Since June 16, 2000

STUDIO KAMADA

English only.

News and updates, March 2006

Mar 30, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
2·10¹⁶⁸-9 = 1(9)₁₆₇1_<169> = 7 · 1087 · 8537489959_<10> · 367694783292840547667053261930530350154041_<42> · C113
C113 = P53 · P61
P53 = 17966034076031944574391153471623679589453353622292711_<53>
P61 = 4660500063909969005743702902671272798968399002082218677735511_<61>

Number: 19991_168 N=83730702959555558644286753585554649649572317505120979221312693092511006979457450320140886370830911981249481160321 ( 113 digits) Divisors found: r1=17966034076031944574391153471623679589453353622292711 (pp53) r2=4660500063909969005743702902671272798968399002082218677735511 (pp61) Version: GGNFS-0.77.1 Total time: 58.38 hours. Scaled time: 34.80 units (timescale=0.596). Factorization parameters were as follows: name: 19991_168 n: 83730702959555558644286753585554649649572317505120979221312693092511006979457450320140886370830911981249481160321 skew: 62536.04 # norm 1.67e+15 c5: 4800 c4: 542418002 c3: -30527202903432 c2: -187460816726501101 c1: 39811099175404160316726 c0: -1109743373310044488384538995 # alpha -5.38 Y1: 185480496509 Y0: -7052262054420382279818 # Murphy_E 6.92e-10 # M 75632762796499756649388024022841439022310180894940132867887513639978626189449917333412097122871594278740117554634 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:7719597, finalFF:707777 Initial matrix: 500741 x 707777 with sparse part having weight 61382861. Pruned matrix : 422570 x 425137 with weight 24650963. Total sieving time: 51.42 hours. Total relation processing time: 0.60 hours. Matrix solve time: 5.83 hours. Time per square root: 0.53 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: 58.38 hours. --------- CPU info (if available) ----------

Mar 29, 2006

By CWI
10²³⁸+1 = 1(0)₂₃₇1_<239> = 29 · 101 · 281 · 2381 · 28559389 · 121499449 · 1491383821_<10> · 275855329893529_<15> · 2324557465671829_<16> · 20087794479102305428621_<23> · C152
C152 = P64 · P89
P64 = 5582637833682557709253612812885341475900082138954691763178176941_<64>
P89 = 13712255219708533473813623053189821987961076229175414555827926545777661379291311684923609_<89> Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(68·10¹⁹⁸+13)/9 = 7(5)₁₉₇7_<199> = 3³ · 2837 · 7305413 · 124068676637_<12> · 403212889427768888832067867_<27> · 1562091434865214888463863633_<28> · C123
C123 = P57 · P66
P57 = 258170928787318894541525466230371667081514748966348106999_<57>
P66 = 669249700255497765647229643415437163131542241223547798847162206127_<66>

Number: 75557_198 N=172780816705596629436477571893915454694951908049723289731935734705261274963726310234006475949636958455314893409923089382873 ( 123 digits) Divisors found: r1=258170928787318894541525466230371667081514748966348106999 (pp57) r2=669249700255497765647229643415437163131542241223547798847162206127 (pp66) Version: GGNFS-0.77.1 Total time: 257.55 hours. Scaled time: 161.74 units (timescale=0.628). Factorization parameters were as follows: name: 75557_198 n: 172780816705596629436477571893915454694951908049723289731935734705261274963726310234006475949636958455314893409923089382873 skew: 242002.32 # norm 4.69e+16 c5: 5040 c4: 620918512 c3: -1283681869942759 c2: -25445850424152104787 c1: 26848786049597838801584727 c0: 58141808848337734262122548867 # alpha -5.97 Y1: 1075588169161 Y0: -509346087624359811646142 # Murphy_E 2.15e-10 # M 4224800078277202070226350581168509253931390803546482563682347130827643033159196813348775910046698793869083997859267081664 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2500000, 7780001) Relations: rels:8271672, finalFF:788713 Initial matrix: 697784 x 788713 with sparse part having weight 89212794. Pruned matrix : 662576 x 666128 with weight 65904764. Total sieving time: 227.99 hours. Total relation processing time: 4.58 hours. Matrix solve time: 24.26 hours. Time per square root: 0.72 hours. Prototype def-par.txt line would be: gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 257.55 hours. --------- CPU info (if available) ----------

Mar 23, 2006

By Kazumaro Aoki / GMP-ECM
(10³⁷¹-1)/9 = (1)_371<371> = 107 · 239 · 2969 · 4649 · 51199 · 1659431 · 1325815267337711173_<19> · 47198858799491425660200071_<26> · C304
C304 = P50 · C255
P50 = 26628696860763170757415075888614691991511099147227_<50>
C255 = [222341721027911715633671961706217915116678982524266600828809108331318320649681568887402437710769278163500186590283610898584016236491957089336867945678571711723875925300701888125177904675751179148227068623232948215760382265117676642381699264210177060167843_<255>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 21, 2006

