Since June 16, 2000

STUDIO KAMADA

English only.

News and updates, August 2006

Aug 31, 2006

By Wataru Sakai / GMP-ECM 6.1, GGNFS-0.77.1-20060513-pentium4 gnfs
(22·10¹⁸⁴-1)/3 = 7(3)_184<185> = 13 · 613 · 2281 · 14868970103047296245613937657_<29> · C150
C150 = P40 · P44 · P67
P40 = 2031080946385714878679659203604090401921_<40>
P44 = 21945234169387169334196823964344482962911429_<44>
P67 = 6087289750244991176881048532900144215876009240110234950082092759569_<67>

-------------------------------------------------------------------------------- Input number is 271326008406630128238872515463149625877354734768189047779930524749980293347074947943662398980732616918692654155507590620036804998472605855111160688021 (150 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1650881922 Step 1 took 349291ms Step 2 took 112389ms ********** Factor found in step 2: 21945234169387169334196823964344482962911429 Found probable prime factor of 44 digits: 21945234169387169334196823964344482962911429 Composite cofactor 12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049 has 107 digits -------------------------------------------------------------------------------- Number: template N=12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049 ( 107 digits) Divisors found: r1=2031080946385714878679659203604090401921 (pp40) r2=6087289750244991176881048532900144215876009240110234950082092759569 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 18.29 hours. Scaled time: 22.99 units (timescale=1.257). Factorization parameters were as follows: name: template n: 12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049 skew: 22789.77 # norm 3.10e+014 c5: 2340 c4: -398302965 c3: -10216058861434 c2: -13884546662538244 c1: 2027046464299948407818 c0: -2007001082567218081705635 # alpha -5.19 Y1: 154384318913 Y0: -350423791053635097226 # Murphy_E 1.50e-009 # M 10817716021220227761602447619130818932091000933110480399993043144783173863818229918415548312281906103274965 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, 2450001) Primes: RFBsize:183072, AFBsize:183087, largePrimes:4569109 encountered Relations: rels:4788587, finalFF:554889 Max relations in full relation-set: 28 Initial matrix: 366236 x 554889 with sparse part having weight 43558978. Pruned matrix : 242243 x 244138 with weight 23035380. Polynomial selection time: 1.08 hours. Total sieving time: 15.61 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.16 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 18.29 hours. --------- CPU info (if available) ---------- --------------------------------------------------------------------------------

Aug 30, 2006

By JMB / GGNFS-0.77.1 gnfs
(2·10¹⁸⁰+43)/9 = (2)₁₇₉7_<180> = 17 · 239 · 113177 · 15272032201952205157_<20> · 136224300968205436467179879754395287_<36> · C117
C117 = P40 · P77
P40 = 5558661540664315482839927301493931936647_<40>
P77 = 41788890014541574244523074808400148246998304107338687225849783582778228178449_<77>

Number: Job N=232290295750883296131439774105626527875056675632797772800763276168416357472031357205659940208252291417037581678720503 ( 117 digits) Divisors found: r1=5558661540664315482839927301493931936647 (pp40) r2=41788890014541574244523074808400148246998304107338687225849783582778228178449 (pp77) Version: GGNFS-0.77.1 Total time: 39.38 hours. Scaled time: 59.14 units (timescale=1.502). Factorization parameters were as follows: name: (2*10^180+43)/9 n: 232290295750883296131439774105626527875056675632797772800763276168416357472031357205659940208252291417037581678720503 skew: 9349.429688 # norm 1.71E+015 c5: 264720 c4: -9523916494 c3: -61337468606242 c2: 22676187366698402 c1: -269265682539014474973 c0: 5121980116927843701921948 #alpha -4.640000 Y1: 318706942937 Y0: -15440057987372811183991 # Murphy_E 4.66E-010 # M 69253233117561781989395062316267320386824023092863487817179644402226643072076701551648395600868986918207942320169534 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 3200001) Relations: rels:6790880, finalFF:559535 Initial matrix: 433737 x 559535 with sparse part having weight 57653840. Pruned matrix : 397949 x 400181 with weight 31074701. Total sieving time: 35.94 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.00 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000 total time: 39.38 hours. --------- CPU info (if available) ----------

Aug 29, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁶⁹-7)/9 = 9(7)_169<170> = 379 · 1277 · 4273 · 475167601 · C152
C152 = P35 · P46 · P72
P35 = 37350460755027633587644875964382999_<35>
P46 = 4409353470751458981059214537553493540306417779_<46>
P72 = 604170426485645551645435173395485943426251747190098266896590237901019043_<72>

Number: 97777_169 N=99501663567416802757943949514997808834996790510533353884050335532583489142338088177622578683020941966164588894667452416472305275977351140857946300585503 ( 152 digits) SNFS difficulty: 171 digits. Divisors found: r1=37350460755027633587644875964382999 (pp35) r2=4409353470751458981059214537553493540306417779 (pp46) r3=604170426485645551645435173395485943426251747190098266896590237901019043 (pp72) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 320.06 hours. Scaled time: 215.08 units (timescale=0.672). Factorization parameters were as follows: name: 97777_169 n: 99501663567416802757943949514997808834996790510533353884050335532583489142338088177622578683020941966164588894667452416472305275977351140857946300585503 m: 10000000000000000000000000000000000 c5: 44 c0: -35 skew: 4 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 9800001) Primes: RFBsize:412849, AFBsize:412837, largePrimes:6333893 encountered Relations: rels:6634339, finalFF:947650 Max relations in full relation-set: 28 Initial matrix: 825752 x 947650 with sparse part having weight 76425953. Pruned matrix : 730966 x 735158 with weight 59238469. Total sieving time: 278.68 hours. Total relation processing time: 1.49 hours. Matrix solve time: 39.52 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 320.06 hours. --------- CPU info (if available) ----------

Aug 28, 2006

By Wataru Sakai / GMP-ECM 6.1, GGNFS-0.77.1-20060513-pentium4 gnfs
(4·10¹⁶⁵-1)/3 = 1(3)_165<166> = 157 · 83297702222519_<14> · 31498475790963799_<17> · C133
C133 = P38 · P39 · P56
P38 = 73734584147276662658901916882345178111_<38>
P39 = 763162496562153777788361534760296511667_<39>
P56 = 57521243829208317483878443841979756256108901163271675277_<56>

