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News and updates, September 2005

Sep 30, 2005

By Makoto Kamada / GGNFS-0.77.1
10¹⁶⁹-9 = (9)₁₆₈1_<169> = C169
C169 = P56 · P114
P56 = 94211591202708488915524241578569786726705726654902440361_<56>
P114 = 106144051621882701124925887117325659671531292461815961898361365027825862303359296356795774245471393139352946460831_<114>

Number: 99991_169 N=9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 ( 169 digits) SNFS difficulty: 170 digits. Divisors found: r1=94211591202708488915524241578569786726705726654902440361 (pp56) r2=106144051621882701124925887117325659671531292461815961898361365027825862303359296356795774245471393139352946460831 (pp114) Version: GGNFS-0.77.1 Total time: 168.51 hours. Scaled time: 144.92 units (timescale=0.860). Factorization parameters were as follows: n: 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 m: 10000000000000000000000000000000000 c5: 1 c0: -90 skew: 3 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [3000000, 7600001) Relations: rels:6364281, finalFF:925392 Initial matrix: 826019 x 925392 with sparse part having weight 57695015. Pruned matrix : 789184 x 793378 with weight 41189257. Total sieving time: 141.03 hours. Total relation processing time: 0.68 hours. Matrix solve time: 26.66 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 168.51 hours. --------- CPU info (if available) ----------

Sep 29, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁵¹+71)/9 = (1)₁₅₀9_<151> = 3 · 23 · 61 · 1163 · 1392536443_<10> · C135
C135 = P52 · P84
P52 = 1435575192424309524768909293072449589412358289040997_<52>
P84 = 113544561029960344981988582475143875453433518727002828818207021463470771560713531067_<84>

Number: 11119_151 N=1630017550493190787306213877005142857399139736124182065763045639252398292930256964576559345971400401608702061247664839746110369961 53799 ( 135 digits) SNFS difficulty: 151 digits. Divisors found: r1=1435575192424309524768909293072449589412358289040997 (pp52) r2=113544561029960344981988582475143875453433518727002828818207021463470771560713531067 (pp84) Version: GGNFS-0.77.1 Total time: 29.11 hours. Scaled time: 19.42 units (timescale=0.667). Factorization parameters were as follows: name: 11119_151 n: 163001755049319078730621387700514285739913973612418206576304563925239829293025696457655934597140040160870206124766483974611036996153 799 m: 1000000000000000000000000000000 c5: 10 c0: 71 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 1900001) Relations: rels:5167413, finalFF:440239 Initial matrix: 352962 x 440239 with sparse part having weight 35869279. Pruned matrix : 329115 x 330943 with weight 19351732. Total sieving time: 25.62 hours. Total relation processing time: 0.24 hours. Matrix solve time: 3.12 hours. Time per square root: 0.13 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: 29.11 hours. --------- CPU info (if available) ----------

Sep 29, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹⁴⁷+63·10⁷³-1)/9 = 111111111111111111111111111111111111111111111111111111111111111111111111181111111111111111111111111111111111111111111111111111111111111111111111111_<147> = 41 · 733 · 5669 · C138
C138 = P59 · P80
P59 = 18043670197968668793984586707577096674672799298135615597639_<59>
P80 = 36144175451666733695082301849669634364211513159356501466289901979180714137743657_<80>

Number: 11811_73 N=652173581427389791594625534819755229694025596885680192259571805404684165289942910179028932880723041736696821275246747216925708611036425823 ( 138 digits) SNFS difficulty: 147 digits. Divisors found: r1=18043670197968668793984586707577096674672799298135615597639 (pp59) r2=36144175451666733695082301849669634364211513159356501466289901979180714137743657 (pp80) Version: GGNFS-0.77.1 Total time: 43.92 hours. Scaled time: 34.43 units (timescale=0.784). Factorization parameters were as follows: name: 11811_73 n: 652173581427389791594625534819755229694025596885680192259571805404684165289942910179028932880723041736696821275246747216925708611036425823 m: 1000000000000000000000000 skew: 1 c6: 1000 c3: 630 c0: -1 type: snfs qintsize: 200000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [750000, 4750001) Relations: rels:3206706, finalFF:261356 Initial matrix: 228140 x 261356 with sparse part having weight 32357297. Pruned matrix : 223464 x 224668 with weight 25007265. Total sieving time: 42.12 hours. Total relation processing time: 0.39 hours. Matrix solve time: 1.25 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,147,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 43.92 hours. --------- CPU info (if available) ----------

Sep 28, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(7·10¹⁴⁹+18·10⁷⁴-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777777777977777777777777777777777777777777777777777777777777777777777777777777777777_<149> = C149
C149 = P46 · P50 · P55
P46 = 5404604503922020712999254263107777804727300539_<46>
P50 = 10192808475155750989833315677764597817385059969119_<50>
P55 = 1411879875419220434906116593970461441967036874923815197_<55>