By Bruce Dodson / GMP-ECM
10²⁸³+1 = 1(0)₂₈₂1_<284> = 11 · 1699 · 241117 · 61945573305222690279363663578823967_<35> · C239
C239 = P51 · C189
P51 = 151168348012920493188164812150408056175148228488823_<51>
C189 = [236981781933948043228112220789227624908212542569354344676500735171191136986262759275099377257787061318322981899812820646487731505276950534191352836827590738081581753192002166353465640625197_<189>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 20, 2006

By Torbjorn Granlund / GMP-ECM
10³⁹⁵+1 = 1(0)₃₉₄1_<396> = 11 · 1423 · 9091 · 9615060929_<10> · 6295632499623851_<16> · 4539787279569136988691351491_<28> · 24966203549341539495819194854679625225811_<41> · 66443174541490579097997510158021076958392938976011506949065646573_<65> · C229
C229 = P47 · P182
P47 = 36135553580039597739744803188558136917651907171_<47>
P182 = 42660530392229903351072436102344244250617560023502875336329183331096805000157530395542396500243031769146588091361465456452731316179986315200680926557940585563325081869311166989363491_<182>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 15, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(32·10¹⁸³-23)/9 = 3(5)₁₈₂3_<184> = 11 · 19 · 17397387712532638583_<20> · 90684212543160708737_<20> · 15029772282548630768461_<23> · C120
C120 = P40 · P81
P40 = 1923668077538699854190851222644599554517_<40>
P81 = 372960566449273440535593005370695937455230440600272291890122994647120883283696071_<81>

Number: 35553_183 N=717452335859218360167438927623765212076802428464127319102516042017826581473819680378277934646358498808266801495823202707 ( 120 digits) Divisors found: r1=1923668077538699854190851222644599554517 (pp40) r2=372960566449273440535593005370695937455230440600272291890122994647120883283696071 (pp81) Version: GGNFS-0.77.1 Total time: 146.56 hours. Scaled time: 87.35 units (timescale=0.596). Factorization parameters were as follows: name: 35553_183 n: 717452335859218360167438927623765212076802428464127319102516042017826581473819680378277934646358498808266801495823202707 skew: 103830.10 # norm 4.16e+16 c5: 18360 c4: 9620368916 c3: 7177488075314 c2: -81657829878091490664 c1: 1933461944338510949361607 c0: -313681924961620863382406111 # alpha -5.66 Y1: 1710720816299 Y0: -131335908490248459876552 # Murphy_E 2.70e-10 # M 481970025387192072510914688544626149162622798462491063577737582196652254614879116165880736905817348899803797752005002797 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, 5190001) Relations: rels:7895878, finalFF:708277 Initial matrix: 631562 x 708277 with sparse part having weight 69096069. Pruned matrix : 599687 x 602908 with weight 50233403. Polynomial selection time: 1.50 hours. Total sieving time: 125.46 hours. Total relation processing time: 2.04 hours. Matrix solve time: 16.85 hours. Time per square root: 0.70 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: 146.56 hours. --------- CPU info (if available) ----------

Mar 15, 2006

By Makoto Kamada / PFGW
(14·10¹¹²⁷⁹-11)/3 = 4(6)₁₁₂₇₈3_<11280> is PRP. This is the 26th prime or PRP of the form 466...663 including 43.
(14·10¹⁹⁶⁷⁷-11)/3 = 4(6)₁₉₆₇₆3_<19678> is PRP. This is the 27th prime or PRP of the form 466...663 including 43.

Primality testing (14*10^11279-11)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 167 Running N-1 test using base 193 Running N-1 test using base 223 Running N+1 test using discriminant 3, base 1+sqrt(3) Running N+1 test using discriminant 3, base 3+sqrt(3) Running N+1 test using discriminant 3, base 4+sqrt(3) Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.13% proof) (14*10^11279-11)/3 is Fermat and Lucas PRP! (136.2094s+0.0010s) Primality testing (14*10^19677-11)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 139 Running N+1 test using discriminant 191, base 2+sqrt(191) Calling N-1 BLS with factored part 0.18% and helper 0.04% (0.57% proof) (14*10^19677-11)/3 is Fermat and Lucas PRP! (208.3531s+0.0015s)

Note:
(14·10¹¹²⁷⁹-11)/3-1 = 42·R₁₁₂₇₉, 11279 is prime.
(14·10¹⁹⁶⁷⁷-11)/3-1 = 42·R₁₉₆₇₇, 19677 = 3 · 7 · 937.

