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News and updates, June 2006

Jun 30, 2006 (2nd)

By Wojciech Florek / GMP-ECM 6.1
10²⁰⁰+3 = 1(0)₁₉₉3_<201> = C201
C201 = P29 · C172
P29 = 16892897616604738393032473779_<29>
C172 = [5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457_<172>]

Jun 30, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(22·10¹⁷²-1)/3 = 7(3)_172<173> = 13 · 84201814666201_<14> · C158
C158 = P28 · C131
P28 = 1272085084357714677202671397_<28>
C131 = [52664802777632128483139943807112499915228136328357345310586727772346381267412255744083863646372276716206868216067462224684412144253_<131>]
10¹⁸⁹+9 = 1(0)₁₈₈9_<190> = 14929 · 269221423 · C177
C177 = P35 · P143
P35 = 12192227834085072186320734367252819_<35>
P143 = 20406879351220085024953499773532182396131297871099978867280706469418636599119483854979393271010719938699602587208502179786539720548754102460333_<143>

Jun 29, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4
(2·10¹⁵⁷+1)/3 = (6)₁₅₆7_<157> = 7 · 23 · 541 · C152
C152 = P27 · P125
P27 = 890782728330524191869166267_<27>
P125 = 85923866571843740803540965749926517381370019113790480690155834870443120275131486394405562940747729082323857462899385910744101_<125>

Number: 66667_157 N=76539496293574891983635855692433688093898654052957677485524467763477648553594868792168478739241417052234379245550185034232289717301370439681136458440967 ( 152 digits) SNFS difficulty: 157 digits. Divisors found: r1=890782728330524191869166267 (pp27) r2=85923866571843740803540965749926517381370019113790480690155834870443120275131486394405562940747729082323857462899385910744101 (pp125) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 48.81 hours. Scaled time: 31.29 units (timescale=0.641). Factorization parameters were as follows: n: 76539496293574891983635855692433688093898654052957677485524467763477648553594868792168478739241417052234379245550185034232289717301370439681136458440967 m: 10000000000000000000000000000000 c5: 200 c0: 1 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:216391, largePrimes:5587411 encountered Relations: rels:5531851, finalFF:540104 Max relations in full relation-set: 28 Initial matrix: 433272 x 540104 with sparse part having weight 41840958. Pruned matrix : 367301 x 369531 with weight 26704226. Total sieving time: 41.91 hours. Total relation processing time: 0.34 hours. Matrix solve time: 6.39 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 48.81 hours. --------- CPU info (if available) ----------

(2·10¹⁶²-11)/9 = (2)₁₆₁1_<162> = 2999 · 13291 · 737369127871_<12> · C142
C142 = P58 · P85
P58 = 3477161523419951142339720131731396316406999807975085010917_<58>
P85 = 2174420563538039342235832474859054013840635530546636646389334682567283354466126851267_<85>

Number: 22221_162 N=7560811519267597547267443095951233885561978836680096060752707770152009100385863396144664462142405057459157349147876168151822386943389530281839 ( 142 digits) SNFS difficulty: 162 digits. Divisors found: r1=3477161523419951142339720131731396316406999807975085010917 (pp58) r2=2174420563538039342235832474859054013840635530546636646389334682567283354466126851267 (pp85) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 80.13 hours. Scaled time: 50.56 units (timescale=0.631). Factorization parameters were as follows: n: 7560811519267597547267443095951233885561978836680096060752707770152009100385863396144664462142405057459157349147876168151822386943389530281839 m: 100000000000000000000000000000000 c5: 200 c0: -11 skew: 1 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4549000 ) Primes: RFBsize:315948, AFBsize:316992, largePrimes:5799465 encountered Relations: rels:5908229, finalFF:740494 Max relations in full relation-set: 28 Initial matrix: 633005 x 740494 with sparse part having weight 45607314. Pruned matrix : 551212 x 554441 with weight 32109977. Total sieving time: 66.12 hours. Total relation processing time: 0.35 hours. Matrix solve time: 13.41 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 80.13 hours. --------- CPU info (if available) ----------

Jun 28, 2006

By Yousuke Koide / GMP-ECM / Jun 13, 2006
(10⁶²⁹-1)/9 = (1)_629<629> = 52837 · 2028119 · 2071723 · 247629013 · 654756293 · 5363222357_<10> · 2212394296770203368013_<22> · C563
C563 = P37 · C527
P37 = 1789869609522556717733652117803369849_<37>
C527 = [14534606650760746267274530737012122249588886991871533480924248527831473439337496631299129179522033276819164732384678553894131236188994972432041295892899181561322393208614711702308252990527266567131722050002675497142409690259209102269418390421674637868575482378208912819748484996888540615006146463031999507378641474887080601161024829052876998932648990033604585060950024365773053544964048384392311758635258298416485361871913055731243696761053009538099247807223175971678734515859190036820748543634426650689638017502134520137543399_<527>]
By Brude Dodson / GMP-ECM / Jun 25, 2006
(10³⁶⁹-1)/9 = (1)_369<369> = 3² · 37 · 83 · 1231 · 333667 · 538987 · 1811791 · 626920594693_<12> · 9425856976319889649_<19> · 1900016393894413508477719_<25> · 201763709900322803748657942361_<30> · 3151445759294008336434146467746716852125711_<43> · 8414640003465161203119978906558054839526493_<43> · C174
C174 = P52 · P122
P52 = 4624740815741021164555032450406356165555243059597323_<52>
P122 = 36075379229129405137442680972370788324414060277012433191198831287911648192680373281921936535843435181632954359677168188643_<122>
By Yousuke Koide / GMP-ECM / Jun 28, 2006
(10⁷⁹¹-1)/9 = (1)_791<791> = 227 · 239 · 4649 · 123397 · 1177009 · 142101569 · 908191467191_<12> · 1793584572599_<13> · 5325832146769_<13> · 827436967363609_<15> · 609308862837834547266089_<24> · 53895712312217719065267103426685397298498705173449226555003346881878523705781079015749721646701723_<98> · C589
C589 = P38 · C552
P38 = 17268952016347267202474461693447627333_<38>
C552 = [524338276467821469306866110640693273267456771354911491249811039886750737206459012463989313027609454624719205006551535049494191144723719815372375176302554242015920402149910500053458715224907875055739914800002691751396537788564528624249078377798631613710343087407520477946788491848531530083964817956899222619192798538490548065449464266022982267809530617447686365811014092939620045876935557367216873409267163582736418854782229284649982294276357936431663242770726403360599987506648872509414316421874236089815724432810048030031264456545314684078313249739241_<552>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁵⁴-7)/9 = 9(7)_154<155> = 739 · 1409 · 89561 · 9944520990408625844894246647_<28> · C117
C117 = P40 · P77
P40 = 5837116682833462849392995823393826958467_<40>
P77 = 18062736791772976438494600135843067934866747134653325808014080402535275160343_<77>

Number: 97777_154 N=105434302264887821200236582241715413873905252645232754612561173722931173696896607522883110803817912699363819426474181 ( 117 digits) SNFS difficulty: 156 digits. Divisors found: r1=5837116682833462849392995823393826958467 (pp40) r2=18062736791772976438494600135843067934866747134653325808014080402535275160343 (pp77) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 61.01 hours. Scaled time: 37.15 units (timescale=0.609). Factorization parameters were as follows: name: 97777_154 n: 105434302264887821200236582241715413873905252645232754612561173722931173696896607522883110803817912699363819426474181 m: 10000000000000000000000000000000 c5: 44 c0: -35 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:216382, largePrimes:5730781 encountered Relations: rels:5731090, finalFF:574418 Max relations in full relation-set: 28 Initial matrix: 433264 x 574418 with sparse part having weight 48987164. Pruned matrix : 363853 x 366083 with weight 31040164. Total sieving time: 53.51 hours. Total relation processing time: 0.53 hours. Matrix solve time: 6.76 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 61.01 hours. --------- CPU info (if available) ----------

Jun 24, 2006 (3rd)

By suberi / GGNFS-0.77.1-20060513-pentium4
(2·10¹⁵⁶+7)/9 = (2)₁₅₅3_<156> = 23 · 3499 · 23646641 · C144
C144 = P61 · P83
P61 = 6926356052576897781946985964283783248377448772933915690211713_<61>
P83 = 16859373684167425982860874223536195143299267692900426968939447864947450149457709003_<83>

Number: 22223_156 N=116774024959988722821062037579716837704602479668438645177019103488857401948400666554562683576727032687209786010840712519018713258848097016152139 ( 144 digits) SNFS difficulty: 156 digits. Divisors found: r1=6926356052576897781946985964283783248377448772933915690211713 (pp61) r2=16859373684167425982860874223536195143299267692900426968939447864947450149457709003 (pp83) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 44.21 hours. Scaled time: 26.92 units (timescale=0.609). Factorization parameters were as follows: n: 116774024959988722821062037579716837704602479668438645177019103488857401948400666554562683576727032687209786010840712519018713258848097016152139 m: 10000000000000000000000000000000 c5: 20 c0: 7 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:215976, largePrimes:5576703 encountered Relations: rels:5572542, finalFF:588575 Max relations in full relation-set: 28 Initial matrix: 432858 x 588575 with sparse part having weight 43819791. Pruned matrix : 321876 x 324104 with weight 27043784. Total sieving time: 37.95 hours. Total relation processing time: 0.73 hours. Matrix solve time: 5.26 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 44.21 hours. --------- CPU info (if available) ----------

10¹⁵⁴-3 = (9)₁₅₃7_<154> = 13 · 11243 · 6067869097_<10> · C140
C140 = P37 · P48 · P56
P37 = 1640121535660974334937516641312705897_<37>
P48 = 632474589733957453044658343116704489644784209341_<48>
P56 = 10869739116142629212501414649177235931983515829671794207_<56>

Number: 99997_154 N=11275562949784345252112605626469572573490020234580540167103938207368024209876467537743006522462110907256030913689041774978331494305994400539 ( 140 digits) SNFS difficulty: 155 digits. Divisors found: r1=1640121535660974334937516641312705897 (pp37) r2=632474589733957453044658343116704489644784209341 (pp48) r3=10869739116142629212501414649177235931983515829671794207 (pp56) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 37.22 hours. Scaled time: 23.49 units (timescale=0.631). Factorization parameters were as follows: n: 11275562949784345252112605626469572573490020234580540167103938207368024209876467537743006522462110907256030913689041774978331494305994400539 m: 10000000000000000000000000000000 c5: 1 c0: -30 skew: 1.97 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2400001) Primes: RFBsize:216816, AFBsize:215581, largePrimes:5481373 encountered Relations: rels:5403721, finalFF:528307 Max relations in full relation-set: 28 Initial matrix: 432461 x 528307 with sparse part having weight 37745359. Pruned matrix : 360063 x 362289 with weight 23851643. Total sieving time: 30.84 hours. Total relation processing time: 0.27 hours. Matrix solve time: 5.94 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 37.22 hours. --------- CPU info (if available) ----------

Jun 24, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
10¹⁵²+9 = 1(0)₁₅₁9_<153> = 29 · 293 · 1640081714429881_<16> · C133
C133 = P33 · P101
P33 = 269884379947565697172496988236741_<33>
P101 = 26588335208574136942682656526949478340363566869268859697120096025992721634714319195150472641068851757_<101>
10¹⁵⁷+9 = 1(0)₁₅₆9_<158> = 103 · 379 · 11025855177473150881_<20> · C134
C134 = P30 · P104
P30 = 489153471136315018633879719917_<30>
P104 = 47496995862766072526492146025536044546152041717277054294283602053960385357153879208150508927116593915441_<104>
10¹⁹⁴+9 = 1(0)₁₉₃9_<195> = 601 · 1669 · 4157 · 102873857153_<12> · C174
C174 = P30 · P144
P30 = 779377879409212880284613409841_<30>
P144 = 299113536682015207303470362477684416309447351856104432130038973632908830947016400385722023444292682919977688505297634840607839940972350056603601_<144>

Jun 24, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁵³-7)/9 = 9(7)_153<154> = 3³ · 19 · 71 · 3260123 · C143
C143 = P38 · P43 · P63
P38 = 99116919537660717344019019386864967843_<38>
P43 = 1546063793752448861604594357599366716472771_<43>
P63 = 537347530384367705748566479582863469498681675372594701184956221_<63>

