Since June 16, 2000

STUDIO KAMADA

English only.

News and updates, April 2006

Apr 30, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(2·10¹⁶⁶+43)/9 = (2)₁₆₅7_<166> = 23 · 239 · 223681 · 4808529001_<10> · 27380724157_<11> · 49555413624314842798663_<23> · C114
C114 = P48 · P67
P48 = 109487586728603959180419389601246000593684286667_<48>
P67 = 2529994022553427102516108528949076661299677585064796901468164965163_<67>

Number: 22227_166 N=277002939967167951016685502103671381318776877865988131419624426806168301114704336309326219472752500352276560381721 ( 114 digits) Divisors found: r1=109487586728603959180419389601246000593684286667 (pp48) r2=2529994022553427102516108528949076661299677585064796901468164965163 (pp67) Version: GGNFS-0.77.1 Total time: 68.07 hours. Scaled time: 40.57 units (timescale=0.596). Factorization parameters were as follows: name: 22227_166 n: 277002939967167951016685502103671381318776877865988131419624426806168301114704336309326219472752500352276560381721 skew: 35022.57 # norm 2.16e+15 c5: 18240 c4: 3324342576 c3: -75210684545821 c2: -3889995031532597485 c1: 41149321063516891001327 c0: 225554783497329843951341475 # alpha -5.11 Y1: 661875331123 Y0: -6859467162763553226608 # Murphy_E 5.83e-10 # M 169113702666968308599370405410246605720862169449212140169193171897561787349105029174955912873471203511474794908184 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, 3050001) Relations: rels:7820687, finalFF:710792 Initial matrix: 500744 x 710792 with sparse part having weight 65707739. Pruned matrix : 426298 x 428865 with weight 27132479. Total sieving time: 60.31 hours. Total relation processing time: 0.73 hours. Matrix solve time: 6.55 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 68.07 hours. --------- CPU info (if available) ----------

Apr 27, 2006 (2nd)

By Yousuke Koide / GMP-ECM
10⁹⁵⁷+1 = 1(0)₉₅₆1_<958> = 7 · 11² · 13 · 23 · 59 · 1277 · 4093 · 8779 · 357281 · 599144041 · 49561573447_<11> · 183411838171_<12> · 638453709757_<12> · 135080726389891_<15> · 8793273568581345414847_<22> · 154083204930662557781201849_<27> · 1274194732898148471766404179653_<31> · [486459602951209423461970749393767073577709990315453869054236545173346054197523047637756449380382360041196303992701358542477479985899282299202659134981413322115768441437335973512015267176836292140179486592703400778357473505777445415009505803673230073891473294849_<261>] · C539
C539 = P33 · C506
P33 = 156318278601913796169958831669567_<33>
C506 = [66203514277021933018367219154147693778936535037473098541895109470133101615260456904766124804243260059004061482523868396627422842510506272739618129760738873068588643277236787555047257507825557038938807521179427472188374447895999544336201041507230424796520553176789792857470904436544840504491242651630080934330545370540473441479395984110121956451559196947095558755351350931089697373180296334055005865225493893072152234214689358450841228924816239504156756948896041357344696275396252307079534359595606264813659_<506>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(4·10¹⁷⁵+23)/9 = (4)₁₇₄7_<175>= 7⁴ · 151 · 4077068417_<10> · 912028673482967_<15> · 18287204296526384115739261382729_<32> · C114
C114 = P43 · P72
P43 = 1474496589385636624872422204643590358428021_<43>
P72 = 122264617559167997611060160283499497988751361155452737911400912906085147_<72>