Number: 77977_74 N=7777777777777777777777777777777777777777777777777777777777777777777777777797777777777777777777777777777777777777777777777777777777 7777777777777777777 ( 149 digits) SNFS difficulty: 150 digits. Divisors found: r1=5404604503922020712999254263107777804727300539 (pp46) r2=10192808475155750989833315677764597817385059969119 (pp50) r3=1411879875419220434906116593970461441967036874923815197 (pp55) Version: GGNFS-0.77.1 Total time: 39.25 hours. Scaled time: 26.14 units (timescale=0.666). Factorization parameters were as follows: name: 77977_74 n: 777777777777777777777777777777777777777777777777777777777777777777777777779777777777777777777777777777777777777777777777777777777777 77777777777777777 m: 10000000000000000000000000 c6: 7 c3: 18 c0: -70 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2100001) Relations: rels:5297545, finalFF:484339 Initial matrix: 352514 x 484339 with sparse part having weight 41780222. Pruned matrix : 319653 x 321479 with weight 18586160. Total sieving time: 35.85 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.84 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,150,6,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 39.25 hours. --------- CPU info (if available) ----------

Sep 27, 2005 (2nd)

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹⁴⁷+54·10⁷³-1)/9 = 111111111111111111111111111111111111111111111111111111111111111111111111171111111111111111111111111111111111111111111111111111111111111111111111111_<147> = 3² · 17 · 19 · C143
C143 = P62 · P81
P62 = 50183216683544210347493719943505384799366983609805300613170571_<62>
P81 = 761647398729307770338953052863586957090523894962597420009504549850879755898450863_<81>

Number: 11711_73 N=38221916446890647097045445858655352979398387035125941214692504682184764764744104269388067117685280739976302411802927798799831823567633681152773 ( 143 digits) SNFS difficulty: 147 digits. Divisors found: r1=50183216683544210347493719943505384799366983609805300613170571 (pp62) r2=761647398729307770338953052863586957090523894962597420009504549850879755898450863 (pp81) Version: GGNFS-0.77.1 Total time: 29.19 hours. Scaled time: 32.46 units (timescale=1.112). Factorization parameters were as follows: name: 11711_73 n: 38221916446890647097045445858655352979398387035125941214692504682184764764744104269388067117685280739976302411802927798799831823567633681152773 m: 1000000000000000000000000 skew: 1 c6: 1000 c3: 540 c0: -1 type: snfs qintsize: 3211000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [750000, 750000) Relations: rels:3080495, finalFF:269591 Initial matrix: 227947 x 269591 with sparse part having weight 31198209. Pruned matrix : 222150 x 223353 with weight 22383978. Total sieving time: 27.82 hours. Total relation processing time: 0.14 hours. Matrix solve time: 1.12 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,147,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 29.19 hours. --------- CPU info (if available) ----------

Sep 27, 2005

By Anton Korobeynikov / GGNFS-0.77.1-20050918-athlon gnfs
(31·10¹⁷⁵-13)/9 = 3(4)₁₇₄3_<176> = 3³ · 11 · 1758714678208981_<16> · 218277674307795096958217_<24> · 33833568313095695481541775239_<29> · C106
C106 = P52 · P55
P52 = 1338118630701493155755390329944470852310677155961119_<52>
P55 = 6672915229960602211087964240079771261594177163348746167_<55>

Number: tst106 N=8929152190302020347429266526432030524488161133378763203396320408660623788598621809325516977041298452280873 ( 106 digits) Divisors found: r1=1338118630701493155755390329944470852310677155961119 (pp52) r2=6672915229960602211087964240079771261594177163348746167 (pp55) Version: GGNFS-0.77.1-20050918-athlon Total time: 23.25 hours. Scaled time: 6.16 units (timescale=0.265). Factorization parameters were as follows: name: tst106 n: 8929152190302020347429266526432030524488161133378763203396320408660623788598621809325516977041298452280873 skew: 13988.75 # norm 9.24e+014 c5: 109200 c4: -124756648 c3: -97486167632234 c2: 70373387485007969 c1: 5966520956209533976686 c0: -9599423711263654546510848 # alpha -6.21 Y1: 137916226933 Y0: -152236085177219492257 # Murphy_E 1.53e-009 # M 4204347915402033042204649121630437412441159100594441987808255706056133265569276024396700002667842788525704 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2010089) Primes: RFBsize:183072, AFBsize:182943, largePrimes:4365341 encountered Relations: rels:4362550, finalFF:391364 Max relations in full relation-set: 28 Initial matrix: 366103 x 391364 with sparse part having weight 32502185. Pruned matrix : 344921 x 346815 with weight 25664956. Total sieving time: 15.74 hours. Total relation processing time: 0.42 hours. Matrix solve time: 6.56 hours. Time per square root: 0.53 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 23.25 hours. --------- CPU info (if available) ----------

Sep 26, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴⁵-5·10⁷²-1 = 9999999999999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999999999999_<145> = 81839 · 98272507 · C133
C133 = P39 · P94
P39 = 152850960360368016481796770480122031721_<39>
P94 = 8134661370956745828048953759976786314450618333909639195969999821733276700744096239942518707403_<94>

Number: 99499_72 N=1243390802757126501296053602554702077688262967135835473292833861150048331817913321440621720655003863799081320556499282362379083530 563 ( 133 digits) SNFS difficulty: 145 digits. Divisors found: r1=152850960360368016481796770480122031721 (pp39) r2=8134661370956745828048953759976786314450618333909639195969999821733276700744096239942518707403 (pp94) Version: GGNFS-0.77.1 Total time: 46.05 hours. Scaled time: 30.71 units (timescale=0.667). Factorization parameters were as follows: name: 99499_72 n: 124339080275712650129605360255470207768826296713583547329283386115004833181791332144062172065500386379908132055649928236237908353056 3 m: 1000000000000000000000000 c6: 10 c3: -5 c0: -1 skew: 2 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 4350001) Relations: rels:3306355, finalFF:225841 Initial matrix: 200206 x 225841 with sparse part having weight 29679208. Pruned matrix : 197120 x 198185 with weight 23952291. Total sieving time: 43.47 hours. Total relation processing time: 0.51 hours. Matrix solve time: 1.91 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,145,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 46.05 hours. --------- CPU info (if available) ----------