Number: 97777_153 N=82343716238265332733845578767001197316759534003740090541991240208597861404143350691125394255272175363383252368085479900141859271017232097820613 ( 143 digits) SNFS difficulty: 154 digits. Divisors found: r1=99116919537660717344019019386864967843 (pp38) r2=1546063793752448861604594357599366716472771 (pp43) r3=537347530384367705748566479582863469498681675372594701184956221 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 50.96 hours. Scaled time: 34.24 units (timescale=0.672). Factorization parameters were as follows: name: 97777_153 n: 82343716238265332733845578767001197316759534003740090541991240208597861404143350691125394255272175363383252368085479900141859271017232097820613 m: 2000000000000000000000000000000 c5: 2750 c0: -7 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:216172, largePrimes:5588683 encountered Relations: rels:5518212, finalFF:527248 Max relations in full relation-set: 28 Initial matrix: 433055 x 527248 with sparse part having weight 41503672. Pruned matrix : 374357 x 376586 with weight 27113464. Total sieving time: 44.17 hours. Total relation processing time: 0.41 hours. Matrix solve time: 6.18 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 50.96 hours. --------- CPU info (if available) ----------

Jun 22, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4
(37·10¹⁵³-1)/9 = 4(1)_153<154> = 19 · 52673 · 6828739 · 53203810549582657_<17> · C125
C125 = P58 · P67
P58 = 1449115186608669999968721909978577884920205127608130753117_<58>
P67 = 7802457274112608923698648032270060088171243614756391036896564625483_<67>

Number: 41111_153 N=11306659328781867934200901863811224235021793204640218687383945073613523898676275009234833635994753050785147831466037839880511 ( 125 digits) SNFS difficulty: 154 digits. Divisors found: r1=1449115186608669999968721909978577884920205127608130753117 (pp58) r2=7802457274112608923698648032270060088171243614756391036896564625483 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 53.40 hours. Scaled time: 34.28 units (timescale=0.642). Factorization parameters were as follows: n: 11306659328781867934200901863811224235021793204640218687383945073613523898676275009234833635994753050785147831466037839880511 m: 1000000000000000000000000000000 c5: 37000 c0: -1 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:217626, largePrimes:5592626 encountered Relations: rels:5485878, finalFF:487203 Max relations in full relation-set: 28 Initial matrix: 434509 x 487203 with sparse part having weight 39884456. Pruned matrix : 411756 x 413992 with weight 30091644. Total sieving time: 44.27 hours. Total relation processing time: 0.40 hours. Matrix solve time: 8.51 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 53.40 hours. --------- CPU info (if available) ----------

8·10¹⁵²-1 = 7(9)_152<153> = 23 · C152
C152 = P40 · P112
P40 = 7901339528982736247439245218030751681423_<40>
P112 = 4402115434739492378122395747854232895486096498939727009935645870272775578543880889791663422087920251843606452631_<112>

Number: 79999_152 N=34782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913 ( 152 digits) SNFS difficulty: 152 digits. Divisors found: r1=7901339528982736247439245218030751681423 (pp40) r2=4402115434739492378122395747854232895486096498939727009935645870272775578543880889791663422087920251843606452631 (pp112) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 33.81 hours. Scaled time: 20.62 units (timescale=0.610). Factorization parameters were as follows: n: 34782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913 m: 2000000000000000000000000000000 c5: 25 c0: -1 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:176093, largePrimes:5463800 encountered Relations: rels:5400866, finalFF:508492 Max relations in full relation-set: 28 Initial matrix: 352459 x 508492 with sparse part having weight 43119422. Pruned matrix : 279663 x 281489 with weight 22308678. Total sieving time: 29.53 hours. Total relation processing time: 0.59 hours. Matrix solve time: 3.46 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 33.81 hours. --------- CPU info (if available) ----------

Jun 22, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁵²-7)/9 = 9(7)_152<153> = 43² · 1699 · 9787 · 26731 · C139
C139 = P36 · P52(1123...) · P52(7199...)
P36 = 147069431940540632633622231942675241_<36>
P52(1123...) = 1123545359101834709721738804452009746749923728439347_<52>
P52(7199...) = 7199992653826193042600639583180770081495925912971633_<52>

Number: 97777_152 N=1189720865726551197046584113282700046958525888139439104529939391718176978625271748994829022891657295537737626613238339384672302925168944891 ( 139 digits) SNFS difficulty: 153 digits. Divisors found: r1=147069431940540632633622231942675241 (pp36) r2=1123545359101834709721738804452009746749923728439347 (pp52) r3=7199992653826193042600639583180770081495925912971633 (pp52) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 44.45 hours. Scaled time: 27.07 units (timescale=0.609). Factorization parameters were as follows: name: 97777_152 n: 1189720865726551197046584113282700046958525888139439104529939391718176978625271748994829022891657295537737626613238339384672302925168944891 m: 2000000000000000000000000000000 c5: 275 c0: -7 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176544, largePrimes:5634915 encountered Relations: rels:5575605, finalFF:493838 Max relations in full relation-set: 28 Initial matrix: 352912 x 493838 with sparse part having weight 45407063. Pruned matrix : 299744 x 301572 with weight 25519786. Total sieving time: 39.81 hours. Total relation processing time: 0.32 hours. Matrix solve time: 4.14 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 44.45 hours. --------- CPU info (if available) ----------

Jun 20, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4
2·10¹⁵³-9 = 1(9)₁₅₂1_<154> = 11 · C153
C153 = P41 · P45 · P68
P41 = 14143455769740740001759009960126743688349_<41>
P45 = 453912657024767148614711372141519336680287959_<45>
P68 = 28321058492200039254937740121739341593546053812714710601460743639391_<68>

Number: 19991_153 N=181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181 ( 153 digits) SNFS difficulty: 153 digits. Divisors found: r1=14143455769740740001759009960126743688349 (pp41) r2=453912657024767148614711372141519336680287959 (pp45) r3=28321058492200039254937740121739341593546053812714710601460743639391 (pp68) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 37.97 hours. Scaled time: 23.05 units (timescale=0.607). Factorization parameters were as follows: n: 181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181 m: 2000000000000000000000000000000 c5: 125 c0: -18 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176188, largePrimes:5665430 encountered Relations: rels:5691661, finalFF:578636 Max relations in full relation-set: 28 Initial matrix: 352556 x 578636 with sparse part having weight 51231586. Pruned matrix : 262318 x 264144 with weight 24854504. Total sieving time: 33.49 hours. Total relation processing time: 0.69 hours. Matrix solve time: 3.55 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 37.97 hours. --------- CPU info (if available) ----------

Jun 20, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
6·10¹⁵¹-1 = 5(9)_151<152> = 61 · 129113 · C145
C145 = P33 · P47 · P66
P33 = 836660367018273797355323968615817_<33>
P47 = 17524625066162102246330727763070206160904572767_<47>
P66 = 519581298814572713681606589033971690588245769057952345724971828437_<66>

Number: 59999_151 N=7618183741196077701919007787434389979650561529975077111890677031798171966023408393181573187954686535228449650090472280413154419441706483315606243 ( 145 digits) SNFS difficulty: 151 digits. Divisors found: r1=836660367018273797355323968615817 (pp33) r2=17524625066162102246330727763070206160904572767 (pp47) r3=519581298814572713681606589033971690588245769057952345724971828437 (pp66) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 32.65 hours. Scaled time: 19.88 units (timescale=0.609). Factorization parameters were as follows: name: 59999_151 n: 7618183741196077701919007787434389979650561529975077111890677031798171966023408393181573187954686535228449650090472280413154419441706483315606243 m: 1000000000000000000000000000000 c5: 60 c0: -1 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:175738, largePrimes:5548666 encountered Relations: rels:5544388, finalFF:557581 Max relations in full relation-set: 28 Initial matrix: 352107 x 557581 with sparse part having weight 49093900. Pruned matrix : 263359 x 265183 with weight 23631186. Total sieving time: 29.11 hours. Total relation processing time: 0.33 hours. Matrix solve time: 3.06 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 32.65 hours. --------- CPU info (if available) ----------

Jun 19, 2006

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10¹⁸²+3 = 1(0)₁₈₁3_<183> = C183
C183 = P27 · P156
P27 = 406739627350936953562388377_<27>
P156 = 245857529671480737053230473791951684664784508684537281437794354233101717382061812791982857492060102011506560855529194447399887136377222705239997696635282939_<156>

Jun 18, 2006 (4th)

By Alfred Reich / Msieve v. 1.06
(2·10¹⁵⁷+43)/9 = (2)₁₅₆7_<157> = 7 · 6011267 · 11340661 · 26297446143827679370836289_<26> · C117
C117 = P54 · P63
P54 = 297907083346305195502362629714985396531415470201105233_<54>
P63 = 594416225273485143935306604924356739743242652295164459113417819_<63>