Number: 44447_175 N=180278761593532432612303389060257361960331553150960921382583597306562657112851496908359299109733878279188096704087 ( 114 digits) Divisors found: r1=1474496589385636624872422204643590358428021 (pp43) r2=122264617559167997611060160283499497988751361155452737911400912906085147 (pp72) Version: GGNFS-0.77.1 Total time: 66.44 hours. Scaled time: 40.99 units (timescale=0.617). Factorization parameters were as follows: name: 44447_175 n: 180278761593532432612303389060257361960331553150960921382583597306562657112851496908359299109733878279188096704087 skew: 37257.24 # norm 1.97e+15 c5: 2640 c4: -3066352960 c3: -2045340552093 c2: 4202550017261824270 c1: 5428663167547359316208 c0: -351827258170714110587019840 # alpha -5.13 Y1: 940460856101 Y0: -9265702850142573753067 # Murphy_E 5.77e-10 # M 73472187332863004272367469093365019774637426525363658693875390400459913791531866622534228469633558335064213728171 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, 3050001) Relations: rels:7715758, finalFF:666113 Initial matrix: 501371 x 666113 with sparse part having weight 60549670. Pruned matrix : 442462 x 445032 with weight 28621695. Polynomial selection time: 0.59 hours. Total sieving time: 57.53 hours. Total relation processing time: 0.71 hours. Matrix solve time: 7.08 hours. Time per square root: 0.52 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 66.44 hours. --------- CPU info (if available) ----------

Apr 24, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(5·10¹⁶⁴-41)/9 = (5)₁₆₃1_<164> = 3 · 117526809611_<12> · 54250638606310858569979433501919015383_<38> · C115
C115 = P43 · P73
P43 = 1474584781590694929005726294763938095505713_<43>
P73 = 1969675536474541734600499776776117471857256864782569029241086440347327593_<73>

Number: 55551_164 N=2904453570756846986973383368766510254862338723725138737049038603407688954012735912987940359365696468744723414038809 ( 115 digits) Divisors found: r1=1474584781590694929005726294763938095505713 (pp43) r2=1969675536474541734600499776776117471857256864782569029241086440347327593 (pp73) Version: GGNFS-0.77.1 Total time: 67.75 hours. Scaled time: 40.38 units (timescale=0.596). Factorization parameters were as follows: name: 55551_164 n: 2904453570756846986973383368766510254862338723725138737049038603407688954012735912987940359365696468744723414038809 skew: 80450.98 # norm 1.20e+16 c5: 17820 c4: 4393654356 c3: -433753330947111 c2: -27350320194916868196 c1: 1177687194802812552792514 c0: 15113021087910275283692837108 # alpha -6.45 Y1: 2090837063779 Y0: -11026236084453321843579 # Murphy_E 5.28e-10 # M 223818122459110710984661179910979783697925729433915265008233972170338542245360401390459830340040811696130589483131 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, 3050001) Relations: rels:7459470, finalFF:591118 Initial matrix: 500042 x 591118 with sparse part having weight 51454791. Pruned matrix : 465016 x 467580 with weight 31354404. Total sieving time: 58.56 hours. Total relation processing time: 0.63 hours. Matrix solve time: 7.92 hours. Time per square root: 0.64 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 67.75 hours. --------- CPU info (if available) ----------

Apr 23, 2006

By Bruce Dodson / GMP-ECM
10³⁹⁹+1 = 1(0)₃₉₈1_<400> = 7² · 11 · 13 · 127 · 2689 · 459691 · 909091 · 1458973 · 425991366045253_<15> · 909090909090909091_<18> · 247025236977306025681323889_<27> · 753201806271328462547977919407_<30> · 61828645758322140842666144519962696417487_<41> · 72021403933746126426491665754465510017877_<41> · 17499101101496101893247811440257935152097401_<44> · C159
C159 = P49 · P110
P49 = 9284668536078237580134472469990637899155265743957_<49>
P110 = 13147963643704652632557279758698587212033283223333451187877069162714784603584406816150353817835190742091970171_<110>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 22, 2006 (2nd)

