News and updates, September 2008

Since June 16, 2000

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News and updates, September 2008	2008-10-01(Wed) 23:15

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News and updates, September 2008

Sep 30, 2008 (4th): By Justin Card / ggnfs/msieve 1.38
(10¹⁸¹+17)/9 = (1)₁₈₀3_<181> = 3 · 157 · 1217 · 158606909 · 387812569 · 1081691731937760857100887471929643_<34> · C125
C125 = P46 · P79
P46 = 7385184232314750943068830580286922326162032853_<46>
P79 = 3944910724671705496959005657530034323166977886486088453196723251979037296752101_<79>

Number: 11113_181 N=29133892481734837183602135697334988973490703807163310757974571749978078052900604926957726939876253751243046373693076558774153 ( 125 digits) Divisors found: r1=7385184232314750943068830580286922326162032853 r2=3944910724671705496959005657530034323166977886486088453196723251979037296752101 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.096). Factorization parameters were as follows: name: 11113_181 n: 29133892481734837183602135697334988973490703807163310757974571749978078052900604926957726939876253751243046373693076558774153 skew: 59306.55 # norm 1.20e+17 c5: 81240 c4: -26753789998 c3: 2671095956360131 c2: 181566292555311624899 c1: -2830291977228100294497705 c0: 6437501435799513345248142525 # alpha -5.47 Y1: 34134483791353 Y0: -814567199780845767882556 # Murphy_E 1.44e-10 # M 11523274213504150547440140399716556813368765874185185755558534481244351005830591973008858940401959649125501491092593456176972 type: gnfs rlim: 8000000 alim: 8000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [4000000, 8300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 977398 x 977646 Total sieving time: 39.40 hours. Total relation processing time: 1.00 hours. Matrix solve time: 4.00 hours. Time per square root: 0.16 hours. total time: 44.73 hours. --------- CPU info (if available) ---------- [ 27.172216] Memory: 3055428k/3111872k available (2523k kernel code, 56056k reserved, 1328k data, 328k init) [ 27.318604] Calibrating delay using timer specific routine.. 3982.80 BogoMIPS (lpj=19914039) [ 28.066173] Calibrating delay using timer specific routine.. 3979.59 BogoMIPS (lpj=19897994)
Sep 30, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(25·10¹⁸¹-43)/9 = 2(7)₁₈₀3_<182> = 199 · C180
C180 = P84 · P96
P84 = 737914540865569522516610635268562488832829093976632609420812249119634895894823895649_<84>
P96 = 189163941450691415519843770805049671097893785124964204776656846922107400108917180888501599597323_<96>

Number: n N=139586823003908431044109436069235064209938581797878280290340591848129536571747627024008933556672250139586823003908431044109436069235064209938581797878280290340591848129536571747627 ( 180 digits) SNFS difficulty: 182 digits. Divisors found: Tue Sep 30 07:28:26 2008 prp84 factor: 737914540865569522516610635268562488832829093976632609420812249119634895894823895649 Tue Sep 30 07:28:27 2008 prp96 factor: 189163941450691415519843770805049671097893785124964204776656846922107400108917180888501599597323 Tue Sep 30 07:28:27 2008 elapsed time 04:32:32 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.65 hours. Scaled time: 89.27 units (timescale=2.045). Factorization parameters were as follows: name: KA_2_7_180_3 n: 139586823003908431044109436069235064209938581797878280290340591848129536571747627024008933556672250139586823003908431044109436069235064209938581797878280290340591848129536571747627 type: snfs skew: 0.70 deg: 5 c5: 250 c0: -43 m: 1000000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 3700001) Primes: RFBsize:539777, AFBsize:540260, largePrimes:13819945 encountered Relations: rels:13443130, finalFF:1142439 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 43.32 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000 total time: 43.65 hours. --------- CPU info (if available) ----------
(8·10¹⁷⁰-71)/9 = (8)₁₆₉1_<170> = 3 · 10039 · 716789 · 2965043 · C154
C154 = P69 · P85
P69 = 443198506540851385333367717395890976633598570600406398617488535633577_<69>
P85 = 3133395045463270610737589355782572374210977477082636826967676595220533524174375587867_<85>

Number: n N=1388716004551824663688127790977244167305559219887100242841409051448755631839236069068098714742279970502100643048354646251438202731220208003585966679010259 ( 154 digits) SNFS difficulty: 170 digits. Divisors found: Tue Sep 30 17:22:35 2008 prp69 factor: 443198506540851385333367717395890976633598570600406398617488535633577 Tue Sep 30 17:22:35 2008 prp85 factor: 3133395045463270610737589355782572374210977477082636826967676595220533524174375587867 Tue Sep 30 17:22:35 2008 elapsed time 01:58:27 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.00 hours. Scaled time: 14.26 units (timescale=2.038). Factorization parameters were as follows: name: KA_8_169_1 n: 1388716004551824663688127790977244167305559219887100242841409051448755631839236069068098714742279970502100643048354646251438202731220208003585966679010259 type: snfs skew: 1.55 deg: 5 c5: 8 c0: -71 m: 10000000000000000000000000000000000 rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 1700001) Primes: RFBsize:425648, AFBsize:425953, largePrimes:12556966 encountered Relations: rels:11858449, finalFF:922632 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 6.74 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000 total time: 7.00 hours. --------- CPU info (if available) ----------
2·10¹⁷¹-7 = 1(9)₁₇₀3_<172> = 69542053866301_<14> · C158
C158 = P37 · P122
P37 = 2207526515260409521358128631916321637_<37>
P122 = 13027964122020918758541442567091441481729149610702735659626025690125388966404642417856907478360011684956625601358894013289_<122>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 28759576239222479445427457166769989217459420861873120828607886411638715838759733339575181195652664367341890322210548946242344000418152022255576564125476234093 (158 digits) Using B1=990000, B2=1045563762, polynomial Dickson(6), sigma=38349962 Step 1 took 12640ms Step 2 took 6438ms ********** Factor found in step 2: 2207526515260409521358128631916321637 Found probable prime factor of 37 digits: 2207526515260409521358128631916321637 Probable prime cofactor 13027964122020918758541442567091441481729149610702735659626025690125388966404642417856907478360011684956625601358894013289 has 122 digits
Sep 30, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁶³-71)/9 = 2(8)₁₆₂1_<164> = 3 · 7 · 17482589 · 742458152998064175019_<21> · C135
C135 = P41 · P94
P41 = 82040906752589392506124571605912668180523_<41>
P94 = 1291824044130121762655087841332987925302619521194453123869004000921846867381372572710987124377_<94>

Number: 28881_163 N=105982415945232243895233769180678939994479004894602568437992066771945436505597759901254384722787348132133665169458489655421436489909171 ( 135 digits) SNFS difficulty: 164 digits. Divisors found: r1=82040906752589392506124571605912668180523 (pp41) r2=1291824044130121762655087841332987925302619521194453123869004000921846867381372572710987124377 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 92.11 hours. Scaled time: 92.66 units (timescale=1.006). Factorization parameters were as follows: name: 28881_163 n: 105982415945232243895233769180678939994479004894602568437992066771945436505597759901254384722787348132133665169458489655421436489909171 m: 200000000000000000000000000000000 c5: 1625 c0: -142 skew: 0.61 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5800001) Primes: RFBsize:348513, AFBsize:347822, largePrimes:6128209 encountered Relations: rels:6437711, finalFF:928519 Max relations in full relation-set: 28 Initial matrix: 696401 x 928519 with sparse part having weight 64868998. Pruned matrix : 512907 x 516453 with weight 47758086. Total sieving time: 89.49 hours. Total relation processing time: 0.11 hours. Matrix solve time: 2.41 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 92.11 hours. --------- CPU info (if available) ----------
Sep 30, 2008: By matsui / GMP-ECM
4·10¹⁹⁸+3 = 4(0)₁₉₇3_<199> = 7³ · 499 · 6623605628946997_<16> · 1337219835698580307_<19> · C160
C160 = P38 · P123
P38 = 22355415272513896662048780081754279783_<38>
P123 = 118028070472771437685486920896484037107828428621451610964475648743976065340805709497284979806314122890506877033820039746847_<123>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 2638566529232341089643546066807989595166818810117536594989975833327270688254378755998477840372259078317921239139584373535543895418449639572065879395910130094201 =22355415272513896662048780081754279783* 118028070472771437685486920896484037107828428621451610964475648743976065340805709497284979806314122890506877033820039746847
Sep 29, 2008 (2nd): By Wataru Sakai / GGNFS
(73·10¹⁹⁴-1)/9 = 8(1)₁₉₄_<195> = C195
C195 = P75 · P121
P75 = 306560981981481704619439698696478142677609707817262304366101661349418983307_<75>
P121 = 2645839355903771034479686515433710428643834762960463161678823519151880019097909680932155803208297225177206761675775557173_<121>

Number: 81111_194 N=811111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 ( 195 digits) SNFS difficulty: 196 digits. Divisors found: r1=306560981981481704619439698696478142677609707817262304366101661349418983307 (pp75) r2=2645839355903771034479686515433710428643834762960463161678823519151880019097909680932155803208297225177206761675775557173 (pp121) Version: GGNFS-0.77.1-20060722-nocona Total time: 4907.46 hours. Scaled time: 9829.64 units (timescale=2.003). Factorization parameters were as follows: n: 811111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 m: 1000000000000000000000000000000000000000 c5: 73 c0: -10 skew: 0.67 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 86400001) Primes: RFBsize:501962, AFBsize:502306, largePrimes:9714699 encountered Relations: rels:11320200, finalFF:1140454 Max relations in full relation-set: 32 Initial matrix: 1004333 x 1140454 with sparse part having weight 216153670. Pruned matrix : 939585 x 944670 with weight 198992522. Total sieving time: 4888.56 hours. Total relation processing time: 0.95 hours. Matrix solve time: 17.53 hours. Time per square root: 0.43 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 4907.46 hours. --------- CPU info (if available) ----------
(16·10¹⁹⁰+11)/9 = 1(7)₁₈₉9_<191> = 163 · C189
C189 = P59 · P130
P59 = 15893897701210748826466356818360065080329541721568770733123_<59>
P130 = 6862138122843942847791922085053418154936259828171101678155392075764498344425374075168875066509622240658600914959115020089323939771_<130>

Number: 17779_190 N=109066121336059986366734832992501704158145875937286980231765507839127471029311520109066121336059986366734832992501704158145875937286980231765507839127471029311520109066121336059986366734833 ( 189 digits) SNFS difficulty: 191 digits. Divisors found: r1=15893897701210748826466356818360065080329541721568770733123 (pp59) r2=6862138122843942847791922085053418154936259828171101678155392075764498344425374075168875066509622240658600914959115020089323939771 (pp130) Version: GGNFS-0.77.1-20060722-nocona Total time: 1211.20 hours. Scaled time: 2426.02 units (timescale=2.003). Factorization parameters were as follows: n: 109066121336059986366734832992501704158145875937286980231765507839127471029311520109066121336059986366734832992501704158145875937286980231765507839127471029311520109066121336059986366734833 m: 200000000000000000000000000000000000000 c5: 1 c0: 22 skew: 1.86 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 20600001) Primes: RFBsize:501962, AFBsize:502487, largePrimes:7199292 encountered Relations: rels:7802974, finalFF:1170083 Max relations in full relation-set: 32 Initial matrix: 1004513 x 1170083 with sparse part having weight 143400992. Pruned matrix : 885927 x 891013 with weight 123578297. Total sieving time: 1199.45 hours. Total relation processing time: 0.14 hours. Matrix solve time: 11.33 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1211.20 hours. --------- CPU info (if available) ----------
Sep 29, 2008: By Sinkiti Sibata / GGNFS
(26·10¹⁶²-71)/9 = 2(8)₁₆₁1_<163> = 1605341 · C157
C157 = P44 · P56 · P57
P44 = 34840843885409601679480678418650111005563801_<44>
P56 = 65612945889179070840638882215639321183998522259344767579_<56>
P57 = 787200458193689081759211506325782501478201241604278678679_<57>

Number: 28881_162 N=1799548437926203148669901839477649227727248534042853754366760014781214015519997862690162955340260348978122958853532607021741106026002505940413213696584643941 ( 157 digits) SNFS difficulty: 163 digits. Divisors found: r1=34840843885409601679480678418650111005563801 (pp44) r2=65612945889179070840638882215639321183998522259344767579 (pp56) r3=787200458193689081759211506325782501478201241604278678679 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 77.77 hours. Scaled time: 78.40 units (timescale=1.008). Factorization parameters were as follows: name: 28881_162 n: 1799548437926203148669901839477649227727248534042853754366760014781214015519997862690162955340260348978122958853532607021741106026002505940413213696584643941 m: 100000000000000000000000000000000 c5: 2600 c0: -71 skew: 0.49 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 5150001) Primes: RFBsize:315948, AFBsize:315767, largePrimes:5897191 encountered Relations: rels:5994983, finalFF:717928 Max relations in full relation-set: 28 Initial matrix: 631782 x 717928 with sparse part having weight 56111003. Pruned matrix : 571221 x 574443 with weight 42764962. Total sieving time: 74.92 hours. Total relation processing time: 0.11 hours. Matrix solve time: 2.65 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 77.77 hours. --------- CPU info (if available) ----------
(26·10¹⁵⁵-71)/9 = 2(8)₁₅₄1_<156> = 761 · 54499 · 30564664990261253_<17> · C132
C132 = P47 · P85
P47 = 63836161460698741419691880404514945920853927423_<47>
P85 = 3570024888040223758946915583946688879184055497902878240186964550332918034067683819241_<85>