prp54 factor: 297907083346305195502362629714985396531415470201105233 prp63 factor: 594416225273485143935306604924356739743242652295164459113417819 Fri Jun 16 15:30:27 2006 Fri Jun 16 15:30:27 2006 Fri Jun 16 15:30:27 2006 Msieve v. 1.06 Fri Jun 16 15:30:27 2006 random seeds: 6e3be7d0 af211ff4 Fri Jun 16 15:30:27 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Fri Jun 16 15:30:28 2006 using multiplier of 17 Fri Jun 16 15:30:28 2006 sieve interval: 19 blocks of size 65536 Fri Jun 16 15:30:28 2006 processing polynomials in batches of 3 Fri Jun 16 15:30:28 2006 using a sieve bound of 10566139 (350000 primes) Fri Jun 16 15:30:28 2006 using large prime bound of 1584920850 (30 bits) Fri Jun 16 15:30:28 2006 using double large prime bound of 36308945412966600 (47-56 bits) Fri Jun 16 15:30:28 2006 using trial factoring cutoff of 68 bits Fri Jun 16 15:30:28 2006 polynomial 'A' values have 16 factors Sat Jun 17 14:47:39 2006 5839 relations (5561 full + 278 combined from 322304 partial), need 350096 Sat Jun 17 14:47:39 2006 elapsed time 23:17:12 Sat Jun 17 14:48:21 2006 Sat Jun 17 14:48:21 2006 Sat Jun 17 14:48:21 2006 Msieve v. 1.06 Sat Jun 17 14:48:21 2006 random seeds: a6d38e10 66593cf6 Sat Jun 17 14:48:21 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Sat Jun 17 14:48:23 2006 using multiplier of 17 Sat Jun 17 14:48:23 2006 sieve interval: 19 blocks of size 65536 Sat Jun 17 14:48:23 2006 processing polynomials in batches of 3 Sat Jun 17 14:48:23 2006 using a sieve bound of 10566139 (350000 primes) Sat Jun 17 14:48:23 2006 using large prime bound of 1584920850 (30 bits) Sat Jun 17 14:48:23 2006 using double large prime bound of 36308945412966600 (47-56 bits) Sat Jun 17 14:48:23 2006 using trial factoring cutoff of 68 bits Sat Jun 17 14:48:23 2006 polynomial 'A' values have 16 factors Sat Jun 17 15:05:03 2006 67 relations (67 full + 0 combined from 3929 partial), need 350096 Sat Jun 17 15:05:03 2006 elapsed time 00:16:42 Sat Jun 17 15:08:44 2006 Sat Jun 17 15:08:44 2006 Sat Jun 17 15:08:44 2006 Msieve v. 1.06 Sat Jun 17 15:08:44 2006 random seeds: 2edef0b0 ff574550 Sat Jun 17 15:08:44 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Sat Jun 17 15:08:46 2006 using multiplier of 17 Sat Jun 17 15:08:46 2006 sieve interval: 19 blocks of size 65536 Sat Jun 17 15:08:46 2006 processing polynomials in batches of 3 Sat Jun 17 15:08:46 2006 using a sieve bound of 10566139 (350000 primes) Sat Jun 17 15:08:46 2006 using large prime bound of 1584920850 (30 bits) Sat Jun 17 15:08:46 2006 using double large prime bound of 36308945412966600 (47-56 bits) Sat Jun 17 15:08:46 2006 using trial factoring cutoff of 68 bits Sat Jun 17 15:08:46 2006 polynomial 'A' values have 16 factors Sat Jun 17 15:08:52 2006 restarting with 45113 full and 2586148 partial relations Sat Jun 17 15:10:15 2006 79829 relations (45115 full + 34714 combined from 2586446 partial), need 350096 Sat Jun 17 15:10:15 2006 elapsed time 00:01:31 Sat Jun 17 15:11:28 2006 Sat Jun 17 15:11:28 2006 Sat Jun 17 15:11:28 2006 Msieve v. 1.06 Sat Jun 17 15:11:28 2006 random seeds: f0c64d78 a1063e8e Sat Jun 17 15:11:28 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Sat Jun 17 15:11:29 2006 using multiplier of 17 Sat Jun 17 15:11:29 2006 sieve interval: 19 blocks of size 65536 Sat Jun 17 15:11:29 2006 processing polynomials in batches of 3 Sat Jun 17 15:11:29 2006 using a sieve bound of 10566139 (350000 primes) Sat Jun 17 15:11:29 2006 using large prime bound of 1584920850 (30 bits) Sat Jun 17 15:11:29 2006 using double large prime bound of 36308945412966600 (47-56 bits) Sat Jun 17 15:11:29 2006 using trial factoring cutoff of 68 bits Sat Jun 17 15:11:29 2006 polynomial 'A' values have 16 factors Sun Jun 18 14:02:17 2006 5722 relations (5458 full + 264 combined from 315736 partial), need 350096 Sun Jun 18 14:02:17 2006 elapsed time 22:50:49 Sun Jun 18 14:53:41 2006 Sun Jun 18 14:53:41 2006 Sun Jun 18 14:53:41 2006 Msieve v. 1.06 Sun Jun 18 14:53:41 2006 random seeds: a7040c00 6bf83931 Sun Jun 18 14:53:41 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Sun Jun 18 14:53:43 2006 using multiplier of 17 Sun Jun 18 14:53:43 2006 sieve interval: 19 blocks of size 65536 Sun Jun 18 14:53:43 2006 processing polynomials in batches of 3 Sun Jun 18 14:53:43 2006 using a sieve bound of 10566139 (350000 primes) Sun Jun 18 14:53:43 2006 using large prime bound of 1584920850 (30 bits) Sun Jun 18 14:53:43 2006 using double large prime bound of 36308945412966600 (47-56 bits) Sun Jun 18 14:53:43 2006 using trial factoring cutoff of 68 bits Sun Jun 18 14:53:43 2006 polynomial 'A' values have 16 factors Sun Jun 18 14:53:58 2006 restarting with 98809 full and 5685171 partial relations Sun Jun 18 14:53:58 2006 489590 relations (98809 full + 390781 combined from 5685171 partial), need 350096 Sun Jun 18 14:54:19 2006 begin with 5685171 relations Sun Jun 18 14:54:35 2006 reduce to 1179398 relations in 14 passes Sun Jun 18 14:54:35 2006 attempting to read 98809 full and 1179398 partial relations Sun Jun 18 14:55:21 2006 recovered 98809 full and 1179398 partial relations Sun Jun 18 14:55:21 2006 recovered 1255866 polynomials Sun Jun 18 14:55:27 2006 attempting to build 390781 cycles Sun Jun 18 14:55:28 2006 found 390781 cycles in 6 passes Sun Jun 18 14:55:30 2006 distribution of cycle lengths: Sun Jun 18 14:55:30 2006 length 2 : 76003 Sun Jun 18 14:55:30 2006 length 3 : 82423 Sun Jun 18 14:55:30 2006 length 4 : 72166 Sun Jun 18 14:55:30 2006 length 5 : 57921 Sun Jun 18 14:55:30 2006 length 6 : 40330 Sun Jun 18 14:55:30 2006 length 7 : 26146 Sun Jun 18 14:55:30 2006 length 8 : 16036 Sun Jun 18 14:55:30 2006 length 9+: 19756 Sun Jun 18 14:55:30 2006 largest cycle: 21 relations Sun Jun 18 14:55:31 2006 350000 x 350064 system, weight 22152847 (avg 63.28/col) Sun Jun 18 14:55:34 2006 reduce to 338708 x 338772 in 4 passes Sun Jun 18 16:11:11 2006 lanczos halted after 5357 iterations Sun Jun 18 16:11:15 2006 recovered 56 nontrivial dependencies Sun Jun 18 16:13:09 2006 prp54 factor: 297907083346305195502362629714985396531415470201105233 Sun Jun 18 16:13:09 2006 prp63 factor: 594416225273485143935306604924356739743242652295164459113417819 Sun Jun 18 16:13:12 2006 elapsed time 01:19:31

Jun 18, 2006 (3rd)

By Wataru Sakai / GMP-ECM 6.1
(25·10¹⁶¹-1)/3 = 8(3)_161<162> = 71 · 627632323902741384517983871_<27> · C134
C134 = P33 · P101
P33 = 402923263960731990459276252411929_<33>
P101 = 46412264609376042963875982573595320846726898199501545598399929674110110204265192309020927313561073797_<101>
(25·10¹⁸⁹-1)/3 = 8(3)_189<190> = 13 · 69481 · 14970782913227_<14> · 86676545786512496411372249_<26> · C145
C145 = P29 · P33 · P85
P29 = 22947665214016491792948713879_<29>
P33 = 263220054799792924810769047222031_<33>
P85 = 1177079381440907821047749257131763892168650187727161937621530953691546230966643693843_<85>
(25·10¹⁹³-1)/3 = 8(3)_193<194> = 2729 · 9431 · 113622631267_<12> · C176
C176 = P37 · P140
P37 = 1234673054650272416503200054655444603_<37>
P140 = 23080258080801038899595047931573006063528336563000814220369471250323182879121823026175822141456825879452373941615318614152585303505844325067_<140>

Jun 18, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(73·10¹⁵¹-1)/9 = 8(1)_151<152> = 3 · 29 · 47 · 193 · 457697 · C141
C141 = P33 · P34 · P75
P33 = 528012984669708627919758887087231_<33>
P34 = 2640623962369281969675262349483603_<34>
P75 = 161055923586852517269688910385341375145213411153442717701673814626750164283_<75>

Number: 81111_151 N=224557655449331640744698222153463653716415037742054456753768335971442934095442031868984712643312221148993545757459799412236334041135414093919 ( 141 digits) SNFS difficulty: 152 digits. Divisors found: r1=528012984669708627919758887087231 (pp33) r2=2640623962369281969675262349483603 (pp34) r3=161055923586852517269688910385341375145213411153442717701673814626750164283 (pp75) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 44.55 hours. Scaled time: 29.98 units (timescale=0.673). Factorization parameters were as follows: name: 81111_151 n: 224557655449331640744698222153463653716415037742054456753768335971442934095442031868984712643312221148993545757459799412236334041135414093919 m: 1000000000000000000000000000000 c5: 730 c0: -1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176503, largePrimes:5534398 encountered Relations: rels:5399634, finalFF:435070 Max relations in full relation-set: 28 Initial matrix: 352872 x 435070 with sparse part having weight 39896073. Pruned matrix : 320448 x 322276 with weight 25707123. Total sieving time: 39.82 hours. Total relation processing time: 0.36 hours. Matrix solve time: 4.20 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 44.55 hours. --------- CPU info (if available) ----------

Jun 18, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4
(8·10¹⁵³-71)/9 = (8)₁₅₂1_<153> = 8825839534511526662522911_<25> · C129
C129 = P46 · P83
P46 = 1296444514871243498998765398449712354381717833_<46>
P83 = 77685061845475214425509536216756309596984840086525079446336201532416456388867813687_<83>

Number: 88881_153 N=100714372316999662567112812918965620315388389942591227612416816485546219492067911197547793034221068381867775300311816362049380271 ( 129 digits) SNFS difficulty: 153 digits. Divisors found: r1=1296444514871243498998765398449712354381717833 (pp46) r2=77685061845475214425509536216756309596984840086525079446336201532416456388867813687 (pp83) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 60.66 hours. Scaled time: 37.13 units (timescale=0.612). Factorization parameters were as follows: n: 100714372316999662567112812918965620315388389942591227612416816485546219492067911197547793034221068381867775300311816362049380271 m: 2000000000000000000000000000000 c5: 250 c0: -71 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2700001) Primes: RFBsize:176302, AFBsize:175124, largePrimes:5822215 encountered Relations: rels:5825108, finalFF:487746 Max relations in full relation-set: 28 Initial matrix: 351492 x 487746 with sparse part having weight 52251534. Pruned matrix : 305361 x 307182 with weight 32152741. Total sieving time: 53.71 hours. Total relation processing time: 1.08 hours. Matrix solve time: 5.58 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 60.66 hours. --------- CPU info (if available) ----------

Jun 17, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4
(4·10¹⁵³+41)/9 = (4)₁₅₂9_<153> = 23 · 29 · 7877 · 873567461478995351_<18> · C128
C128 = P53 · P76
P53 = 10278202000310109853026337644927666384593872391970911_<53>
P76 = 9421438220178605267247787803414490154127967731184104140712790580208553504351_<76>

Number: 44449_153 N=96835445160437861836793054504352665974763358359367105494199949648027977115227878216143159883536675005810147600085224164703933761 ( 128 digits) SNFS difficulty: 153 digits. Divisors found: r1=10278202000310109853026337644927666384593872391970911 (pp53) r2=9421438220178605267247787803414490154127967731184104140712790580208553504351 (pp76) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 36.61 hours. Scaled time: 23.54 units (timescale=0.643). Factorization parameters were as follows: n: 96835445160437861836793054504352665974763358359367105494199949648027977115227878216143159883536675005810147600085224164703933761 m: 2000000000000000000000000000000 c5: 125 c0: 41 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176674, largePrimes:5475359 encountered Relations: rels:5331530, finalFF:432026 Max relations in full relation-set: 28 Initial matrix: 353041 x 432026 with sparse part having weight 38289105. Pruned matrix : 319991 x 321820 with weight 24785869. Total sieving time: 31.58 hours. Total relation processing time: 0.31 hours. Matrix solve time: 4.55 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 36.61 hours. --------- CPU info (if available) ----------

(5·10¹⁵⁷-41)/9 = (5)₁₅₆1_<157> = 31638006853_<11> · 127308301733038781811409_<24> · C124
C124 = P47 · P77
P47 = 62177795589380677359547676171051471759978319277_<47>
P77 = 22183309247072798284455041381076813661365827752047238245813949734174421655119_<77>

Number: 55551_157 N=1379309267860510631923280660454483985542807005995371878444954987504570972707580675762406732618983047945197528669850163428963 ( 124 digits) SNFS difficulty: 157 digits. Divisors found: r1=62177795589380677359547676171051471759978319277 (pp47) r2=22183309247072798284455041381076813661365827752047238245813949734174421655119 (pp77) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 53.50 hours. Scaled time: 36.75 units (timescale=0.687). Factorization parameters were as follows: n: 1379309267860510631923280660454483985542807005995371878444954987504570972707580675762406732618983047945197528669850163428963 m: 10000000000000000000000000000000 c5: 500 c0: -41 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3300001) Primes: RFBsize:216816, AFBsize:216877, largePrimes:5686463 encountered Relations: rels:5613572, finalFF:490335 Max relations in full relation-set: 28 Initial matrix: 433759 x 490335 with sparse part having weight 45003353. Pruned matrix : 410960 x 413192 with weight 34410874. Total sieving time: 43.92 hours. Total relation processing time: 0.31 hours. Matrix solve time: 9.07 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 53.50 hours. --------- CPU info (if available) ----------

Jun 16, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(28·10¹⁵¹-1)/9 = 3(1)_151<152> = 31 · 19843 · 434831 · C141
C141 = P60 · P81
P60 = 974853410034804062561219744184438708636042947181325656020147_<60>
P81 = 119312702335017997752212094830142486881715593155366467314651908260291633099814831_<81>

Number: 31111_151 N=116312394731759824276532451135704508184575224005721352126402868892503361415954444774635572442848479083945663759064809382402290241666105400157 ( 141 digits) SNFS difficulty: 152 digits. Divisors found: r1=974853410034804062561219744184438708636042947181325656020147 (pp60) r2=119312702335017997752212094830142486881715593155366467314651908260291633099814831 (pp81) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 36.44 hours. Scaled time: 24.31 units (timescale=0.667). Factorization parameters were as follows: name: 31111_151 n: 116312394731759824276532451135704508184575224005721352126402868892503361415954444774635572442848479083945663759064809382402290241666105400157 m: 1000000000000000000000000000000 c5: 280 c0: -1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176603, largePrimes:5432957 encountered Relations: rels:5288454, finalFF:437164 Max relations in full relation-set: 28 Initial matrix: 352972 x 437164 with sparse part having weight 38153671. Pruned matrix : 312776 x 314604 with weight 23827219. Total sieving time: 32.14 hours. Total relation processing time: 0.34 hours. Matrix solve time: 3.80 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 36.44 hours. --------- CPU info (if available) ----------