By Yousuke Koide / GMP-ECM
10⁹⁰³+1 = 1(0)₉₀₂1_<904> = 7² · 11 · 13 · 127 · 2689 · 3613 · 459691 · 909091 · 57009401 · 2182600451_<10> · 212057054080446499_<18> · 120525789336558438197_<21> · 7306116556571817748755241_<25> · 304768036847074491064894608014695867632997_<42> · 3605696680890791382725432167911038465896663_<43> · 6798855735656881396055959081077830421892567_<43> · 1752088930844817629923654387608505754917704006063078641900632201094124478044555887071171166365583553287053602700568010683873135238140340718711012045219107751867190380847_<169> · C504
C504 = P38 · C467
P38 = 43304701938592897922269981296083376277_<38>
C467 = [21013886489517971344330040348864764437934906646797649893170202970198245328335882505499980396675911865555101856779577300554075531457771872695017237088972173632109249163225374752369335580275541978505985802453671153658648150573384500193528998265661485199395999980819844420791561304482876541398168140686809355351611618717081565145452820471364641262390976246981616092354714230772892990579479051048942179341131112862748124387554407607082664991040927358250555874030530718383_<467>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 22, 2006

Jason Papadopoulos's Msieve Version 1.06 was released.

Apr 21, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(2·10¹⁶⁷-17)/3 = (6)₁₆₆1_<167> = 7 · 7461472332473_<13> · 431563732881502259_<18> · 5375549665816933543013_<22> · C114
C114 = P35 · P37 · P44
P35 = 13261436963852796014111335957348117_<35>
P37 = 1573557102101571405377857101955399229_<37>
P44 = 26366061185051453095178144268786977977763221_<44>

Number: 66661_167 N=550197165033613611769376863626601856258906596716272891854586217441612353242352244972984468385524424237232803855253 ( 114 digits) Divisors found: r1=13261436963852796014111335957348117 (pp35) r2=1573557102101571405377857101955399229 (pp37) r3=26366061185051453095178144268786977977763221 (pp44) Version: GGNFS-0.77.1 Total time: 61.41 hours. Scaled time: 36.60 units (timescale=0.596). Factorization parameters were as follows: name: 66661_167 n: 550197165033613611769376863626601856258906596716272891854586217441612353242352244972984468385524424237232803855253 skew: 70471.01 # norm 4.20e+15 c5: 1800 c4: 1368602079 c3: -12250040256487 c2: -1093635789305396793 c1: 39849855690633737457906 c0: -1783344159885267576523734080 # alpha -5.53 Y1: 805473164171 Y0: -12503883379418569316817 # Murphy_E 5.79e-10 # M 529423451654234320505526908635372534366477001369404131995810074889560862579154671691751730713159012157786351594722 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, 2950001) Relations: rels:7611348, finalFF:653939 Initial matrix: 500098 x 653939 with sparse part having weight 56597179. Pruned matrix : 441743 x 444307 with weight 26893096. Total sieving time: 53.70 hours. Total relation processing time: 0.64 hours. Matrix solve time: 6.54 hours. Time per square root: 0.53 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 61.41 hours. --------- CPU info (if available) ----------

Apr 19, 2006

By Yousuke Koide / GMP-ECM
10⁸⁸⁸+1 = 1(0)₈₈₇1_<889> = 17 · 593 · 1777 · 5882353 · 7228321 · 9999999900000001_<16> · 14645119755678294049_<20> · 1686340623946037268128160202360893760539460370996627318701517706745362561551433406408094266441822934232698145025463743674536256340640809274873526138279915682968128161887015177082630691231028669477234384485666273187182124789224283305059021924114671146711635919055647554806087689713153457_<286> · C547
C547 = P34 · P514
P34 = 2430356574005120498845908043009873_<34>
P514 = 2187319485856065660460480283212234313654078652411870459451330169647543812240431617143716447792186692975247051510538424479092940669136785288465781753693717009207146283270615110366556378727360748704592078063629885737548293485907528075546515396905912717472464716164833417809029422074335902030196371245199471373470169818790769381981258258611278976650676287419191207657093916768283363951628318877273133525031558244951861839766442570991470244423599118239355710932138403326127489420348476636642367374646669593814227877889_<514>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 18, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10¹⁶²+11)/3 = (3)₁₆₁7_<162> = 1433 · 124841369 · 1336592833641954403_<19> · 36720308617555078459_<20> · C113
C113 = P35 · P79
P35 = 15839391943642481226131981562976091_<35>
P79 = 2396790507959344653148912568029143521446310165683450943135628493061398785885083_<79>

