matrix: 367037 x 412079 with sparse part having weight 29666911. Pruned matrix : 344995 x 346894 with weight 19885069. Polynomial selection time: 0.50 hours. Total sieving time: 17.10 hours. Total relation processing time: 0.30 hours. Matrix solve time: 3.12 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 21.35 hours. --------- CPU info (if available) ----------

Jul 13, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹⁴³+27·10⁷¹-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111111111411111111111111111111111111111111111111111111111111111111111111111111111_<143> = 347 · 10691 · C136
C136 = P47 · P90
P47 = 15914364112759625740263793294061180343689180989_<47>
P90 = 188200336645953221237336848625512956963451186790808407736477939103129232513949203654597987_<90>

Number: 11411_71 N=2995088683527638214132847098656094722435098150403949108291714329759204235486691278508414686680927481924415163259438804842207796078069143 ( 136 digits) SNFS difficulty: 144 digits. Divisors found: r1=15914364112759625740263793294061180343689180989 (pp47) r2=188200336645953221237336848625512956963451186790808407736477939103129232513949203654597987 (pp90) Version: GGNFS-0.77.1 Total time: 126.44 hours. Scaled time: 99.38 units (timescale=0.786). Factorization parameters were as follows: n: 2995088683527638214132847098656094722435098150403949108291714329759204235486691278508414686680927481924415163259438804842207796078069143 m: 1000000000000000000000000000000000000 c4: 1 c2: 27 c0: -10 skew: 1 type: snfs qintsize: 14450000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 15100001) Relations: rels:4493677, finalFF:224737 Initial matrix: 200220 x 224737 with sparse part having weight 34853767. Pruned matrix : 196913 x 197978 with weight 29246889. Total sieving time: 124.98 hours. Total relation processing time: 0.26 hours. Matrix solve time: 1.15 hours. Time per square root: 0.06 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: 126.44 hours. --------- CPU info (if available) ----------

Jul 12, 2005

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10¹⁵⁹-7)/3 = (3)₁₅₈1_<159> = 218417 · 27524743 · 4049888683661543_<16> · 146342914665017035903297_<24> · C107
C107 = P46 · P62
P46 = 1437241274453822339930106600253026833902238939_<46>
P62 = 65091543130661698240983562654299215624196046775187187189769129_<62>

Number: 33331_159 N=93552252405278164056093123002242187278556911562047528926414562232061920013364791286396112008530147603914131 ( 107 digits) Divisors found: r1=1437241274453822339930106600253026833902238939 (pp46) r2=65091543130661698240983562654299215624196046775187187189769129 (pp62) Version: GGNFS-0.77.1 Total time: 22.80 hours. Scaled time: 15.16 units (timescale=0.665). Factorization parameters were as follows: name: 33331_159 n: 93552252405278164056093123002242187278556911562047528926414562232061920013364791286396112008530147603914131 skew: 9012.57 # norm 2.80e+14 c5: 171780 c4: -736144756 c3: -40002967490366 c2: 9797259494568875 c1: 1725079583276220128486 c0: -552403386950124191411875 # alpha -5.36 Y1: 135665563319 Y0: -222441880033545947406 # Murphy_E 1.37e-09 # M 60963646720127694611986479636083141002695212684264197567402216133526579579768781913627043647677979834881598 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 2450001) Relations: rels:4650778, finalFF:492472 Initial matrix: 367188 x 492472 with sparse part having weight 39431197. Pruned matrix : 324884 x 326783 with weight 17475231. Polynomial selection time: 0.50 hours. Total sieving time: 18.98 hours. Total relation processing time: 0.36 hours. Matrix solve time: 2.65 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 22.80 hours. --------- CPU info (if available) ----------

Jul 11, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10¹⁴⁷+15·10⁷³-1)/3 = 333333333333333333333333333333333333333333333333333333333333333333333333383333333333333333333333333333333333333333333333333333333333333333333333333_<147> = 21045023536608059_<17> · 2943338195446139826253_<22> · C109
C109 = P35 · P74
P35 = 61663742529777984145787311663377961_<35>
P74 = 87268856142282606568015304626665065775597133889887534234132816390578397939_<74>