Input number is 3236804907430004528606917948362126891424658553679801203805105246107656670221796513073490090353393840110682144058628658834319679302249 (133 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=93173744 Step 1 took 279290ms Step 2 took 96017ms ********** Factor found in step 2: 73734584147276662658901916882345178111 Found probable prime factor of 38 digits: 73734584147276662658901916882345178111 Composite cofactor 43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759 has 95 digits --------------------------------------------------------------- Number: template N=43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759 ( 95 digits) Divisors found: r1=763162496562153777788361534760296511667 (pp39) r2=57521243829208317483878443841979756256108901163271675277 (pp56) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 8.83 hours. Scaled time: 11.17 units (timescale=1.265). Factorization parameters were as follows: name: template n: 43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759 m: 5555252496116222501049 deg: 4 c4: 46092480 c3: -97993599572 c2: 595858358302098957 c1: -165953902866421130 c0: -851764011351318078373880 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.637 # E(F1,F2) = 3.551640e-005 # GGNFS version 0.77.1-20060513-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1156655070. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1440001) Primes: RFBsize:92938, AFBsize:93056, largePrimes:1920708 encountered Relations: rels:2025755, finalFF:251251 Max relations in full relation-set: 28 Initial matrix: 186075 x 251251 with sparse part having weight 22285816. Pruned matrix : 159264 x 160258 with weight 11995849. Total sieving time: 8.34 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.32 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 8.83 hours. --------- CPU info (if available) ----------

Aug 27, 2006

By JMB / GGNFS-0.77.1 gnfs, GGNFS-0.77.1-20050930-prescott gnfs
(19·10¹⁵²-1)/9 = 2(1)_152<153> = 59 · 67 · 179 · 211 · 209919090707_<12> · 23255047412505613_<17> · C117
C117 = P45 · P73
P45 = 103466483476477569371883659837304092315490593_<45>
P73 = 2799496547093994558129967204266584630456496784372432258039009023750741721_<73>

Number: N N=289654063232356797575174326723012494182204658797247957617870812204664068855517973508513921321914344063894921748130553 ( 117 digits) Divisors found: r1=103466483476477569371883659837304092315490593 (pp45) r2=2799496547093994558129967204266584630456496784372432258039009023750741721 (pp73) Version: GGNFS-0.77.1 Total time: 39.11 hours. Scaled time: 71.29 units (timescale=1.823). Factorization parameters were as follows: name: (19*10^152-1)/9 n: 289654063232356797575174326723012494182204658797247957617870812204664068855517973508513921321914344063894921748130553 skew: 33281.148438 # norm 1.31E+016 c5: 146760 c4: 8776090268 c3: -378888624324306 c2: 2008532010338895485 c1: 181500397538308165856108 c0: -9512360289270801960444615 #alpha -6.180000 Y1: 1353449699413 Y0: -18157414057605125091206 # Murphy_E 4.39E-010 # M 57804010562778641285000682977123609322272133912438546446115654711394932009165525472078479225981090915205914161475441 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2000000, 3600001) Relations: rels:6482955, finalFF:650007 Initial matrix: 566651 x 650007 with sparse part having weight 48490135. Pruned matrix : 527816 x 530713 with weight 30728326. Total sieving time: 35.03 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.65 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 39.11 hours. --------- CPU info (if available) ----------

(16·10¹⁶⁷-7)/9 = 1(7)_167<168> = 3² · 401 · 1129 · 731121689659444742569_<21> · 288186292597430549439121_<24> · C117
C117 = P54 · P63
P54 = 466603873318081534951944598024969453319073680131135729_<54>
P63 = 443797980480291249951903306203053836868259406908879789548246217_<63>

Number: N N=207077856662846240235313334079932768382063026764942737221802202305784699021628764915860564562697346780044408337787193 ( 117 digits) Divisors found: r1=466603873318081534951944598024969453319073680131135729 (pp54) r2=443797980480291249951903306203053836868259406908879789548246217 (pp63) Version: GGNFS-0.77.1-20050930-prescott Total time: 61.26 hours. Scaled time: 34.73 units (timescale=0.567). Factorization parameters were as follows: name: (16*10^167-7)/9 n: 207077856662846240235313334079932768382063026764942737221802202305784699021628764915860564562697346780044408337787193 skew: 15523.200195 # norm 3.87E+015 c5: 95760 c4: -22188300468 c3: -68028203400212 c2: 5340600972906269443 c1: 8989035250724614085172 c0: -50635669207311551042279145 #alpha -5.510000 Y1: 660506461483 Y0: -18492286938618375162754 # Murphy_E 4.50E-010 # M 181309531116944392876346575739884961409984050243104986523315894074131008584101572192481570234445987008852354289724910 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3450001) Primes: RFBsize:283146, AFBsize:283160, largePrimes:6597661 encountered Relations: rels:6649891, finalFF:727592 Max relations in full relation-set: 40 Initial matrix: 566388 x 727592 with sparse part having weight 60993166. Pruned matrix : 431545 x 434440 with weight 33848319. Total sieving time: 55.21 hours. Total relation processing time: 0.47 hours. Matrix solve time: 4.84 hours. Time per square root: 0.74 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 61.26 hours. --------- CPU info (if available) ----------

Aug 24, 2006

By Bruce Dodson / GMP-ECM
10³⁸¹+1 = 1(0)₃₈₀1_<382> = 7 · 11 · 13 · 2287 · 3557 · 857772733 · 1094479651_<10> · 1125629957_<10> · 451897625287_<12> · 616896149073719728613_<21> · 10860110813777339731289_<23> · 1053449334720579590200819_<25> · 36099531273603138218699301565567581705151216702113889_<53> · C214
C214 = P67 · P147
P67 = 4444349792156709907895752551798631908946180608768737946280238078881_<67>
P147 = 227106988265159616528571981140572415396122551755756282296008613353922816015404819504625289055134338407924996143023758066472872886277706507970899321_<147>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 22, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(85·10¹⁵²+41)/9 = 9(4)₁₅₁9_<153> = 13 · 197 · 647467307 · 47985896085289799139356507_<26> · C116
C116 = P45 · P71
P45 = 170725642594225454451474174348792505239958339_<45>
P71 = 69524300558461150094284117980194046531241851609895069471577519549231219_<71>