Number: 28881_155 N=227896685171648671109267995127880791600813825571543173727625987550571717872159185551505336201973631147175443328833813898063264945943 ( 132 digits) SNFS difficulty: 156 digits. Divisors found: r1=63836161460698741419691880404514945920853927423 (pp47) r2=3570024888040223758946915583946688879184055497902878240186964550332918034067683819241 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 42.65 hours. Scaled time: 33.26 units (timescale=0.780). Factorization parameters were as follows: name: 28881_155 n: 227896685171648671109267995127880791600813825571543173727625987550571717872159185551505336201973631147175443328833813898063264945943 m: 10000000000000000000000000000000 c5: 26 c0: -71 skew: 1.22 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:218152, largePrimes:5706068 encountered Relations: rels:5661084, finalFF:528212 Max relations in full relation-set: 28 Initial matrix: 435034 x 528212 with sparse part having weight 46997049. Pruned matrix : 392905 x 395144 with weight 32227067. Total sieving time: 40.43 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.94 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 42.65 hours. --------- CPU info (if available) ----------
(26·10¹³⁴-71)/9 = 2(8)₁₃₃1_<135> = 1801897 · 265450281363670856539_<21> · C108
C108 = P49 · P60
P49 = 2151771244658802648860981132723919893684815718567_<49>
P60 = 280686539850995217773316080340193459612811030104024615577821_<60>

Number: 28881_134 N=603973225214148590339598242124486865273569787328277014085649480739015184344731316431305397368734430023102507 ( 108 digits) Divisors found: r1=2151771244658802648860981132723919893684815718567 (pp49) r2=280686539850995217773316080340193459612811030104024615577821 (pp60) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 19.00 hours. Scaled time: 8.97 units (timescale=0.472). Factorization parameters were as follows: name: 28881_134 n: 603973225214148590339598242124486865273569787328277014085649480739015184344731316431305397368734430023102507 skew: 9031.63 # norm 8.65e+14 c5: 132480 c4: -9655136832 c3: 3073901148074 c2: 788244391354358951 c1: 755654046763763982904 c0: -3914555308130336395968572 # alpha -6.44 Y1: 184659791063 Y0: -340233371806463795427 # Murphy_E 1.39e-09 # M 528174875071408094852850298995715238680787298333444263874278964954547222542074420587388804359136793122955655 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, 2300001) Primes: RFBsize:183072, AFBsize:182771, largePrimes:4380791 encountered Relations: rels:4391242, finalFF:413456 Max relations in full relation-set: 28 Initial matrix: 365923 x 413456 with sparse part having weight 29385875. Pruned matrix : 328573 x 330466 with weight 19750900. Total sieving time: 15.57 hours. Total relation processing time: 0.29 hours. Matrix solve time: 2.92 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 19.00 hours. --------- CPU info (if available) ----------
Sep 28, 2008 (5th): By Serge Batalov / Msieve-1.38
(26·10¹⁴⁰-71)/9 = 2(8)₁₃₉1_<141> = 258551 · C136
C136 = P58 · P79
P58 = 1061457857440639884285723044526980992447605343813900560013_<58>
P79 = 1052644826720225490937098572168106297601845969296447812929710800726211325127987_<79>

SNFS difficulty: 141 digits. Divisors found: r1=1061457857440639884285723044526980992447605343813900560013 r2=1052644826720225490937098572168106297601845969296447812929710800726211325127987 Version: Total time: 5.70 hours. Scaled time: 14.70 units (timescale=2.579). Factorization parameters were as follows: n: 1117338122416424182806830717687763299654183851112116715421285892875637258757030098080799876577112016154990268414699184643992438199383831 Y1: 1 Y0: -10000000000000000000000000000 c5: 26 c0: -71 skew: 1.22 type: snfs lss: 1 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved rational special-q in [650000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 215541 x 215782 Total sieving time: 5.70 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 5.70 hours.
Sep 28, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
5·10¹⁸¹-7 = 4(9)₁₈₀3_<182> = 107 · 167 · C178
C178 = P79 · P99
P79 = 5349247229374462217450139738261038814734050044867358474115901989701104007451021_<79>
P99 = 523090803940434651997243625173949810907397035980386998037130621336689305210083737010025418468122257_<99>

Number: n N=2798142033689630085623146230902680620068274665622026974089204768034025407129665901841177458167776596340030219933963848004924729979293748950696737366388717891320163411494767474397 ( 178 digits) SNFS difficulty: 181 digits. Divisors found: Sun Sep 28 04:54:25 2008 prp79 factor: 5349247229374462217450139738261038814734050044867358474115901989701104007451021 Sun Sep 28 04:54:25 2008 prp99 factor: 523090803940434651997243625173949810907397035980386998037130621336689305210083737010025418468122257 Sun Sep 28 04:54:25 2008 elapsed time 05:08:16 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 42.26 hours. Scaled time: 83.51 units (timescale=1.976). Factorization parameters were as follows: name: KA_4_9_180_3 n: 2798142033689630085623146230902680620068274665622026974089204768034025407129665901841177458167776596340030219933963848004924729979293748950696737366388717891320163411494767474397 type: snfs skew: 0.67 deg: 5 c5: 50 c0: -7 m: 1000000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 4500001) Primes: RFBsize:539777, AFBsize:540740, largePrimes:13860963 encountered Relations: rels:13460271, finalFF:1117649 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 41.94 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000 total time: 42.26 hours. --------- CPU info (if available) ----------
Sep 28, 2008 (3rd): By Justin Card / msieve 1.38
(26·10¹²⁶-71)/9 = 2(8)₁₂₅1_<127> = 401 · 3354622878026888455049_<22> · C103
C103 = P44 · P60
P44 = 16283299902589791600249813240195129893581187_<44>
P60 = 131886498973573202679378662889306990910980844571318172595187_<60>

Number: 28881_126 N=2147547415889293181059921809418318585188055202701289383214912889185222223648914042877205066401069946969 ( 103 digits) SNFS difficulty: 127 digits. Divisors found: r1=16283299902589791600249813240195129893581187 r2=131886498973573202679378662889306990910980844571318172595187 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.090). Factorization parameters were as follows: n: 2147547415889293181059921809418318585188055202701289383214912889185222223648914042877205066401069946969 Y1: 1 Y0: -10000000000000000000000000 c5: 260 c0: -71 skew: 0.77 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 131945 x 132185 Total sieving time: 1.22 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours.
(26·10¹²⁴-71)/9 = 2(8)₁₂₃1_<125> = 3 · 163 · 57162358247_<11> · 4863987289960456051_<19> · C93
C93 = P44 · P49
P44 = 82711241811099317326869797485718892733761469_<44>
P49 = 2568945372540053678056380379294551958469473628953_<49>

Sat Sep 27 00:44:53 2008 Sat Sep 27 00:44:53 2008 Sat Sep 27 00:44:53 2008 Msieve v. 1.38 Sat Sep 27 00:44:53 2008 random seeds: 5731128c 633662a3 Sat Sep 27 00:44:53 2008 factoring 212480661907664999835916436228413132121070297399683627848151251731890808162658241713314211957 (93 digits) Sat Sep 27 00:44:55 2008 no P-1/P+1/ECM available, skipping Sat Sep 27 00:44:55 2008 commencing quadratic sieve (93-digit input) Sat Sep 27 00:44:55 2008 using multiplier of 37 Sat Sep 27 00:44:55 2008 using 64kb Athlon XP sieve core Sat Sep 27 00:44:55 2008 sieve interval: 18 blocks of size 65536 Sat Sep 27 00:44:55 2008 processing polynomials in batches of 6 Sat Sep 27 00:44:55 2008 using a sieve bound of 1883627 (70588 primes) Sat Sep 27 00:44:55 2008 using large prime bound of 220384359 (27 bits) Sat Sep 27 00:44:55 2008 using double large prime bound of 1041658353184527 (42-50 bits) Sat Sep 27 00:44:55 2008 using trial factoring cutoff of 50 bits Sat Sep 27 00:44:55 2008 polynomial 'A' values have 12 factors Sat Sep 27 11:40:31 2008 Sat Sep 27 11:40:31 2008 Sat Sep 27 11:40:31 2008 Msieve v. 1.38 Sat Sep 27 11:40:31 2008 random seeds: 367b5676 c75d7466 Sat Sep 27 11:40:31 2008 factoring 212480661907664999835916436228413132121070297399683627848151251731890808162658241713314211957 (93 digits) Sat Sep 27 11:40:32 2008 no P-1/P+1/ECM available, skipping Sat Sep 27 11:40:32 2008 commencing quadratic sieve (93-digit input) Sat Sep 27 11:40:33 2008 using multiplier of 37 Sat Sep 27 11:40:33 2008 using 64kb Athlon XP sieve core Sat Sep 27 11:40:33 2008 sieve interval: 18 blocks of size 65536 Sat Sep 27 11:40:33 2008 processing polynomials in batches of 6 Sat Sep 27 11:40:33 2008 using a sieve bound of 1883627 (70588 primes) Sat Sep 27 11:40:33 2008 using large prime bound of 220384359 (27 bits) Sat Sep 27 11:40:33 2008 using double large prime bound of 1041658353184527 (42-50 bits) Sat Sep 27 11:40:33 2008 using trial factoring cutoff of 50 bits Sat Sep 27 11:40:33 2008 polynomial 'A' values have 12 factors Sat Sep 27 11:40:37 2008 restarting with 12109 full and 628657 partial relations Sat Sep 27 14:00:31 2008 71068 relations (17856 full + 53212 combined from 924337 partial), need 70684 Sat Sep 27 14:00:32 2008 begin with 942193 relations Sat Sep 27 14:00:34 2008 reduce to 180710 relations in 10 passes Sat Sep 27 14:00:34 2008 attempting to read 180710 relations Sat Sep 27 14:00:39 2008 recovered 180710 relations Sat Sep 27 14:00:39 2008 recovered 163046 polynomials Sat Sep 27 14:00:40 2008 attempting to build 71068 cycles Sat Sep 27 14:00:40 2008 found 71068 cycles in 6 passes Sat Sep 27 14:00:40 2008 distribution of cycle lengths: Sat Sep 27 14:00:40 2008 length 1 : 17856 Sat Sep 27 14:00:40 2008 length 2 : 13079 Sat Sep 27 14:00:40 2008 length 3 : 12068 Sat Sep 27 14:00:40 2008 length 4 : 9612 Sat Sep 27 14:00:40 2008 length 5 : 7147 Sat Sep 27 14:00:40 2008 length 6 : 4619 Sat Sep 27 14:00:40 2008 length 7 : 2916 Sat Sep 27 14:00:41 2008 length 9+: 3771 Sat Sep 27 14:00:41 2008 largest cycle: 18 relations Sat Sep 27 14:00:41 2008 matrix is 70588 x 71068 (17.9 MB) with weight 4411696 (62.08/col) Sat Sep 27 14:00:41 2008 sparse part has weight 4411696 (62.08/col) Sat Sep 27 14:00:44 2008 filtering completed in 3 passes Sat Sep 27 14:00:44 2008 matrix is 66723 x 66786 (16.9 MB) with weight 4156271 (62.23/col) Sat Sep 27 14:00:44 2008 sparse part has weight 4156271 (62.23/col) Sat Sep 27 14:00:46 2008 saving the first 48 matrix rows for later Sat Sep 27 14:00:46 2008 matrix is 66675 x 66786 (10.3 MB) with weight 3184238 (47.68/col) Sat Sep 27 14:00:46 2008 sparse part has weight 2309093 (34.57/col) Sat Sep 27 14:00:46 2008 matrix includes 64 packed rows Sat Sep 27 14:00:46 2008 using block size 10922 for processor cache size 256 kB Sat Sep 27 14:00:47 2008 commencing Lanczos iteration Sat Sep 27 14:00:47 2008 memory use: 10.3 MB Sat Sep 27 14:25:49 2008 Sat Sep 27 14:25:49 2008 Sat Sep 27 14:25:49 2008 Msieve v. 1.38 Sat Sep 27 14:25:49 2008 random seeds: 6394e89c b1852f11 Sat Sep 27 14:25:49 2008 factoring 212480661907664999835916436228413132121070297399683627848151251731890808162658241713314211957 (93 digits) Sat Sep 27 14:25:51 2008 no P-1/P+1/ECM available, skipping Sat Sep 27 14:25:51 2008 commencing quadratic sieve (93-digit input) Sat Sep 27 14:25:51 2008 using multiplier of 37 Sat Sep 27 14:25:51 2008 using 64kb Athlon XP sieve core Sat Sep 27 14:25:51 2008 sieve interval: 18 blocks of size 65536 Sat Sep 27 14:25:51 2008 processing polynomials in batches of 6 Sat Sep 27 14:25:51 2008 using a sieve bound of 1883627 (70588 primes) Sat Sep 27 14:25:51 2008 using large prime bound of 220384359 (27 bits) Sat Sep 27 14:25:51 2008 using double large prime bound of 1041658353184527 (42-50 bits) Sat Sep 27 14:25:51 2008 using trial factoring cutoff of 50 bits Sat Sep 27 14:25:51 2008 polynomial 'A' values have 12 factors Sat Sep 27 14:25:54 2008 restarting with 17856 full and 924337 partial relations Sat Sep 27 14:25:54 2008 71068 relations (17856 full + 53212 combined from 924337 partial), need 70684 Sat Sep 27 14:25:55 2008 begin with 942193 relations Sat Sep 27 14:25:58 2008 reduce to 180710 relations in 10 passes Sat Sep 27 14:25:58 2008 attempting to read 180710 relations Sat Sep 27 14:26:03 2008 recovered 180710 relations Sat Sep 27 14:26:03 2008 recovered 163046 polynomials Sat Sep 27 14:26:03 2008 attempting to build 71068 cycles Sat Sep 27 14:26:04 2008 found 71068 cycles in 6 passes Sat Sep 27 14:26:04 2008 distribution of cycle lengths: Sat Sep 27 14:26:04 2008 length 1 : 17856 Sat Sep 27 14:26:04 2008 length 2 : 13079 Sat Sep 27 14:26:04 2008 length 3 : 12068 Sat Sep 27 14:26:04 2008 length 4 : 9612 Sat Sep 27 14:26:04 2008 length 5 : 7147 Sat Sep 27 14:26:04 2008 length 6 : 4619 Sat Sep 27 14:26:04 2008 length 7 : 2916 Sat Sep 27 14:26:04 2008 length 9+: 3771 Sat Sep 27 14:26:04 2008 largest cycle: 18 relations Sat Sep 27 14:26:04 2008 matrix is 70588 x 71068 (17.9 MB) with weight 4411696 (62.08/col) Sat Sep 27 14:26:04 2008 sparse part has weight 4411696 (62.08/col) Sat Sep 27 14:26:08 2008 filtering completed in 3 passes Sat Sep 27 14:26:08 2008 matrix is 66723 x 66786 (16.9 MB) with weight 4156271 (62.23/col) Sat Sep 27 14:26:08 2008 sparse part has weight 4156271 (62.23/col) Sat Sep 27 14:26:09 2008 saving the first 48 matrix rows for later Sat Sep 27 14:26:09 2008 matrix is 66675 x 66786 (10.3 MB) with weight 3184238 (47.68/col) Sat Sep 27 14:26:09 2008 sparse part has weight 2309093 (34.57/col) Sat Sep 27 14:26:09 2008 matrix includes 64 packed rows Sat Sep 27 14:26:09 2008 using block size 10922 for processor cache size 256 kB Sat Sep 27 14:26:10 2008 commencing Lanczos iteration Sat Sep 27 14:26:10 2008 memory use: 10.3 MB Sat Sep 27 14:27:52 2008 lanczos halted after 1056 iterations (dim = 66674) Sat Sep 27 14:27:53 2008 recovered 17 nontrivial dependencies Sat Sep 27 14:27:54 2008 prp44 factor: 82711241811099317326869797485718892733761469 Sat Sep 27 14:27:54 2008 prp49 factor: 2568945372540053678056380379294551958469473628953 Sat Sep 27 14:27:54 2008 elapsed time 00:02:05
Sep 28, 2008 (2nd): By Jo Yeong Uk / GMP-ECM, GGNFS
(26·10¹⁶⁵-71)/9 = 2(8)₁₆₄1_<166> = 17 · 13309 · 71671 · 101477581746372523_<18> · C139
C139 = P37 · P102
P37 = 1787383004449952594789773835754260083_<37>
P102 = 982212133326409521576440542949381649398350348153586585505016074608770961266853317136037014383074679043_<102>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 1755589273872155261233718370285448343873266326860841413940094147862817828579285028494983879753180712516018684386238936660834341115171540569 (139 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1501512258 Step 1 took 4703ms Step 2 took 2604ms ********** Factor found in step 2: 1787383004449952594789773835754260083 Found probable prime factor of 37 digits: 1787383004449952594789773835754260083 Probable prime cofactor 982212133326409521576440542949381649398350348153586585505016074608770961266853317136037014383074679043 has 102 digits
(13·10¹⁷⁹+41)/9 = 1(4)₁₇₈9_<180> = 23 · 42015451969_<11> · 78770911838628725351_<20> · 46992713266751930707073011577_<29> · C119
C119 = P53 · P67
P53 = 30311897398836633926595718252104305336929992466250467_<53>
P67 = 1332154054820807868883060706294827597729163358841002375824024699203_<67>