Number: 33337_162 N=37963704262370013974982229977530646773584991859960923446485591042890017200918324520218776946038568609153002550553 ( 113 digits) Divisors found: r1=15839391943642481226131981562976091 (pp35) r2=2396790507959344653148912568029143521446310165683450943135628493061398785885083 (pp79) Version: GGNFS-0.77.1 Total time: 57.23 hours. Scaled time: 37.88 units (timescale=0.662). Factorization parameters were as follows: name: 33337_162 n: 37963704262370013974982229977530646773584991859960923446485591042890017200918324520218776946038568609153002550553 skew: 82628.90 # norm 5.80e+15 c5: 5400 c4: 2402492435 c3: -113085781430568 c2: -14669915217540964944 c1: 360170614013768543148208 c0: 13321767032890434723398144064 # alpha -6.38 Y1: 693271831747 Y0: -5880177126467717739035 # Murphy_E 6.89e-10 # M 34645119737512916872622338715117151998917211253417099047843164366198507059196910860745581897837412972482767998816 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2850001) Relations: rels:7665727, finalFF:700241 Initial matrix: 500331 x 700241 with sparse part having weight 60604941. Pruned matrix : 422361 x 424926 with weight 24830799. Polynomial selection time: 0.52 hours. Total sieving time: 50.08 hours. Total relation processing time: 0.70 hours. Matrix solve time: 5.45 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 57.23 hours. --------- CPU info (if available) ----------

Apr 16, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(82·10¹⁶⁵-1)/9 = 9(1)_165<166> = 3 · 4651 · 3815909 · 109337069 · 24597499837_<11> · 119473647151415430355631209_<27> · C111
C111 = P44 · P68
P44 = 52584546422938872199993496426580755318657669_<44>
P68 = 10127846063825475829007266635111227567710236342483257149233524822111_<68>

Number: 91111_165 N=532568191507609461751810844266510060172332169466526373634275624269343840855863338282742074685691230272530919259 ( 111 digits) Divisors found: r1=52584546422938872199993496426580755318657669 (pp44) r2=10127846063825475829007266635111227567710236342483257149233524822111 (pp68) Version: GGNFS-0.77.1 Total time: 47.69 hours. Scaled time: 28.42 units (timescale=0.596). Factorization parameters were as follows: name: 91111_165 n: 532568191507609461751810844266510060172332169466526373634275624269343840855863338282742074685691230272530919259 skew: 44253.41 # norm 2.76e+15 c5: 13260 c4: -2952571022 c3: -64159933967618 c2: 5169908297278730197 c1: 65757180348379498133862 c0: -972969186385581959161825911 # alpha -6.14 Y1: 183357985723 Y0: -2092994245773555980588 # Murphy_E 8.58e-10 # M 266349246250008411579281465016211195175095228656302106749506815357893863129981722202192551134409014791788528244 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1600000, 2500001) Relations: rels:7502896, finalFF:632541 Initial matrix: 459786 x 632541 with sparse part having weight 56622491. Pruned matrix : 394614 x 396976 with weight 24147845. Polynomial selection time: 0.50 hours. Total sieving time: 41.44 hours. Total relation processing time: 0.68 hours. Matrix solve time: 4.57 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 47.69 hours. --------- CPU info (if available) ----------

Apr 13, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(83·10¹⁷⁶+61)/9 = 9(2)₁₇₅9_<177> = 977189933 · 677436880567_<12> · 4398981358728402973_<19> · 4561677112603872026693843_<25> · C113
C113 = P40 · P73
P40 = 7192656946027737524918319855947986687571_<40>
P73 = 9652098648828096511437545492127071883766346870809662669210109599313691731_<73>