Number: N N=11869580888757347476677473220519036107142951936630492926951713697053493324085561964441889112990282999987147038185241 ( 116 digits) Divisors found: r1=170725642594225454451474174348792505239958339 (pp45) r2=69524300558461150094284117980194046531241851609895069471577519549231219 (pp71) Version: GGNFS-0.77.1-20050930-prescott Total time: 57.90 hours. Scaled time: 37.86 units (timescale=0.654). Factorization parameters were as follows: name: N n: 11869580888757347476677473220519036107142951936630492926951713697053493324085561964441889112990282999987147038185241 skew: 77179.72 # norm 1.06e+16 c5: 28500 c4: -1605905960 c3: -548908396432052 c2: 7781721018062958274 c1: 1362966716976629355637771 c0: 710581451553397893524894505 # alpha -6.08 Y1: 652928892803 Y0: -13302042930398130801026 # Murphy_E 4.80e-10 # M 8449198108053675294351358438215934681689131985295566294009697841106082365994216984520945583606473255174825235480823 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3500001) Primes: RFBsize:283146, AFBsize:283339, largePrimes:6781742 encountered Relations: rels:7035319, finalFF:894776 Max relations in full relation-set: 40 Initial matrix: 566568 x 894776 with sparse part having weight 74170174. Pruned matrix : 326506 x 329402 with weight 45123261. Total sieving time: 53.51 hours. Total relation processing time: 0.41 hours. Matrix solve time: 3.47 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 57.90 hours. --------- CPU info (if available) ----------

Aug 20, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(82·10¹⁷³-1)/9 = 9(1)_173<174> = 17 · 31 · 19429 · 19681 · 446657 · 2013294557_<10> · 78950206397_<11> · 1126772355818365857299_<22> · C116
C116 = P49 · P68
P49 = 1571702898001461970102304550267406109116965542297_<49>
P68 = 35960170890831727400644102888162433825269692846803398137464594472023_<68>

Number: N N=56518704801748040280654501946968595175553050255691308769059931493973136174743292493725036143767525833564358589656831 ( 116 digits) Divisors found: r1=1571702898001461970102304550267406109116965542297 (pp49) r2=35960170890831727400644102888162433825269692846803398137464594472023 (pp68) Version: GGNFS-0.77.1-20050930-prescott Total time: 62.22 hours. Scaled time: 40.32 units (timescale=0.648). Factorization parameters were as follows: name: N n: 56518704801748040280654501946968595175553050255691308769059931493973136174743292493725036143767525833564358589656831 skew: 50027.61 # norm 2.07e+16 c5: 31200 c4: -147363988 c3: -781844286702183 c2: 2754728581108013796 c1: 352679167912523767114844 c0: -2293971195865843122762610752 # alpha -5.89 Y1: 1067130078613 Y0: -17848739285818037536723 # Murphy_E 4.47e-10 # M 48101014183249661044274227258519366403604948342237387695100379056370372856318552282656444115075891531416884556421210 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3450001) Primes: RFBsize:283146, AFBsize:282427, largePrimes:6542520 encountered Relations: rels:6563316, finalFF:702600 Max relations in full relation-set: 40 Initial matrix: 565654 x 702600 with sparse part having weight 57603385. Pruned matrix : 450451 x 453343 with weight 32528559. Total sieving time: 56.51 hours. Total relation processing time: 0.52 hours. Matrix solve time: 4.62 hours. Time per square root: 0.57 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 62.22 hours. --------- CPU info (if available) ----------

Aug 19, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(64·10¹⁶⁴+53)/9 = 7(1)₁₆₃7_<165> = 3 · 53503 · 940054483999_<12> · 48314243429010383503977289365067_<32> · C116
C116 = P43 · P74
P43 = 1236425327944059453891143340199750359794291_<43>
P74 = 78893636386011202413634291580709861715696520613238084327309376292733676671_<74>

Number: N N=97546090241273282452005139478114991165570138671605243661933236313861034028750412443788439979037553951353899665685261 ( 116 digits) Divisors found: r1=1236425327944059453891143340199750359794291 (pp43) r2=78893636386011202413634291580709861715696520613238084327309376292733676671 (pp74) Version: GGNFS-0.77.1-20050930-prescott Total time: 70.33 hours. Scaled time: 45.79 units (timescale=0.651). Factorization parameters were as follows: name: N n: 97546090241273282452005139478114991165570138671605243661933236313861034028750412443788439979037553951353899665685261 skew: 80764.59 # norm 5.65e+15 c5: 8340 c4: -2213261435 c3: -160091135790358 c2: 12519422774154137710 c1: 589488626580099139001148 c0: -2075649157121883264460470960 # alpha -5.35 Y1: 329529074237 Y0: -25918451818514317799591 # Murphy_E 4.36e-10 # M 27211831738470055975133877654146693096996886542471751876593738751162646426142430179529429567875903904370129517859170 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3750001) Primes: RFBsize:283146, AFBsize:284148, largePrimes:6627799 encountered Relations: rels:6697658, finalFF:733495 Max relations in full relation-set: 40 Initial matrix: 567373 x 733495 with sparse part having weight 64372911. Pruned matrix : 434499 x 437399 with weight 36901761. Total sieving time: 64.04 hours. Total relation processing time: 0.42 hours. Matrix solve time: 4.65 hours. Time per square root: 1.22 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 70.33 hours. --------- CPU info (if available) ----------

Aug 18, 2006

By Yousuke Koide / GMP-ECM
10⁷⁴⁹+1 = 1(0)₇₄₈1_<750> = 11 · 1499 · 28463 · 32957 · 74687 · 392263 · 795653 · 909091 · 280267614929_<12> · 194749234429526109677_<21> · 75477148962003664034473049_<26> · 9140689231828972552925524522037823147045937571379494322686226282352288670801988451_<82> · C574
C574 = P33 · C542
P33 = 628293465283949443537007319053023_<33>
C542 = [12894908452100944414773295073237073300097153241069055774583676737987242414978167908170745727915227967124884330106729412910004744110688873186180052252315852704258881528632513902371451144536293287065361925405261134609289404751378279953125297836822595137476253746855502501879820915343255108864259910503445366286746174398958106605930707640542374737365384945958881525381230321897275240619255078705928789062325522127169718285243629639148526956551496372360311580957215245892505084246451683751602241720569665488251213588481612988433384522783514936053_<542>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 17, 2006