Number: 14449_179 N=40380117029172520674769513188321069808478594187938313449637188262684915551986256553904977186681940701330222198933277801 ( 119 digits) Divisors found: r1=30311897398836633926595718252104305336929992466250467 (pp53) r2=1332154054820807868883060706294827597729163358841002375824024699203 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 34.61 hours. Scaled time: 82.51 units (timescale=2.384). Factorization parameters were as follows: name: 14449_179 n: 40380117029172520674769513188321069808478594187938313449637188262684915551986256553904977186681940701330222198933277801 skew: 59519.84 # norm 5.30e+16 c5: 90180 c4: 37114906902 c3: -1064109571462834 c2: -114583571740201368031 c1: 1888116932644638843692268 c0: 14072364541878315912665194068 # alpha -6.66 Y1: 10050004274557 Y0: -53728508162727730627147 # Murphy_E 3.17e-10 # M 1546977283922582777487438798546142938538458754200649131652727350868351272901527820115965843604045265077433363727393309 type: gnfs rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2100000, 4050001) Primes: RFBsize:296314, AFBsize:295837, largePrimes:7735710 encountered Relations: rels:7843064, finalFF:755394 Max relations in full relation-set: 28 Initial matrix: 592232 x 755394 with sparse part having weight 67118714. Pruned matrix : 463583 x 466608 with weight 42170854. Polynomial selection time: 2.29 hours. Total sieving time: 30.40 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.64 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4200000,4200000,27,27,50,50,2.4,2.4,75000 total time: 34.61 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343) Calibrating delay using timer specific routine.. 5344.63 BogoMIPS (lpj=2672318) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)
Sep 28, 2008: By Sinkiti Sibata / GGNFS
(26·10¹²⁷-71)/9 = 2(8)₁₂₆1_<128> = 3 · 7 · 4177 · C123
C123 = P33 · P91
P33 = 113230714718788553945893724491447_<33>
P91 = 2908592098095199284156292274582063675219090371694461454439845943319274746957258978219884619_<91>

Number: 28881_127 N=329341962092740163125607224242608489675762838319697309402839687733151941914211485674257998892904327426711913185458792353693 ( 123 digits) SNFS difficulty: 128 digits. Divisors found: r1=113230714718788553945893724491447 (pp33) r2=2908592098095199284156292274582063675219090371694461454439845943319274746957258978219884619 (pp91) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 5.33 hours. Scaled time: 2.52 units (timescale=0.473). Factorization parameters were as follows: name: 28881_127 n: 329341962092740163125607224242608489675762838319697309402839687733151941914211485674257998892904327426711913185458792353693 m: 10000000000000000000000000 c5: 2600 c0: -71 skew: 0.49 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:63854, largePrimes:1453713 encountered Relations: rels:1433520, finalFF:156420 Max relations in full relation-set: 28 Initial matrix: 127872 x 156420 with sparse part having weight 10645432. Pruned matrix : 118915 x 119618 with weight 6495540. Total sieving time: 5.06 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.16 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.33 hours. --------- CPU info (if available) ----------
(26·10¹⁴²-71)/9 = 2(8)₁₄₁1_<143> = 3 · 23 · 281 · 1277 · 351887 · 1043876039_<10> · C121
C121 = P54 · P67
P54 = 318812637521068164983566579422495812535445874888122847_<54>
P67 = 9963154172558509622279112283921622547309975069751848442172384313887_<67>

Number: 28881_142 N=3176379459782413951612104998475795623034111084218794263647507738095092102518673699145472039926316940831767873865464076289 ( 121 digits) SNFS difficulty: 143 digits. Divisors found: r1=318812637521068164983566579422495812535445874888122847 (pp54) r2=9963154172558509622279112283921622547309975069751848442172384313887 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.38 hours. Scaled time: 13.48 units (timescale=0.776). Factorization parameters were as follows: name: 28881_142 n: 3176379459782413951612104998475795623034111084218794263647507738095092102518673699145472039926316940831767873865464076289 m: 10000000000000000000000000000 c5: 2600 c0: -71 skew: 0.49 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2550001) Primes: RFBsize:100021, AFBsize:100034, largePrimes:2828558 encountered Relations: rels:2813811, finalFF:228562 Max relations in full relation-set: 28 Initial matrix: 200122 x 228562 with sparse part having weight 25448559. Pruned matrix : 192472 x 193536 with weight 20041376. Total sieving time: 16.84 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.37 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 17.38 hours. --------- CPU info (if available) ----------
(26·10¹⁵¹-71)/9 = 2(8)₁₅₀1_<152> = 3 · 7 · 263 · 13679 · 3226777 · 17209986945207499_<17> · C121
C121 = P34 · P88
P34 = 2745596514435287531823283642891597_<34>
P88 = 2507928999895546296791005056224527982607687054515900884400907699433831261610761528623203_<88>

Number: 28881_151 N=6885761120564388500947561397500272791597190120780410367728327785360043793953985345335262886302990052218560958181187925191 ( 121 digits) SNFS difficulty: 152 digits. Divisors found: r1=2745596514435287531823283642891597 (pp34) r2=2507928999895546296791005056224527982607687054515900884400907699433831261610761528623203 (pp88) Version: GGNFS-0.77.1-20050930-nocona Total time: 31.07 hours. Scaled time: 31.35 units (timescale=1.009). Factorization parameters were as follows: name: 28881_151 n: 6885761120564388500947561397500272791597190120780410367728327785360043793953985345335262886302990052218560958181187925191 m: 1000000000000000000000000000000 c5: 260 c0: -71 skew: 0.77 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2500001) Primes: RFBsize:176302, AFBsize:175109, largePrimes:6378422 encountered Relations: rels:6891323, finalFF:940324 Max relations in full relation-set: 28 Initial matrix: 351478 x 940324 with sparse part having weight 106935468. Pruned matrix : 239768 x 241589 with weight 53592392. Total sieving time: 30.17 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.73 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 31.07 hours. --------- CPU info (if available) ----------
Sep 27, 2008 (7th): By Sinkiti Sibata / GGNFS
(26·10¹²⁵-71)/9 = 2(8)₁₂₄1_<126> = 19 · 613 · 91823 · 153407 · C112
C112 = P41 · P72
P41 = 15699580490746648722017623746645943623109_<41>
P72 = 112158465934766181512722569942161506774982710985048339315616976232886227_<72>

Number: 28881_125 N=1760840863661527731242588303029745571382012232491529812649018974750700959809037491808401556805124013624565019743 ( 112 digits) SNFS difficulty: 126 digits. Divisors found: r1=15699580490746648722017623746645943623109 (pp41) r2=112158465934766181512722569942161506774982710985048339315616976232886227 (pp72) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.95 hours. Scaled time: 1.87 units (timescale=0.473). Factorization parameters were as follows: name: 28881_125 n: 1760840863661527731242588303029745571382012232491529812649018974750700959809037491808401556805124013624565019743 m: 10000000000000000000000000 c5: 26 c0: -71 skew: 1.22 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:49098, AFBsize:64324, largePrimes:2208963 encountered Relations: rels:2289393, finalFF:185176 Max relations in full relation-set: 28 Initial matrix: 113488 x 185176 with sparse part having weight 18384705. Pruned matrix : 101189 x 101820 with weight 7567708. Total sieving time: 3.68 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.15 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.95 hours. --------- CPU info (if available) ----------
Sep 27, 2008 (6th): By Robert Backstrom / GGNFS, GMP-ECM
(26·10¹³³-71)/9 = 2(8)₁₃₂1_<134> = 3 · 7² · 17 · 151 · 1061 · 37783 · 99011812111_<11> · C110
C110 = P43 · P67
P43 = 1965547559984367689019258871317555515695451_<43>
P67 = 9813077914068196935358138454323876101771621519472202609560133578483_<67>

Number: n N=19288071349933233074261710240111886312422696827531398603739748930210286351177246600319447391698166441034580833 ( 110 digits) SNFS difficulty: 134 digits. Divisors found: r1=1965547559984367689019258871317555515695451 (pp43) r2=9813077914068196935358138454323876101771621519472202609560133578483 (pp67) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.06 hours. Scaled time: 5.58 units (timescale=1.823). Factorization parameters were as follows: name: KA_2_8_132_1 n: 19288071349933233074261710240111886312422696827531398603739748930210286351177246600319447391698166441034580833 type: snfs skew: 0.31 deg: 5 c5: 26000 c0: -71 m: 100000000000000000000000000 rlim: 900000 alim: 900000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved algebraic special-q in [100000, 540001) Primes: RFBsize:71274, AFBsize:71446, largePrimes:6627165 encountered Relations: rels:5704800, finalFF:179357 Max relations in full relation-set: 48 Initial matrix: 142787 x 179357 with sparse part having weight 22618482. Pruned matrix : 132920 x 133697 with weight 12851718. Total sieving time: 2.80 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.13 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,900000,900000,28,28,52,52,2.5,2.5,75000 total time: 3.06 hours. --------- CPU info (if available) ----------
(26·10¹³⁸-71)/9 = 2(8)₁₃₇1_<139> = 120949069 · 41467906931283023773_<20> · C111
C111 = P35 · P77
P35 = 35541916653799466686224456599258869_<35>
P77 = 16205981899812491349119706433005180738013612088106238598294885611831440295477_<77>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 575991657976118306505152747026865159701331253253282035051336670437456519531720961945340575972665515620572835513 (111 digits) Using B1=962000, B2=871244232, polynomial Dickson(3), sigma=110969026 Step 1 took 7547ms Step 2 took 3375ms ********** Factor found in step 2: 35541916653799466686224456599258869 Found probable prime factor of 35 digits: 35541916653799466686224456599258869 Probable prime cofactor 16205981899812491349119706433005180738013612088106238598294885611831440295477 has 77 digits
Sep 27, 2008 (5th): By Sinkiti Sibata / GGNFS
(2·10¹⁶⁷+43)/9 = (2)₁₆₆7_<167> = 3 · 43577 · 6890591 · 114764843449205755577_<21> · C135
C135 = P53 · P83
P53 = 11279471825173337406649938800073870329587734408745733_<53>
P83 = 19057011588196652779014261179465989128269937645311151180852735600411117204477421907_<83>