Number: 33833_73 N=5381324276025948628264789591339838362751594049171286745485802590192048962658866690069049686584029264420422379 ( 109 digits) Divisors found: r1=61663742529777984145787311663377961 (pp35) r2=87268856142282606568015304626665065775597133889887534234132816390578397939 (pp74) Version: GGNFS-0.77.1 Total time: 29.54 hours. Scaled time: 17.66 units (timescale=0.598). Factorization parameters were as follows: name: 33833_73 n: 5381324276025948628264789591339838362751594049171286745485802590192048962658866690069049686584029264420422379 skew: 22965.87 # norm 3.24e+15 c5: 63180 c4: -2354866206 c3: -196521512139646 c2: 3142903222265383123 c1: 38224404509356591504146 c0: -1401084493545404024478072 # alpha -6.53 Y1: 15249752903 Y0: -611029234085923076071 # Murphy_E 1.09e-09 # M 2400683074171014488282108658979366985264222852706522840103408779063430082332428060153359032052580550833211202 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, 2900001) Relations: rels:6965797, finalFF:529710 Initial matrix: 460592 x 529710 with sparse part having weight 40085239. Pruned matrix : 428098 x 430464 with weight 25148310. Polynomial selection time: 0.51 hours. Total sieving time: 22.85 hours. Total relation processing time: 0.57 hours. Matrix solve time: 5.19 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 29.54 hours. --------- CPU info (if available) ----------

Jul 11, 2005

By Samuel Chong / GMP-ECM 6.0.1, GGNFS-0.77.1-050703
(10¹⁶⁸+53)/9 = (1)₁₆₇7_<168> = 3 · C167
C167 = P36 · P38 · P95
P36 = 261878964938555063242744473807304607_<36>
P38 = 11515180136795295248507748540824609267_<38>
P95 = 12281880964654498189309969065968311562811764670747209318989527925662296843913202781884529405131_<95>
(23·10¹⁶⁰+1)/3 = 7(6)₁₅₉7_<161> = C161
C161 = P53 · P109
P53 = 74162648820128283692300826847968772682286328601604349_<53>
P109 = 1033763867477435275629351214656637596846353731784895260192061546747433303133364923712335701819135369025949383_<109>

Number: 76667_160 N=76666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667 ( 161 digits) SNFS difficulty: 161 digits. Divisors found: r1=74162648820128283692300826847968772682286328601604349 (pp53) r2=1033763867477435275629351214656637596846353731784895260192061546747433303133364923712335701819135369025949383 (pp109) Version: GGNFS-0.77.1-050703 Total time: 76.08 hours. Scaled time: 65.35 units (timescale=0.859). Factorization parameters were as follows: name: 76667_160 n: 76666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667 m: 100000000000000000000000000000000 c5: 23 c0: 1 type: snfs skew: 0.9 lss: 1 mrif: 24 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved rational special-q in [2000000, 3100001) Primes: RFBsize:283146, AFBsize:283082, largePrimes:5799177 encountered Relations: rels:5914757, finalFF:716943 Max relations in full relation-set: 24 Initial matrix: 566293 x 716943 with sparse part having weight 43490331. Pruned matrix : 438661 x 441556 with weight 25817526. Total sieving time: 66.80 hours. Total relation processing time: 0.41 hours. Matrix solve time: 8.67 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 76.08 hours. --------- CPU info (if available) ---------- dual Pentium 3 (1.4GHz Tualatins), 1GB RAM total elapsed time: 44h28m9s

Jul 9, 2005 (2nd)

By Anton Korobeynikov / GGNFS-0.77.1-050628 gnfs
8·10¹⁸⁶-1 = 7(9)_186<187> = 7 · 47 · 504034073 · 1220285033049641423_<19> · 1709433494016512071_<19> · 6918484257964090228128626296689623_<34> · C106
C106 = P50 · P56
P50 = 43460179064912309703242130945598534289867760101911_<50>
P56 = 76916272754778138630365695931283055966594931721405006103_<56>