Jun 16, 2006 (2nd)

By Alexander Mkrtychyan / ggnfs-0.77.1-20060513-win32
(10¹⁸⁶+71)/9 = (1)₁₈₅9_<186> = C186
C186 = P53 · P133
P53 = 21956285956390994430963419957738743694747827961903819_<53>
P133 = 5060560394039188481932328242445842739178885005851611298737492037561232350261294769209243502470606386060971130677592702162720129986701_<133>

From dependence 1, sqrt obtained: r1=21956285956390994430963419957738743694747827961903819 (p53) r2=5060560394039188481932328242445842739178885005851611298737492037561232350261294769209243502470606386060971130677592702162720129986701 (p133) sieving params: n: 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119 m: 10000000000000000000000000000000000000 c5: 10 c0: 71 skew: 1.48 type: snfs rlim: 11000000 alim: 11000000 lbpr: 28 lbpa: 28 mfbr: 48 mfba: 48 rlambda: 2.2 alambda: 2.2 CPU RAM Process: (GHz days) (Max RSS) ----------------- ---------- --------- gnfs-lasieve4I14e 562 58MB procrels 0.06 ??MB matbuild 0.06 672MB matsolve 5.17 348MB sqrt 0.08 ??MB ---------- total 567.37 Special-q: ~[6M;51M) Processing with different factor bases (with additional(+1M) special-q sieving): -------- 13M/13M unique relations: 3134973 full relation sets: 1730732 Pruning matrix with wt=0.700 Initial matrix is 1696502 x 1730732 with sparse part having weight 39373085. (total weight is 106462937) Matrix pruned to 1670902 x 1679448 with weight 39534812. matsolve found only trivial dependencies. 6M/6M unique relations: 3362796 full relation sets: 949650 Pruning matrix with wt=0.700 Initial matrix is 825087 x 949650 with sparse part having weight 107831245. (total weight is 172292685) Matrix pruned to 780833 x 785022 with weight 77805320.

(4·10¹⁸⁹-7)/3 = 1(3)₁₈₈1_<190> = 11 · C189
C189 = P77 · P112
P77 = 22727342670242448304921294300019680181558260484479909955238866999770020899617_<77>
P112 = 5333316920100283702649243746356914291163645388535270424514041824457524502483749417048804695185211155141229296313_<112>

From dependence 0, sqrt obtained: r1=5333316920100283702649243746356914291163645388535270424514041824457524502483749417048804695185211155141229296313 (p112) r2=22727342670242448304921294300019680181558260484479909955238866999770020899617 (p77) sieving params: m: 100000000000000000000000000000000000000 c5: 2 c0: -35 skew: 1.77 type: snfs rlim: 14000000 alim: 14000000 lbpr: 29 lbpa: 29 mfbr: 54 mfba: 54 rlambda: 2.3 alambda: 2.3 Special-q: ~[6M;60M) Processing with different factor bases (with additional(+0.3M) special-q sieving): -------- 8M/8M unique relations: 3691813 full relation sets: 1245850 Pruning matrix with wt=0.700 Initial matrix is 1079262 x 1245850 with sparse part having weight 81530763. (total weight is 145966109) Matrix pruned to 1004047 x 1009507 with weight 56671324. 7M/7M unique relations: 3837154 full relation sets: 1169049 Pruning matrix with wt=0.700 Initial matrix is 952777 x 1169049 with sparse part having weight 105082045. (total weight is 174741652) Matrix pruned to 868214 x 873041 with weight 67229090. !Solved successfully CPU RAM Process: (GHz days) (Max RSS) ----------------- ---------- --------- gnfs-lasieve4I14e 675 62MB procrels 0.06 ??MB matbuild 0.08 765MB matsolve 5.38 300MB sqrt 0.04 132MB ---------- total 680.56

These are the largest number and the second largest number factored by GGNFS in our tables so far. Congratulations!

Jun 16, 2006

By Alfred Reich / Msieve v. 1.06
10¹⁶¹+9 = 1(0)₁₆₀9_<162> = 7 · 13 · 23 · 157 · 8059 · 13415957160051517_<17> · 33227221889480924019367_<23> · C113
C113 = P47 · P67
P47 = 37811313891994346064305264570354822948081755411_<47>
P67 = 2240332608851730481538608681856319442213805555106852747449191086419_<67>