By JMB / GGNFS-0.77.1 gnfs
(68·10¹⁷⁶+13)/9 = 7(5)₁₇₅7_<177> = 16223 · 17119019860271735061587461_<26> · 619193651836871434301224119229241_<33> · C115
C115 = P57 · P58
P57 = 548948053972127355988942710985004349672426023173799306821_<57>
P58 = 8003843611567193197494230112384504996406675622815584431179_<58>

Number: N N=4393694374867054312301107826304771911374972036279600016021736599645847049491465120275629018011759197571909779771959 ( 115 digits) Divisors found: r1=548948053972127355988942710985004349672426023173799306821 (pp57) r2=8003843611567193197494230112384504996406675622815584431179 (pp58) Version: GGNFS-0.77.1 Total time: 32.28 hours. Scaled time: 58.21 units (timescale=1.803). Factorization parameters were as follows: name: N n: 4393694374867054312301107826304771911374972036279600016021736599645847049491465120275629018011759197571909779771959 skew: 53771.14 # norm 3.67e+15 c5: 14820 c4: 2364063772 c3: -125507969059803 c2: -6212088143643651894 c1: 142181987154929592317020 c0: 4332116672479151476518939000 # alpha -6.03 Y1: 1352439577637 Y0: -12427816160811681721229 # Murphy_E 6.10e-10 # M 1802485709720975932650912060256348315066217203872719209037178881701464471070355288236397841569812479480893529323810 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2800001) Relations: rels:5518218, finalFF:548008 Initial matrix: 434577 x 548008 with sparse part having weight 43296502. Pruned matrix : 392771 x 395007 with weight 22476050. Total sieving time: 30.00 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.94 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000 total time: 32.28 hours. --------- CPU info (if available) ----------

Aug 15, 2006 (4th)

By JMB / GGNFS-0.77.1-20050930-prescott gnfs, GGNFS-0.77.1 gnfs
(5·10¹⁷⁵-41)/9 = (5)₁₇₄1_<175> = 489133 · 1403517697_<10> · 2435964161_<10> · 64249247182044594022865768916254657_<35> · C116
C116 = P53 · P64
P53 = 11432280413830847705222617918639919503658191618454389_<53>
P64 = 4522835909054636966935411318813189352741986783000127616479400367_<64>

Number: N N=51706328378056163380057929616176601960754010322432217032605771561958673172388892161904595921026362579749982059360763 ( 116 digits) Divisors found: r1=11432280413830847705222617918639919503658191618454389 (pp53) r2=4522835909054636966935411318813189352741986783000127616479400367 (pp64) Version: GGNFS-0.77.1-20050930-prescott Total time: 67.22 hours. Scaled time: 43.82 units (timescale=0.652). Factorization parameters were as follows: name: N n: 51706328378056163380057929616176601960754010322432217032605771561958673172388892161904595921026362579749982059360763 skew: 48471.32 # norm 3.13e+16 c5: 62640 c4: -25535682078 c3: -506576515487491 c2: 39285307741783792721 c1: 883264678769304412824603 c0: -5539902059876483682909070875 # alpha -7.01 Y1: 1235812731637 Y0: -15252507920133843820594 # Murphy_E 4.57e-10 # M 29043992165356704836730301334734947366103788037605666308576012135096877153525389509722854916494244119203075603669450 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3450001) Primes: RFBsize:283146, AFBsize:284128, largePrimes:6820518 encountered Relations: rels:7099104, finalFF:911668 Max relations in full relation-set: 40 Initial matrix: 567353 x 911668 with sparse part having weight 77857218. Pruned matrix : 328657 x 331557 with weight 50217778. Total sieving time: 62.74 hours. Total relation processing time: 0.48 hours. Matrix solve time: 3.46 hours. Time per square root: 0.54 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 67.22 hours. --------- CPU info (if available) ----------

(5·10¹⁷¹-41)/9 = (5)₁₇₀1_<171> = 29 · 31 · 720497 · 1160893 · 1389257819416175659_<19> · 30759678135525993098827_<23> · C116
C116 = P49 · P68
P49 = 1136655398395752973921842937526529232079565032873_<49>
P68 = 15210727229336895157226227619434966245190813056156538561963023879721_<68>

Number: N N=17289355218751056377545280878875714628143017402531836624568896246743444355039258118995609342080638646672485363068433 ( 116 digits) Divisors found: r1=1136655398395752973921842937526529232079565032873 (pp49) r2=15210727229336895157226227619434966245190813056156538561963023879721 (pp68) Version: GGNFS-0.77.1 Total time: 34.84 hours. Scaled time: 63.17 units (timescale=1.813). Factorization parameters were as follows: name: N n: 17289355218751056377545280878875714628143017402531836624568896246743444355039258118995609342080638646672485363068433 skew: 41329.98 # norm 1.43e+16 c5: 45360 c4: 17199219306 c3: -361286661039353 c2: -30330523569186455797 c1: 147135491563252297346847 c0: 2812009785225248206216779777 # alpha -6.81 Y1: 3459577597769 Y0: -13068099480518898224536 # Murphy_E 5.16e-10 # M 2825033727445633616920687394495604557664583264776442097248695246583418859121758722048738749391100367416691389534089 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2000000, 3400001) Relations: rels:6519610, finalFF:684370 Initial matrix: 566316 x 684370 with sparse part having weight 52581928. Pruned matrix : 512474 x 515369 with weight 28888924. Total sieving time: 31.34 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.08 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 34.84 hours. --------- CPU info (if available) ----------

Aug 15, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁶⁸-7)/9 = 9(7)_168<169> = 3 · 3047423 · 16256750647861_<14> · C149
C149 = P55 · P95
P55 = 1161650092196977606911825290197250998288654336989039493_<55>
P95 = 56633981075298388052167979569831042502150003956481301205335843212489749948759816365886195227421_<95>