Number: tst106 N=3342794986928293928439711298315328817078274017058526064300434345723697116171884783306122260523044856962833 ( 106 digits) Divisors found: r1=43460179064912309703242130945598534289867760101911 (pp50) r2=76916272754778138630365695931283055966594931721405006103 (pp56) Version: GGNFS-0.77.1-050628 Total time: 36.76 hours. Scaled time: 20.81 units (timescale=0.566). Factorization parameters were as follows: name: tst106 n: 3342794986928293928439711298315328817078274017058526064300434345723697116171884783306122260523044856962833 skew: 22980.06 # norm 8.68e+014 c5: 30600 c4: -1740003667 c3: -32467901597076 c2: 654242532677148186 c1: 13394235132160573893740 c0: 36538250124711699962490585 # alpha -6.50 Y1: 39769527721 Y0: -161316533433319433986 # Murphy_E 1.66e-009 # M 56150422288104883049063045575509703078018856389528110844811427753787327203841613591346077155156319932432 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2300001) Primes: RFBsize:183072, AFBsize:183400, largePrimes:4475736 encountered Relations: rels:4611750, finalFF:500978 Max relations in full relation-set: 28 Initial matrix: 366553 x 500978 with sparse part having weight 38609386. Pruned matrix : 316753 x 318649 with weight 15939717. Total sieving time: 31.89 hours. Total relation processing time: 0.52 hours. Matrix solve time: 3.91 hours. Time per square root: 0.45 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 36.76 hours. --------- CPU info (if available) ----------

Jul 9, 2005

By Kenichiro Yamaguchi / msieve.exe 0.88
(4·10¹⁶³+41)/9 = (4)₁₆₂9_<163> = 3² · 449 · 12791459 · 339418278537910189_<18> · 229015775528644936079_<21> · C115
C115 = P43 · P72
P43 = 1501711131465614823052960975609372409365361_<43>
P72 = 736582713701113557971116973157308599992470800719116072776400587601760481_<72>

Msieve v. 0.88 Tue May 10 13:02:21 2005 random seeds: f8379780 a1d52400 factoring 1106134460410112267004053938425590422740448760975684649017855331687415017137528661799083521671787787034735540098641 (115 digits) using multiplier of 21 using sieve block of 65536 using a sieve bound of 2010923 (75000 primes) using large prime bound of 603276900 using double large prime bound of 6381606628102200 sieving in progress (press Ctrl-C to pause) found 75129 relations (13111 full + 62018 partial), need 75096 found 75129 relations (13111 full + 62018 partial), need 75096 begin with 1701662 relations reduce to 210934 relations in 14 passes attempting to read 13111 full and 210934 partial relations recovered 13111 full and 210934 partial relations recovered 223991 polynomials attempting to build 62018 cycles found 62018 cycles in 6 passes distribution of cycle lengths: length 2 : 10643 length 3 : 11401 length 4 : 10352 length 5 : 8929 length 6 : 6946 length 7 : 4908 length 8 : 3391 length 9+: 5448 largest cycle: 25 relations 75000 x 75064 system, weight 7220674 (avg 96.19/col) reduce to 74822 x 74886 in 3 passes lanczos halted after 1184 iterations recovered 63 nontrivial dependencies prp43 factor: 1501711131465614823052960975609372409365361 prp72 factor: 736582713701113557971116973157308599992470800719116072776400587601760481 elapsed time 1349:25:37

Jul 8, 2005 (3rd)

By Wataru Sakai / GMP-ECM 6.0.1
(28·10¹⁷⁹-1)/9 = 3(1)_179<180> = 17 · 158980370820846386325091_<24> · C156
C156 = P33 · C123
P33 = 130636323549165510465523960184309_<33>
C123 = [881168868410478910122156183182007485081616751855695907325787140382716064689547642860087787997396259439449517750318095543657_<123>]

Jul 8, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
10¹³⁷-2·10⁶⁸-1 = 99999999999999999999999999999999999999999999999999999999999999999999799999999999999999999999999999999999999999999999999999999999999999999_<137> = 7 · 19 · 506600706529_<12> · C124
C124 = P47 · P77
P47 = 38441493794379124235296597148224755847178273731_<47>
P77 = 38608445186394108523037268509940384027364224838065637538612437090089075939697_<77>

Number: 99799_68 N=1484166306043395693283781916997564678996258611726252697225202884766580785126185686120553035776283831475482882848471115199507 ( 124 digits) SNFS difficulty: 137 digits. Divisors found: r1=38441493794379124235296597148224755847178273731 (pp47) r2=38608445186394108523037268509940384027364224838065637538612437090089075939697 (pp77) Version: GGNFS-0.77.1 Total time: 35.10 hours. Scaled time: 20.92 units (timescale=0.596). Factorization parameters were as follows: name: 99799_68 n: 1484166306043395693283781916997564678996258611726252697225202884766580785126185686120553035776283831475482882848471115199507 m: 10000000000000000000000000000000000 c4: 10 c2: -2 c0: -1 skew: 2 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 4525001) Relations: rels:1843421, finalFF:165720 Initial matrix: 142193 x 165720 with sparse part having weight 21722790. Pruned matrix : 140008 x 140782 with weight 16736465. Total sieving time: 33.90 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.88 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,137,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 35.10 hours. --------- CPU info (if available) ----------