Mar 12, 2006

By Yousuke Koide / GMP-ECM
10⁵⁶³+1 = 1(0)₅₆₂1_<564> = 11 · 12498601 · 579098423 · 5089082809028683211_<19> · 29283791702184825961_<20> · C508
C508 = P35 · P474
P35 = 36265008707438890601092610924794499_<35>
P474 = 232401494054570096143564993567696213375160353588417043090684984008451459670563877848647221789116648084601933880604986363761579421580159899581971059471764334988754554032162111036734709558829222890387903668986840084368851089124293184850568488971261475110622313574444779882860262870083592445443612475383694609460996337539641013578225997858543638658915937776380907660097061600787534395165252920449980799649154737825244060326194223564696221792437925158704683354257701429283783173_<474>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 9, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, Msieve v. 1.03
(86·10¹⁵⁹+31)/9 = 9(5)₁₅₈9_<160> = 11 · 79 · 11174459 · 1502356653904533350741_<22> · C129
C129 = P35 · P95
P35 = 32925940611028209913897631506414729_<35>
P95 = 19892914848838805121187170889842741939087687000043733872145367908159923963535199308109148910261_<95>
(86·10¹⁹⁷+31)/9 = 9(5)₁₉₆9_<198> = 11 · 383 · 389 · 6551821 · 889779406597_<12> · 16240097980183799_<17> · 6326590128437676415873_<22> · C135
C135 = P36 · P50 · P51
P36 = 257061712718000124573629082190241723_<36>
P50 = 17202872520442432210877384770546939996230403362031_<50>
P51 = 220127243508692213597620396060520447620885683353701_<51>
(83·10¹⁵²+61)/9 = 9(2)₁₅₁9_<153> = 53 · 49553849717_<11> · 317701005474431_<15> · C127
C127 = P34 · P47(1095...) · P47(2796...)
P34 = 3608239190673295798991471185907989_<34>
P47(1095...) = 10951667146070503349365880660080570035257139853_<47>
P47(2796...) = 27969723271484245196929127184512281242928180627_<47>
(83·10¹⁵⁸+61)/9 = 9(2)₁₅₇9_<159> = C159
C159 = P39 · C121
P39 = 117545651888135840815842818880953169751_<39>
C121 = [7845651518440422046274124148055206572053296058018576850355756519442414234698093136206369834368093919414710356459458036979_<121>]
(83·10¹⁶⁵+61)/9 = 9(2)₁₆₄9_<166> = 11 · 53 · 15467 · 624066075792757767593189_<24> · C136
C136 = P32 · P43 · P62
P32 = 77015221797071783144018776142779_<32>
P43 = 1363983398260425583802572468420050762256249_<43>
P62 = 15600722535588390596249739026257013695088784067038703180701031_<62>
(83·10¹⁷⁰+61)/9 = 9(2)₁₆₉9_<171> = 7883 · 19441 · 2000351 · 2106457109_<10> · C148
C148 = P32 · P117
P32 = 10246654667775461302966534591093_<32>
P117 = 139374886901991284309920528691380173177220939093427095206182914573598399192602401679574826904949867314936196243568889_<117>
(83·10¹⁸²+61)/9 = 9(2)₁₈₁9_<183> = 773 · 5849 · C177
C177 = P26 · P152
P26 = 18323924688912353458934957_<26>
P152 = 11131558409804658552975136550245961802897585754926764622588590174425550785078755590086633257634460716644299002312941445512090775542751313517232875571261_<152>
(83·10¹⁸⁷+61)/9 = 9(2)₁₈₆9_<188> = 3 · 11 · 92051 · 30067547 · C175
C175 = P32 · C143
P32 = 84311270917687423566615482497229_<32>
C143 = [11975936863183358248554497011506440623051685644174883289393187724496404341718218435134527037287517064098894745988460538796464883046662025611401_<143>]
(83·10¹⁸⁸+61)/9 = 9(2)₁₈₇9_<189> = 446309 · 1434847 · 11812329767321731_<17> · C162
C162 = P33 · P129
P33 = 813358403948275531485764881346537_<33>
P129 = 149891436995987972781929490337435011368175402050551513955225614585203280820778471440295188112515448467155816910188061801267258909_<129>

Mar 9, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
3·10¹⁶⁷-1 = 2(9)_167<168> = 7 · 7643 · 5308447 · 22854213927330216399615920416772214007_<38> · C119
C119 = P59 · P61
P59 = 39688758719895871031552328771144713882109670630545445702193_<59>
P61 = 1164549798963657623144995222566231913164712125722393092919267_<61>