Sep 26, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(7·10¹⁴⁵-54·10⁷²-7)/9 = 7777777777777777777777777777777777777777777777777777777777777777777777771777777777777777777777777777777777777777777777777777777777777777777777777_<145> = 71 · 199 · 12188058719659076574629_<23> · C119
C119 = P38 · P81
P38 = 87564312641068638841591256231009360261_<38>
P81 = 515801290798649563626167419342575214155540733512744334738972726184941404656543177_<81>

Number: 77177_72 N=45165785488159710973051639553481235178894347636073938747091935366976442830753362823507269199197784011139077746494489197 ( 119 digits) SNFS difficulty: 145 digits. Divisors found: r1=87564312641068638841591256231009360261 (pp38) r2=515801290798649563626167419342575214155540733512744334738972726184941404656543177 (pp81) Version: GGNFS-0.77.1 Total time: 37.81 hours. Scaled time: 29.65 units (timescale=0.784). Factorization parameters were as follows: n: 45165785488159710973051639553481235178894347636073938747091935366976442830753362823507269199197784011139077746494489197 m: 1000000000000000000000000 c6: 70 c3: -54 c0: -7 skew: 1 type: snfs qintsize: 1000000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 3650001) Relations: rels:3437217, finalFF:375900 Initial matrix: 199834 x 375900 with sparse part having weight 48486997. Pruned matrix : 180127 x 181190 with weight 17117184. Total sieving time: 36.78 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.60 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,145,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 37.81 hours. --------- CPU info (if available) ----------

(7·10¹⁴⁵+9·10⁷²-7)/9 = 7777777777777777777777777777777777777777777777777777777777777777777777778777777777777777777777777777777777777777777777777777777777777777777777777_<145> = 383 · 811 · 6089 · 383303 · 30615034603619_<14> · C117
C117 = P47 · P70
P47 = 68431689554799209491887690638309240442707468639_<47>
P70 = 5121010810333912608676067303823655313256339089261174668305011424165007_<70>

Number: 77877_72 N=350439421979541043162765261875902491018760357666792585244047074023727465476969676295663708562855325114746563213715473 ( 117 digits) SNFS difficulty: 145 digits. Divisors found: r1=68431689554799209491887690638309240442707468639 (pp47) r2=5121010810333912608676067303823655313256339089261174668305011424165007 (pp70) Version: GGNFS-0.77.1 Total time: 26.81 hours. Scaled time: 31.27 units (timescale=1.166). Factorization parameters were as follows: name: 77877_72 n: 350439421979541043162765261875902491018760357666792585244047074023727465476969676295663708562855325114746563213715473 m: 1000000000000000000000000 skew: 1 c6: 70 c3: 9 c0: -7 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 650000) Relations: rels:3227183, finalFF:235032 Initial matrix: 200272 x 235032 with sparse part having weight 31149252. Pruned matrix : 196449 x 197514 with weight 23376361. Total sieving time: 25.10 hours. Total relation processing time: 0.21 hours. Matrix solve time: 1.40 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,145,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 26.81 hours. --------- CPU info (if available) ----------

Sep 25, 2005

By Yousuke Koide / GMP-ECM
10⁸¹³+1 = 1(0)₈₁₂1_<814> = 7 · 11 · 13 · 3253 · 552841 · 19633880890121399344333447_<26> · 13631530938380353975492092299_<29> · 14346353391098975362754290118329_<32> · [20501168633968077420390421455900537416512106676015038595458938603899332424835605523789625881227292636110398733891106068420502643126152428485587118151289391354644442883108526231851914140398775265277914355386154457410781202931638298697376453_<239>] · C478
C478 = P31 · C448
P31 = 2361737551129877719236265175893_<31>
C448 = [2987989399810057508411697668537843230685904546968886714785913544639262176423349267540393423600641107955945711718667808297490501982995472460023087397475031054256432025881599821473701742777134386732202923316988614285929048322906335004497621807933390515190689769147539503399177490134391121645439759838460130448210790819755325400398847235279158669521963122308750439333340886505739740439362538048686918294309352845678727261200193655372973522655537261569_<448>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 24, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴³-5·10⁷¹-1 = 99999999999999999999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999999999999999999_<143> = 7 · 829 · 51157 · C135
C135 = P64 · P71
P64 = 4226983455085368113131838522651325280201438948126519944281685689_<64>
P71 = 79691465468688137474165323187199380282822368311237342631970794505834321_<71>