number: 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) prp47 factor: 37811313891994346064305264570354822948081755411 prp67 factor: 2240332608851730481538608681856319442213805555106852747449191086419 Tue Jun 06 14:10:29 2006 Tue Jun 06 14:10:29 2006 Tue Jun 06 14:10:29 2006 Msieve v. 1.06 Tue Jun 06 14:10:29 2006 random seeds: 82bb10e0 ef1ee166 Tue Jun 06 14:10:29 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Tue Jun 06 14:10:30 2006 using multiplier of 1 Tue Jun 06 14:10:30 2006 sieve interval: 17 blocks of size 65536 Tue Jun 06 14:10:31 2006 processing polynomials in batches of 3 Tue Jun 06 14:10:31 2006 using a sieve bound of 8423407 (282760 primes) Tue Jun 06 14:10:31 2006 using large prime bound of 1263511050 (30 bits) Tue Jun 06 14:10:31 2006 using double large prime bound of 24145837678737600 (47-55 bits) Tue Jun 06 14:10:31 2006 using trial factoring cutoff of 65 bits Tue Jun 06 14:10:31 2006 polynomial 'A' values have 15 factors Tue Jun 06 14:10:31 2006 restarting with 563 full and 34999 partial relations Tue Jun 06 14:26:35 2006 579 relations (576 full + 3 combined from 36265 partial), need 282856 Tue Jun 06 14:26:35 2006 elapsed time 00:16:06 Tue Jun 06 14:27:05 2006 Tue Jun 06 14:27:05 2006 Tue Jun 06 14:27:05 2006 Msieve v. 1.06 Tue Jun 06 14:27:05 2006 random seeds: 14acdaf0 f2db2c6e Tue Jun 06 14:27:05 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Tue Jun 06 14:27:06 2006 using multiplier of 1 Tue Jun 06 14:27:06 2006 sieve interval: 17 blocks of size 65536 Tue Jun 06 14:27:06 2006 processing polynomials in batches of 3 Tue Jun 06 14:27:06 2006 using a sieve bound of 8423407 (282760 primes) Tue Jun 06 14:27:06 2006 using large prime bound of 1263511050 (30 bits) Tue Jun 06 14:27:06 2006 using double large prime bound of 24145837678737600 (47-55 bits) Tue Jun 06 14:27:06 2006 using trial factoring cutoff of 65 bits Tue Jun 06 14:27:06 2006 polynomial 'A' values have 15 factors Wed Jun 07 10:19:26 2006 1110 relations (1097 full + 13 combined from 66807 partial), need 282856 Wed Jun 07 10:19:26 2006 elapsed time 19:52:21 Wed Jun 07 10:23:45 2006 Wed Jun 07 10:23:45 2006 Wed Jun 07 10:23:45 2006 Msieve v. 1.06 Wed Jun 07 10:23:45 2006 random seeds: b353bbc0 876a3e65 Wed Jun 07 10:23:45 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 07 10:23:46 2006 using multiplier of 1 Wed Jun 07 10:23:46 2006 sieve interval: 17 blocks of size 65536 Wed Jun 07 10:23:46 2006 processing polynomials in batches of 3 Wed Jun 07 10:23:46 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 07 10:23:46 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 07 10:23:46 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 07 10:23:46 2006 using trial factoring cutoff of 65 bits Wed Jun 07 10:23:46 2006 polynomial 'A' values have 15 factors Wed Jun 07 12:03:49 2006 5 relations (5 full + 0 combined from 375 partial), need 282856 Wed Jun 07 12:03:49 2006 elapsed time 01:40:04 Wed Jun 07 12:05:32 2006 Wed Jun 07 12:05:32 2006 Wed Jun 07 12:05:32 2006 Msieve v. 1.06 Wed Jun 07 12:05:32 2006 random seeds: d4971db8 71711aba Wed Jun 07 12:05:32 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 07 12:05:34 2006 using multiplier of 1 Wed Jun 07 12:05:34 2006 sieve interval: 17 blocks of size 65536 Wed Jun 07 12:05:34 2006 processing polynomials in batches of 3 Wed Jun 07 12:05:34 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 07 12:05:34 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 07 12:05:34 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 07 12:05:34 2006 using trial factoring cutoff of 65 bits Wed Jun 07 12:05:34 2006 polynomial 'A' values have 15 factors Wed Jun 07 12:05:34 2006 restarting with 251 full and 16479 partial relations Sun Jun 11 18:34:58 2006 2339 relations (2267 full + 72 combined from 140829 partial), need 282856 Sun Jun 11 18:34:58 2006 elapsed time 102:29:26 Sun Jun 11 18:35:59 2006 Sun Jun 11 18:35:59 2006 Sun Jun 11 18:35:59 2006 Msieve v. 1.06 Sun Jun 11 18:35:59 2006 random seeds: cefb7950 3127a798 Sun Jun 11 18:35:59 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Sun Jun 11 18:36:00 2006 using multiplier of 1 Sun Jun 11 18:36:00 2006 sieve interval: 17 blocks of size 65536 Sun Jun 11 18:36:00 2006 processing polynomials in batches of 3 Sun Jun 11 18:36:00 2006 using a sieve bound of 8423407 (282760 primes) Sun Jun 11 18:36:00 2006 using large prime bound of 1263511050 (30 bits) Sun Jun 11 18:36:00 2006 using double large prime bound of 24145837678737600 (47-55 bits) Sun Jun 11 18:36:00 2006 using trial factoring cutoff of 65 bits Sun Jun 11 18:36:00 2006 polynomial 'A' values have 15 factors Mon Jun 12 08:41:31 2006 1024 relations (1015 full + 9 combined from 63554 partial), need 282856 Mon Jun 12 08:41:31 2006 elapsed time 14:05:32 Mon Jun 12 08:42:14 2006 Mon Jun 12 08:42:14 2006 Mon Jun 12 08:42:14 2006 Msieve v. 1.06 Mon Jun 12 08:42:14 2006 random seeds: 79f08e3c 332b9a51 Mon Jun 12 08:42:14 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Mon Jun 12 08:42:16 2006 using multiplier of 1 Mon Jun 12 08:42:16 2006 sieve interval: 17 blocks of size 65536 Mon Jun 12 08:42:16 2006 processing polynomials in batches of 3 Mon Jun 12 08:42:16 2006 using a sieve bound of 8423407 (282760 primes) Mon Jun 12 08:42:16 2006 using large prime bound of 1263511050 (30 bits) Mon Jun 12 08:42:16 2006 using double large prime bound of 24145837678737600 (47-55 bits) Mon Jun 12 08:42:16 2006 using trial factoring cutoff of 65 bits Mon Jun 12 08:42:16 2006 polynomial 'A' values have 15 factors Mon Jun 12 17:08:38 2006 647 relations (645 full + 2 combined from 38538 partial), need 282856 Mon Jun 12 17:08:38 2006 elapsed time 08:26:24 Mon Jun 12 17:09:29 2006 Mon Jun 12 17:09:29 2006 Mon Jun 12 17:09:29 2006 Msieve v. 1.06 Mon Jun 12 17:09:29 2006 random seeds: f3d65b18 0b843bac Mon Jun 12 17:09:29 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Mon Jun 12 17:09:31 2006 using multiplier of 1 Mon Jun 12 17:09:31 2006 sieve interval: 17 blocks of size 65536 Mon Jun 12 17:09:31 2006 processing polynomials in batches of 3 Mon Jun 12 17:09:31 2006 using a sieve bound of 8423407 (282760 primes) Mon Jun 12 17:09:31 2006 using large prime bound of 1263511050 (30 bits) Mon Jun 12 17:09:31 2006 using double large prime bound of 24145837678737600 (47-55 bits) Mon Jun 12 17:09:31 2006 using trial factoring cutoff of 65 bits Mon Jun 12 17:09:31 2006 polynomial 'A' values have 15 factors Mon Jun 12 19:20:38 2006 3 relations (3 full + 0 combined from 307 partial), need 282856 Mon Jun 12 19:20:38 2006 elapsed time 02:11:09 Tue Jun 13 20:38:45 2006 Tue Jun 13 20:38:45 2006 Tue Jun 13 20:38:45 2006 Msieve v. 1.06 Tue Jun 13 20:38:45 2006 random seeds: a273f300 21eb8982 Tue Jun 13 20:38:45 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Tue Jun 13 20:38:46 2006 using multiplier of 1 Tue Jun 13 20:38:46 2006 sieve interval: 17 blocks of size 65536 Tue Jun 13 20:38:46 2006 processing polynomials in batches of 3 Tue Jun 13 20:38:46 2006 using a sieve bound of 8423407 (282760 primes) Tue Jun 13 20:38:46 2006 using large prime bound of 1263511050 (30 bits) Tue Jun 13 20:38:46 2006 using double large prime bound of 24145837678737600 (47-55 bits) Tue Jun 13 20:38:46 2006 using trial factoring cutoff of 65 bits Tue Jun 13 20:38:46 2006 polynomial 'A' values have 15 factors Tue Jun 13 20:39:13 2006 restarting with 65188 full and 4084882 partial relations Tue Jun 13 20:39:13 2006 283482 relations (65188 full + 218294 combined from 4084882 partial), need 282856 Tue Jun 13 20:39:35 2006 begin with 4084882 relations Tue Jun 13 20:41:14 2006 reduce to 682551 relations in 11 passes Tue Jun 13 20:41:14 2006 attempting to read 65188 full and 682551 partial relations Tue Jun 13 20:42:40 2006 Tue Jun 13 20:42:40 2006 Tue Jun 13 20:42:40 2006 Msieve v. 1.06 Tue Jun 13 20:42:40 2006 random seeds: d70a9350 476c372a Tue Jun 13 20:42:40 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Tue Jun 13 20:42:42 2006 using multiplier of 1 Tue Jun 13 20:42:42 2006 sieve interval: 17 blocks of size 65536 Tue Jun 13 20:42:42 2006 processing polynomials in batches of 3 Tue Jun 13 20:42:42 2006 using a sieve bound of 8423407 (282760 primes) Tue Jun 13 20:42:42 2006 using large prime bound of 1263511050 (30 bits) Tue Jun 13 20:42:42 2006 using double large prime bound of 24145837678737600 (47-55 bits) Tue Jun 13 20:42:42 2006 using trial factoring cutoff of 65 bits Tue Jun 13 20:42:42 2006 polynomial 'A' values have 15 factors Tue Jun 13 20:42:42 2006 restarting with 40 full and 2846 partial relations Wed Jun 14 08:18:35 2006 869 relations (861 full + 8 combined from 55706 partial), need 282856 Wed Jun 14 08:18:36 2006 elapsed time 11:35:56 Wed Jun 14 08:35:10 2006 Wed Jun 14 08:35:10 2006 Wed Jun 14 08:35:10 2006 Msieve v. 1.06 Wed Jun 14 08:35:10 2006 random seeds: e8029fd8 a91fd695 Wed Jun 14 08:35:10 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 14 08:35:12 2006 using multiplier of 1 Wed Jun 14 08:35:12 2006 sieve interval: 17 blocks of size 65536 Wed Jun 14 08:35:12 2006 processing polynomials in batches of 3 Wed Jun 14 08:35:12 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 14 08:35:12 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 14 08:35:12 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 14 08:35:12 2006 using trial factoring cutoff of 65 bits Wed Jun 14 08:35:12 2006 polynomial 'A' values have 15 factors Wed Jun 14 08:35:12 2006 restarting with 861 full and 55706 partial relations Wed Jun 14 10:07:52 2006 982 relations (969 full + 13 combined from 62762 partial), need 282856 Wed Jun 14 10:07:52 2006 elapsed time 01:32:42 Wed Jun 14 10:20:08 2006 Wed Jun 14 10:20:08 2006 Wed Jun 14 10:20:08 2006 Msieve v. 1.06 Wed Jun 14 10:20:08 2006 random seeds: 5238bafc 871b85b0 Wed Jun 14 10:20:08 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 14 10:20:09 2006 using multiplier of 1 Wed Jun 14 10:20:10 2006 sieve interval: 17 blocks of size 65536 Wed Jun 14 10:20:10 2006 processing polynomials in batches of 3 Wed Jun 14 10:20:10 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 14 10:20:10 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 14 10:20:10 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 14 10:20:10 2006 using trial factoring cutoff of 65 bits Wed Jun 14 10:20:10 2006 polynomial 'A' values have 15 factors Wed Jun 14 10:20:10 2006 restarting with 969 full and 62762 partial relations Wed Jun 14 13:12:30 2006 1209 relations (1193 full + 16 combined from 75765 partial), need 282856 Wed Jun 14 13:12:30 2006 elapsed time 02:52:22 Wed Jun 14 18:50:58 2006 Wed Jun 14 18:50:58 2006 Wed Jun 14 18:50:58 2006 Msieve v. 1.06 Wed Jun 14 18:50:58 2006 random seeds: 8c3ee704 426cdfd2 Wed Jun 14 18:50:58 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 14 18:50:59 2006 using multiplier of 1 Wed Jun 14 18:50:59 2006 sieve interval: 17 blocks of size 65536 Wed Jun 14 18:50:59 2006 processing polynomials in batches of 3 Wed Jun 14 18:50:59 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 14 18:50:59 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 14 18:50:59 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 14 18:50:59 2006 using trial factoring cutoff of 65 bits Wed Jun 14 18:50:59 2006 polynomial 'A' values have 15 factors Wed Jun 14 18:51:00 2006 restarting with 1193 full and 75765 partial relations Wed Jun 14 19:51:59 2006 1271 relations (1255 full + 16 combined from 80189 partial), need 282856 Wed Jun 14 19:52:00 2006 elapsed time 01:01:02 Wed Jun 14 22:17:46 2006 Wed Jun 14 22:17:46 2006 Wed Jun 14 22:17:46 2006 Msieve v. 1.06 Wed Jun 14 22:17:46 2006 random seeds: 2dad8c00 a44d233d Wed Jun 14 22:17:46 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 14 22:17:48 2006 using multiplier of 1 Wed Jun 14 22:17:48 2006 sieve interval: 17 blocks of size 65536 Wed Jun 14 22:17:48 2006 processing polynomials in batches of 3 Wed Jun 14 22:17:48 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 14 22:17:48 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 14 22:17:48 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 14 22:17:48 2006 using trial factoring cutoff of 65 bits Wed Jun 14 22:17:48 2006 polynomial 'A' values have 15 factors Wed Jun 14 22:17:51 2006 restarting with 1255 full and 80189 partial relations Thu Jun 15 00:50:04 2006 1436 relations (1415 full + 21 combined from 90611 partial), need 282856 Thu Jun 15 00:50:05 2006 elapsed time 02:32:19 Thu Jun 15 11:31:23 2006 Thu Jun 15 11:31:23 2006 Thu Jun 15 11:31:23 2006 Msieve v. 1.06 Thu Jun 15 11:31:23 2006 random seeds: 8e6443e4 c4db7961 Thu Jun 15 11:31:23 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Thu Jun 15 11:31:25 2006 using multiplier of 1 Thu Jun 15 11:31:25 2006 sieve interval: 17 blocks of size 65536 Thu Jun 15 11:31:25 2006 processing polynomials in batches of 3 Thu Jun 15 11:31:25 2006 using a sieve bound of 8423407 (282760 primes) Thu Jun 15 11:31:25 2006 using large prime bound of 1263511050 (30 bits) Thu Jun 15 11:31:25 2006 using double large prime bound of 24145837678737600 (47-55 bits) Thu Jun 15 11:31:25 2006 using trial factoring cutoff of 65 bits Thu Jun 15 11:31:25 2006 polynomial 'A' values have 15 factors Thu Jun 15 11:31:57 2006 restarting with 1684 full and 106708 partial relations Thu Jun 15 11:56:42 2006 1745 relations (1712 full + 33 combined from 108446 partial), need 282856 Thu Jun 15 11:56:42 2006 elapsed time 00:25:19 Thu Jun 15 11:57:29 2006 Thu Jun 15 11:57:29 2006 Thu Jun 15 11:57:29 2006 Msieve v. 1.06 Thu Jun 15 11:57:29 2006 random seeds: 2b5719bc ac70f93d Thu Jun 15 11:57:29 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Thu Jun 15 11:57:30 2006 using multiplier of 1 Thu Jun 15 11:57:30 2006 sieve interval: 17 blocks of size 65536 Thu Jun 15 11:57:30 2006 processing polynomials in batches of 3 Thu Jun 15 11:57:30 2006 using a sieve bound of 8423407 (282760 primes) Thu Jun 15 11:57:30 2006 using large prime bound of 1263511050 (30 bits) Thu Jun 15 11:57:30 2006 using double large prime bound of 24145837678737600 (47-55 bits) Thu Jun 15 11:57:30 2006 using trial factoring cutoff of 65 bits Thu Jun 15 11:57:30 2006 polynomial 'A' values have 15 factors Thu Jun 15 11:57:31 2006 restarting with 1415 full and 90611 partial relations Thu Jun 15 13:24:02 2006 1536 relations (1511 full + 25 combined from 96442 partial), need 282856 Thu Jun 15 13:24:03 2006 elapsed time 01:26:34 Thu Jun 15 14:41:32 2006 Thu Jun 15 14:41:32 2006 Thu Jun 15 14:41:32 2006 Msieve v. 1.06 Thu Jun 15 14:41:32 2006 random seeds: 2bf13d00 55c23d38 Thu Jun 15 14:41:32 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Thu Jun 15 14:41:34 2006 using multiplier of 1 Thu Jun 15 14:41:34 2006 sieve interval: 17 blocks of size 65536 Thu Jun 15 14:41:34 2006 processing polynomials in batches of 3 Thu Jun 15 14:41:34 2006 using a sieve bound of 8423407 (282760 primes) Thu Jun 15 14:41:34 2006 using large prime bound of 1263511050 (30 bits) Thu Jun 15 14:41:34 2006 using double large prime bound of 24145837678737600 (47-55 bits) Thu Jun 15 14:41:34 2006 using trial factoring cutoff of 65 bits Thu Jun 15 14:41:34 2006 polynomial 'A' values have 15 factors Thu Jun 15 14:42:02 2006 restarting with 66448 full and 4166452 partial relations Thu Jun 15 14:42:02 2006 288182 relations (66448 full + 221734 combined from 4166452 partial), need 282856 Thu Jun 15 14:42:24 2006 begin with 4166452 relations Thu Jun 15 14:43:44 2006 reduce to 700937 relations in 11 passes Thu Jun 15 14:43:44 2006 attempting to read 66448 full and 700937 partial relations Thu Jun 15 14:44:56 2006 recovered 66448 full and 700937 partial relations Thu Jun 15 14:44:56 2006 recovered 756557 polynomials Thu Jun 15 14:45:51 2006 attempting to build 221734 cycles Thu Jun 15 14:45:54 2006 found 221734 cycles in 6 passes Thu Jun 15 14:52:54 2006 distribution of cycle lengths: Thu Jun 15 14:52:54 2006 length 2 : 47366 Thu Jun 15 14:52:54 2006 length 3 : 47173 Thu Jun 15 14:52:54 2006 length 4 : 39485 Thu Jun 15 14:52:54 2006 length 5 : 31205 Thu Jun 15 14:52:54 2006 length 6 : 21691 Thu Jun 15 14:52:54 2006 length 7 : 14202 Thu Jun 15 14:52:54 2006 length 8 : 8893 Thu Jun 15 14:52:54 2006 length 9+: 11719 Thu Jun 15 14:52:54 2006 largest cycle: 23 relations Thu Jun 15 14:53:30 2006 282760 x 282824 system, weight 19624908 (avg 69.39/col) Thu Jun 15 14:53:49 2006 reduce to 278846 x 278910 in 3 passes Thu Jun 15 19:56:16 2006 lanczos halted after 4412 iterations Thu Jun 15 19:56:26 2006 recovered 60 nontrivial dependencies Thu Jun 15 20:07:51 2006 prp47 factor: 37811313891994346064305264570354822948081755411 Thu Jun 15 20:07:51 2006 prp67 factor: 2240332608851730481538608681856319442213805555106852747449191086419 Thu Jun 15 20:08:04 2006 elapsed time 05:26:32

Jun 15, 2006 (3rd)