Number: 92229_176 N=69424234390238348459735580768786661626522690519560994858731457507032720590703701430297457624005875684018103175401 ( 113 digits) Divisors found: r1=7192656946027737524918319855947986687571 (pp40) r2=9652098648828096511437545492127071883766346870809662669210109599313691731 (pp73) Version: GGNFS-0.77.1 Total time: 60.14 hours. Scaled time: 39.99 units (timescale=0.665). Factorization parameters were as follows: name: 92229_176 n: 69424234390238348459735580768786661626522690519560994858731457507032720590703701430297457624005875684018103175401 skew: 34725.81 # norm 9.38e+15 c5: 27840 c4: 1952949260 c3: 239570943857341 c2: 28653622092714987 c1: 4208411463039264573491 c0: -524927595336302835681939143 # alpha -6.17 Y1: 829057423733 Y0: -4779333281932956287892 # Murphy_E 6.01e-10 # M 1944097459749997755277490881319499555332311992419460999696824029213840783552124833372077496272187035996537581197 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, 2950001) Relations: rels:7512522, finalFF:623442 Initial matrix: 499633 x 623442 with sparse part having weight 54825480. Pruned matrix : 451822 x 454384 with weight 29284529. Polynomial selection time: 0.50 hours. Total sieving time: 51.68 hours. Total relation processing time: 0.79 hours. Matrix solve time: 6.71 hours. Time per square root: 0.46 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 60.14 hours. --------- CPU info (if available) ----------

Apr 12, 2006

By Yousuke Koide / GMP-ECM
10⁸¹⁶+1 = 1(0)₈₁₅1_<817> = 97 · 353 · 449 · 641 · 1409 · 69857 · 206209 · 58627969 · 3156663361_<10> · 66554101249_<11> · 75118313082913_<14> · 39127329514182768921189838418689_<32> · 8274466617334672110426476083265843201_<37> · [20613661601050142213000575997849301836417547662874985098970766781932900988120507408603473644982986488160619644274811516746717894883553676903578704941377044565165542482689618096760494994922455997632250274389555329_<212>] · C471
C471 = P37 · P435
P37 = 4444442797021732533861519689020084897_<37>
P435 = 182168885688800471032070314606442908018600300417083944518739710393647902382617378829742666164078393724922058999479539245587167427080499185116669904781913921946772253903767015005946741838709655930349163084737589584381983926389625045094948824590259228606134828950677303795021460411056135766667281810175120746691826141507834669471110707839979934576289109001841823875933756134673970083682689775540524930437792688282436257038622290979346977_<435>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 11, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(22·10¹⁶⁸-1)/3 = 7(3)_168<169> = 7 · 56123 · 446327841017_<12> · 430461185535167573_<18> · 1409905188331436013487_<22> · C113
C113 = P56 · P58
P56 = 13084049258809821588896439090996621938307031288296648457_<56>
P58 = 5266746964258109491400138988161479038453646038826462079387_<58>

Number: 73333_168 N=68910376714040195406347745240503361261758316416576282636203495308149851640887510416264286216165380927075165055859 ( 113 digits) Divisors found: r1=13084049258809821588896439090996621938307031288296648457 (pp56) r2=5266746964258109491400138988161479038453646038826462079387 (pp58) Version: GGNFS-0.77.1 Total time: 53.51 hours. Scaled time: 31.89 units (timescale=0.596). Factorization parameters were as follows: name: 73333_168 n: 68910376714040195406347745240503361261758316416576282636203495308149851640887510416264286216165380927075165055859 skew: 36941.64 # norm 5.22e+15 c5: 15600 c4: 4190341915 c3: 3039365141531 c2: -8922979585383379554 c1: 94148034217382755246189 c0: -5421494257068971161432225 # alpha -6.41 Y1: 975922912999 Y0: -5358309014913334727634 # Murphy_E 7.37e-10 # M 6599696211979593814265749664234017177559052514922972069100058083737370758216219483967420220531197055536338039220 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:7879379, finalFF:790755 Initial matrix: 500653 x 790755 with sparse part having weight 69627103. Pruned matrix : 390126 x 392693 with weight 22520690. Polynomial selection time: 0.53 hours. Total sieving time: 46.94 hours. Total relation processing time: 0.63 hours. Matrix solve time: 4.96 hours. Time per square root: 0.46 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 53.51 hours. --------- CPU info (if available) ----------