Number: 97777_168 N=65788869337602257470354512709932976498964658419801366922367938905952098946499946563937605731014460005019249788707206813716626708384762770883485537553 ( 149 digits) SNFS difficulty: 169 digits. Divisors found: r1=1161650092196977606911825290197250998288654336989039493 (pp55) r2=56633981075298388052167979569831042502150003956481301205335843212489749948759816365886195227421 (pp95) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 307.87 hours. Scaled time: 207.19 units (timescale=0.673). Factorization parameters were as follows: name: 97777_168 n: 65788869337602257470354512709932976498964658419801366922367938905952098946499946563937605731014460005019249788707206813716626708384762770883485537553 m: 2000000000000000000000000000000000 c5: 2750 c0: -7 skew: 3 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 9400001) Primes: RFBsize:412849, AFBsize:412242, largePrimes:6265476 encountered Relations: rels:6545172, finalFF:932138 Max relations in full relation-set: 28 Initial matrix: 825158 x 932138 with sparse part having weight 72124302. Pruned matrix : 741740 x 745929 with weight 55940787. Total sieving time: 267.84 hours. Total relation processing time: 1.59 hours. Matrix solve time: 38.06 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 307.87 hours. --------- CPU info (if available) ----------

Aug 15, 2006 (2nd)

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4
(2·10¹⁵⁸+7)/9 = (2)₁₅₇3_<158> = 191 · C156
C156 = P36 · P120
P36 = 131762990689564553924901894505812253_<36>
P120 = 882999942521541802647808796269686171357208978670046129416456874646530567606892048042407142275493669636303904492109195301_<120>

Number: test N=116346713205351948807446189645142524723676556137289121582315299592786503781268179173938336242001163467132053519488074461896451425247236765561372891215823153 ( 156 digits) SNFS difficulty: 158 digits. Divisors found: r1=131762990689564553924901894505812253 (pp36) r2=882999942521541802647808796269686171357208978670046129416456874646530567606892048042407142275493669636303904492109195301 (pp120) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 60.11 hours. Scaled time: 76.03 units (timescale=1.265). Factorization parameters were as follows: n: 116346713205351948807446189645142524723676556137289121582315299592786503781268179173938336242001163467132053519488074461896451425247236765561372891215823153 m: 20000000000000000000000000000000 c5: 125 c0: 14 skew: 1 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3800001) Primes: RFBsize:283146, AFBsize:283727, largePrimes:5772505 encountered Relations: rels:5857015, finalFF:699322 Max relations in full relation-set: 28 Initial matrix: 566938 x 699322 with sparse part having weight 46601840. Pruned matrix : 465701 x 468599 with weight 31108907. Total sieving time: 54.10 hours. Total relation processing time: 0.29 hours. Matrix solve time: 5.54 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 60.11 hours. --------- CPU info (if available) ----------

Aug 15, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10¹⁶³-1)/3 = 1(3)_163<164> = 13 · 1617029653_<10> · C153
C153 = P28 · C126
P28 = 4089127132463729329999260241_<28>
C126 = [155112496265691502702356326760306526844120861180050281869646762856380657373483770708019727853353298989247112858037210723680117_<126>]

Aug 14, 2006 (2nd)

By Bruce Dodson / GMP-ECM
10³²⁸+1 = 1(0)₃₂₇1_<329> = 17 · 5882353 · 6051298241_<10> · 48656086054529_<14> · 669995415570582921859463287135169_<33> · C264
C264 = P56 · C209
P56 = 18798124481332409484502894235050519095834690259132073729_<56>
C209 = [26966706888061228309314861584452783093449979584971248841728716375604431259788120714089993744450304753814274573818260830964443146927438209553380971499989034253234857050497492661619432197590261828134053458180609_<209>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 14, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(10¹⁷²+71)/9 = (1)₁₇₁9_<172> = 3² · 4391 · 4919 · 6337 · 503573969713352179_<18> · 4894102405193232341523799_<25> · C117
C117 = P50 · P68
P50 = 15441280903831977725272445863464931495519706268391_<50>
P68 = 23701256234827907885716605563878213283252164799721868829312661738797_<68>

Number: N N=365977755295676774775510425752865543407563187811110276370278426136480960683749215044820881215418051861192830419465627 ( 117 digits) Divisors found: r1=15441280903831977725272445863464931495519706268391 (pp50) r2=23701256234827907885716605563878213283252164799721868829312661738797 (pp68) Version: GGNFS-0.77.1-20050930-prescott Total time: 63.00 hours. Scaled time: 40.44 units (timescale=0.642). Factorization parameters were as follows: name: N n: 365977755295676774775510425752865543407563187811110276370278426136480960683749215044820881215418051861192830419465627 skew: 46221.68 # norm 2.11e+15 c5: 8880 c4: 800381912 c3: 48637968167417 c2: -2591345113024835856 c1: -66628290509630989647114 c0: 676846138220199379674969111 # alpha -4.77 Y1: 3658631464037 Y0: -33343215984948588542900 # Murphy_E 4.21e-10 # M 132425972767365485666788243273465066850953504834744825058251254902605105935877722859492830520304156857092881157938327 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3550001) Primes: RFBsize:283146, AFBsize:282237, largePrimes:6531912 encountered Relations: rels:6522365, finalFF:676176 Max relations in full relation-set: 40 Initial matrix: 565464 x 676176 with sparse part having weight 55755486. Pruned matrix : 474048 x 476939 with weight 33468131. Total sieving time: 57.16 hours. Total relation processing time: 0.41 hours. Matrix solve time: 4.88 hours. Time per square root: 0.55 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 63.00 hours. --------- CPU info (if available) ----------

Aug 13, 2006 (2nd)

By JMB / GGNFS-0.77.1 gnfs
(5·10¹⁵⁸-17)/3 = 1(6)₁₅₇1_<159> = 7² · 227 · 587117 · 28302487 · 4405758911640887447737379_<25> · C117
C117 = P50 · P67
P50 = 67621902109110330371869937121494348175237496572533_<50>
P67 = 3026700483864348901223166729369813676797114347757361309491810095819_<67>