Number: 99499_71 N=3368545060476516876978352830039846755318530951493958324111239450057935758079663335210410154349732676137827403168637406444513792307 32169 ( 135 digits) SNFS difficulty: 144 digits. Divisors found: r1=4226983455085368113131838522651325280201438948126519944281685689 (pp64) r2=79691465468688137474165323187199380282822368311237342631970794505834321 (pp71) Version: GGNFS-0.77.1 Total time: 29.81 hours. Scaled time: 19.82 units (timescale=0.665). Factorization parameters were as follows: name: 99499_71 n: 336854506047651687697835283003984675531853095149395832411123945005793575807966333521041015434973267613782740316863740644451379230732 169 m: 1000000000000000000000000 c6: 1 c3: -5 c0: -10 skew: 2 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 3150001) Relations: rels:3013005, finalFF:231737 Initial matrix: 200200 x 231737 with sparse part having weight 27088785. Pruned matrix : 196177 x 197242 with weight 20373082. Total sieving time: 27.65 hours. Total relation processing time: 0.37 hours. Matrix solve time: 1.66 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,144,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 29.81 hours. --------- CPU info (if available) ----------

Sep 24, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹⁴³+36·10⁷¹-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111111111511111111111111111111111111111111111111111111111111111111111111111111111_<143> = 3 · 23908939 · 25810517 · C127
C127 = P46 · P82
P46 = 2607668807327004985161783467552891735050687879_<46>
P82 = 2301583820944128487085008688078452990774158844979393223368239060897835128041394781_<82>
(10¹⁴⁵+72·10⁷²-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111111119111111111111111111111111111111111111111111111111111111111111111111111111_<145> = 3² · 2107327 · 2723333 · 10118441480393_<14> · C118
C118 = P58 · P60
P58 = 4061310944478199450935127095296114671511035658753832154961_<58>
P60 = 523482822214804830828357706751542295784338038432502503653253_<60>

Number: 11911_72 N=2126026515107322376424368162911387965905961350419462213637544985698108336765616243172222324940307551568433484107738133 ( 118 digits) SNFS difficulty: 145 digits. Divisors found: r1=4061310944478199450935127095296114671511035658753832154961 (pp58) r2=523482822214804830828357706751542295784338038432502503653253 (pp60) Version: GGNFS-0.77.1 Total time: 36.58 hours. Scaled time: 28.68 units (timescale=0.784). Factorization parameters were as follows: n: 2126026515107322376424368162911387965905961350419462213637544985698108336765616243172222324940307551568433484107738133 m: 1000000000000000000000000 c6: 10 c3: 72 c0: -1 skew: 1 type: snfs qintsize: 1000000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 3650001) Relations: rels:3399791, finalFF:386171 Initial matrix: 200402 x 386171 with sparse part having weight 49013167. Pruned matrix : 179494 x 180560 with weight 16551419. Total sieving time: 35.63 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.59 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,145,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 36.58 hours. --------- CPU info (if available) ----------

Sep 23, 2005

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴⁹-5·10⁷⁴-1 = 99999999999999999999999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999999999999999999999_<149> = 73 · 1697 · 4253 · 94379 · 140363 · 419683619 · C122
C122 = P49 · P73
P49 = 7607082794944975537132889579438640845935478194747_<49>
P73 = 4487781874349498160146767447626885491119476257355891326606162986068662363_<73>

Number: 99499_74 N=34138928283829981483835794161021640466040291417085193935654332119712915240943444241925776849647744784377979912928303207161 ( 122 digits) SNFS difficulty: 150 digits. Divisors found: r1=7607082794944975537132889579438640845935478194747 (pp49) r2=4487781874349498160146767447626885491119476257355891326606162986068662363 (pp73) Version: GGNFS-0.77.1 Total time: 67.74 hours. Scaled time: 45.12 units (timescale=0.666). Factorization parameters were as follows: name: 99499_74 n: 34138928283829981483835794161021640466040291417085193935654332119712915240943444241925776849647744784377979912928303207161 m: 10000000000000000000000000 c6: 1 c3: -5 c0: -10 skew: 2 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [750000, 2650001) Relations: rels:3003478, finalFF:284308 Initial matrix: 228589 x 284308 with sparse part having weight 32723180. Pruned matrix : 220909 x 222115 with weight 20791093. Total sieving time: 65.15 hours. Total relation processing time: 0.38 hours. Matrix solve time: 2.05 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,150,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 67.74 hours. --------- CPU info (if available) ----------

Sep 22, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(7·10¹⁴³-18·10⁷¹-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777777577777777777777777777777777777777777777777777777777777777777777777777777_<143> = 3³ · 811 · 16126223813047_<14> · C126
C126 = P41 · P86
P41 = 16713088988339994082589554888842125451283_<41>
P86 = 13178971039368712383242077555833066132886647279685469526123716787222619190917368268741_<86>

Number: 77577_71 N=220261315755724913572106880169066606847972296952932304551593314722275727161329532239306795331791596332030899244084219047244703 ( 126 digits) SNFS difficulty: 144 digits. Divisors found: r1=16713088988339994082589554888842125451283 (pp41) r2=13178971039368712383242077555833066132886647279685469526123716787222619190917368268741 (pp86) Version: GGNFS-0.77.1 Total time: 25.58 hours. Scaled time: 20.11 units (timescale=0.786). Factorization parameters were as follows: n: 220261315755724913572106880169066606847972296952932304551593314722275727161329532239306795331791596332030899244084219047244703 m: 1000000000000000000000000 c6: 7 c3: -18 c0: -70 skew: 1 type: snfs qintsize: 1000000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 2650001) Relations: rels:2893823, finalFF:282437 Initial matrix: 199870 x 282437 with sparse part having weight 31188111. Pruned matrix : 188368 x 189431 with weight 15596429. Total sieving time: 24.69 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.58 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,144,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 25.58 hours. --------- CPU info (if available) ----------