Number: 22227_167 N=214953025281065940547395149502201290586118762475115084677179939782782050610010468173133158100944549423320604633635433583123437326972831 ( 135 digits) SNFS difficulty: 167 digits. Divisors found: r1=11279471825173337406649938800073870329587734408745733 (pp53) r2=19057011588196652779014261179465989128269937645311151180852735600411117204477421907 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 115.79 hours. Scaled time: 116.48 units (timescale=1.006). Factorization parameters were as follows: name: 22227_167 n: 214953025281065940547395149502201290586118762475115084677179939782782050610010468173133158100944549423320604633635433583123437326972831 m: 1000000000000000000000000000000000 c5: 200 c0: 43 skew: 0.74 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, 6850001) Primes: RFBsize:380800, AFBsize:380632, largePrimes:6097586 encountered Relations: rels:6324207, finalFF:873305 Max relations in full relation-set: 28 Initial matrix: 761497 x 873305 with sparse part having weight 61105444. Pruned matrix : 674396 x 678267 with weight 45815347. Total sieving time: 111.93 hours. Total relation processing time: 0.11 hours. Matrix solve time: 3.64 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 115.79 hours. --------- CPU info (if available) ----------
(26·10¹³⁶-71)/9 = 2(8)₁₃₅1_<137> = 3 · 2741 · C133
C133 = P47 · P86
P47 = 92372285975211434631537057344098560567670446839_<47>
P86 = 38032848797379633248033194711881967676062087393154102007966129723213945990007458206473_<86>

Number: 28881_136 N=3513181185563527774399718945505154917778048022484359587606577756158201251232991473779507343899901360682097639412488007891145432188847 ( 133 digits) SNFS difficulty: 137 digits. Divisors found: r1=92372285975211434631537057344098560567670446839 (pp47) r2=38032848797379633248033194711881967676062087393154102007966129723213945990007458206473 (pp86) Version: GGNFS-0.77.1-20050930-nocona Total time: 12.79 hours. Scaled time: 10.05 units (timescale=0.786). Factorization parameters were as follows: name: 28881_136 n: 3513181185563527774399718945505154917778048022484359587606577756158201251232991473779507343899901360682097639412488007891145432188847 m: 1000000000000000000000000000 c5: 260 c0: -71 skew: 0.77 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 2125001) Primes: RFBsize:78498, AFBsize:63419, largePrimes:1663569 encountered Relations: rels:1683191, finalFF:159116 Max relations in full relation-set: 28 Initial matrix: 141984 x 159116 with sparse part having weight 17826188. Pruned matrix : 137921 x 138694 with weight 14425970. Total sieving time: 12.53 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.14 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 12.79 hours. --------- CPU info (if available) ----------
(26·10¹⁴⁶-71)/9 = 2(8)₁₄₅1_<147> = 17681 · 23242459 · C135
C135 = P56 · P80
P56 = 17943666279248153726359854426579738150064948201372651529_<56>
P80 = 39176962177511276591329105438819030419134508058060721100657357913796416293078491_<80>

Number: 28881_146 N=702978335147989415065882633006451840646443720183542402084529045134097378966611414274165384547692051817047065827290671468580902788162739 ( 135 digits) SNFS difficulty: 147 digits. Divisors found: r1=17943666279248153726359854426579738150064948201372651529 (pp56) r2=39176962177511276591329105438819030419134508058060721100657357913796416293078491 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 28.94 hours. Scaled time: 29.20 units (timescale=1.009). Factorization parameters were as follows: name: 28881_146 n: 702978335147989415065882633006451840646443720183542402084529045134097378966611414274165384547692051817047065827290671468580902788162739 m: 100000000000000000000000000000 c5: 260 c0: -71 skew: 0.77 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 4850001) Primes: RFBsize:114155, AFBsize:113433, largePrimes:3262406 encountered Relations: rels:3446743, finalFF:323228 Max relations in full relation-set: 28 Initial matrix: 227655 x 323228 with sparse part having weight 43074247. Pruned matrix : 205449 x 206651 with weight 27908579. Total sieving time: 28.49 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.33 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 28.94 hours. --------- CPU info (if available) ----------
Sep 27, 2008 (4th): By Justin Card / msieve 1.38
(26·10¹¹⁰-71)/9 = 2(8)₁₀₉1_<111> = 127 · 1951 · 7886623688988353_<16> · C90
C90 = P37 · P53
P37 = 9671736314603461057887965599847505751_<37>
P53 = 15285311076956761976885931758180371769621907771691351_<53>

Fri Sep 26 23:47:52 2008 Msieve v. 1.38 Fri Sep 26 23:47:52 2008 random seeds: 7df286b6 f127304e Fri Sep 26 23:47:52 2008 factoring 147835498223013253412349061166493597442944842892249770825188005060303286665934263969459601 (90 digits) Fri Sep 26 23:47:52 2008 no P-1/P+1/ECM available, skipping Fri Sep 26 23:47:52 2008 commencing quadratic sieve (90-digit input) Fri Sep 26 23:47:52 2008 using multiplier of 1 Fri Sep 26 23:47:52 2008 using 64kb Opteron sieve core Fri Sep 26 23:47:52 2008 sieve interval: 18 blocks of size 65536 Fri Sep 26 23:47:52 2008 processing polynomials in batches of 6 Fri Sep 26 23:47:52 2008 using a sieve bound of 1575281 (59491 primes) Fri Sep 26 23:47:52 2008 using large prime bound of 126022480 (26 bits) Fri Sep 26 23:47:52 2008 using double large prime bound of 380896014563600 (42-49 bits) Fri Sep 26 23:47:52 2008 using trial factoring cutoff of 49 bits Fri Sep 26 23:47:52 2008 polynomial 'A' values have 11 factors Fri Sep 26 23:47:53 2008 restarting with 760 full and 30262 partial relations Sat Sep 27 01:12:36 2008 59841 relations (15780 full + 44061 combined from 636896 partial), need 59587 Sat Sep 27 01:12:36 2008 begin with 652676 relations Sat Sep 27 01:12:37 2008 reduce to 147025 relations in 10 passes Sat Sep 27 01:12:37 2008 attempting to read 147025 relations Sat Sep 27 01:12:38 2008 failed to read relation 88569 Sat Sep 27 01:12:38 2008 recovered 147024 relations Sat Sep 27 01:12:38 2008 recovered 124630 polynomials Sat Sep 27 01:12:38 2008 attempting to build 59840 cycles Sat Sep 27 01:12:38 2008 found 59840 cycles in 5 passes Sat Sep 27 01:12:38 2008 distribution of cycle lengths: Sat Sep 27 01:12:38 2008 length 1 : 15780 Sat Sep 27 01:12:38 2008 length 2 : 11165 Sat Sep 27 01:12:38 2008 length 3 : 10262 Sat Sep 27 01:12:38 2008 length 4 : 8151 Sat Sep 27 01:12:38 2008 length 5 : 5865 Sat Sep 27 01:12:38 2008 length 6 : 3768 Sat Sep 27 01:12:38 2008 length 7 : 2170 Sat Sep 27 01:12:38 2008 length 9+: 2679 Sat Sep 27 01:12:38 2008 largest cycle: 17 relations Sat Sep 27 01:12:39 2008 matrix is 59491 x 59840 (15.7 MB) with weight 3627865 (60.63/col) Sat Sep 27 01:12:39 2008 sparse part has weight 3627865 (60.63/col) Sat Sep 27 01:12:39 2008 filtering completed in 3 passes Sat Sep 27 01:12:39 2008 matrix is 55644 x 55708 (14.7 MB) with weight 3402133 (61.07/col) Sat Sep 27 01:12:39 2008 sparse part has weight 3402133 (61.07/col) Sat Sep 27 01:12:40 2008 saving the first 48 matrix rows for later Sat Sep 27 01:12:40 2008 matrix is 55596 x 55708 (11.1 MB) with weight 2851124 (51.18/col) Sat Sep 27 01:12:40 2008 sparse part has weight 2355787 (42.29/col) Sat Sep 27 01:12:40 2008 matrix includes 64 packed rows Sat Sep 27 01:12:40 2008 using block size 10922 for processor cache size 256 kB Sat Sep 27 01:12:40 2008 commencing Lanczos iteration Sat Sep 27 01:12:40 2008 memory use: 9.3 MB Sat Sep 27 01:13:00 2008 lanczos halted after 881 iterations (dim = 55592) Sat Sep 27 01:13:00 2008 recovered 14 nontrivial dependencies Sat Sep 27 01:13:00 2008 prp37 factor: 9671736314603461057887965599847505751 Sat Sep 27 01:13:00 2008 prp53 factor: 15285311076956761976885931758180371769621907771691351 Sat Sep 27 01:13:00 2008 elapsed time 01:25:08
Sep 27, 2008 (3rd): By Serge Batalov / Msieve-1.36, Msieve-1.38
(26·10¹⁵⁰-71)/9 = 2(8)₁₄₉1_<151> = 43 · 59 · 39511 · 156236473309783_<15> · 306806534558417_<15> · 90996090683978972051700665489_<29> · C85
C85 = P42 · P44
P42 = 278892062287133994385679444936173651725679_<42>
P44 = 23691165618220695016170882191532431070649463_<44>

Fri Sep 26 20:08:09 2008 Msieve v. 1.36 Fri Sep 26 20:08:09 2008 random seeds: 3070926c edda5a26 Fri Sep 26 20:08:09 2008 factoring 6607278037251613419745403617730917584902354733438686568219298506923381764817244660377 (85 digits) Fri Sep 26 20:08:09 2008 no P-1/P+1/ECM available, skipping Fri Sep 26 20:08:09 2008 commencing quadratic sieve (85-digit input) Fri Sep 26 20:08:09 2008 using multiplier of 17 Fri Sep 26 20:08:09 2008 using 64kb Opteron sieve core Fri Sep 26 20:08:09 2008 sieve interval: 6 blocks of size 65536 Fri Sep 26 20:08:09 2008 processing polynomials in batches of 17 Fri Sep 26 20:08:09 2008 using a sieve bound of 1434229 (54704 primes) Fri Sep 26 20:08:09 2008 using large prime bound of 116172549 (26 bits) Fri Sep 26 20:08:09 2008 using double large prime bound of 328992642862119 (41-49 bits) Fri Sep 26 20:08:09 2008 using trial factoring cutoff of 49 bits Fri Sep 26 20:08:09 2008 polynomial 'A' values have 11 factors Fri Sep 26 20:46:26 2008 54970 relations (16331 full + 38639 combined from 567574 partial), need 54800 Fri Sep 26 20:46:27 2008 begin with 583905 relations Fri Sep 26 20:46:27 2008 reduce to 127831 relations in 10 passes Fri Sep 26 20:46:27 2008 attempting to read 127831 relations Fri Sep 26 20:46:28 2008 recovered 127831 relations Fri Sep 26 20:46:28 2008 recovered 106406 polynomials Fri Sep 26 20:46:29 2008 attempting to build 54970 cycles Fri Sep 26 20:46:29 2008 found 54970 cycles in 5 passes Fri Sep 26 20:46:29 2008 distribution of cycle lengths: Fri Sep 26 20:46:29 2008 length 1 : 16331 Fri Sep 26 20:46:29 2008 length 2 : 11450 Fri Sep 26 20:46:29 2008 length 3 : 9750 Fri Sep 26 20:46:29 2008 length 4 : 6906 Fri Sep 26 20:46:29 2008 length 5 : 4543 Fri Sep 26 20:46:29 2008 length 6 : 2755 Fri Sep 26 20:46:29 2008 length 7 : 1559 Fri Sep 26 20:46:29 2008 length 9+: 1676 Fri Sep 26 20:46:29 2008 largest cycle: 18 relations Fri Sep 26 20:46:29 2008 matrix is 54704 x 54970 (12.7 MB) with weight 2895459 (52.67/col) Fri Sep 26 20:46:29 2008 sparse part has weight 2895459 (52.67/col) Fri Sep 26 20:46:30 2008 filtering completed in 3 passes Fri Sep 26 20:46:30 2008 matrix is 49166 x 49230 (11.5 MB) with weight 2617484 (53.17/col) Fri Sep 26 20:46:30 2008 sparse part has weight 2617484 (53.17/col) Fri Sep 26 20:46:30 2008 saving the first 48 matrix rows for later Fri Sep 26 20:46:30 2008 matrix is 49118 x 49230 (7.0 MB) with weight 1976889 (40.16/col) Fri Sep 26 20:46:30 2008 sparse part has weight 1351761 (27.46/col) Fri Sep 26 20:46:30 2008 matrix includes 64 packed rows Fri Sep 26 20:46:30 2008 using block size 19692 for processor cache size 1024 kB Fri Sep 26 20:46:31 2008 commencing Lanczos iteration Fri Sep 26 20:46:31 2008 memory use: 6.6 MB Fri Sep 26 20:47:02 2008 lanczos halted after 778 iterations (dim = 49118) Fri Sep 26 20:47:02 2008 recovered 18 nontrivial dependencies Fri Sep 26 20:47:02 2008 prp42 factor: 278892062287133994385679444936173651725679 Fri Sep 26 20:47:02 2008 prp44 factor: 23691165618220695016170882191532431070649463 Fri Sep 26 20:47:02 2008 elapsed time 00:38:53
(26·10¹⁰²-71)/9 = 2(8)₁₀₁1_<103> = 67 · C101
C101 = P43 · P58
P43 = 4538946310673361934203419529586170464160589_<43>
P58 = 9499505316661328483693123081125976474462217351123397421287_<58>