Number: N N=204671243833471872423458363170935132549848443077825215001952886645519860774092659259664652641538107318116138813539527 ( 117 digits) Divisors found: r1=67621902109110330371869937121494348175237496572533 (pp50) r2=3026700483864348901223166729369813676797114347757361309491810095819 (pp67) Version: GGNFS-0.77.1 Total time: 41.48 hours. Scaled time: 75.41 units (timescale=1.818). Factorization parameters were as follows: name: N n: 204671243833471872423458363170935132549848443077825215001952886645519860774092659259664652641538107318116138813539527 skew: 40873.77 # norm 5.27e+15 c5: 29340 c4: 1476685827 c3: -284808719427086 c2: -1625016887507574014 c1: 139298769983634584929104 c0: -300252010840174442528395056 # alpha -5.13 Y1: 456887006213 Y0: -23373258294493079571857 # Murphy_E 4.33e-10 # M 69218691873820054618000039397568631155747605271065307352011942265970179923676763177576565812296351208189263969084310 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2000000, 3680001) Relations: rels:6458002, finalFF:634911 Initial matrix: 565919 x 634911 with sparse part having weight 48642764. Pruned matrix : 533302 x 536195 with weight 32985209. Total sieving time: 37.05 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.99 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,60000 total time: 41.48 hours. --------- CPU info (if available) ----------

Aug 13, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10¹⁷⁷-1)/3 = 1(3)_177<178> = 4409 · 22961 · C170
C170 = P29 · C141
P29 = 43665368763292497076610163467_<29>
C141 = [301627341967929378435673111291397900932534777570343251996445617288863617272291852009571123885313428683074596057961228788786605535514717262151_<141>]

Aug 12, 2006

By JMB / Msieve v. 2.04
(34·10¹⁵⁵-43)/9 = 3(7)₁₅₄3_<156> = 11 · 520702915570613_<15> · 5555018987718121828955407_<25> · 4441619662273433601989908731614767_<34> · C82
C82 = P35 · P47
P35 = 35949300598985833824141852183554201_<35>
P47 = 74359481489915926639112034917743709079659453219_<47>

Msieve v. 2.04 Fri Aug 11 07:21:22 2006 random seeds: 16034e40 0065c729 factoring 2673171352465710644495563497271882852656939209210070623777550975107357 875710423019 (82 digits) using multiplier of 1 using sieve block of 65536 using a sieve bound of 1508867 (57131 primes) using large prime bound of 15088670 (23 bits) prp35 factor: 35949300598985833824141852183554201 prp47 factor: 74359481489915926639112034917743709079659453219 elapsed time 01:12:29

Aug 11, 2006 (2nd)

By JMB / GMP-ECM 6.0.1 B1=11000000
(34·10¹⁵⁵-43)/9 = 3(7)₁₅₄3_<156> = 11 · 520702915570613_<15> · 5555018987718121828955407_<25> · C116
C116 = P34 · C82
P34 = 4441619662273433601989908731614767_<34>
C82 = [2673171352465710644495563497271882852656939209210070623777550975107357875710423019_<82>]

Aug 11, 2006

By JMB / GMP-ECM 6.0.1 B1=11000000
10¹⁷¹+9 = 1(0)₁₇₀9_<172> = 114870713498291_<15> · 152103797335211_<15> · 1077903296318851813591058561693_<31> · C113
C113 = P39 · P75
P39 = 119386461467535400538961423925754434819_<39>
P75 = 444749782753570053864318452769186104647351235367140088183461389738755377327_<75>

Aug 10, 2006

By JMB / GMP-ECM 6.0.1 B1=11000000
(28·10¹⁶²+17)/9 = 3(1)₁₆₁3_<163> = 196961 · 76407693552855061_<17> · 615007859440361597069371583_<27> · C114
C114 = P35 · P80
P35 = 14985999353401319166603348866934571_<35>
P80 = 22430131294455821462057713883010980947736349572806097941827659523032229508329521_<80>

Aug 9, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs
10¹⁶²+9 = 1(0)₁₆₁9_<163> = 5573 · 735595652772776933_<18> · C141
C141 = P32 · P47 · P63
P32 = 44574910306875039119713293503029_<32>
P47 = 15796214831501458885442791692067196909108663273_<47>
P63 = 346440210180306140299079585071546545979928246632083029744358053_<63>

Number: template N=5472443986278634559182270530295372853227297441893538310967286061401558754596631170156064966170636476322887469 ( 109 digits) Divisors found: r1=15796214831501458885442791692067196909108663273 (pp47) r2=346440210180306140299079585071546545979928246632083029744358053 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 23.20 hours. Scaled time: 29.24 units (timescale=1.260). Factorization parameters were as follows: name: template n: 5472443986278634559182270530295372853227297441893538310967286061401558754596631170156064966170636476322887469 skew: 11018.09 # norm 3.20e+014 c5: 15000 c4: 2049539905 c3: -16085797091712 c2: -213274340734910712 c1: 131380839582017791300 c0: -170902177794463511226600 # alpha -4.86 Y1: 62487254993 Y0: -817367011602365383949 # Murphy_E 1.12e-009 # M 5004784583434845831078841956713121671236324974689500294609609848605805097246009678817654938417451410693748427 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 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2900001) Primes: RFBsize:230209, AFBsize:230832, largePrimes:7319197 encountered Relations: rels:7139177, finalFF:579821 Max relations in full relation-set: 28 Initial matrix: 461116 x 579821 with sparse part having weight 43420824. Pruned matrix : 363223 x 365592 with weight 24332046. Polynomial selection time: 1.35 hours. Total sieving time: 18.27 hours. Total relation processing time: 0.42 hours. Matrix solve time: 2.90 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 23.20 hours. --------- CPU info (if available) ----------

Aug 9, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(4·10¹⁶⁶-31)/9 = (4)₁₆₅1_<166> = 43 · 421 · 11489 · 13063 · 219281 · 2114323 · 1401498638512800602338683574933_<31> · C112
C112 = P44 · P68
P44 = 73852723653066632145630012304772718105985831_<44>
P68 = 34088684369438135938395966419974474187769342866960086047456527452129_<68>