Sep 21, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(7·10¹⁴³-45·10⁷¹-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777777277777777777777777777777777777777777777777777777777777777777777777777777_<143>

= 3 · 97 · 167 · 220169 · 1193809768201760719_<19> · C115
C115 = P45 · P71
P45 = 403057793911824167022356193780204947197145521_<45>
P71 = 15107320712864825916941842087195959008317378609606036377161301236408411_<71>

Number: 77277_71 N=6089123358445703566359338445691733135195466081478896948086918682260578617109915516309164751062799007898897355377131 ( 115 digits) SNFS difficulty: 144 digits. Divisors found: r1=403057793911824167022356193780204947197145521 (pp45) r2=15107320712864825916941842087195959008317378609606036377161301236408411 (pp71) Version: GGNFS-0.77.1 Total time: 36.13 hours. Scaled time: 28.29 units (timescale=0.783). Factorization parameters were as follows: n: 6089123358445703566359338445691733135195466081478896948086918682260578617109915516309164751062799007898897355377131 m: 1000000000000000000000000 c6: 7 c3: -45 c0: -70 skew: 1 type: snfs qintsize: 1000000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 3650001) Relations: rels:3149530, finalFF:284155 Initial matrix: 200442 x 284155 with sparse part having weight 35293446. Pruned matrix : 190418 x 191484 with weight 18747386. Total sieving time: 35.05 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.73 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,144,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 36.13 hours. --------- CPU info (if available) ----------

Sep 20, 2005 (2nd)

By Makoto Kamada / GGNFS-0.77.1
(10¹⁵²-7)/3 = (3)₁₅₁1_<152> = 31 · 877 · 17333 · 15137587596899_<14> · 105778309518031_<15> · C116
C116 = P57 · P60
P57 = 247445620284419286332024260400277258105853174549257067019_<57>
P60 = 178529775276009541114346689149194427116014977593144491500851_<60>

Number: 33331_152 N=44176410982410163299974310599844589781710735107169108719596941998844558831709354455120517448624649334307593602533169 ( 116 digits) SNFS difficulty: 152 digits. Divisors found: r1=247445620284419286332024260400277258105853174549257067019 (pp57) r2=178529775276009541114346689149194427116014977593144491500851 (pp60) Version: GGNFS-0.77.1 Total time: 26.58 hours. Scaled time: 22.96 units (timescale=0.864). Factorization parameters were as follows: n: 44176410982410163299974310599844589781710735107169108719596941998844558831709354455120517448624649334307593602533169 m: 1000000000000000000000000000000 c5: 100 c0: -7 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2100001) Relations: rels:5323108, finalFF:450213 Initial matrix: 353124 x 450213 with sparse part having weight 38399849. Pruned matrix : 332963 x 334792 with weight 20317823. Total sieving time: 23.60 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.70 hours. Time per square root: 0.08 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: 26.58 hours. --------- CPU info (if available) ----------

Sep 20, 2005

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴⁹-7·10⁷⁴-1 = 99999999999999999999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999999999999999999_<149> = 9721 · 4189623909880529_<16> · C130
C130 = P58 · P72
P58 = 7690770857933312118597753750628516117910872540228607770081_<58>
P72 = 319259732546553198230034160874462037912072645302944776190499583078669031_<72>

Number: 99299_74a N=2455353447180614710113666508161868422147013669430768580779628319622623794987516791058193652895797157987678638831283467974343061511 ( 130 digits) SNFS difficulty: 150 digits. Divisors found: r1=7690770857933312118597753750628516117910872540228607770081 (pp58) r2=319259732546553198230034160874462037912072645302944776190499583078669031 (pp72) Version: GGNFS-0.77.1 Total time: 64.62 hours. Scaled time: 38.58 units (timescale=0.597). Factorization parameters were as follows: name: 99299_74a n: 2455353447180614710113666508161868422147013669430768580779628319622623794987516791058193652895797157987678638831283467974343061511 m: 10000000000000000000000000 c6: 1 c3: -7 c0: -10 skew: 2 type: snfsFactor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [750000, 2550001) Relations: rels:2963705, finalFF:277804 Initial matrix: 227971 x 277804 with sparse part having weight 31390705. Pruned matrix : 220823 x 222026 with weight 20682772. Total sieving time: 62.19 hours. Total relation processing time: 0.30 hours. Matrix solve time: 1.96 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,150,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 64.62 hours. --------- CPU info (if available) ----------

Sep 19, 2005 (2nd)

By Makoto Kamada / GGNFS-0.77.1
(10¹⁵¹+53)/9 = (1)₁₅₀7_<151> = 7³ · 109 · 12170033 · 1474257115384270604354669957_<28> · C112
C112 = P41 · P72
P41 = 13895338835485101820598178988327586760611_<41>
P72 = 119207270151444009334181713166925566184534569334425892610231192042679801_<72>