SNFS difficulty: 103 digits. Divisors found: r1=4538946310673361934203419529586170464160589 r2=9499505316661328483693123081125976474462217351123397421287 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.944). Factorization parameters were as follows: n: 43117744610281923714759535655058043117744610281923714759535655058043117744610281923714759535655058043 Y1: 1 Y0: -100000000000000000000 c5: 2600 c0: -71 skew: 0.49 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [225000, 305001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 43400 x 43627 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 0.30 hours.
(26·10¹¹²-71)/9 = 2(8)₁₁₁1_<113> = 3² · 29147 · C108
C108 = P43 · P65
P43 = 4769177979227823799073881807117328228690591_<43>
P65 = 23091435821474135828457919814168101536665195947355131326279552917_<65>

SNFS difficulty: 113 digits. Divisors found: r1=4769177979227823799073881807117328228690591 r2=23091435821474135828457919814168101536665195947355131326279552917 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 110127167228527002546055393117983893478226800123850706529312675171025372875763424819359678293130563804503947 Y1: 1 Y0: -10000000000000000000000 c5: 2600 c0: -71 skew: 0.49 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 99584 x 99802 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.65 hours.
(26·10¹²¹-71)/9 = 2(8)₁₂₀1_<122> = 3² · 7 · 47 · 142543003 · C110
C110 = P54 · P57
P54 = 222364605027963289594960585610198951220800558531666759_<54>
P57 = 307808683726998816731583533019641595302396302718066515573_<57>

SNFS difficulty: 122 digits. Divisors found: r1=222364605027963289594960585610198951220800558531666759 r2=307808683726998816731583533019641595302396302718066515573 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.744). Factorization parameters were as follows: n: 68445756381131363080887663085460098626256994430630041422322275180521774617167939449170434442331404815119937907 Y1: 1 Y0: -1000000000000000000000000000000 c4: 260 c0: -71 skew: 0.77 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 725001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 91856 x 92076 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,122,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 1.20 hours.
Sep 27, 2008 (2nd): By Robert Backstrom / GMP-ECM
(34·10¹⁹⁶-7)/9 = 3(7)₁₉₆_<197> = 37 · 47 · 6173 · 118373 · 31219384748723_<14> · 1473811541368567_<16> · 2242132689060816180407_<22> · C135
C135 = P43 · P92
P43 = 8818435865982917766354331139100370909728421_<43>
P92 = 32678997856966163491820964161711557583797401265091727332837787241185572405703184609703490221_<92>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 288177646766249323807994780014805681086201286651911030677961221351613989107380858450475712007537724154169055689087760689539206939271041 (135 digits) Using B1=4866000, B2=11416155670, polynomial Dickson(12), sigma=1204317703 Step 1 took 48318ms Step 2 took 21169ms ********** Factor found in step 2: 8818435865982917766354331139100370909728421 Found probable prime factor of 43 digits: 8818435865982917766354331139100370909728421 Probable prime cofactor 32678997856966163491820964161711557583797401265091727332837787241185572405703184609703490221 has 92 digits
Sep 27, 2008: Factorizations of 288...881 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Sep 26, 2008 (2nd): By Sinkiti Sibata / GGNFS
(13·10¹⁶⁶+41)/9 = 1(4)₁₆₅9_<167> = 431 · 659 · 67211 · 34187057 · 109318474575529_<15> · C135
C135 = P50 · P85
P50 = 34142122029434846349176131188868061554306868171903_<50>
P85 = 5929963384398578517109566018319591899379255541236213307569733895313595568330293252969_<85>

Number: 14449_166 N=202461533500216725433746524290492280498300806327822604511062313669686113177108949960264126600183931185734180294575384666460492157130007 ( 135 digits) SNFS difficulty: 167 digits. Divisors found: r1=34142122029434846349176131188868061554306868171903 (pp50) r2=5929963384398578517109566018319591899379255541236213307569733895313595568330293252969 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 124.34 hours. Scaled time: 125.46 units (timescale=1.009). Factorization parameters were as follows: name: 14449_166 n: 202461533500216725433746524290492280498300806327822604511062313669686113177108949960264126600183931185734180294575384666460492157130007 m: 1000000000000000000000000000000000 c5: 130 c0: 41 skew: 0.79 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, 7250001) Primes: RFBsize:380800, AFBsize:379893, largePrimes:6183848 encountered Relations: rels:6450049, finalFF:907035 Max relations in full relation-set: 28 Initial matrix: 760760 x 907035 with sparse part having weight 68399919. Pruned matrix : 645283 x 649150 with weight 50746737. Total sieving time: 120.50 hours. Total relation processing time: 0.12 hours. Matrix solve time: 3.61 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 124.34 hours. --------- CPU info (if available) ----------
Sep 26, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(4·10¹⁸²-7)/3 = 1(3)₁₈₁1_<183> = 51473 · C178
C178 = P33 · P66 · P80
P33 = 111674969858577488476968435205091_<33>
P66 = 410923244146929474573211564906433238336504047888161145678797662857_<66>
P80 = 56447238927081583452010133015677952938829702727247218171506201584513543966479481_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 2590354813850627189659303583108296258880060096231681334550800095843128112473206017394232575006961578562223560572209378379603546195740161508622643586605275257578406802271741171747 (178 digits) Using B1=782000, B2=696767622, polynomial Dickson(3), sigma=2644948554 Step 1 took 12144ms Step 2 took 4526ms ********** Factor found in step 2: 111674969858577488476968435205091 Found probable prime factor of 33 digits: 111674969858577488476968435205091 Composite cofactor 23195482543053206881421353751404610349519007646345770007549762402992329345957190547132777743367728994353508496397809803285168273674330253046337217 has 146 digits Number: n N=23195482543053206881421353751404610349519007646345770007549762402992329345957190547132777743367728994353508496397809803285168273674330253046337217 ( 146 digits) SNFS difficulty: 182 digits. Divisors found: Fri Sep 26 04:28:28 2008 prp66 factor: 410923244146929474573211564906433238336504047888161145678797662857 Fri Sep 26 04:28:28 2008 prp80 factor: 56447238927081583452010133015677952938829702727247218171506201584513543966479481 Fri Sep 26 04:28:29 2008 elapsed time 04:37:09 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 39.64 hours. Scaled time: 81.07 units (timescale=2.045). Factorization parameters were as follows: name: KA_1_3_181_1 n: 23195482543053206881421353751404610349519007646345770007549762402992329345957190547132777743367728994353508496397809803285168273674330253046337217 type: snfs skew: 0.89 deg: 5 c5: 25 c0: -14 m: 2000000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 3700001) Primes: RFBsize:539777, AFBsize:539275, largePrimes:13622239 encountered Relations: rels:13313889, finalFF:1206082 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 39.33 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000 total time: 39.64 hours. --------- CPU info (if available) ----------
Sep 25, 2008: By Serge Batalov / **Msieve 1.38**
(5·10¹⁶⁹-41)/9 = (5)₁₆₈1_<169> = 5851 · 13267 · 1027853 · 73870523 · C147
C147 = P57 · P91
P57 = 696980304571246698535520900058861516042355649025352830041_<57>
P91 = 1352390091424003573905931189189861414444936573068295525332680772365816186487388077452104457_<91>

SNFS difficulty: 170 digits. Divisors found: r1=696980304571246698535520900058861516042355649025352830041 r2=1352390091424003573905931189189861414444936573068295525332680772365816186487388077452104457 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.724). Factorization parameters were as follows: n: 942589257819838178696155706168661683360821107017404276607244976674025274365182068018460893385781710775435724423885085318984473409680541616099592737 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 1 c0: -82 skew: 2.41 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [3000000, 5100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 988373 x 988621 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 38.00 hours.
Sep 24, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
9·10¹⁸⁰-7 = 8(9)₁₇₉3_<181> = 10891 · C177
C177 = P76 · P102
P76 = 5486819574558925029152624668200693996930258823313386814434120700542015883423_<76>
P102 = 150610091392044818382883472006373182746590680311053182451698963556980981251397542935784243994273255701_<102>

Number: n N=826370397575980167110458176475989349003764576255623909650169865026168395923239371958497842255072996051785878248094757138922045725828665870902580112019098338077311541639886144523 ( 177 digits) SNFS difficulty: 180 digits. Divisors found: Wed Sep 24 11:08:36 2008 prp76 factor: 5486819574558925029152624668200693996930258823313386814434120700542015883423 Wed Sep 24 11:08:36 2008 prp102 factor: 150610091392044818382883472006373182746590680311053182451698963556980981251397542935784243994273255701 Wed Sep 24 11:08:37 2008 elapsed time 03:49:38 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.61 hours. Scaled time: 60.78 units (timescale=1.707). Factorization parameters were as follows: name: KA_8_9_179_3 n: 826370397575980167110458176475989349003764576255623909650169865026168395923239371958497842255072996051785878248094757138922045725828665870902580112019098338077311541639886144523 type: snfs skew: 0.95 deg: 5 c5: 9 c0: -7 m: 1000000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 3000001) Primes: RFBsize:539777, AFBsize:539995, largePrimes:13973574 encountered Relations: rels:13965082, finalFF:1414887 Max relations in full relation-set: 28 Initial matrix: 1079836 x 1414887 with sparse part having weight 138132887. Pruned matrix : Total sieving time: 35.29 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000 total time: 35.61 hours. --------- CPU info (if available) ----------
Sep 24, 2008 (3rd): By Sinkiti Sibata / GGNFS
(5·10¹⁶⁶-23)/9 = (5)₁₆₅3_<166> = 3² · 334610021 · 733322295128893182421_<21> · C136
C136 = P36 · P100
P36 = 954966188692478370261835870373955259_<36>
P100 = 2634287420039296053564941005908420267092205878181191973670272490843357273239995457115579925801892643_<100>

Number: 55553_166 N=2515655417435468421906423529418482767298588603498122386763350799680220456382663824939484925376682675948872275090986001914951956003259537 ( 136 digits) SNFS difficulty: 166 digits. Divisors found: r1=954966188692478370261835870373955259 (pp36) r2=2634287420039296053564941005908420267092205878181191973670272490843357273239995457115579925801892643 (pp100) Version: GGNFS-0.77.1-20050930-nocona Total time: 101.01 hours. Scaled time: 101.82 units (timescale=1.008). Factorization parameters were as follows: name: 55553_166 n: 2515655417435468421906423529418482767298588603498122386763350799680220456382663824939484925376682675948872275090986001914951956003259537 m: 1000000000000000000000000000000000 c5: 50 c0: -23 skew: 0.86 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 6200001) Primes: RFBsize:348513, AFBsize:348791, largePrimes:6077777 encountered Relations: rels:6316953, finalFF:862311 Max relations in full relation-set: 28 Initial matrix: 697369 x 862311 with sparse part having weight 64492968. Pruned matrix : 571242 x 574792 with weight 47124797. Total sieving time: 97.95 hours. Total relation processing time: 0.11 hours. Matrix solve time: 2.86 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 101.01 hours. --------- CPU info (if available) ----------
(25·10¹⁶²+11)/9 = 2(7)₁₆₁9_<163> = 956996067485339718144137108196685667_<36> · C127
C127 = P44 · P83
P44 = 82764568509156828642850056701654905874238953_<44>
P83 = 35070575358147688261227157636411129948137439908546697720503815691536272272514529929_<83>

Number: 27779_162 N=2902601036884961627173699119809625917037467027349604362385456802139104947986390088924478788941052925770284265498185067416124337 ( 127 digits) SNFS difficulty: 164 digits. Divisors found: r1=82764568509156828642850056701654905874238953 (pp44) r2=35070575358147688261227157636411129948137439908546697720503815691536272272514529929 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 61.07 hours. Scaled time: 47.63 units (timescale=0.780). Factorization parameters were as follows: name: 27779_162 n: 2902601036884961627173699119809625917037467027349604362385456802139104947986390088924478788941052925770284265498185067416124337 m: 500000000000000000000000000000000 c5: 4 c0: 55 skew: 1.69 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4150001) Primes: RFBsize:315948, AFBsize:315287, largePrimes:5705479 encountered Relations: rels:5818145, finalFF:746133 Max relations in full relation-set: 28 Initial matrix: 631299 x 746133 with sparse part having weight 43557527. Pruned matrix : 536894 x 540114 with weight 29054475. Total sieving time: 58.07 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.71 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 61.07 hours. --------- CPU info (if available) ----------
Sep 24, 2008 (2nd): By Justin Card / GGNFS
7·10¹⁶⁶+1 = 7(0)₁₆₅1_<167> = 23 · 53 · 31327 · 34726262056239405863392591_<26> · C134
C134 = P55 · P80
P55 = 1913290242196232539268012066652201280412112493917178819_<55>
P80 = 27589042770237067407217839796789774556735213612294539601853969868354417611828713_<80>

Number: 70001_166 N=52785846323829097015703542990556850979883528135952978084427866439294004697060090080086165672931785725911862903245367422061368419629947 ( 134 digits) SNFS difficulty: 166 digits. Divisors found: r1=1913290242196232539268012066652201280412112493917178819 r2=27589042770237067407217839796789774556735213612294539601853969868354417611828713 Version: Total time: 90.40 hours. Scaled time: 189.48 units (timescale=2.096). Factorization parameters were as follows: n: 52785846323829097015703542990556850979883528135952978084427866439294004697060090080086165672931785725911862903245367422061368419629947 m: 1000000000000000000000000000000000 c5: 70 c4: 0 c3: 0 c2: 0 c1: 0 c0: 1 Y1: 1 Y0: -1000000000000000000000000000000000 skew: 0.43 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 603990 x 604208 Total sieving time: 90.40 hours. Total relation processing time: 1.58 hours. Matrix solve time: 1.25 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 93.42 hours. --------- CPU info (if available) ---------- [ 27.172216] Memory: 3055428k/3111872k available (2523k kernel code, 56056k reserved, 1328k data, 328k init) [ 27.318604] Calibrating delay using timer specific routine.. 3982.80 BogoMIPS (lpj=19914039) [ 28.066173] Calibrating delay using timer specific routine.. 3979.59 BogoMIPS (lpj=19897994)
Sep 24, 2008: By Serge Batalov / Msieve-1.37 QS
(4·10¹⁷²+41)/9 = (4)₁₇₁9_<172> = 3² · 47 · 220793663 · 262458105583_<12> · 487196685878876428730725467376703_<33> · 398845555197803023949777099556339851_<36> · C81
C81 = P34 · P48
P34 = 2449842135058899424657127232517211_<34>
P48 = 380875764020883110409902511467730416896409998609_<48>