Jul 8, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1, GMP-ECM 6.0
(7·10¹³⁷-45·10⁶⁸-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777277777777777777777777777777777777777777777777777777777777777777777777_<137> = 3² · 1187 · 83165363 · 33715779863_<11> · C115
C115 = P57 · P58
P57 = 261916745177383314877528648985844868003430140154044524611_<57>
P58 = 9913416204895503222150086051146754399161046075676293950141_<58>

Number: 77277_68 N=2596489705974957897267536554345254312471558114972188002436074720437635301385207442774309289275158481611765681420151 ( 115 digits) SNFS difficulty: 137 digits. Divisors found: r1=261916745177383314877528648985844868003430140154044524611 (pp57) r2=9913416204895503222150086051146754399161046075676293950141 (pp58) Version: GGNFS-0.77.1 Total time: 38.49 hours. Scaled time: 30.22 units (timescale=0.785). Factorization parameters were as follows: n: 2596489705974957897267536554345254312471558114972188002436074720437635301385207442774309289275158481611765681420151 m: 10000000000000000000000000000000000 c4: 70 c2: -45 c0: -7 skew: 1 type: snfs qintsize: 50000 Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 4950001) Relations: rels:1875197, finalFF:163000 Initial matrix: 142526 x 163000 with sparse part having weight 21649316. Pruned matrix : 140549 x 141325 with weight 17256639. Total sieving time: 37.95 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.37 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,137,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 38.49 hours. --------- CPU info (if available) ----------

10¹⁴³-7·10⁷¹-1 = 99999999999999999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999999999999999_<143> = 631 · 4993 · 113021 · 711889 · 8174189 · 1018445325323_<13> · C107
C107 = P36 · P72
P36 = 124081059014402609188910712167753797_<36>
P72 = 381900090388147519926382272844193239916998973958499765471774268565374743_<72>

Jul 6, 2005 (3rd)

Details of the factoring of 10³⁶⁰+1 are available at NP193 report (Tomoya Adachi).

Jul 6, 2005 (2nd)

By Yousuke Koide / GMP-ECM
10⁷⁷⁴+1 = 1(0)₇₇₃1_<775> = 101 · 1549 · 9901 · 100621 · 338669 · 999999000001_<12> · 1596501606879721_<16> · 6056569717114034438093089_<25> · 279060762796539348792116809_<27> · 8045181580990560114237163201_<28> · 13441721102334727627682496494535257828666281_<44> · 202026760686388880964731015757788959143121139209_<48> · 46229724820742226005075125617528225785246749164469_<50> · 2923500556298303355222653948542706598448925085853709961673200056984872843366529_<79> · C430
C430 = P36 · C395
P36 = 115309033658716156289440262332960681_<36>
C395 = [20620642695014350337975511260833292822488981904790966335112045379351063410791322312127504657601590276065370336707976715926498689674117490793516947745259213581845996865577233865053026635087556515181985962133162273828679367877568982626950433111620559067673836746851895118649988765130904273037926649784665694675341659036165386071624318996351026405778496712183868965164454623203112092834169036219169_<395>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 6, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹³⁷+15·10⁶⁸-1)/3 = 33333333333333333333333333333333333333333333333333333333333333333333833333333333333333333333333333333333333333333333333333333333333333333_<137> = 23 · 1301 · C133
C133 = P36 · P97
P36 = 267585440783358957736467000710402543_<36>
P97 = 4163045262442537352797969001234701845700259730698574326340078542301228772173015352281880886073097_<97>

Number: 33833_68 N=1113970301551760630061602557675812362842406621439472423665185086165619534583208011674408760262451403045594804442513562588421392685671 ( 133 digits) SNFS difficulty: 137 digits. Divisors found: r1=267585440783358957736467000710402543 (pp36) r2=4163045262442537352797969001234701845700259730698574326340078542301228772173015352281880886073097 (pp97) Version: GGNFS-0.77.1 Total time: 35.69 hours. Scaled time: 28.02 units (timescale=0.785). Factorization parameters were as follows: n: 1113970301551760630061602557675812362842406621439472423665185086165619534583208011674408760262451403045594804442513562588421392685671 m: 10000000000000000000000000000000000 c4: 10 c2: 15 c0: -1 skew: 1 type: snfs qintsize: 50000 Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 4650001) Relations: rels:1837054, finalFF:160049 Initial matrix: 142315 x 160049 with sparse part having weight 21226657. Pruned matrix : 140547 x 141322 with weight 17398011. Total sieving time: 35.16 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.38 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,137,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 35.69 hours. --------- CPU info (if available) ----------