Number: 11117_151 N=1656425410407523938008362100731804302338694799025320828075910612347370794803640653528089475607271904065112118411 ( 112 digits) SNFS difficulty: 151 digits. Divisors found: r1=13895338835485101820598178988327586760611 (pp41) r2=119207270151444009334181713166925566184534569334425892610231192042679801 (pp72) Version: GGNFS-0.77.1 Total time: 23.80 hours. Scaled time: 20.52 units (timescale=0.862). Factorization parameters were as follows: n: 1656425410407523938008362100731804302338694799025320828075910612347370794803640653528089475607271904065112118411 m: 1000000000000000000000000000000 c5: 10 c0: 53 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2000001) Relations: rels:5606912, finalFF:570395 Initial matrix: 352511 x 570395 with sparse part having weight 50641858. Pruned matrix : 303423 x 305249 with weight 16702260. Total sieving time: 21.61 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.92 hours. Time per square root: 0.07 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: 23.80 hours. --------- CPU info (if available) ----------

Sep 19, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹⁴³+54·10⁷¹-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111111111711111111111111111111111111111111111111111111111111111111111111111111111_<143> = 83 · 615542356384709107_<18> · C123
C123 = P44 · P80
P44 = 16197706322224665168921392016601227322415057_<44>
P80 = 13426658248042374703718480358757697751184371777828778917717953298882176929884383_<80>

Number: 11711_71 N=217481067190665919305659947718591517014168410662205738485389977121150613582384490369998327579625463670744837070699348354831 ( 123 digits) SNFS difficulty: 144 digits. Divisors found: r1=16197706322224665168921392016601227322415057 (pp44) r2=13426658248042374703718480358757697751184371777828778917717953298882176929884383 (pp80) Version: GGNFS-0.77.1 Total time: 25.39 hours. Scaled time: 19.88 units (timescale=0.783). Factorization parameters were as follows: n: 217481067190665919305659947718591517014168410662205738485389977121150613582384490369998327579625463670744837070699348354831 m: 1000000000000000000000000 c6: 1 c3: 54 c0: -10 skew: 1 type: snfs qintsize: 1000000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 2650001) Relations: rels:2901329, finalFF:277370 Initial matrix: 199736 x 277370 with sparse part having weight 30762538. Pruned matrix : 189016 x 190078 with weight 15898623. Total sieving time: 24.50 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.61 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,144,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 25.39 hours. --------- CPU info (if available) ----------

(7·10¹⁴³-54·10⁷¹-7)/9 = 77777777777777777777777777777777777777777777777777777777777777777777777177777777777777777777777777777777777777777777777777777777777777777777777_<143> = 13 · 239 · 398456431 · C131
C131 = P38 · P93
P38 = 66093701362031281001731974225870390331_<38>
P93 = 950546490842008147042688248625215333783327711118993319756406892329103327678906354661218607151_<93>

Number: 77177_71 N=62825135896438488441436771449779334797836466675272274335222651757497832551376624905031688189002553707685874429427514139316517856981 ( 131 digits) SNFS difficulty: 144 digits. Divisors found: r1=66093701362031281001731974225870390331 (pp38) r2=950546490842008147042688248625215333783327711118993319756406892329103327678906354661218607151 (pp93) Version: GGNFS-0.77.1 Total time: 28.48 hours. Scaled time: 22.33 units (timescale=0.784). Factorization parameters were as follows: n: 62825135896438488441436771449779334797836466675272274335222651757497832551376624905031688189002553707685874429427514139316517856981 m: 1000000000000000000000000 c6: 7 c3: -54 c0: -70 skew: 1 type: snfs qintsize: 2275000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 2925001) Relations: rels:2876776, finalFF:253359 Initial matrix: 199830 x 253359 with sparse part having weight 28229248. Pruned matrix : 192552 x 193615 with weight 17525880. Total sieving time: 27.46 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.70 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,144,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 28.48 hours. --------- CPU info (if available) ----------

Sep 18, 2005

Wataru Sakai's 56 digits factor was placed on eighth of the largest factor found by ECM. Congratulations!
See Large Factors Found By ECM (Richard Brent).

Sep 14, 2005 (2nd)

By Wataru Sakai / GMP-ECM 6.0.1
3·10¹⁶⁶-1 = 2(9)_166<167> = 47 · 71 · 2667289 · 10991159 · 627960539 · 2137781721901653563_<19> · C123
C123 = P56 · P68
P56 = 10345389693582740479529989859541374220406006881752101849_<56>
P68 = 22080500640751102476087504432625828948573909939464280318314247588489_<68>
Note: P56 is the second largest prime factor found by GMP-ECM in our tables. Congratulations!

Sep 14, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹⁴³+45·10⁷¹-1)/9 = 11111111111111111111111111111111111111111111111111111111111111111111111611111111111111111111111111111111111111111111111111111111111111111111111_<143> = 31 · 3067 · C138
C138 = P56 · P82
P56 = 20200641684724245754250086231892578489308178227109512851_<56>
P82 = 5785179724796597502347433085972931672675889015378672672873247829853702152891246393_<82>

Number: 11611_71 N=116864342702347687780547462699823417978176752643763592783860566815434980185650694816949536808177699244939481800131589249882843496440896443 ( 138 digits) SNFS difficulty: 144 digits. Divisors found: r1=20200641684724245754250086231892578489308178227109512851 (pp56) r2=5785179724796597502347433085972931672675889015378672672873247829853702152891246393 (pp82) Version: GGNFS-0.77.1 Total time: 25.50 hours. Scaled time: 19.97 units (timescale=0.783). Factorization parameters were as follows: n: 116864342702347687780547462699823417978176752643763592783860566815434980185650694816949536808177699244939481800131589249882843496440896443 m: 1000000000000000000000000 c6: 1 c3: 45 c0: -10 skew: 1 type: snfs qintsize: 1000000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 2650001) Relations: rels:3000030, finalFF:315372 Initial matrix: 200165 x 315372 with sparse part having weight 34901610. Pruned matrix : 184321 x 185385 with weight 14536167. Total sieving time: 24.68 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.54 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,144,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 25.50 hours. --------- CPU info (if available) ----------