Tue Sep 23 11:56:13 2008 Msieve v. 1.37 Tue Sep 23 11:56:13 2008 random seeds: 53d42b0a 75560bf7 Tue Sep 23 11:56:13 2008 factoring 933085494921109827158710069754359573279758458138952040836991150992465132078559499 (81 digits) Tue Sep 23 11:56:13 2008 searching for 15-digit factors Tue Sep 23 11:56:14 2008 commencing quadratic sieve (81-digit input) Tue Sep 23 11:56:14 2008 using multiplier of 1 Tue Sep 23 11:56:14 2008 using 64kb Opteron sieve core Tue Sep 23 11:56:14 2008 sieve interval: 6 blocks of size 65536 Tue Sep 23 11:56:14 2008 processing polynomials in batches of 17 Tue Sep 23 11:56:14 2008 using a sieve bound of 1325923 (50864 primes) Tue Sep 23 11:56:14 2008 using large prime bound of 127288608 (26 bits) Tue Sep 23 11:56:14 2008 using trial factoring cutoff of 27 bits Tue Sep 23 11:56:14 2008 polynomial 'A' values have 10 factors Tue Sep 23 12:08:02 2008 51110 relations (26192 full + 24918 combined from 272885 partial), need 50960 Tue Sep 23 12:08:02 2008 begin with 299077 relations Tue Sep 23 12:08:02 2008 reduce to 72955 relations in 2 passes Tue Sep 23 12:08:02 2008 attempting to read 72955 relations Tue Sep 23 12:08:03 2008 recovered 72955 relations Tue Sep 23 12:08:03 2008 recovered 63005 polynomials Tue Sep 23 12:08:03 2008 attempting to build 51110 cycles Tue Sep 23 12:08:03 2008 found 51110 cycles in 1 passes Tue Sep 23 12:08:03 2008 distribution of cycle lengths: Tue Sep 23 12:08:03 2008 length 1 : 26192 Tue Sep 23 12:08:03 2008 length 2 : 24918 Tue Sep 23 12:08:03 2008 largest cycle: 2 relations Tue Sep 23 12:08:03 2008 matrix is 50864 x 51110 (7.6 MB) with weight 1580108 (30.92/col) Tue Sep 23 12:08:03 2008 sparse part has weight 1580108 (30.92/col) Tue Sep 23 12:08:03 2008 filtering completed in 3 passes Tue Sep 23 12:08:03 2008 matrix is 36125 x 36188 (5.9 MB) with weight 1256316 (34.72/col) Tue Sep 23 12:08:03 2008 sparse part has weight 1256316 (34.72/col) Tue Sep 23 12:08:03 2008 saving the first 48 matrix rows for later Tue Sep 23 12:08:03 2008 matrix is 36077 x 36188 (4.5 MB) with weight 995457 (27.51/col) Tue Sep 23 12:08:03 2008 sparse part has weight 804953 (22.24/col) Tue Sep 23 12:08:03 2008 matrix includes 64 packed rows Tue Sep 23 12:08:03 2008 using block size 14475 for processor cache size 1024 kB Tue Sep 23 12:08:04 2008 commencing Lanczos iteration Tue Sep 23 12:08:04 2008 memory use: 4.2 MB Tue Sep 23 12:08:08 2008 lanczos halted after 572 iterations (dim = 36076) Tue Sep 23 12:08:08 2008 recovered 17 nontrivial dependencies Tue Sep 23 12:08:08 2008 prp34 factor: 2449842135058899424657127232517211 Tue Sep 23 12:08:08 2008 prp48 factor: 380875764020883110409902511467730416896409998609 Tue Sep 23 12:08:08 2008 elapsed time 00:11:55
Sep 23, 2008 (2nd): By Sinkiti Sibata / GGNFS
(25·10¹⁶⁵+11)/9 = 2(7)₁₆₄9_<166> = 7² · 71 · 1229 · 156799 · 86859680114923_<14> · 141208653207553585741_<21> · C120
C120 = P59 · P62
P59 = 16074984290793976464998006648109533726617375552718845662617_<59>
P62 = 21014439226186271746727555583827699417119049826464020217738801_<62>

Number: 27779_165 N=337806780440789045113039137220969559081629068252855899137979087861381973412324924977923686904046145934723285022276102217 ( 120 digits) Divisors found: r1=16074984290793976464998006648109533726617375552718845662617 (pp59) r2=21014439226186271746727555583827699417119049826464020217738801 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 64.36 hours. Scaled time: 49.49 units (timescale=0.769). Factorization parameters were as follows: name: 27779_165 n: 337806780440789045113039137220969559081629068252855899137979087861381973412324924977923686904046145934723285022276102217 skew: 95898.23 # norm 1.67e+16 c5: 30060 c4: -74717654 c3: -705030454434139 c2: 8050922963625462632 c1: 3155243119129826402614188 c0: -64504785277031888812155507520 # alpha -5.98 Y1: 7426006963723 Y0: -102361323587563003671847 # Murphy_E 3.18e-10 # M 285492000409818898872953286248517410567252442636728159563327865228391630836454600444674685956951115206410069923986873559 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4110001) Primes: RFBsize:315948, AFBsize:316989, largePrimes:7774050 encountered Relations: rels:7972494, finalFF:848401 Max relations in full relation-set: 28 Initial matrix: 633016 x 848401 with sparse part having weight 71702901. Pruned matrix : 457851 x 461080 with weight 42942460. Total sieving time: 60.49 hours. Total relation processing time: 0.43 hours. Matrix solve time: 3.08 hours. Time per square root: 0.36 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: 64.36 hours. --------- CPU info (if available) ----------
Sep 23, 2008: By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.37
(4·10¹⁷²+41)/9 = (4)₁₇₁9_<172> = 3² · 47 · 220793663 · 262458105583_<12> · C150
C150 = P33 · P36 · C81
P33 = 487196685878876428730725467376703_<33>
P36 = 398845555197803023949777099556339851_<36>
C81 = [933085494921109827158710069754359573279758458138952040836991150992465132078559499_<81>]

# two ECM factors: # Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3260962697 Step 1 took 14297ms Step 2 took 12741ms ********** Factor found in step 2: 398845555197803023949777099556339851 Found probable prime factor of 36 digits: 398845555197803023949777099556339851 Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2979693243 Step 1 took 16485ms Step 2 took 12965ms ********** Factor found in step 2: 487196685878876428730725467376703 Found probable prime factor of 33 digits: 487196685878876428730725467376703
(13·10¹⁷⁹+41)/9 = 1(4)₁₇₈9_<180> = 23 · 42015451969_<11> · 78770911838628725351_<20> · C148
C148 = P29 · C119
P29 = 46992713266751930707073011577_<29>
C119 = [40380117029172520674769513188321069808478594187938313449637188262684915551986256553904977186681940701330222198933277801_<119>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=843826318 Step 1 took 14245ms Step 2 took 12917ms ********** Factor found in step 2: 46992713266751930707073011577 Found probable prime factor of 29 digits: 46992713266751930707073011577 Composite cofactor 40380117029172520674769513188321069808478594187938313449637188262684915551986256553904977186681940701330222198933277801 has 119 digits
4·10¹⁹⁵-9 = 3(9)₁₉₄1_<196> = 13 · 107 · 317 · 683 · 4813 · 34945726168123_<14> · 235346907565680687670001_<24> · C147
C147 = P35 · P112
P35 = 84023102213882289455105713911646201_<35>
P112 = 3993335105848129845498334339702023428427294782244533437466867913637243996141634999335678685464308070534367797009_<112>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3729024413 Step 1 took 18539ms Step 2 took 16998ms ********** Factor found in step 2: 84023102213882289455105713911646201 Found probable prime factor of 35 digits: 84023102213882289455105713911646201 Probable prime cofactor 3993335105848129845498334339702023428427294782244533437466867913637243996141634999335678685464308070534367797009 has 112 digits
(8·10¹⁹⁸-53)/9 = (8)₁₉₇3_<198> = 443² · 509 · 54001 · 781721 · 23743506773317561028947_<23> · 2580754674706962971246952203_<28> · C130
C130 = P29 · P102
P29 = 32368523515701041820822572173_<29>
P102 = 106280646441674238900428385238379104570468681385301477094082044361402629538958719229812675579724825371_<102>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3529257140 Step 1 took 12445ms Step 2 took 11241ms ********** Factor found in step 2: 32368523515701041820822572173 Found probable prime factor of 29 digits: 32368523515701041820822572173 Probable prime cofactor 106280646441674238900428385238379104570468681385301477094082044361402629538958719229812675579724825371 has 102 digits
(13·10¹⁶⁷+41)/9 = 1(4)₁₆₆9_<168> = 480185983 · 28444017767816011987_<20> · C140
C140 = P60 · P80
P60 = 255495494090934243398138407064825919513157133359958105353597_<60>
P80 = 41392073043566976748716370443946057031311344967750540425260269537821998787807977_<80>

SNFS difficulty: 168 digits. Divisors found: r1=255495494090934243398138407064825919513157133359958105353597 r2=41392073043566976748716370443946057031311344967750540425260269537821998787807977 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.729). Factorization parameters were as follows: n: 10575488153714185091397046009582798434739843055341525642692804920734214201457798874370694763287755300109417664211267870586842810176122243269 Y1: 1 Y0: -1000000000000000000000000000000000 c5: 1300 c0: 41 skew: 0.5 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [2750000, 5050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1009651 x 1009899 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 4.00 hours. Time per square root: 0.30 hours * 3 Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,54,54,2.6,2.6,100000 total time: 39.00 hours.
8·10¹⁸⁹-7 = 7(9)₁₈₈3_<190> = 1403785393_<10> · 1947272813871401270971_<22> · C160
C160 = P30 · P131
P30 = 259434316310048883009749966749_<30>
P131 = 11280673929515482410186744031856075693766227254925575504050922917780974235338007459650081318927619624208279244239261693510134938119_<131>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1724537978 Step 1 took 20561ms Step 2 took 2944ms ********** Factor found in step 2: 259434316310048883009749966749 Found probable prime factor of 30 digits: 259434316310048883009749966749 Probable prime cofactor 11280673929515482410186744031856075693766227254925575504050922917780974235338007459650081318927619624208279244239261693510134938119 has 131 digits
Sep 23, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
7·10¹⁷⁸-9 = 6(9)₁₇₇1_<179> = 19 · 2539 · C175
C175 = P65 · P111
P65 = 12897341641762311482225721924377786620072960817038184469508152023_<65>
P111 = 112507515436489482196909605851330785043044214218396095102143177575566128872215934971677861051720757848691700337_<111>

Number: n N=1451047863850251860450654008001492506374245973342177815551087249435127795858294811467423975456561845732882817520366493231898177898468108040878091250181380982981281482556331751 ( 175 digits) SNFS difficulty: 178 digits. Divisors found: Mon Sep 22 18:53:36 2008 prp65 factor: 12897341641762311482225721924377786620072960817038184469508152023 Mon Sep 22 18:53:36 2008 prp111 factor: 112507515436489482196909605851330785043044214218396095102143177575566128872215934971677861051720757848691700337 Mon Sep 22 18:53:36 2008 elapsed time 05:54:33 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 57.99 hours. Scaled time: 118.94 units (timescale=2.051). Factorization parameters were as follows: name: KA_6_9_177_1 n: 1451047863850251860450654008001492506374245973342177815551087249435127795858294811467423975456561845732882817520366493231898177898468108040878091250181380982981281482556331751 type: snfs skew: 0.26 deg: 5 c5: 7000 c0: -9 m: 100000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 11400001) Primes: RFBsize:539777, AFBsize:539075, largePrimes:15392040 encountered Relations: rels:15911037, finalFF:1641017 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 57.50 hours. Total relation processing time: 0.49 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,178,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000 total time: 57.99 hours. --------- CPU info (if available) ----------
Sep 23, 2008 (3rd): By Serge Batalov / GMP-ECM 6.2.1
(8·10¹⁹⁸-53)/9 = (8)₁₉₇3_<198> = 443² · 509 · 54001 · 781721 · 23743506773317561028947_<23> · C157
C157 = P28 · C130
P28 = 2580754674706962971246952203_<28>
C130 = [3440147603611240855717915265739196737191480416785639942379705043877609846496446141839893018288901405432125844676826299567469001183_<130>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1884473842 Step 1 took 24308ms ********** Factor found in step 1: 2580754674706962971246952203 Found probable prime factor of 28 digits: 2580754674706962971246952203 Composite cofactor 3440147603611240855717915265739196737191480416785639942379705043877609846496446141839893018288901405432125844676826299567469001183 has 130 digits
Sep 22, 2008 (2nd): By matsui / GMP-ECM
4·10¹⁸²+9 = 4(0)₁₈₁9_<183> = 593 · 1328642261_<10> · 23666791403837444777_<20> · C152
C152 = P38 · P114
P38 = 30538114624651788954583755347034152657_<38>
P114 = 702450347822345188677038220687379849426066288977031773444331177142414305322712815983768134833633739828814217175997_<114>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 21451509239925295538168421795102247653439573588875108420209533505822891969985296592779292726269424313705399400454705326894779927663246219481894334174029 =30538114624651788954583755347034152657* 702450347822345188677038220687379849426066288977031773444331177142414305322712815983768134833633739828814217175997
Sep 22, 2008: By Sinkiti Sibata / GGNFS
(25·10¹⁵⁷+11)/9 = 2(7)₁₅₆9_<158> = 9542909 · 2914206752057_<13> · 9138747720366349_<16> · C123
C123 = P58 · P65
P58 = 1324246518820340916190100054706676378801923457295730611749_<58>
P65 = 82535507900081281232126800634121927761333411590662336194211534983_<65>