By Wojciech Florek / GMP-ECM 6.0.1 B1=50000
10²⁰⁰+9 = 1(0)₁₉₉9_<201> = 27793 · 1619861 · C190
C190 = P26 · C164
P26 = 67747437129266000269703021_<26>
C164 = [32786416573339916713456581271610480336366936402832697536081978826368233931128306550623785015488259274779087861845908056248255213200999357697362157495980354472120073_<164>]

Jun 15, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
3·10¹⁵¹-1 = 2(9)_151<152> = 103 · 15607 · 35159 · 14094323 · C134
C134 = P48 · P86
P48 = 803919452098002873794823857201688324440053056001_<48>
P86 = 46845872075351073831628759072931045137614880228706167557837224075618406020863534117667_<86>

Number: 29999_151 N=37660307811869368071143626717392891077148245893848443905585408084269631973112722238396669205370621661836143893933492373568490474469667 ( 134 digits) SNFS difficulty: 151 digits. Divisors found: r1=803919452098002873794823857201688324440053056001 (pp48) r2=46845872075351073831628759072931045137614880228706167557837224075618406020863534117667 (pp86) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 32.36 hours. Scaled time: 19.77 units (timescale=0.611). Factorization parameters were as follows: name: 29999_151 n: 37660307811869368071143626717392891077148245893848443905585408084269631973112722238396669205370621661836143893933492373568490474469667 m: 1000000000000000000000000000000 c5: 30 c0: -1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:175423, largePrimes:5562413 encountered Relations: rels:5551679, finalFF:551257 Max relations in full relation-set: 28 Initial matrix: 351792 x 551257 with sparse part having weight 48702916. Pruned matrix : 264444 x 266266 with weight 23590245. Total sieving time: 28.86 hours. Total relation processing time: 0.28 hours. Matrix solve time: 3.04 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 32.36 hours. --------- CPU info (if available) ----------

Jun 15, 2006

By Wojciech Florek / GMP-ECM 6.0.1 B1=50000
10¹⁵⁵+9 = 1(0)₁₅₄9_<156> = 7 · 13 · 36819899903_<11> · C143
C143 = P26 · P117
P26 = 79017600284684020776597601_<26>
P117 = 377704507649203485094138150729343418582135548032657891156331722185962796664870047824029441603130922378771354117137333_<117>
10¹⁸⁵+9 = 1(0)₁₈₄9_<186> = 7 · 13 · 229846571 · 1275374768743384691_<19> · C157
C157 = P31 · C127
P31 = 2601396325020582930122538337721_<31>
C127 = [1441040661382525705417821587285663316407691187456963366088056617767879156058816313976715675551433626176389802439909676048900179_<127>]

Jun 14, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4
(4·10¹⁵²-13)/9 = (4)₁₅₁3_<152> = 17 · 157 · 6476783 · C142
C142 = P68 · P74
P68 = 70051112394180511931099325798622432992902701888617624858258185590861_<68>
P74 = 36702405181637427368617502969073420790220101845842707621638501963536194669_<74>

Number: 44443_152 N=2571044310515636631591363642344402560399099518358547822280233718276022116764197533447168630264726143496554443438364403140703983099575283320009 ( 142 digits) SNFS difficulty: 152 digits. Divisors found: r1=70051112394180511931099325798622432992902701888617624858258185590861 (pp68) r2=36702405181637427368617502969073420790220101845842707621638501963536194669 (pp74) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 37.42 hours. Scaled time: 23.50 units (timescale=0.628). Factorization parameters were as follows: n: 2571044310515636631591363642344402560399099518358547822280233718276022116764197533447168630264726143496554443438364403140703983099575283320009 m: 2000000000000000000000000000000 c5: 25 c0: -26 skew: 1.01 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2200001) Primes: RFBsize:176302, AFBsize:176748, largePrimes:5547592 encountered Relations: rels:5457284, finalFF:473655 Max relations in full relation-set: 28 Initial matrix: 353114 x 473655 with sparse part having weight 41920058. Pruned matrix : 304103 x 305932 with weight 24002656. Total sieving time: 32.17 hours. Total relation processing time: 0.29 hours. Matrix solve time: 4.80 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 37.42 hours. --------- CPU info (if available) ----------

Jun 13, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(25·10¹⁵¹-1)/3 = 8(3)_151<152> = 40213 · 31173893 · 13946968278689_<14> · C127
C127 = P46 · P81
P46 = 8173120943122339742908571543763108966367651147_<46>
P81 = 583167752877706836532991362620680694133049760946451667127882465043575940344860839_<81>

Number: 83333_151 N=4766300574398378856441697253711236415813730164095873758343781948185529731621724242828907536094532267344007114712574137013732333 ( 127 digits) SNFS difficulty: 152 digits. Divisors found: r1=8173120943122339742908571543763108966367651147 (pp46) r2=583167752877706836532991362620680694133049760946451667127882465043575940344860839 (pp81) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 39.49 hours. Scaled time: 26.61 units (timescale=0.674). Factorization parameters were as follows: name: 83333_151 n: 4766300574398378856441697253711236415813730164095873758343781948185529731621724242828907536094532267344007114712574137013732333 m: 1000000000000000000000000000000 c5: 250 c0: -1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2200001) Primes: RFBsize:176302, AFBsize:175838, largePrimes:5676207 encountered Relations: rels:5686431, finalFF:561341 Max relations in full relation-set: 28 Initial matrix: 352206 x 561341 with sparse part having weight 51177717. Pruned matrix : 270625 x 272450 with weight 25638975. Total sieving time: 35.78 hours. Total relation processing time: 0.33 hours. Matrix solve time: 3.24 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 39.49 hours. --------- CPU info (if available) ----------

Jun 12, 2006 (3rd)

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10¹⁷¹+3 = 1(0)₁₇₀3_<172> = C172
C172 = P26 · C146
P26 = 11766503516695099357653883_<26>
C146 = [84987014076113040368276240003085477274619465136310452297603910182168194570059311533447910927491502082842012464686661684313334515329656218133967641_<146>]

Jun 12, 2006 (2nd)

By Wojciech Florek / GGNFS-0.77.1
10¹⁵⁵+3 = 1(0)₁₅₄3_<156> = C156
C156 = P77 · P79
P77 = 82104127886814499369024993996312311665706556142420410416782489897012262753547_<77>
P79 = 1217965558782331157844625900310263781587935921261132202891162537797114525084649_<79>

Number: 10,310-M N=100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 156 digits) SNFS difficulty: 155 digits. Divisors found: r1=82104127886814499369024993996312311665706556142420410416782489897012262753547 (pp77) r2=1217965558782331157844625900310263781587935921261132202891162537797114525084649 (pp79) Version: GGNFS-0.77.1 Total time: 88.84 hours. Scaled time: 48.68 units (timescale=0.548). Factorization parameters were as follows: name: 10^155+3 10,310-M n: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 type: snfs m: 10000000000000000000000000000000 skew: 1.2 c5: 1 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 rlim: 4000000 alim: 3700000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 qintsize: 50000 Factor base limits: 4000000/3700000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1850000, 2300001) Relations: rels:5171311, finalFF:626344 Initial matrix: 546367 x 626344 with sparse part having weight 32686910. Pruned matrix : 502764 x 505559 with weight 19259495. Total sieving time: 77.41 hours. Total relation processing time: 0.59 hours. Matrix solve time: 10.59 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,4000000,3700000,27,27,48,48,2.3,2.3,100000 total time: 88.84 hours. --------- CPU info (if available) ---------- CPU0: Intel Pentium III (Coppermine) stepping 06 CPU1: Intel Pentium III (Coppermine) stepping 06 Memory: 514812k/524224k available (1676k kernel code, 8652k reserved, 708k data, 180k init, 0k highmem) Calibrating delay loop... 1851.39 BogoMIPS Calibrating delay loop... 1867.77 BogoMIPS Total of 2 processors activated (3719.16 BogoMIPS). x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 2 CPUs -------------------------------------------------------------------------- CPU #1 Family: 6 Model: 8 Stepping: 6 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cC0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 950MHz processor (estimate). -------------------------------------------------------------------------- CPU #2 Family: 6 Model: 8 Stepping: 6 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cC0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 950MHz processor (estimate). -------------------------------------------------------------------------- WARNING: Detected SMP, but unable to access cpuid driver. Used Uniprocessor CPU routines. Results inaccurate.

P77 is the largest factor found by GGNFS in our tables so far. Congratulations!

Jun 12, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4 gnfs
(2·10¹⁷⁷+61)/9 = (2)₁₇₆9_<177> = 373 · 52452310739_<11> · 122313301254781630237_<21> · 698935614467460981599711_<24> · C120
C120 = P39 · P82
P39 = 102274804112509011932166621876688728607_<39>
P82 = 1299075864221558361306831248327523719975317527188803043876725435794660391001753143_<82>

Number: 22229_177 N=132862729540548235885710325806135088341175371249479339168970742759531835213425691441068602652953432293108269044736261801 ( 120 digits) Divisors found: r1=102274804112509011932166621876688728607 (pp39) r2=1299075864221558361306831248327523719975317527188803043876725435794660391001753143 (pp82) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 94.67 hours. Scaled time: 60.78 units (timescale=0.642). Factorization parameters were as follows: name: 22229_177 n: 132862729540548235885710325806135088341175371249479339168970742759531835213425691441068602652953432293108269044736261801 skew: 118264.19 # norm 2.48e+016 c5: 16380 c4: 2906053828 c3: -842318987455755 c2: -31805894219144108025 c1: 3829700256869416762366795 c0: 61382773760292758874608119257 # alpha -6.53 Y1: 11968793848913 Y0: -95899409147692607700800 # Murphy_E 3.46e-010 # M 97739709333115584892434197029876455362571111405703888251707455578910987395730840374213972981668836923260695644624972375 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 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4110001) Primes: RFBsize:315948, AFBsize:315964, largePrimes:7684067 encountered Relations: rels:7782590, finalFF:772270 Max relations in full relation-set: 28 Initial matrix: 631997 x 772270 with sparse part having weight 65670693. Pruned matrix : 514290 x 517513 with weight 40913071. Total sieving time: 76.06 hours. Total relation processing time: 1.04 hours. Matrix solve time: 17.06 hours. Time per square root: 0.52 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 94.67 hours. --------- CPU info (if available) ----------

Jun 11, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(16·10¹⁵¹-1)/3 = 5(3)_151<152> = 152311 · 715209641 · 313198861778351_<15> · C124
C124 = P55 · P69
P55 = 4492114583152676075568292046791383513694243521858826159_<55>
P69 = 347987062260942870395968830956400479517277155958985376021550782808187_<69>

Number: 53333_151 N=1563197757130839718450150233073190481919155646304989399336964917055382221284358227647965491014654792583752170529025474963733 ( 124 digits) SNFS difficulty: 152 digits. Divisors found: r1=4492114583152676075568292046791383513694243521858826159 (pp55) r2=347987062260942870395968830956400479517277155958985376021550782808187 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 33.13 hours. Scaled time: 22.33 units (timescale=0.674). Factorization parameters were as follows: name: 53333_151 n: 1563197757130839718450150233073190481919155646304989399336964917055382221284358227647965491014654792583752170529025474963733 m: 1000000000000000000000000000000 c5: 160 c0: -1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:176093, largePrimes:5402411 encountered Relations: rels:5275796, finalFF:456173 Max relations in full relation-set: 28 Initial matrix: 352462 x 456173 with sparse part having weight 38619267. Pruned matrix : 299185 x 301011 with weight 22581981. Total sieving time: 29.04 hours. Total relation processing time: 0.34 hours. Matrix solve time: 3.59 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 33.13 hours. --------- CPU info (if available) ----------

Jun 10, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4
(2·10¹⁵⁸-11)/9 = (2)₁₅₇1_<158> = 3² · 7 · 3373 · 244846033 · C144
C144 = P48 · P97
P48 = 136373220163038473408001030523801101796795796597_<48>
P97 = 3131903903250503659877494912285800041740438149611919544242941413416214051230896603159433989608979_<97>