Jul 4, 2005 (3rd)

By Tomoya Adachi
10³⁶⁰+1 = 1(0)₃₅₉1_<361> = 17 · 8929 · 5070721 · 5882353 · 1132716961_<10> · 9999999900000001_<16> · 19721061166646717498359681_<26> · 281259985248437790051014401_<27> · 31388506438433752927908678241_<29> · 111994624258035614290513943330720125433979169_<45> · C193
C193 = P52 · P141
P52 = 2582785559040998185916696136639544586696154922477921_<52>
P141 = 387178872244935905889772080780710293688045544881430361754684573270941224160164698232378629400751141017399632124896823872033355066626985720481_<141>
Reference: NP193 report (Tomoya Adachi)

Jul 4, 2005 (2nd)

By Samuel Chong / GGNFS-0.77.1-050612 gnfs
(4·10¹⁶⁹-7)/3 = 1(3)₁₆₈1_<170> = 11 · 61 · 97 · 659 · 54096433 · 54290441 · 64308106981_<11> · 3765965069522130999796999696397_<31> · C105
C105 = P45 · P60
P45 = 687458054229396231638810565700743919885244773_<45>
P60 = 635738994891674777504228524674028850752300643056700335656779_<60>

Number: 13331_169 N=437043892425982813077935152545705581918969058064574850936440789645498900517989233477364470144410131766167 ( 105 digits) Divisors found: r1=687458054229396231638810565700743919885244773 (pp45) r2=635738994891674777504228524674028850752300643056700335656779 (pp60) Version: GGNFS-0.77.1-050612 Total time: 12.67 hours. Scaled time: 15.19 units (timescale=1.199). Factorization parameters were as follows: name: 13331_169 n: 437043892425982813077935152545705581918969058064574850936440789645498900517989233477364470144410131766167 skew: 3275.14 # norm 6.26e+014 c5: 954720 c4: -15574121622 c3: 37178338993774 c2: 208878367728459544 c1: 57838636510205381169 c0: -331890594985075502529 # alpha -6.11 Y1: 82518468697 Y0: -53967459406002339472 # Murphy_E 2.01e-009 # M 194674284298753262814761309149263309265107036091190640020265067214269292704064162381532010415288947872535 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2150001) Primes: RFBsize:183072, AFBsize:182604, largePrimes:4439867 encountered Relations: rels:4561010, finalFF:508893 Max relations in full relation-set: 32 Initial matrix: 365760 x 508893 with sparse part having weight 38261347. Pruned matrix : 254279 x 256171 with weight 17951282. Polynomial selection time: 0.95 hours. Total sieving time: 10.77 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.59 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 12.67 hours. --------- CPU info (if available) ---------- Pentium M 745 (1.8GHz Dothan), 1GB RAM total elapsed time: 13h5m7.618s

Jul 4, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(10¹³⁷+6·10⁶⁸-1)/3 = 33333333333333333333333333333333333333333333333333333333333333333333533333333333333333333333333333333333333333333333333333333333333333333_<137> = 431 · C134
C134 = P60 · P75
P60 = 752933367455375140891409663863210594909534577360491740045359_<60>
P75 = 102717615977560843468390580689681339283912919142680246353484793776583549877_<75>

Number: 33533_68 N=77339520494972931167826759474091260634184068058778035576179427687548801237432327919566898685228151585460170146945088940448569218870843 ( 134 digits) SNFS difficulty: 137 digits. Divisors found: r1=752933367455375140891409663863210594909534577360491740045359 (pp60) r2=102717615977560843468390580689681339283912919142680246353484793776583549877 (pp75) Version: GGNFS-0.77.0 Total time: 38.49 hours. Scaled time: 25.60 units (timescale=0.665). Factorization parameters were as follows: n: 77339520494972931167826759474091260634184068058778035576179427687548801237432327919566898685228151585460170146945088940448569218870843 m: 10000000000000000000000000000000000 c4: 10 c2: 6 c0: -1 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 4825001) Relations: rels:1886029, finalFF:162916 Initial matrix: 142156 x 162916 with sparse part having weight 21913619. Pruned matrix : 140301 x 141075 with weight 17429400. Total sieving time: 37.61 hours. Total relation processing time: 0.47 hours. Matrix solve time: 0.37 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,137,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 38.49 hours. --------- CPU info (if available) ----------