Number: 27779_157 N=109297359015751382757590584761681435097761745318418345552443725745543683153018309251137026627824848955651477944234904315267 ( 123 digits) Divisors found: r1=1324246518820340916190100054706676378801923457295730611749 (pp58) r2=82535507900081281232126800634121927761333411590662336194211534983 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 82.43 hours. Scaled time: 83.18 units (timescale=1.009). Factorization parameters were as follows: name: 27779_157 n: 109297359015751382757590584761681435097761745318418345552443725745543683153018309251137026627824848955651477944234904315267 skew: 62000.91 # norm 9.42e+15 c5: 1560 c4: 1495301999 c3: -237801306897353 c2: -6516794873467408648 c1: 46696468715858655525789 c0: 428876002410578610703489620 # alpha -4.43 Y1: 11440970936461 Y0: -587618408973170623261291 # Murphy_E 2.39e-10 # M 100730276207215881327981099032047925236957950976150459045887497600095574624645597788010714685658071890436466215979834840367 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 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5440001) Primes: RFBsize:348513, AFBsize:348010, largePrimes:7962731 encountered Relations: rels:8330423, finalFF:925608 Max relations in full relation-set: 28 Initial matrix: 696602 x 925608 with sparse part having weight 90657732. Pruned matrix : 519652 x 523199 with weight 62536167. Total sieving time: 79.00 hours. Total relation processing time: 0.23 hours. Matrix solve time: 2.92 hours. Time per square root: 0.28 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: 82.43 hours. --------- CPU info (if available) ----------
Sep 21, 2008 (3rd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(43·10¹⁸⁰-7)/9 = 4(7)₁₈₀_<181> = 7717 · C177
C177 = P37 · P140
P37 = 7974850129236699611743439999799043481_<37>
P140 = 77634527787228389847918815078532026524742425012288827865479837265962584100748133165695301835012008917167725311213692593828248802988299673701_<140>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 619123723957208471916259916778252919240349588930643744690654111413473860020445481116726419305141606554072538263285963169337537615365786935049601889047269376412825939844211193181 (177 digits) Using B1=3834000, B2=8561443810, polynomial Dickson(6), sigma=936150032 Step 1 took 59850ms Step 2 took 21227ms ********** Factor found in step 2: 7974850129236699611743439999799043481 Found probable prime factor of 37 digits: 7974850129236699611743439999799043481 Probable prime cofactor 77634527787228389847918815078532026524742425012288827865479837265962584100748133165695301835012008917167725311213692593828248802988299673701 has 140 digits
(22·10¹⁹⁵+41)/9 = 2(4)₁₉₄9_<196> = C196
C196 = P48 · P149
P48 = 133847907008974165416726785238473125656386676331_<48>
P149 = 18262851463792785302404893664396092758157756934387695704742235137911239465916250049387416609237886485726480277100893540116149440927005054900514665379_<149>

Number: n N=2444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 ( 196 digits) SNFS difficulty: 196 digits. Divisors found: Sun Sep 21 23:31:43 2008 prp48 factor: 133847907008974165416726785238473125656386676331 Sun Sep 21 23:31:43 2008 prp149 factor: 18262851463792785302404893664396092758157756934387695704742235137911239465916250049387416609237886485726480277100893540116149440927005054900514665379 Sun Sep 21 23:31:43 2008 elapsed time 24:58:19 (Msieve 1.37) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 183.83 hours. Scaled time: 236.96 units (timescale=1.289). Factorization parameters were as follows: name: KA_2_4_194_9 n: 2444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 type: snfs skew: 1.13 deg: 5 c5: 22 c0: 41 m: 1000000000000000000000000000000000000000 rlim: 9600000 alim: 9600000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9600000/9600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 16100001) Primes: RFBsize:639851, AFBsize:639690, largePrimes:15700927 encountered Relations: rels:16181449, finalFF:1303141 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 182.76 hours. Total relation processing time: 1.08 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,9600000,9600000,28,28,52,52,2.5,2.5,100000 total time: 183.83 hours. --------- CPU info (if available) ----------
Sep 21, 2008 (2nd): By Serge Batalov / Msieve-1.37
(25·10¹⁵⁸+11)/9 = 2(7)₁₅₇9_<159> = 3 · 163 · 448801 · C151
C151 = P39 · P112
P39 = 137389628695179787605418180755763657877_<39>
P112 = 9212571560698381077396463062817283198373662941165977110800670318580503998459757629198423949102641490029724479343_<112>

SNFS difficulty: 159 digits. Divisors found: r1=137389628695179787605418180755763657877 r2=9212571560698381077396463062817283198373662941165977110800670318580503998459757629198423949102641490029724479343 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.720). Factorization parameters were as follows: n: 1265711786052123537291755711705811059148731331941557665959847133426148586146192857342235679715462077090018193295647088925848584354096853706755005734811 Y1: 1 Y0: -50000000000000000000000000000000 c5: 8 c0: 11 skew: 1.07 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [2000000, 2800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 648365 x 648613 Total sieving time: 12.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 1.50 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,54,54,2.5,2.5,100000 total time: 14.00 hours.
(25·10¹⁵⁹+11)/9 = 2(7)₁₅₈9_<160> = 7 · C159
C159 = P43 · P117
P43 = 2657780922364980442038543388644686126602807_<43>
P117 = 149307037869881540490495888397203652439490230060489375653475306412910625822390022203824618445561134554266447970512371_<117>

SNFS difficulty: 160 digits. Divisors found: r1=2657780922364980442038543388644686126602807 r2=149307037869881540490495888397203652439490230060489375653475306412910625822390022203824618445561134554266447970512371 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.703). Factorization parameters were as follows: n: 396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825397 Y1: 1 Y0: -100000000000000000000000000000000 c5: 5 c0: 22 skew: 1.34 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [2000000, 3200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 715410 x 715658 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,54,54,2.5,2.5,100000 total time: 19.00 hours.
Sep 21, 2008: By Sinkiti Sibata / GGNFS, Msieve
(25·10¹⁶⁸+11)/9 = 2(7)₁₆₇9_<169> = 60737823877_<11> · 2391245651153087_<16> · 88327195955309617_<17> · 11269454630239385869_<20> · C107
C107 = P44 · P63
P44 = 99636796677422281629691745530908874418949017_<44>
P63 = 192839935983067964860238605035402472643939209453310925694585381_<63>

Number: 27779_168 N=19213953492832071691888356432134441574295306649176679790741819525345351703318048554011557238677581592520477 ( 107 digits) Divisors found: r1=99636796677422281629691745530908874418949017 (pp44) r2=192839935983067964860238605035402472643939209453310925694585381 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 19.68 hours. Scaled time: 15.17 units (timescale=0.771). Factorization parameters were as follows: name: 27779_168 n: 19213953492832071691888356432134441574295306649176679790741819525345351703318048554011557238677581592520477 skew: 9817.78 # norm 1.43e+14 c5: 6840 c4: -1293420660 c3: 965728069439 c2: 125523965749091149 c1: 284947326891434748589 c0: -4579311507562674711556 # alpha -4.62 Y1: 7631626717 Y0: -308825058652731342747 # Murphy_E 1.46e-09 # M 17111148031494828095272157669907087589765217394301232366704600631807007446817858694000563667479322053158049 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, 2600001) Primes: RFBsize:183072, AFBsize:183200, largePrimes:4619239 encountered Relations: rels:4875921, finalFF:565343 Max relations in full relation-set: 28 Initial matrix: 366351 x 565343 with sparse part having weight 48074444. Pruned matrix : 245460 x 247355 with weight 26390764. Total sieving time: 18.67 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.68 hours. Time per square root: 0.16 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: 19.68 hours. --------- CPU info (if available) ----------
(25·10¹³⁵+11)/9 = 2(7)₁₃₄9_<136> = 7 · 17 · 24618943 · 829455593933613949664672311_<27> · C100
C100 = P33 · P68
P33 = 101760642791834943232640563376777_<33>
P68 = 11233320577193988996054868802362165629420963942890486212300213105621_<68>

Sat Sep 20 16:03:00 2008 Msieve v. 1.36 Sat Sep 20 16:03:00 2008 random seeds: a78bf2a4 352f1807 Sat Sep 20 16:03:00 2008 factoring 1143109922622006640335934320858230741322564114655730564054913482556917003342965340126485297919563517 (100 digits) Sat Sep 20 16:03:02 2008 no P-1/P+1/ECM available, skipping Sat Sep 20 16:03:02 2008 commencing quadratic sieve (100-digit input) Sat Sep 20 16:03:02 2008 using multiplier of 3 Sat Sep 20 16:03:02 2008 using 64kb Pentium 4 sieve core Sat Sep 20 16:03:02 2008 sieve interval: 18 blocks of size 65536 Sat Sep 20 16:03:02 2008 processing polynomials in batches of 6 Sat Sep 20 16:03:02 2008 using a sieve bound of 2681729 (97571 primes) Sat Sep 20 16:03:02 2008 using large prime bound of 402259350 (28 bits) Sat Sep 20 16:03:02 2008 using double large prime bound of 3076883377187400 (43-52 bits) Sat Sep 20 16:03:02 2008 using trial factoring cutoff of 52 bits Sat Sep 20 16:03:02 2008 polynomial 'A' values have 13 factors Sat Sep 20 16:03:06 2008 restarting with 8177 full and 518198 partial relations Sun Sep 21 03:25:34 2008 97777 relations (23198 full + 74579 combined from 1477182 partial), need 97667 Sun Sep 21 03:25:39 2008 begin with 1500380 relations Sun Sep 21 03:25:41 2008 reduce to 258871 relations in 12 passes Sun Sep 21 03:25:41 2008 attempting to read 258871 relations Sun Sep 21 03:25:50 2008 recovered 258871 relations Sun Sep 21 03:25:50 2008 recovered 249493 polynomials Sun Sep 21 03:25:50 2008 attempting to build 97777 cycles Sun Sep 21 03:25:51 2008 found 97777 cycles in 6 passes Sun Sep 21 03:25:51 2008 distribution of cycle lengths: Sun Sep 21 03:25:51 2008 length 1 : 23198 Sun Sep 21 03:25:51 2008 length 2 : 16628 Sun Sep 21 03:25:51 2008 length 3 : 16331 Sun Sep 21 03:25:51 2008 length 4 : 13312 Sun Sep 21 03:25:51 2008 length 5 : 10105 Sun Sep 21 03:25:51 2008 length 6 : 7105 Sun Sep 21 03:25:51 2008 length 7 : 4567 Sun Sep 21 03:25:51 2008 length 9+: 6531 Sun Sep 21 03:25:51 2008 largest cycle: 22 relations Sun Sep 21 03:25:51 2008 matrix is 97571 x 97777 (26.0 MB) with weight 6414114 (65.60/col) Sun Sep 21 03:25:51 2008 sparse part has weight 6414114 (65.60/col) Sun Sep 21 03:25:53 2008 filtering completed in 3 passes Sun Sep 21 03:25:53 2008 matrix is 93701 x 93765 (25.0 MB) with weight 6179719 (65.91/col) Sun Sep 21 03:25:53 2008 sparse part has weight 6179719 (65.91/col) Sun Sep 21 03:25:54 2008 saving the first 48 matrix rows for later Sun Sep 21 03:25:54 2008 matrix is 93653 x 93765 (13.8 MB) with weight 4676238 (49.87/col) Sun Sep 21 03:25:54 2008 sparse part has weight 3067094 (32.71/col) Sun Sep 21 03:25:54 2008 matrix includes 64 packed rows Sun Sep 21 03:25:54 2008 using block size 21845 for processor cache size 512 kB Sun Sep 21 03:25:55 2008 commencing Lanczos iteration Sun Sep 21 03:25:55 2008 memory use: 14.5 MB Sun Sep 21 03:27:25 2008 lanczos halted after 1482 iterations (dim = 93647) Sun Sep 21 03:27:25 2008 recovered 15 nontrivial dependencies Sun Sep 21 03:27:28 2008 prp33 factor: 101760642791834943232640563376777 Sun Sep 21 03:27:28 2008 prp68 factor: 11233320577193988996054868802362165629420963942890486212300213105621 Sun Sep 21 03:27:28 2008 elapsed time 11:24:28
Sep 20, 2008 (6th): By Jo Yeong Uk / GGNFS
(25·10¹⁷⁷+11)/9 = 2(7)₁₇₆9_<178> = 7 · 401 · 2677468327_<10> · 845137723820723_<15> · 545382280341452033_<18> · 384200698398579815600737_<24> · C109
C109 = P46 · P63
P46 = 6157197430675453532424056643451057039223485303_<46>
P63 = 338969797703252851359735909773659729555343992931588939572392839_<63>