Number: 22221_158 N=427107820527460481965800659937090806025710492398582629787910040201168839154848698242923514230339462348863549244998158835338352432003242848844463 ( 144 digits) SNFS difficulty: 158 digits. Divisors found: r1=136373220163038473408001030523801101796795796597 (pp48) r2=3131903903250503659877494912285800041740438149611919544242941413416214051230896603159433989608979 (pp97) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 61.35 hours. Scaled time: 42.08 units (timescale=0.686). Factorization parameters were as follows: n: 427107820527460481965800659937090806025710492398582629787910040201168839154848698242923514230339462348863549244998158835338352432003242848844463 m: 20000000000000000000000000000000 c5: 125 c0: -22 skew: 1 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:282598, largePrimes:5660000 encountered Relations: rels:5693705, finalFF:658134 Max relations in full relation-set: 28 Initial matrix: 565809 x 658134 with sparse part having weight 41765004. Pruned matrix : 492727 x 495620 with weight 28196709. Total sieving time: 50.11 hours. Total relation processing time: 0.26 hours. Matrix solve time: 10.76 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 61.35 hours. --------- CPU info (if available) ----------

Jun 9, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1
(28·10¹⁵⁴-1)/9 = 3(1)_154<155> = 29 · 523 · 356947 · 1279301069_<10> · 329796478307462684783_<21> · C116
C116 = P51 · P65
P51 = 300621016513776590359526923103344706640342409501697_<51>
P65 = 45307905222633353862121896072140996414543098670746516403110579681_<65>

Number: 31111_154 N=13620508524137886095135775437549085410611631881407400493766199272054663054717943584997443021365877512209360023218657 ( 116 digits) SNFS difficulty: 156 digits. Divisors found: r1=300621016513776590359526923103344706640342409501697 (pp51) r2=45307905222633353862121896072140996414543098670746516403110579681 (pp65) Version: GGNFS-0.77.1 Total time: 48.44 hours. Scaled time: 32.22 units (timescale=0.665). Factorization parameters were as follows: name: 31111_154 n: 13620508524137886095135775437549085410611631881407400493766199272054663054717943584997443021365877512209360023218657 m: 10000000000000000000000000000000 c5: 14 c0: -5 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2700001) Relations: rels:5727743, finalFF:603263 Initial matrix: 434263 x 603263 with sparse part having weight 48582766. Pruned matrix : 391440 x 393675 with weight 21231753. Total sieving time: 43.42 hours. Total relation processing time: 0.32 hours. Matrix solve time: 4.55 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 48.44 hours. --------- CPU info (if available) ----------

Jun 9, 2006 (2nd)

By Bryan Koen / GGNFS-0.77.1-20060513-pentium3 gnfs
10¹⁵¹+9 = 1(0)₁₅₀9_<152> = 47 · 59 · 1259 · 7127 · 2966921 · 11067807493_<11> · 72688089600520497603686170777972481_<35> · C90
C90 = P42 · P48
P42 = 304041896967341114744845407635505771861889_<42>
P48 = 553800538862497459614953502422358377149435369453_<48>

Number: 10009_151 N=168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717 ( 90 digits) Divisors found: r1=304041896967341114744845407635505771861889 (pp42) r2=553800538862497459614953502422358377149435369453 (pp48) Version: GGNFS-0.77.1-20060513-pentium3 Total time: 7.78 hours. Scaled time: 4.87 units (timescale=0.626). Factorization parameters were as follows: name: 10009_151 n: 168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717 m: 397102947624127176218 deg: 4 c4: 6771336 c3: -9421734641 c2: -17097857456607989 c1: 52700057966859489 c0: 20139528042945550388527 skew: 1635.250 type: gnfs # adj. I(F,S) = 50.521 # E(F1,F2) = 2.015879e-04 # GGNFS version 0.77.1-20060513-pentium3 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1149781811. # maxskew=2000.0 # These parameters should be manually set: rlim: 700000 alim: 700000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.4 alambda: 2.4 qintsize: 40000 type: gnfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [350000, 750001) Primes: RFBsize:56543, AFBsize:56325, largePrimes:1619047 encountered Relations: rels:1627644, finalFF:155272 Max relations in full relation-set: 28 Initial matrix: 112945 x 155272 with sparse part having weight 13574909. Pruned matrix : 100318 x 100946 with weight 6869840. Polynomial selection time: 0.17 hours. Total sieving time: 6.85 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.47 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,89,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000 total time: 7.78 hours. --------- CPU info (if available) ---------- x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 1.0Ghz processor (estimate).

Jun 9, 2006

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10¹⁹⁹+3 = 1(0)₁₉₈3_<200> = 13 · 4533299 · 259556761 · 111011352372742720485057131_<27> · C157
C157 = P33 · C125
P33 = 505135145839533539009957298516389_<33>
C125 = [11658292768317820781554389954230436794449000313821548811563233466427335134152895851328952839749423751087120161554182716468331_<125>]

Jun 8, 2006 (5th)

By Yousuke Koide / GMP-ECM
(10⁶⁰⁷-1)/9 = (1)_607<607> = 10857536471_<11> · C597
C597 = P34 · C563
P34 = 8030222013165659643947340265695409_<34>
C563 = [12743791025705280337647107449763389196590743381995489997602359492550670282914658786866644132251081530183945513634942367344940945849768823651695138554796618106799788799265038643749276286863772813091423307583327488336703425138962767003020761379082230966326019896681052112375556339576356383468466444597317090588231683659499086434219490053020977894894071243326908124169207137882751682358057098873428276903560922268298083613125322614771267815515696194827324894983730224274660295001335913828824662433094826344709281811146432335327830920101507170509517110651808908417249_<563>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 8, 2006 (4th)

By Bryan Koen / GMP-ECM 6.1 B1=3000000
10¹⁵¹+9 = 1(0)₁₅₀9_<152> = 47 · 59 · 1259 · 7127 · 2966921 · 11067807493_<11> · C125
C125 = P35 · C90
P35 = 72688089600520497603686170777972481_<35>
C90 = [168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717_<90>]

Jun 8, 2006 (3rd)

By Bryan Koen / GMP-ECM 6.1 B1=3000000
10¹⁴⁹+9 = 1(0)₁₄₈9_<150> = 7 · 13 · 1289 · 14111809 · 2038469620239917_<16> · C122
C122 = P26 · P96
P26 = 80577406982383442189446811_<26>
P96 = 367794702512173851463405661443194990091070675569301662648266498490154427340333411671971726316077_<96>

Jun 8, 2006 (2nd)

By Wojciech Florek / Msieve v. 1.03
10¹⁴⁰+9 = 1(0)₁₃₉9_<141> = 47017 · 74498093 · 6280399637_<10> · 378185559992276358710822426933737_<33> · C86
C86 = P36 · P50
P36 = 275290255655372346657479721190470389_<36>
P50 = 43663331382360791758121439349427121020054742354629_<50>

Jun 8, 2006

By Bryan Koen / GMP-ECM 6.1 B1=3000000
10¹⁴⁰+9 = 1(0)₁₃₉9_<141> = 47017 · 74498093 · 6280399637_<10> · C118
C118 = P33 · C86
P33 = 378185559992276358710822426933737_<33>
C86 = [12020089659015344816036119415930027908760447367801456885997889765522261556089961580681_<86>]

Jun 7, 2006 (2nd)

By Bryan Koen / GGNFS-0.77.1-20060513-pentium3
10¹³⁸+9 = 1(0)₁₃₇9_<139> = 876233 · 3884165579644422661_<19> · C114
C114 = P44 · P70
P44 = 78273652233899717283899884219650481533344701_<44>
P70 = 3753764830682790162556690001403905303929149813189408310793058874824593_<70>

Number: 10009_138 N=293820882924708172219936720052802603554401992112281932163797281493515360316752301778857178250591701547951981031693 ( 114 digits) SNFS difficulty: 138 digits. Divisors found: r1=78273652233899717283899884219650481533344701 (pp44) r2=3753764830682790162556690001403905303929149813189408310793058874824593 (pp70) Version: GGNFS-0.77.1-20060513-pentium3 Total time: 17.78 hours. Scaled time: 11.13 units (timescale=0.626). Factorization parameters were as follows: n: 293820882924708172219936720052802603554401992112281932163797281493515360316752301778857178250591701547951981031693 m: 1000000000000000000000000000 c5: 1000 c0: 9 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1525001) Primes: RFBsize:78498, AFBsize:63873, largePrimes:1570583 encountered Relations: rels:1573135, finalFF:171984 Max relations in full relation-set: 28 Initial matrix: 142438 x 171984 with sparse part having weight 15803147. Pruned matrix : 133995 x 134771 with weight 10765947. Total sieving time: 16.39 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.04 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 17.78 hours. --------- CPU info (if available) ---------- x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 1.0Ghz processor (estimate).

Jun 7, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(5·10¹⁶³+13)/9 = (5)₁₆₂7_<163> = 7 · 491 · 1046680382986660661_<19> · 26988494111082482595723749_<26> · C116
C116 = P33 · P35 · P49
P33 = 217331380417265405385792427178641_<33>
P35 = 55344255753515407497857400669052247_<35>
P49 = 4757296669612601389627040223185439915807754519687_<49>

Number: 55557_163 N=57220971289632372895013854360486568742682462018091052842231747397803851776811199836976065406658831179664130202209649 ( 116 digits) Divisors found: r1=217331380417265405385792427178641 (pp33) r2=55344255753515407497857400669052247 (pp35) r3=4757296669612601389627040223185439915807754519687 (pp49) Version: GGNFS-0.77.1 Total time: 72.54 hours. Scaled time: 48.24 units (timescale=0.665). Factorization parameters were as follows: name: 55557_163 n: 57220971289632372895013854360486568742682462018091052842231747397803851776811199836976065406658831179664130202209649 skew: 63091.21 # norm 1.03e+16 c5: 10980 c4: -567513282 c3: -288483363928883 c2: -42686857066294 c1: -10217904753094925098120 c0: 805345242548038392245007424 # alpha -6.11 Y1: 920218306469 Y0: -22049094785443788512841 # Murphy_E 5.16e-10 # M 21548108821676313080445840778074574074874607909847815919519715036737519808444584049118282893032989879028308785080208 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, 3630001) Relations: rels:7694457, finalFF:806287 Initial matrix: 631773 x 806287 with sparse part having weight 63262568. Pruned matrix : 555050 x 558272 with weight 30385169. Polynomial selection time: 1.52 hours. Total sieving time: 60.64 hours. Total relation processing time: 1.09 hours. Matrix solve time: 8.75 hours. Time per square root: 0.54 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: 72.54 hours. --------- CPU info (if available) ----------

Jun 6, 2006 (3rd)

By Wojciech Florek / Msieve v. 1.03
10¹⁵²+3 = 1(0)₁₅₁3_<153> = 43613668999_<11> · 12179717710063_<14> · 128492693814335713_<18> · 2456091372331436862367783336363_<31> · C81
C81 = P38 · P44
P38 = 15820959142195526790315426273379632223_<38>
P44 = 37703736485632074700837740810673485387490687_<44>

Jun 6, 2006 (2nd)

By Alfred Reich / Msieve v. 1.06
10¹⁴⁴+3 = 1(0)₁₄₃3_<145> = 134060221 · 895346379774329815520794224163_<30> · C106
C106 = P43 · P64
P43 = 3312794646750731247992525345573307418477327_<43>
P64 = 2514863810750094284798767186768560521807692068531696374269371643_<64>

Jun 6, 2006

By Bryan Koen / GMP-ECM 6.1 B1=1000000
10¹⁵²+3 = 1(0)₁₅₁3_<153> = 43613668999_<11> · 12179717710063_<14> · 128492693814335713_<18> · C112
C112 = P31 · C81
P31 = 2456091372331436862367783336363_<31>
C81 = [596509274447291814464580040316696780259376731908870341805954675607430656897607201_<81>]
10¹²²+9 = 1(0)₁₂₁9_<123> = 797 · 87324709 · C112
C112 = P32 · P80
P32 = 46442319103878729137347867918441_<32>
P80 = 30937885895272059997914839937905492541094892096918455339201066688438011910438513_<80>
10¹²⁹+9 = 1(0)₁₂₈9_<130> = 383 · 470957 · 925380361 · C112
C112 = P29 · P84
P29 = 26662284559638260051010569411_<29>
P84 = 224699616945787993015228728987794854226294266940075097993481422453900414417478640009_<84>

Jun 5, 2006 (3rd)

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10¹⁶⁰+3 = 1(0)₁₅₉3_<161> = 7² · 823 · C156
C156 = P28 · P129
P28 = 2418343914073834818913548979_<28>
P129 = 102538278668961192433911894438328850160845843852041786502290291129164567462464059585048892813551072785448461295685350000183704391_<129>

Jun 5, 2006 (2nd)

By Bryan Koen / GGNFS-0.77.1-20060513-pentium3
10¹⁴¹+3 = 1(0)₁₄₀3_<142> = 23 · 179 · 644783 · 1095239290136891_<16> · C117
C117 = P51 · P66
P51 = 803739638634605270206280169488592754569025676064749_<51>
P66 = 427938295026116307934098302562270778494869844206815199155275017447_<66>

Number: 10003_141 N=343950970602199819231512078234382265236200797813972452208461451756224073663979763523341432993779852136795871276675803 ( 117 digits) SNFS difficulty: 141 digits. Divisors found: r1=803739638634605270206280169488592754569025676064749 (pp51) r2=427938295026116307934098302562270778494869844206815199155275017447 (pp66) Version: GGNFS-0.77.1-20060513-pentium3 Total time: 21.59 hours. Scaled time: 13.51 units (timescale=0.626). Factorization parameters were as follows: n: 343950970602199819231512078234382265236200797813972452208461451756224073663979763523341432993779852136795871276675803 m: 10000000000000000000000000000 c5: 10 c0: 3 skew: 1 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1750001) Primes: RFBsize:100021, AFBsize:99998, largePrimes:2680955 encountered Relations: rels:2643376, finalFF:256210 Max relations in full relation-set: 28 Initial matrix: 200085 x 256210 with sparse part having weight 22916201. Pruned matrix : 182362 x 183426 with weight 14089073. Total sieving time: 19.25 hours. Total relation processing time: 0.24 hours. Matrix solve time: 1.90 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 21.59 hours. --------- CPU info (if available) ---------- x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 1.0Ghz processor (estimate).