Sep 13, 2005 (2nd)

By Kenichiro Yamaguchi / GGNFS-0.77.1
(7·10¹⁴¹-45·10⁷⁰-7)/9 = 777777777777777777777777777777777777777777777777777777777777777777777727777777777777777777777777777777777777777777777777777777777777777777777_<141> = 3089 · 8563 · 283909 · C129
C129 = P41 · P88
P41 = 58652798393860565815370026873212851538391_<41>
P88 = 1765809221960943255769182473012586637075182623140275690951647167662713926381035549130169_<88>

Number: 77277_70 N=103569652297694987953627625628198793313050449057259381408529923443451276790035858088726254060204366784359552640911552933559818079 ( 129 digits) SNFS difficulty: 141 digits. Divisors found: r1=58652798393860565815370026873212851538391 (pp41) r2=1765809221960943255769182473012586637075182623140275690951647167662713926381035549130169 (pp88) Version: GGNFS-0.77.1 Total time: 56.05 hours. Scaled time: 43.89 units (timescale=0.783). Factorization parameters were as follows: n: 103569652297694987953627625628198793313050449057259381408529923443451276790035858088726254060204366784359552640911552933559818079 m: 100000000000000000000000000000000000 c4: 70 c2: -45 c0: -7 skew: 1 type: snfs qintsize: 1500000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 6650001) Relations: rels:3442872, finalFF:353628 Initial matrix: 200453 x 353628 with sparse part having weight 50737412. Pruned matrix : 184335 x 185401 with weight 21626407. Total sieving time: 55.03 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.79 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,141,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 56.05 hours. --------- CPU info (if available) ----------

Sep 13, 2005

By Wataru Sakai / GMP-ECM 6.0.1
3·10¹⁹⁰-1 = 2(9)_190<191> = 97 · 29924824213_<11> · 7668447060104434870881489582121_<31> · 512358733922895524489343752888689_<33> · C115
C115 = P30 · P86
P30 = 247984694771318430568948981693_<30>
P86 = 10607461577425281731753905244766737614406396259890391295260540539167282031764330723127_<86>

Sep 11, 2005

By Yousuke Koide / GMP-ECM
10⁴⁴³+1 = 1(0)₄₄₂1_<444> = 11 · 887 · 2659 · C436
C436 = P43 · C394
P43 = 3646836465960880692292201915543408162476049_<43>
C394 = [1056936920749964722929828576624217604146887673567661698146974403860730882430792714566017124364090647084708761042672412110583342292077804307482388499001109008194875836195841990475402074719478633242189283412047635153545645032028344137331511134704077687538175641102136020445005471151998617932091877877913277007525468543178676185089859186550080677532355108510234998991838967281973483348896796755223_<394>]
10⁸⁶⁷+1 = 1(0)₈₆₆1_<868> = 7 · 11 · 13 · 103 · 4013 · 511438099 · 21993833369_<11> · 291078844423_<12> · 27608334534637_<14> · 587063793048979091_<18> · 1972638068686670089_<19> · 377526955309799110357_<21> · 3434599112338341945743041_<25> · 6794665217550790190548807_<25> · 42323992639419349049079264521_<29> · [7869279963898584873704619876952650437142766041101303960599340958747338060623170735596454466404569560841011834013635808394002588995226791041455798312938104095919627533925117419483939626462647532409864836445929031936209_<217>] · C463
C463 = P40 · C424
P40 = 1363267285346876343226104657933729291571_<40>
C424 = [5771480751840582985388703945235891831356446142487405897303743318091745656755051377264513126243290873378949031599534144611358216682091492341982494653037487954847487958865608089116229717391924859653909955930092381188858868218525451033067471663209025482216765524003510399287087429319214038031758031389789240471012973007854634416272473325141435641906859906515344002960351254023639639973631305490078314347823590160221993138672441_<424>]
10⁸⁹⁷+1 = 1(0)₈₉₆1_<898> = 7 · 11 · 13² · 47 · 139 · 157 · 859 · 2531 · 6397 · 31051 · 41263 · 107641 · 216451 · 1058313049_<10> · 32494323733_<11> · 388847808493_<12> · 564362592691_<12> · 40118979906877_<14> · 143574021480139_<15> · 549797184491917_<15> · 24649445347649059192745899_<26> · 20186272871950202514968048148247_<32> · [33852066257429811148979390609187539760850944806763555795340084882048986912482949506591909041130651770779842162499482875755533111808276172876211496409325473343590723224081353129229935527059488811457730702694849036693756201766866018562295004353153066430367_<254>] · C462
C462 = P37 · C425
P37 = 8506605834248913330852032305919581849_<37>
C425 = [52696566310890555059713785468295190337713032880561252126403680211073068279889235080696182420195019443948876494177803199989194580453076606218572165233875780462433235647111602082924714786418624232604391875035984478489504597896289611496485775684278517583435313708524108203303317049386792124699967604877994728261228242507820430044905622878998990477030983559308742252183606941967762023641179505430404889630469419258650277762546437_<425>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 8, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
(10¹⁴⁵+27·10⁷²-1)/9 = 1111111111111111111111111111111111111111111111111111111111111111111111114111111111111111111111111111111111111111111111111111111111111111111111111_<145> = 89 · 113 · C141
C141 = P51 · P90
P51 = 231765555870207670623710560918298164819618843538357_<51>
P90 = 476694506664627985476181685621420487293201128856842553222172695669351321716815243796911539_<90>