Apr 9, 2006

By Yousuke Koide / GMP-ECM
10⁸⁴⁹+1 = 1(0)₈₄₈1_<850> = 7 · 11 · 13 · 1699 · 241117 · 9170899 · 715880197 · 7198295568559013885196835567543447_<34> · 61945573305222690279363663578823967_<35> · 151168348012920493188164812150408056175148228488823_<51> · [236981781933948043228112220789227624908212542569354344676500735171191136986262759275099377257787061318322981899812820646487731505276950534191352836827590738081581753192002166353465640625197_<189>] · C515
C515 = P34 · C482
P34 = 1941850545413860134349140850659019_<34>
C482 = [11974596042808172532294983252939558878410189694663843068971765344308532913676645715309213363442627278076993492211166595880998184306177956628823075306750747898909101048339462363861018906574913448147471222095530123865763276293471254728437236511524459858068517800257650185047651380759211520548387242736820413514544025166081207894531393549080448211783134185139166833148694113912674297086397341821453080768324146339882473885456877565040591000305223469402926705116035907018404340127773009_<482>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 8, 2006 (2nd)

By Yousuke Koide / GMP-ECM
10⁸¹⁶+1 = 1(0)₈₁₅1_<817> = 97 · 353 · 449 · 641 · 1409 · 69857 · 206209 · 58627969 · 3156663361_<10> · 66554101249_<11> · 75118313082913_<14> · 8274466617334672110426476083265843201_<37> · [20613661601050142213000575997849301836417547662874985098970766781932900988120507408603473644982986488160619644274811516746717894883553676903578704941377044565165542482689618096760494994922455997632250274389555329_<212>] · C503
C503 = P32 · C471
P32 = 39127329514182768921189838418689_<32>
C471 = [809639191841064628525439231464999860397773607701980496081352666339504925459847421412079302897545851796994671960772729238488139832762235263695725908656072122047265685298946436141716959730769253735737488429705565187437664314635095937428340389980720185899033798436170265716087449200924809607342324420823123105586292160476218717903066160195563389157166475672526475982627558029455580472138762318157710719436530508723203208044400504432618748282362705740783507784354366160306369_<471>]
10⁸²²+1 = 1(0)₈₂₁1_<823> = 101 · 9901 · 718606649 · 40160350429_<11> · 144389656548047821_<18> · 2834523818368583744706086149_<28> · [3430756550790484778909640352209879033892610315578901813821345434990400007261052844057102137330186660253398361164679549479441003751370060990401385264590147924466884786339105844110638415462294590233248989402615229312388735660453351624541145759819967937881_<253>] · C500
C500 = P35 · C466
P35 = 16254031864650930002850269462824009_<35>
C466 = [1518251219423747541558249786341574895284479899305883251990246801255766909229333395434458469693549966383795065664136418817339096752250299235950034967670343929013892055001964056060297891256021051404942653075694117320359458606226902427876452489321855322434222068318126282515684656661189152027802914755789408960326502178798522971472567196598942110678827737509377973305601271034834784135339840915115044044544939389765778113496729595022312073212316740002281949880005471741_<466>]
10⁸³⁷+1 = 1(0)₈₃₆1_<838> = 7 · 11 · 13 · 19 · 373 · 1117 · 5023 · 44641 · 52579 · 70541929 · 3590254957_<10> · 14175966169_<11> · 261315626851_<12> · 909090909090909090909090909091_<30> · 183372282864547916749018225828651_<33> · 18381907262281244633158190677786966663091011_<44> · 4887054837129490444185770642291712106451445708466643483270887621857163512076927093556902832792696796518529880218993484798134507347686651311824503_<145> · C525
C525 = P36 · C490
P36 = 108131551600520034721722272883130729_<36>
C490 = [7045616588486799878229908819910336923888220571062351357216159107348231895397024661050209344237746338927104332618758413991185539098879237656670503260201568098865214938494573500927612773398337686887554455654975502630496905550466931864411689596634310312025533326809689061042921776515817300848267597128380147428873265628242289520724784622861753110448953054107116821206466090015933935448825960415332332679426815216857782017220038922288778308959959611010035857100841026102213598239576198581831053_<490>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 8, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(34·10¹⁹⁰-7)/9 = 3(7)_190<191> = 37 · 109 · 6609437 · 60793981 · 16209889148099957_<17> · 3026164475092149900973_<22> · 5559395425785366046547_<22> · C113
C113 = P47 · P67
P47 = 17700270697562795473798575278495575252228893343_<47>
P67 = 4829510199492607911626007156104654630552733041153862475787361617117_<67>