Number: (4·10166-31)/9 C112 N=2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199 ( 112 digits) Divisors found: r1=73852723653066632145630012304772718105985831 (pp44) r2=34088684369438135938395966419974474187769342866960086047456527452129 (pp68) Version: GGNFS-0.77.1-20050930-prescott Total time: 32.53 hours. Scaled time: 19.81 units (timescale=0.609). Factorization parameters were as follows: name: (4·10166-31)/9 C112 n: 2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199 skew: 20807.37 # norm 5.54e+15 c5: 38400 c4: -5696422944 c3: -270524084185390 c2: 2834749926957496277 c1: 13883696403005631212110 c0: -33266943953232428779977728 # alpha -6.34 Y1: 673389653299 Y0: -2308515873579294509673 # Murphy_E 8.40e-10 # M 1689938327551674534910204802217113629727040156762154475652360671688288051808192850060885510573294732167029196891 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2450001) Primes: RFBsize:216816, AFBsize:216527, largePrimes:5456723 encountered Relations: rels:5350941, finalFF:537741 Max relations in full relation-set: 40 Initial matrix: 433419 x 537741 with sparse part having weight 40511458. Pruned matrix : 345227 x 347458 with weight 21610858. Total sieving time: 28.65 hours. Total relation processing time: 0.48 hours. Matrix solve time: 3.03 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000 total time: 32.53 hours. --------- CPU info (if available) ---------- 3.2ghz P4, 2gb DDR, 7200 RPM IDE

Aug 7, 2006

Daniel Heuer found the largest known near-repdigit prime number 3·10¹¹⁹²⁹²-1 = 2(9)_{119292<119293>}. Congratulations!
References:

• The Top Twenty: Near-repdigit (Chris K. Caldwell)
• The Prime Database: 3*10^119292-1 (Chris K. Caldwell)

Aug 6, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4
(19·10¹⁶⁷-1)/9 = 2(1)_167<168> = 48761 · 7783163 · C156
C156 = P52 · P104
P52 = 9213779069369765001437791549262278092034656923926957_<52>
P104 = 60373251713664375579895563454106435402505689903757733131520095501842512209171123875885660397963312420961_<104>

Number: 21111_167 N=556265802989153120515703738711098287930938971259492519112654427574545887025752040989524841887031236074654193034645440519108902890194259867325067154799745677 ( 156 digits) SNFS difficulty: 168 digits. Divisors found: r1=9213779069369765001437791549262278092034656923926957 (pp52) r2=60373251713664375579895563454106435402505689903757733131520095501842512209171123875885660397963312420961 (pp104) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 247.08 hours. Scaled time: 150.72 units (timescale=0.610). Factorization parameters were as follows: n: 556265802989153120515703738711098287930938971259492519112654427574545887025752040989524841887031236074654193034645440519108902890194259867325067154799745677 m: 1000000000000000000000000000000000 c5: 1900 c0: -1 skew: 1 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2750000, 7850001) Primes: RFBsize:380800, AFBsize:380927, largePrimes:6183340 encountered Relations: rels:6431532, finalFF:886589 Max relations in full relation-set: 28 Initial matrix: 761794 x 886589 with sparse part having weight 68124049. Pruned matrix : 666101 x 669973 with weight 51560289. Total sieving time: 209.69 hours. Total relation processing time: 3.21 hours. Matrix solve time: 33.74 hours. Time per square root: 0.44 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 247.08 hours. --------- CPU info (if available) ----------

Aug 6, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(22·10¹⁶³-1)/3 = 7(3)_163<164> = 197 · 84948082135073744830961689889_<29> · C133
C133 = P31 · P102
P31 = 5766978834890632029154858016207_<31>
P102 = 759859441556857392031887053491686419668387447209216643623736091892709102130571496823704046528074412543_<102>

Aug 5, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000, Msieve v. 1.07, GGNFS-0.77.1-20060513-pentium4 gnfs
(8·10¹⁸¹+1)/9 = (8)₁₈₀9_<181> = 3² · 162703 · 436529 · 198685966079416987465648073668331204609_<39> · C131
C131 = P33 · P39 · P60
P33 = 542441679016241624644644490188229_<33>
P39 = 496477762884048622818601277837137881409_<39>
P60 = 259882036616767224751131892084058161800893633111811279277667_<60>

Wed Aug 02 23:25:50 2006 Msieve v. 1.07 Wed Aug 02 23:25:50 2006 random seeds: e7b26820 9874fbc3 Wed Aug 02 23:25:50 2006 factoring 129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803 (99 digits) Wed Aug 02 23:25:51 2006 using multiplier of 35 Wed Aug 02 23:25:51 2006 sieve interval: 9 blocks of size 65536 Wed Aug 02 23:25:51 2006 processing polynomials in batches of 6 Wed Aug 02 23:25:51 2006 using a sieve bound of 2542933 (92576 primes) Wed Aug 02 23:25:51 2006 using large prime bound of 381439950 (28 bits) Wed Aug 02 23:25:51 2006 using double large prime bound of 2796192470588850 (43-52 bits) Wed Aug 02 23:25:51 2006 using trial factoring cutoff of 57 bits Wed Aug 02 23:25:51 2006 polynomial 'A' values have 13 factors Thu Aug 03 10:52:49 2006 93021 relations (22595 full + 70426 combined from 1375827 partial), need 92672 Thu Aug 03 10:52:51 2006 begin with 1375827 relations Thu Aug 03 10:52:52 2006 reduce to 219529 relations in 11 passes Thu Aug 03 10:52:52 2006 attempting to read 22595 full and 219529 partial relations Thu Aug 03 10:52:57 2006 recovered 22595 full and 219529 partial relations Thu Aug 03 10:52:57 2006 recovered 231943 polynomials Thu Aug 03 10:52:57 2006 attempting to build 70426 cycles Thu Aug 03 10:52:57 2006 found 70426 cycles in 5 passes Thu Aug 03 10:52:58 2006 distribution of cycle lengths: Thu Aug 03 10:52:58 2006 length 2 : 16312 Thu Aug 03 10:52:58 2006 length 3 : 15721 Thu Aug 03 10:52:58 2006 length 4 : 12700 Thu Aug 03 10:52:58 2006 length 5 : 9570 Thu Aug 03 10:52:58 2006 length 6 : 6390 Thu Aug 03 10:52:58 2006 length 7 : 3981 Thu Aug 03 10:52:58 2006 length 8 : 2563 Thu Aug 03 10:52:58 2006 length 9+: 3189 Thu Aug 03 10:52:58 2006 largest cycle: 21 relations Thu Aug 03 10:52:58 2006 92576 x 92640 system, weight 5982638 (avg 64.58/col) Thu Aug 03 10:52:58 2006 reduce to 91077 x 91141 in 3 passes Thu Aug 03 10:55:46 2006 lanczos halted after 1442 iterations Thu Aug 03 10:55:46 2006 recovered 63 nontrivial dependencies Thu Aug 03 10:56:18 2006 prp39 factor: 496477762884048622818601277837137881409 Thu Aug 03 10:56:18 2006 prp60 factor: 259882036616767224751131892084058161800893633111811279277667 Thu Aug 03 10:56:18 2006 elapsed time 11:30:28