Number: 11411_72 N=110481367317401920166163976445372487929910620573840221846585573343055693955564394064940947709168848673671185354589948405201462773303282401423 ( 141 digits) SNFS difficulty: 145 digits. Divisors found: r1=231765555870207670623710560918298164819618843538357 (pp51) r2=476694506664627985476181685621420487293201128856842553222172695669351321716815243796911539 (pp90) Version: GGNFS-0.77.1 Total time: 219.73 hours. Scaled time: 165.46 units (timescale=0.753). Factorization parameters were as follows: n: 110481367317401920166163976445372487929910620573840221846585573343055693955564394064940947709168848673671185354589948405201462773303282401423 m: 1000000000000000000000000000000000000 c4: 10 c2: 27 c0: -1 skew: 1 type: snfs qintsize: 2000000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 24650001) Relations: rels:5746658, finalFF:225648 Initial matrix: 199560 x 225648 with sparse part having weight 36716766. Pruned matrix : 196561 x 197622 with weight 30648658. Total sieving time: 217.96 hours. Total relation processing time: 0.50 hours. Matrix solve time: 1.19 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,145,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 219.73 hours. --------- CPU info (if available) ----------

Sep 7, 2005

By Wataru Sakai / GMP-ECM 6.0.1
3·10¹⁵³-1 = 2(9)_153<154> = 72019 · 1472927109551_<13> · 6437899768974245773_<19> · C118
C118 = P41 · P77
P41 = 45425367911692522245626027985214885364243_<41>
P77 = 96705293648696981037155654696825961344230797647139452351613239823428072265389_<77>

Sep 6, 2005

By Sinkiti Sibata / GGNFS-0.77.1
10¹⁴³-8·10⁷¹-1 = 99999999999999999999999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999999999999999999999_<143> = 939623 · 692765651 · C129
C129 = P40 · P89
P40 = 5545315714417291165686064725832927750643_<40>
P89 = 27703442430900092553537300647051906583048198294477171096908738767897374226177031471283041_<89>

Number: 99199_71 N=153624334655525044186691865819496479895855337929403934446979662530604532822145983919217173587198722294170547473315529189322745363 ( 129 digits) SNFS difficulty: 144 digits. Divisors found: r1=5545315714417291165686064725832927750643 (pp40) r2=27703442430900092553537300647051906583048198294477171096908738767897374226177031471283041 (pp89) Version: GGNFS-0.77.1 Total time: 174.95 hours. Scaled time: 116.52 units (timescale=0.666). Factorization parameters were as follows: name: 99199_71 n: 153624334655525044186691865819496479895855337929403934446979662530604532822145983919217173587198722294170547473315529189322745363 m: 1000000000000000000000000000000000000 c4: 1 c2: -8 c0: -10 skew: 2 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 21650001) Relations: rels:5428768, finalFF:224431 Initial matrix: 200191 x 224431 with sparse part having weight 36189694. Pruned matrix : 197524 x 198588 with weight 30573016. Total sieving time: 170.54 hours. Total relation processing time: 1.72 hours. Matrix solve time: 2.62 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,144,4,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 174.95 hours. --------- CPU info (if available) ----------

Sep 5, 2005

By K. Aoki & T. Shimoyama / GMP-ECM
(10³¹¹-1)/9 = (1)_311<311> = C311
C311 = P64 · P247
P64 = 4344673058714954477761314793437392900672885445361103905548950933_<64>
P247 = 2557410180456133012695296509537372979376491356924379552525114935669331084986752230647446546259197479934221837065635648510025350381215759674118823641087628274237766333894639357732286152115312924645292259846495854098673368096039697255340580355564267_<247>
See also ECMNET (Paul Zimmermann).

Sep 4, 2005

By Yousuke Koide / GMP-ECM
10⁴³⁶+1 = 1(0)₄₃₅1_<437> = 73 · 137 · 86403431489_<11> · 456439977353_<12> · C410
C410 = P43 · C368
P43 = 1710994186565875947530228779349674860535337_<43>
C368 = [14818129057462283853775654812618861131040955555183331815585265901844180195589373882781414035305246121771793257893061987415246466288899349926740285270435373507399657836785754508325906681454120568644765969951040233484222186645607824518987973529073072608461765668778863598874116839743777665033781655901259905226059546949834048270069032481393898474950498707497744212479169_<368>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 1, 2005

By Wataru Sakai / GMP-ECM 6.0.1
3·10¹⁷²-1 = 2(9)_172<173>

= C173
C173 = P35 · C138
P35 = 38122987748499595028686163894145203_<35>
C138 = [786926780186075758268741106446345233058414651262593009833784935602647827417065446546566009104898212188196236218414523309890529326286496133_<138>]