Number: 37777_190 N=85483637867659658567202674170495654476226505771174948815394154314847353949058264254404667624789110546175796152131 ( 113 digits) Divisors found: r1=17700270697562795473798575278495575252228893343 (pp47) r2=4829510199492607911626007156104654630552733041153862475787361617117 (pp67) Version: GGNFS-0.77.1 Total time: 57.54 hours. Scaled time: 38.27 units (timescale=0.665). Factorization parameters were as follows: name: 37777_190 n: 85483637867659658567202674170495654476226505771174948815394154314847353949058264254404667624789110546175796152131 skew: 29076.08 # norm 1.07e+16 c5: 36540 c4: -12185242756 c3: 256023137714363 c2: 11051642456086268502 c1: 18000780073429467449288 c0: -153367693679452411321236672 # alpha -6.17 Y1: 878574755927 Y0: -4718764285096744772323 # Murphy_E 6.34e-10 # M 75966605504227469208499904048510806763470040437426901577401200590832189731289766473179388615073537509657719698494 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2850001) Relations: rels:7507727, finalFF:633645 Initial matrix: 500994 x 633645 with sparse part having weight 54977270. Pruned matrix : 448761 x 451329 with weight 28155882. Total sieving time: 50.19 hours. Total relation processing time: 0.63 hours. Matrix solve time: 6.24 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 57.54 hours. --------- CPU info (if available) ----------

Apr 6, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(61·10¹⁷³-7)/9 = 6(7)_173<174> = 71 · 233 · 24742957991_<11> · 31809119701353051742109_<23> · 39660267116313906346259099_<26> · C112
C112 = P28 · P29 · P56
P28 = 3760357206641161646188454939_<28>
P29 = 17434053596101093960844893121_<29>
P56 = 20021041886655596186926329100373757874861254953098046101_<56>

Number: 67777_173 N=1312544851288681061657320385726742235100077386920141929455960788027209627857570783929880133267056183525631510519 ( 112 digits) Divisors found: r1=3760357206641161646188454939 (pp28) r2=17434053596101093960844893121 (pp29) r3=20021041886655596186926329100373757874861254953098046101 (pp56) Version: GGNFS-0.77.1 Total time: 43.90 hours. Scaled time: 26.21 units (timescale=0.597). Factorization parameters were as follows: name: 67777_173 n: 1312544851288681061657320385726742235100077386920141929455960788027209627857570783929880133267056183525631510519 skew: 24484.59 # norm 3.26e+15 c5: 20160 c4: -6931159530 c3: -62708438404343 c2: 2275074974729497200 c1: 32786546490054575521986 c0: 5415945762602193956372053 # alpha -6.42 Y1: 308438021903 Y0: -2305306742891941527290 # Murphy_E 8.41e-10 # M 54595772227758935359404905948683395924693960067717954361230432600020289149931447345402724142563475095733714275 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, 2550001) Relations: rels:7400610, finalFF:656339 Initial matrix: 500217 x 656339 with sparse part having weight 52225852. Pruned matrix : 433326 x 435891 with weight 23330329. Total sieving time: 37.25 hours. Total relation processing time: 0.59 hours. Matrix solve time: 5.59 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: 43.90 hours. --------- CPU info (if available) ----------