Number: template N=129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803 ( 99 digits) Divisors found: r1=496477762884048622818601277837137881409 (pp39) r2=259882036616767224751131892084058161800893633111811279277667 (pp60) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.16 hours. Scaled time: 7.73 units (timescale=1.254). Factorization parameters were as follows: name: template n: 129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803 skew: 9546.64 # norm 5.82e+013 c5: 25440 c4: 327356204 c3: -2756380090446 c2: -26695770066661670 c1: 13726476804124437779 c0: 730114543638448319289596 # alpha -6.09 Y1: 10835548823 Y0: -5508452295331048625 # Murphy_E 4.07e-009 # M 43647947722120531491045537206099770873096300206510332994071869368876871426009741108841708977697337 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1300001) Primes: RFBsize:135072, AFBsize:135627, largePrimes:3897401 encountered Relations: rels:3987587, finalFF:468705 Max relations in full relation-set: 28 Initial matrix: 270777 x 468705 with sparse part having weight 31420460. Pruned matrix : 135986 x 137403 with weight 11779890. Polynomial selection time: 0.45 hours. Total sieving time: 5.17 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.27 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 6.16 hours. --------- CPU info (if available) ----------

Aug 5, 2006

By Yousuke Koide / GMP-ECM
10⁶³¹+1 = 1(0)₆₃₀1_<632> = 11 · 111478771 · 7144726022423651_<16> · 25275592878679576093_<20> · 324340568278356513982411_<24> · C564
C564 = P33 · C531
P33 = 215007779702918011813855565694983_<33>
C531 = [647549189090766885539933216048953381766282962756191273299208190433157850091993991879210354251404437260181512652894093774881642980661569572938361554582904065808145062221178935594264088903446558313933923951452627617040506754385034509397492029650065938555770272362685341300381208344171606718543565358130740121026865773917747329408645838090080628394617515583502194446165611330220785781361533250749575952629581355453371379965611509754045286244674853219793092966102089424772461223062153805403748147135382956547785370167119053568537747219_<531>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 4, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs, GMP-ECM 6.0.1
(61·10¹⁷⁰-7)/9 = 6(7)_170<171> = 89 · 59149 · 73106034559740600637_<20> · 455443373077175325700179430733987_<33> · C112
C112 = P54 · P59
P54 = 259634246889555898861112235610888816344185272851756101_<54>
P59 = 14893621763832231129772178482053300115800386287663092493903_<59>

Number: N N=3866894270110480495299331929349939555976910470220605286134629327779460046947883016645268141896942460825185552203 ( 112 digits) Divisors found: r1=259634246889555898861112235610888816344185272851756101 (pp54) r2=14893621763832231129772178482053300115800386287663092493903 (pp59) Version: GGNFS-0.77.1-20050930-prescott Total time: 38.99 hours. Scaled time: 25.62 units (timescale=0.657). Factorization parameters were as follows: name: N n: 3866894270110480495299331929349939555976910470220605286134629327779460046947883016645268141896942460825185552203 skew: 40962.73 # norm 5.21e+15 c5: 17400 c4: -239661230 c3: -193594578520121 c2: 459645264047848230 c1: 12630770380130446786544 c0: -185397841779260423540488128 # alpha -6.15 Y1: 526615703819 Y0: -2946882526904680098125 # Murphy_E 7.99e-10 # M 906621222046150642737111880646727832873613351095034764872743174328229588823611973950586077300151454670273150662 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2400001) Primes: RFBsize:216816, AFBsize:216754, largePrimes:5420312 encountered Relations: rels:5291749, finalFF:520517 Max relations in full relation-set: 40 Initial matrix: 433648 x 520517 with sparse part having weight 36906463. Pruned matrix : 359939 x 362171 with weight 20487459. Total sieving time: 36.43 hours. Total relation processing time: 0.27 hours. Matrix solve time: 1.93 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000 total time: 38.99 hours. --------- CPU info (if available) ----------

(86·10¹⁹²+31)/9 = 9(5)₁₉₁9_<193> = 13 · 79801 · 113754799183_<12> · 1840989671002883_<16> · 64478288440428854599_<20> · 477664605616311721510870585903_<30> · C112
C112 = P48 · P64
P48 = 544743413352596587064461975415669241172263459607_<48>
P64 = 2621528754462436339398526557224274787788408344875291572559019753_<64>

Aug 2, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10¹⁶⁷-7)/9 = 9(7)_167<168> = 547 · 255917 · 62987719 · 168095479 · C144
C144 = P36 · P109
P36 = 173057865665730828088779240795479581_<36>
P109 = 3811978501475933954155211857611104093457904408402378553499026213538586627283954077584331779888287710077425683_<109>

Number: 97777_167 N=659692863429076083431306133363648261064622208616886952777689858266262337273979785875087842161434570070362767114570543284589051713060979871478823 ( 144 digits) SNFS difficulty: 168 digits. Divisors found: r1=173057865665730828088779240795479581 (pp36) r2=3811978501475933954155211857611104093457904408402378553499026213538586627283954077584331779888287710077425683 (pp109) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 237.31 hours. Scaled time: 144.52 units (timescale=0.609). Factorization parameters were as follows: name: 97777_167 n: 659692863429076083431306133363648261064622208616886952777689858266262337273979785875087842161434570070362767114570543284589051713060979871478823 m: 2000000000000000000000000000000000 c5: 275 c0: -7 skew: 3 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2750000, 7750001) Primes: RFBsize:380800, AFBsize:381318, largePrimes:6147199 encountered Relations: rels:6384742, finalFF:880495 Max relations in full relation-set: 28 Initial matrix: 762184 x 880495 with sparse part having weight 65754152. Pruned matrix : 670303 x 674177 with weight 49760472. Total sieving time: 206.57 hours. Total relation processing time: 1.11 hours. Matrix solve time: 29.28 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 237.31 hours. --------- CPU info (if available) ----------