Number: 29999_167 N=46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531 ( 119 digits) Divisors found: r1=39688758719895871031552328771144713882109670630545445702193 (pp59) r2=1164549798963657623144995222566231913164712125722393092919267 (pp61) Version: GGNFS-0.77.1 Total time: 127.93 hours. Scaled time: 76.25 units (timescale=0.596). Factorization parameters were as follows: name: 29999_167 n: 46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531 skew: 124276.53 # norm 6.35e+16 c5: 3780 c4: 9000258924 c3: -554045092292200 c2: -39482819237992107286 c1: 3932121986615762035288899 c0: 70617401508006264190233896568 # alpha -6.80 Y1: 977912957527 Y0: -104103375987437644398895 # Murphy_E 3.22e-10 # M 38938266427990170016457106322341826580574242911371250299063807152482269131899914371350670090841862042894144699664069961 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, 4770001) Relations: rels:7833087, finalFF:739482 Initial matrix: 632170 x 739482 with sparse part having weight 66718778. Pruned matrix : 591810 x 595034 with weight 42684964. Polynomial selection time: 1.71 hours. Total sieving time: 109.90 hours. Total relation processing time: 1.73 hours. Matrix solve time: 13.85 hours. Time per square root: 0.75 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 127.93 hours. --------- CPU info (if available) ----------

Mar 6, 2006 (2nd)

By Bruce Dodson / GMP-ECM
10⁶¹⁰+1 = 1(0)₆₀₉1_<611> = 101 · 3541 · 6101 · 21961 · 27961 · 51241 · 1587221 · 9818561 · 81183810541_<11> · 217345835281_<12> · 555818110301_<12> · 28474644365651641_<17> · 8950221294967070861_<19> · 17751033585336286181_<20> · 17716886277230798340041_<23> · 101444162656037151745878558385892753596849_<42> · 75743388768260974116327848920184337528059461788181539337429709_<62> · [24117462560776940857674798510867129035516104161041003845211930699998253738773357627145166937584558542746371549244626963892247670300659074689156318263222623146762142584127818541_<176>] · C185
C185 = P50 · P136
P50 = 39069669288697789469488625615834711944836425801981_<50>
P136 = [1642269048916396301246801744101379821902073519810571143520576971928815724659633161556699837755221303434764527770131486856721570324295821_<136>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 6, 2006

By Yousuke Koide / GMP-ECM
10⁵⁵⁷+1 = 1(0)₅₅₆1_<558> = 11 · 88007 · 179268223 · 344577275324047_<15> · C529
C529 = P38 · C491
P38 = 20862619931001299769258280552030071437_<38>
C491 = [80155126803992958974081271951622621798563080439375689086151511748888857024774801881444988889327039297111156006793190146899843106382703618789533002233930062113834145634448902443144669556151584614671871116613397376475754027410164847877952704878442901102913032214159979400648826552464374616727772570384213045693621664436916530380113597719242206587830138898336553329158672161855285016711264338141948902686341480347249217048265971292294117681897203483787177184016190823523188622792220861985797929_<491>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 3, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(14·10¹⁷⁸-41)/9 = 1(5)₁₇₇1_<179> = 18077 · 970583 · 1735406205257_<13> · 1745824177303_<13> · 390328319148709270682251559_<27> · C117
C117 = P41 · P76
P41 = 82809502531065408728209262767741242648467_<41>
P76 = 9053460294396930637785159619418341915179225744274958113717340351294912094247_<76>

Number: 15551_178 N=749712543163762808092051180657424884788820203073702176064721437535025801283241160904783569650296980815170595794069349 ( 117 digits) Divisors found: r1=82809502531065408728209262767741242648467 (pp41) r2=9053460294396930637785159619418341915179225744274958113717340351294912094247 (pp76) Version: GGNFS-0.77.1 Total time: 90.52 hours. Scaled time: 60.19 units (timescale=0.665). Factorization parameters were as follows: name: 15551_178 n: 749712543163762808092051180657424884788820203073702176064721437535025801283241160904783569650296980815170595794069349 skew: 37242.91 # norm 6.09e+15 c5: 64800 c4: 6759976239 c3: -240101464909709 c2: -7631822091175545737 c1: 136429241778261841168464 c0: 1961043974935176328332864300 # alpha -5.23 Y1: 3236659220977 Y0: -25862042449072322628529 # Murphy_E 4.05e-10 # M 349385423445357336464828299975167497040480146975800760950577244763433429412923324641596525897204278449812482008715321 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, 3990001) Relations: rels:7690204, finalFF:756389 Initial matrix: 631392 x 756389 with sparse part having weight 61408642. Pruned matrix : 578158 x 581378 with weight 35000223. Polynomial selection time: 2.42 hours. Total sieving time: 74.78 hours. Total relation processing time: 1.15 hours. Matrix solve time: 11.46 hours. Time per square root: 0.70 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 90.52 hours. --------- CPU info (if available) ----------