Jul 3, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹³⁷+12·10⁶⁸-1)/3 = 33333333333333333333333333333333333333333333333333333333333333333333733333333333333333333333333333333333333333333333333333333333333333333_<137> = 7 · 59 · 216015925796663_<15> · C120
C120 = P48 · P72
P48 = 433966982010329182008430441728765593758343711477_<48>
P72 = 860966463396356312426055258598349988964676061853126175816825690309059091_<72>

Number: 33733_68 N=373631017732223298003759928827137458608805528199800698744377777259181496818183259206815312632016168818390425264647887407 ( 120 digits) SNFS difficulty: 137 digits. Divisors found: r1=433966982010329182008430441728765593758343711477 (pp48) r2=860966463396356312426055258598349988964676061853126175816825690309059091 (pp72) Version: GGNFS-0.77.1 Total time: 28.14 hours. Scaled time: 26.85 units (timescale=0.954). Factorization parameters were as follows: name: 33733_68 n: 373631017732223298003759928827137458608805528199800698744377777259181496818183259206815312632016168818390425264647887407 m: 10000000000000000000000000000000000 c4: 10 c2: 12 c0: -1 skew: 1 type: snfs qintsize: 300000 Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 4300001) Relations: rels:1813869, finalFF:172676 Initial matrix: 142279 x 172676 with sparse part having weight 22257568. Pruned matrix : 139729 x 140504 with weight 15929721. Total sieving time: 27.77 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.22 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,137,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 28.14 hours. --------- CPU info (if available) ----------

Jul 2, 2005 (2nd)

By Wataru Sakai / GMP-ECM 6.0.1
(28·10¹⁹¹-1)/9 = 3(1)_191<192> = 6197 · 17839635938857_<14> · 257151644189669463738913_<24> · C152
C152 = P31 · P121
P31 = 6640250143350598462463268599219_<31>
P121 = 1648064835818731819503175566093799461463906092440925968516339312383305952539020121973929333839216181356636543190133684097_<121>
(79·10¹⁷⁰-7)/9 = 8(7)_170<171> = 1765641831386057_<16> · C156
C156 = P30 · C126
P30 = 519984567881869875839623965217_<30>
C126 = [956074021105397536437342755056849754612201290610974264349641650804121960025424871623231611685371025112062981295261387784719433_<126>]

Jul 2, 2005

By Makoto Kamada / PFGW 1.2
(505·10¹⁸⁴⁷⁰-1)/9 = 56(1)_18470<18472> is PRP.
This is the second largest known PRP of the smallest prime or PRP of a quasi-repdigit sequence. The largest one is (2·10¹⁹¹⁵³+691)/9 = (2)₁₉₁₅₁99_<19153>, and the third largest one is (64·10¹⁰⁹⁰⁶+53)/9 = 7(1)₁₀₉₀₅7_<10907>

Jul 1, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.0
(10¹³⁷+45·10⁶⁸-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111111611111111111111111111111111111111111111111111111111111111111111111111_<137> = 559166411 · C128
C128 = P45 · P83
P45 = 704654122261087194924139620175139766287597353_<45>
P83 = 28199435724179175393788787025494771519765673504676048833953469555595431725123255917_<83>

Number: 11611_68 N=19870848628479422579463756650989379816505307059853262736683071457079368651689471939885729493703639346661527405499167422470787701 ( 128 digits) SNFS difficulty: 137 digits. Divisors found: r1=704654122261087194924139620175139766287597353 (pp45) r2=28199435724179175393788787025494771519765673504676048833953469555595431725123255917 (pp83) Version: GGNFS-0.77.0 Total time: 59.56 hours. Scaled time: 39.61 units (timescale=0.665). Factorization parameters were as follows: n: 19870848628479422579463756650989379816505307059853262736683071457079368651689471939885729493703639346661527405499167422470787701 m: 10000000000000000000000000000000000 c4: 10 c2: 45 c0: -1 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 7450001) Relations: rels:2229625, finalFF:162723 Initial matrix: 142652 x 162723 with sparse part having weight 23393520. Pruned matrix : 140936 x 141713 with weight 19021909. Total sieving time: 58.23 hours. Total relation processing time: 0.87 hours. Matrix solve time: 0.41 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,137,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 59.56 hours. --------- CPU info (if available) ----------