Jun 5, 2006

By Tyler Cadigan / PRIMO 2.2.0 beta 6
The prime number (34·10⁷⁷³-7)/9 was certified by PRIMO. All prime numbers under 1000 digits in our tables have been certified.

Jun 4, 2006 (4th)

By Alexander Mkrtychyan / Msieve v. 1.06
10¹⁶⁷+3 = 1(0)₁₆₆3_<168> = 613 · 3042701 · 5418606523951_<13> · 210504879244969399_<18> · 104420640192739457415377_<24> · C105
C105 = P50 · P56
P50 = 12671007740661978399849262965676367229484426614023_<50>
P56 = 35524907704428477072483751792823172988116747462504646589_<56>

Thu Jun 01 07:44:48 2006 Msieve v. 1.06 Thu Jun 01 07:44:48 2006 random seeds: b14be000 1f671996 Thu Jun 01 07:44:48 2006 factoring 450136380509115586818824476925994457819859020646634121016333059079851013391762916786707134979013526517547 (105 digits) Thu Jun 01 07:44:49 2006 using multiplier of 13 Thu Jun 01 07:44:49 2006 sieve interval: 9 blocks of size 65536 Thu Jun 01 07:44:49 2006 processing polynomials in batches of 6 Thu Jun 01 07:44:49 2006 using a sieve bound of 3943937 (140000 primes) Thu Jun 01 07:44:49 2006 using large prime bound of 591590550 (29 bits) Thu Jun 01 07:44:49 2006 using double large prime bound of 6160815113841750 (44-53 bits) Thu Jun 01 07:44:49 2006 using trial factoring cutoff of 60 bits Thu Jun 01 07:44:49 2006 polynomial 'A' values have 14 factors Thu Jun 01 07:44:49 2006 restarting with 3042 full and 194490 partial relations Sat Jun 03 05:48:23 2006 140203 relations (33009 full + 107194 combined from 2073320 partial), need 140096 Sat Jun 03 05:48:47 2006 begin with 2073320 relations Sat Jun 03 05:48:50 2006 reduce to 338226 relations in 11 passes Sat Jun 03 05:48:50 2006 attempting to read 33009 full and 338226 partial relations Sat Jun 03 05:49:15 2006 recovered 33009 full and 338226 partial relations Sat Jun 03 05:49:15 2006 recovered 364498 polynomials Sat Jun 03 05:49:16 2006 attempting to build 107194 cycles Sat Jun 03 05:49:17 2006 found 107194 cycles in 6 passes Sat Jun 03 05:49:17 2006 distribution of cycle lengths: Sat Jun 03 05:49:17 2006 length 2 : 23465 Sat Jun 03 05:49:17 2006 length 3 : 23358 Sat Jun 03 05:49:17 2006 length 4 : 19359 Sat Jun 03 05:49:17 2006 length 5 : 14682 Sat Jun 03 05:49:17 2006 length 6 : 10184 Sat Jun 03 05:49:17 2006 length 7 : 6633 Sat Jun 03 05:49:17 2006 length 8 : 4199 Sat Jun 03 05:49:17 2006 length 9+: 5314 Sat Jun 03 05:49:17 2006 largest cycle: 21 relations Sat Jun 03 05:49:18 2006 140000 x 140064 system, weight 9718057 (avg 69.38/col) Sat Jun 03 05:49:19 2006 reduce to 138118 x 138182 in 3 passes Sat Jun 03 06:08:39 2006 lanczos halted after 2185 iterations Sat Jun 03 06:08:41 2006 recovered 58 nontrivial dependencies Sat Jun 03 06:10:00 2006 prp50 factor: 12671007740661978399849262965676367229484426614023 Sat Jun 03 06:10:00 2006 prp56 factor: 35524907704428477072483751792823172988116747462504646589 Sat Jun 03 06:10:01 2006 elapsed time 46:25:13

Jun 4, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(34·10¹⁷⁶-7)/9 = 3(7)_176<177> = 13 · 829 · 318683 · 11176757 · 3948411858562751_<16> · 428211044560044339671392979782357_<33> · C112
C112 = P38 · P75
P38 = 11694279611466984831142203943332807419_<38>
P75 = 497748584082412889125755168559358506745646837820266378957660155569774344887_<75>

Number: 37777_176 N=5820811118471521231475918967207027515179168849013239199862519224248461311165696923761581519214488363575258316653 ( 112 digits) Divisors found: r1=11694279611466984831142203943332807419 (pp38) r2=497748584082412889125755168559358506745646837820266378957660155569774344887 (pp75) Version: GGNFS-0.77.1 Total time: 53.33 hours. Scaled time: 35.47 units (timescale=0.665). Factorization parameters were as follows: name: 37777_176 n: 5820811118471521231475918967207027515179168849013239199862519224248461311165696923761581519214488363575258316653 skew: 32740.23 # norm 7.73e+14 c5: 7800 c4: 790299208 c3: -34647393104357 c2: -702585806193034208 c1: 6659086119635802079482 c0: 123094738763234464057267500 # alpha -5.03 Y1: 484020890317 Y0: -3754712135906934550109 # Murphy_E 8.03e-10 # M 4302948463608880647102223092922936267994757185578952181911465511761176268904489859460161461822645693421840905721 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:7677602, finalFF:705015 Initial matrix: 499803 x 705015 with sparse part having weight 61142504. Pruned matrix : 419449 x 422012 with weight 24554381. Polynomial selection time: 0.52 hours. Total sieving time: 45.83 hours. Total relation processing time: 0.77 hours. Matrix solve time: 5.74 hours. Time per square root: 0.47 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: 53.33 hours. --------- CPU info (if available) ----------

Jun 4, 2006 (2nd)

By Tyler Cadigan / PRIMO 2.2.0 beta 6
The following 11 prime numbers under 1000 digits were certified by PRIMO.
10⁷⁰⁰+7, 10⁹⁹⁹+7, (5·10⁴⁶¹+1)/3, (5·10⁸⁴⁰+1)/3, (5·10⁸⁴⁷+1)/3, (7·10⁵²²-1)/3, (7·10⁵⁹⁷-1)/3, (13·10⁷²⁷-1)/3, (53·10⁴³⁹+1)/9, (61·10⁷⁸⁵-7)/9, (61·10⁷⁹⁹-7)/9.

Jun 4, 2006

By Bryan Koen / GGNFS-0.77.1-20060513-pentium3
10¹³⁸+3 = 1(0)₁₃₇3_<139> = 103 · 990513749998083607_<18> · 34585142462197870945875655226509_<32> · C87
C87 = P42 · P45
P42 = 515100320152004920978466573096213025512461_<42>
P45 = 550200369707475541148787748643398354924032907_<45>

Number: 10003_138 N=283408386584072121357621650236515295775168451662180323194828514316327126544738502554127 ( 87 digits) SNFS difficulty: 138 digits. Divisors found: r1=515100320152004920978466573096213025512461 (pp42) r2=550200369707475541148787748643398354924032907 (pp45) Version: GGNFS-0.77.1-20060513-pentium3 Total time: 21.08 hours. Scaled time: 13.20 units (timescale=0.626). Factorization parameters were as follows: n: 283408386584072121357621650236515295775168451662180323194828514316327126544738502554127 m: 1000000000000000000000000000 c5: 1000 c0: 3 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1750001) Primes: RFBsize:78498, AFBsize:64158, largePrimes:1602887 encountered Relations: rels:1611027, finalFF:169149 Max relations in full relation-set: 28 Initial matrix: 142722 x 169149 with sparse part having weight 16717764. Pruned matrix : 135569 x 136346 with weight 11997191. Total sieving time: 19.46 hours. Total relation processing time: 0.24 hours. Matrix solve time: 1.25 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 21.08 hours. --------- CPU info (if available) ---------- x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 1.0Ghz processor (estimate).

Jun 3, 2006

By Tyler Cadigan / PRIMO 2.2.0 beta 6
The following 227 prime numbers under 1000 digits were certified by PRIMO.
(10⁷⁶⁷+53)/9, (10⁶⁸⁴+71)/9, (10⁷²⁰+71)/9, (11·10⁸⁷⁶+7)/9, (11·10⁸¹¹+43)/9, (11·10⁸¹²+43)/9, (11·10⁵⁴⁷+61)/9, (4·10⁸⁸⁷+11)/3, (13·10⁷³⁵+23)/9, (13·10⁵²⁹+41)/9, (14·10⁵³⁷+31)/9, (14·10⁸³¹+31)/9, (5·10⁶²⁹+7)/3, (5·10⁷²⁰+7)/3, (17·10⁸⁴³+1)/9, 2·10⁷⁶¹+9, (19·10⁵⁴³-1)/9, (19·10⁵⁸⁴-1)/9, (19·10⁸³³-1)/9, (19·10⁷⁵⁴+17)/9, (19·10⁹⁵¹+17)/9, (7·10⁶⁵⁷+17)/3, (22·10⁴⁹⁹+41)/9, (23·10⁷³³+31)/9, (25·10⁹³⁶-61)/9, (25·10⁴⁸²-7)/9, (26·10⁸⁷⁶-71)/9, (26·10⁴⁹⁴-53)/9, (26·10⁵⁹⁸-53)/9, (26·10⁴⁴⁹-17)/9, 3·10⁴⁸⁴-7, 3·10⁸⁶⁵-7, 3·10⁵⁹³+7, (28·10⁶⁹²+53)/9, (28·10⁷⁹⁷+71)/9, (29·10⁶⁴⁹-11)/9, (29·10⁹⁴⁹-11)/9, (29·10⁹⁶³-11)/9, (29·10⁵¹⁹+61)/9, (29·10⁶⁰³+61)/9, (10⁹⁷⁸+11)/3, (31·10⁷⁵⁸+23)/9, (31·10⁵¹²+41)/9, (32·10⁹⁵⁷+31)/9, (11·10⁶⁷³-17)/3, (11·10⁷⁸⁰-17)/3, (11·10⁴⁹⁸+1)/3, (34·10⁷⁷⁶+11)/9, (35·10⁵³⁸-71)/9, (35·10⁵⁰⁹+1)/9, (35·10⁷¹⁰+1)/9, 4·10⁹⁴⁹-9, (37·10⁵⁸⁹-1)/9, (37·10⁹⁷³-1)/9, (37·10⁵¹³+53)/9, (38·10⁶³⁰+7)/9, (38·10⁷²⁴+7)/9, (13·10⁷¹⁵-7)/3, (13·10⁸⁰⁴-7)/3, (13·10⁴⁵⁶+11)/3, (13·10⁴⁶⁷+11)/3, (13·10⁶⁰⁷+11)/3, (13·10⁸²⁸+11)/3, (13·10⁶³⁸+17)/3, (4·10⁷²²+23)/9, (41·10⁷⁰²-23)/9, (41·10⁶²¹+31)/9, (14·10⁶⁵²+1)/3,