Apr 4, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(25·10¹⁸⁹-7)/9 = 2(7)_189<190> = 23 · 53 · 37013 · 547635411247_<12> · 330088629807359_<15> · 3327653778948571_<16> · 22683909170999073431738750101_<29> · C112
C112 = P39 · P73
P39 = 856086520823564452415849992209116593237_<39>
P73 = 5270401796810904687788561074505843101960974063751693547717781294407477621_<73>

Number: 27777_189 N=4511919937574110062022680359046714142686606807038938468754742182604387963067074666966204626047764872601837449177 ( 112 digits) Divisors found: r1=856086520823564452415849992209116593237 (pp39) r2=5270401796810904687788561074505843101960974063751693547717781294407477621 (pp73) Version: GGNFS-0.77.1 Total time: 57.21 hours. Scaled time: 34.09 units (timescale=0.596). Factorization parameters were as follows: name: 27777_189 n: 4511919937574110062022680359046714142686606807038938468754742182604387963067074666966204626047764872601837449177 skew: 148044.23 # norm 4.56e+15 c5: 720 c4: -73626874 c3: -110867117727798 c2: 454455646419441839 c1: 510055059250966394606382 c0: 3954090739576303650823513256 # alpha -5.57 Y1: 234260784469 Y0: -5746536105901399508307 # Murphy_E 7.19e-10 # M 3185822251552743801476745947087601288349612792255263001652175728055263652166107759270387802466612664245102359504 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2850001) Relations: rels:7502977, finalFF:656719 Initial matrix: 500172 x 656719 with sparse part having weight 54894770. Pruned matrix : 438101 x 440665 with weight 25287702. Polynomial selection time: 0.50 hours. Total sieving time: 50.16 hours. Total relation processing time: 0.64 hours. Matrix solve time: 5.43 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 57.21 hours. --------- CPU info (if available) ----------

Apr 1, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(83·10¹⁶⁹+61)/9 = 9(2)₁₆₈9_<170> = 3 · 11² · 306725482387_<12> · 158097431899383477583_<21> · 5128036316381592220298959_<25> · C112
C112 = P50 · P62
P50 = 19700081684465458593403806555789969994895088533657_<50>
P62 = 51860316780454489279897084658059454426917923044301608049721421_<62>

Number: 92229_168 N=1021652476757208163560581079259281054181213711730300692671570682687015568804053712776559333447913768270232366597 ( 112 digits) Divisors found: r1=19700081684465458593403806555789969994895088533657 (pp50) r2=51860316780454489279897084658059454426917923044301608049721421 (pp62) Version: GGNFS-0.77.1 Total time: 48.14 hours. Scaled time: 28.69 units (timescale=0.596). Factorization parameters were as follows: name: 92229_168 n: 1021652476757208163560581079259281054181213711730300692671570682687015568804053712776559333447913768270232366597 skew: 42379.53 # norm 2.26e+15 c5: 5700 c4: 2476189901 c3: 2818036125079 c2: -3965150761651559721 c1: 20159536553490602897396 c0: 628219114223343985647383680 # alpha -5.92 Y1: 299274416299 Y0: -2822810127643404054087 # Murphy_E 8.41e-10 # M 998581722717076005120486833807822888215121894318500192856457073627922103911622034888560960264551830549271253187 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, 2650001) Relations: rels:7817263, finalFF:794068 Initial matrix: 500946 x 794068 with sparse part having weight 68271744. Pruned matrix : 385474 x 388042 with weight 21626578. Polynomial selection time: 0.52 hours. Total sieving time: 41.98 hours. Total relation processing time: 0.73 hours. Matrix solve time: 4.45 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: 48.14 hours. --------- CPU info (if available) ----------