Number: 27779_177 N=2087103967495046706276067970122419419022511455953998279647936986802817671321789654961798929535928625058945217 ( 109 digits) Divisors found: r1=6157197430675453532424056643451057039223485303 (pp46) r2=338969797703252851359735909773659729555343992931588939572392839 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.74 hours. Scaled time: 27.28 units (timescale=2.323). Factorization parameters were as follows: name: 27779_177 n: 2087103967495046706276067970122419419022511455953998279647936986802817671321789654961798929535928625058945217 skew: 32823.13 # norm 4.71e+14 c5: 4140 c4: -71364416 c3: -11634601779911 c2: -437449399023178436 c1: 2192614406917375491624 c0: 51523026074077021222366080 # alpha -5.51 Y1: 53450399057 Y0: -871984650797901441577 # Murphy_E 1.24e-09 # M 1324511941542110147642404859276676481618277862522208959679582391092161274809532009101863003961825845040641987 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1700001) Primes: RFBsize:148933, AFBsize:148689, largePrimes:5135535 encountered Relations: rels:5333563, finalFF:456369 Max relations in full relation-set: 28 Initial matrix: 297703 x 456369 with sparse part having weight 47715445. Pruned matrix : 224563 x 226115 with weight 22753216. Polynomial selection time: 0.68 hours. Total sieving time: 10.69 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.22 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,26,26,50,50,2.6,2.6,50000 total time: 11.74 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343) Calibrating delay using timer specific routine.. 5344.63 BogoMIPS (lpj=2672318) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)
Sep 20, 2008 (5th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(14·10¹⁷⁸-23)/9 = 1(5)₁₇₇3_<179> = 17 · C177
C177 = P43 · P135
P43 = 2225841655194472268016781853809366714396313_<43>
P135 = 411095136800562521541539475829738868608002274427477071385840597838998349260485047470252329367328208883411589540139084008392762907660793_<135>

Number: n N=915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209 ( 177 digits) SNFS difficulty: 179 digits. Divisors found: Sat Sep 20 16:52:55 2008 prp43 factor: 2225841655194472268016781853809366714396313 Sat Sep 20 16:52:55 2008 prp135 factor: 411095136800562521541539475829738868608002274427477071385840597838998349260485047470252329367328208883411589540139084008392762907660793 Sat Sep 20 16:52:55 2008 elapsed time 06:44:14 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 103.73 hours. Scaled time: 87.34 units (timescale=0.842). Factorization parameters were as follows: name: KA_1_5_177_3 n: 915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209 type: snfs skew: 0.55 deg: 5 c5: 875 c0: -46 m: 200000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 13800001) Primes: RFBsize:539777, AFBsize:540340, largePrimes:15352877 encountered Relations: rels:15599595, finalFF:1126756 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 103.04 hours. Total relation processing time: 0.69 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,179,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000 total time: 103.73 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(79·10¹⁷¹-7)/9 = 8(7)₁₇₁_<172> = 455849 · 5458373 · 67309522537_<11> · 1478323965043_<13> · 21868648504691_<14> · C124
C124 = P39 · P85
P39 = 205933584244552585437467949053421910141_<39>
P85 = 7872363074833719679020067199964325911944706977770586747781253428175946317375962633481_<85>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 1621183944474974841004973167630623544618770286330625649993113352858042939934854174924508403146115135259070343188195700030821 (124 digits) Using B1=5472000, B2=11416630690, polynomial Dickson(12), sigma=1768681715 Step 1 took 48726ms Step 2 took 20109ms ********** Factor found in step 2: 205933584244552585437467949053421910141 Found probable prime factor of 39 digits: 205933584244552585437467949053421910141 Probable prime cofactor 7872363074833719679020067199964325911944706977770586747781253428175946317375962633481 has 85 digits
Sep 20, 2008 (4th): By Serge Batalov / Msieve 1.37, GMP-ECM 6.2.1, Msieve-1.37
(25·10¹⁴⁵+11)/9 = 2(7)₁₄₄9_<146> = 39119 · C141
C141 = P65 · P77
P65 = 22018123084442256945601181842870458576967444925337048195952914377_<65>
P77 = 32249980746513672256233897182103678492771023523845280466382534623925440318133_<77>

Number: 27779_145 N=710084045547631017607243993399058712589222060323059837362350207770591727236835751879592468564579303606374850527308412223670793675139389498141 ( 141 digits) SNFS difficulty: 146 digits. Divisors found: r1=22018123084442256945601181842870458576967444925337048195952914377 r2=32249980746513672256233897182103678492771023523845280466382534623925440318133 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.723). Factorization parameters were as follows: n: 710084045547631017607243993399058712589222060323059837362350207770591727236835751879592468564579303606374850527308412223670793675139389498141 Y1: 1 Y0: -100000000000000000000000000000 c5: 25 c0: 11 skew: 0.85 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved rational special-q in [750000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 217022 x 217241 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 4.90 hours.
(25·10¹⁸¹+11)/9 = 2(7)₁₈₀9_<182> = 489343 · 210435473 · 429402721073_<12> · 182964771137591_<15> · 43944186772223093519_<20> · C122
C122 = P32 · P91
P32 = 23598479575400327060190027268979_<32>
P91 = 3310910530014099084884003286660786026675819476626077776496236615555080721288380919172566327_<91>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1615171658 Step 1 took 4421ms Step 2 took 2396ms ********** Factor found in step 2: 23598479575400327060190027268979 Found probable prime factor of 32 digits: 23598479575400327060190027268979 Probable prime cofactor 3310910530014099084884003286660786026675819476626077776496236615555080721288380919172566327 has 91 digits
(25·10¹⁴⁹+11)/9 = 2(7)₁₄₈9_<150> = 3 · C149
C149 = P44 · P48 · P58
P44 = 89422569745722268375593254754751733693202109_<44>
P48 = 284115817265519624811828721956934316858888334641_<48>
P58 = 3644464179724676150814281014736489200665629737281618159797_<58>

SNFS difficulty: 150 digits. Divisors found: r1=89422569745722268375593254754751733693202109 r2=284115817265519624811828721956934316858888334641 r3=3644464179724676150814281014736489200665629737281618159797 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.726). Factorization parameters were as follows: n: 92592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593 Y1: 1 Y0: -1000000000000000000000000000000 c5: 5 c0: 22 skew: 1.34 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [1200000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 451014 x 451254 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,54,54,2.5,2.5,100000 total time: 9.50 hours.
Sep 20, 2008 (3rd): By Sinkiti Sibata / GGNFS, Msieve
(25·10¹⁴⁴+11)/9 = 2(7)₁₄₃9_<145> = 2179652333_<10> · 555525169807_<12> · C124
C124 = P34 · P41 · P49
P34 = 6555616797040220553503787469828621_<34>
P41 = 73975542567038708308894989343115810707013_<41>
P49 = 4730475671659868972131894097385159232743234787633_<49>

Number: 27779_144 N=2294069293066095745670137846707089174646054183142057512760829022119782349751523968362806955211662464140409618998272826924209 ( 124 digits) SNFS difficulty: 145 digits. Divisors found: r1=6555616797040220553503787469828621 (pp34) r2=73975542567038708308894989343115810707013 (pp41) r3=4730475671659868972131894097385159232743234787633 (pp49) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.88 hours. Scaled time: 17.02 units (timescale=1.008). Factorization parameters were as follows: name: 27779_144 n: 2294069293066095745670137846707089174646054183142057512760829022119782349751523968362806955211662464140409618998272826924209 m: 100000000000000000000000000000 c5: 5 c0: 22 skew: 1.34 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 3150001) Primes: RFBsize:100021, AFBsize:100104, largePrimes:3076799 encountered Relations: rels:3208992, finalFF:311014 Max relations in full relation-set: 28 Initial matrix: 200190 x 311014 with sparse part having weight 39232556. Pruned matrix : 176682 x 177746 with weight 22487174. Total sieving time: 16.56 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.22 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 16.88 hours. --------- CPU info (if available) ----------
(25·10¹⁰⁹+11)/9 = 2(7)₁₀₈9_<110> = 621059 · 60520133 · C96
C96 = P37 · P59
P37 = 8518541216079366642207800998712558843_<37>
P59 = 86756003328650734930201809343394393921066217104696711721799_<59>

Fri Sep 19 21:48:34 2008 Msieve v. 1.36 Fri Sep 19 21:48:34 2008 random seeds: 6141f597 886cea6a Fri Sep 19 21:48:34 2008 factoring 739034590097430011847178811447724966016948771754630731479696239768907048998575629325791633318557 (96 digits) Fri Sep 19 21:48:36 2008 no P-1/P+1/ECM available, skipping Fri Sep 19 21:48:36 2008 commencing quadratic sieve (96-digit input) Fri Sep 19 21:48:36 2008 using multiplier of 5 Fri Sep 19 21:48:36 2008 using 64kb Pentium 4 sieve core Fri Sep 19 21:48:36 2008 sieve interval: 18 blocks of size 65536 Fri Sep 19 21:48:36 2008 processing polynomials in batches of 6 Fri Sep 19 21:48:36 2008 using a sieve bound of 2298889 (84706 primes) Fri Sep 19 21:48:36 2008 using large prime bound of 344833350 (28 bits) Fri Sep 19 21:48:36 2008 using double large prime bound of 2331828631036500 (43-52 bits) Fri Sep 19 21:48:36 2008 using trial factoring cutoff of 52 bits Fri Sep 19 21:48:36 2008 polynomial 'A' values have 12 factors Sat Sep 20 05:02:55 2008 84910 relations (21169 full + 63741 combined from 1268574 partial), need 84802 Sat Sep 20 05:03:00 2008 begin with 1289743 relations Sat Sep 20 05:03:01 2008 reduce to 219896 relations in 10 passes Sat Sep 20 05:03:01 2008 attempting to read 219896 relations Sat Sep 20 05:03:09 2008 recovered 219896 relations Sat Sep 20 05:03:09 2008 recovered 203990 polynomials Sat Sep 20 05:03:09 2008 attempting to build 84910 cycles Sat Sep 20 05:03:09 2008 found 84910 cycles in 6 passes Sat Sep 20 05:03:09 2008 distribution of cycle lengths: Sat Sep 20 05:03:09 2008 length 1 : 21169 Sat Sep 20 05:03:09 2008 length 2 : 14932 Sat Sep 20 05:03:09 2008 length 3 : 14313 Sat Sep 20 05:03:09 2008 length 4 : 11452 Sat Sep 20 05:03:09 2008 length 5 : 8668 Sat Sep 20 05:03:09 2008 length 6 : 5678 Sat Sep 20 05:03:09 2008 length 7 : 3710 Sat Sep 20 05:03:09 2008 length 9+: 4988 Sat Sep 20 05:03:09 2008 largest cycle: 21 relations Sat Sep 20 05:03:10 2008 matrix is 84706 x 84910 (23.5 MB) with weight 5816551 (68.50/col) Sat Sep 20 05:03:10 2008 sparse part has weight 5816551 (68.50/col) Sat Sep 20 05:03:11 2008 filtering completed in 3 passes Sat Sep 20 05:03:11 2008 matrix is 80313 x 80375 (22.4 MB) with weight 5547279 (69.02/col) Sat Sep 20 05:03:11 2008 sparse part has weight 5547279 (69.02/col) Sat Sep 20 05:03:12 2008 saving the first 48 matrix rows for later Sat Sep 20 05:03:12 2008 matrix is 80265 x 80375 (16.9 MB) with weight 4712491 (58.63/col) Sat Sep 20 05:03:12 2008 sparse part has weight 3959309 (49.26/col) Sat Sep 20 05:03:12 2008 matrix includes 64 packed rows Sat Sep 20 05:03:12 2008 using block size 21845 for processor cache size 512 kB Sat Sep 20 05:03:13 2008 commencing Lanczos iteration Sat Sep 20 05:03:13 2008 memory use: 14.7 MB Sat Sep 20 05:04:34 2008 lanczos halted after 1270 iterations (dim = 80265) Sat Sep 20 05:04:34 2008 recovered 18 nontrivial dependencies Sat Sep 20 05:04:36 2008 prp37 factor: 8518541216079366642207800998712558843 Sat Sep 20 05:04:36 2008 prp59 factor: 86756003328650734930201809343394393921066217104696711721799 Sat Sep 20 05:04:36 2008 elapsed time 07:16:02
(25·10¹⁴⁶+11)/9 = 2(7)₁₄₅9_<147> = 3² · 311 · 815280920042379045817_<21> · C123
C123 = P36 · P87
P36 = 217157733583248726770838103900749061_<36>
P87 = 560546985914951290774332227279129798735530007314797011598600521856481772063274777635233_<87>

Number: 27779_146 N=121727113028212068940104061530922353894609120636416006266835333908723404409672394991179681058140998472858620222918925266213 ( 123 digits) SNFS difficulty: 147 digits. Divisors found: r1=217157733583248726770838103900749061 (pp36) r2=560546985914951290774332227279129798735530007314797011598600521856481772063274777635233 (pp87) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.59 hours. Scaled time: 15.71 units (timescale=1.008). Factorization parameters were as follows: name: 27779_146 n: 121727113028212068940104061530922353894609120636416006266835333908723404409672394991179681058140998472858620222918925266213 m: 100000000000000000000000000000 c5: 250 c0: 11 skew: 0.54 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 2850001) Primes: RFBsize:114155, AFBsize:114243, largePrimes:2880134 encountered Relations: rels:2875007, finalFF:270616 Max relations in full relation-set: 28 Initial matrix: 228464 x 270616 with sparse part having weight 29150397. Pruned matrix : 215839 x 217045 with weight 21581657. Total sieving time: 15.19 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.29 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 15.59 hours. --------- CPU info (if available) ----------
(25·10¹⁵³+11)/9 = 2(7)₁₅₂9_<154> = 7 · 1619 · 26249 · 121001 · 9629191476013162601_<19> · C121
C121 = P47 · P75
P47 = 17089294561179909609497895907997512028577048257_<47>
P75 = 468961218759818144911743241615271591080346751331129510155707954444981636591_<75>

Number: 27779_153 N=8014216405156462018926099823156586249159542824660379557516458721325017323013340800025073267558580653489159472339843971887 ( 121 digits) SNFS difficulty: 154 digits. Divisors found: r1=17089294561179909609497895907997512028577048257 (pp47) r2=468961218759818144911743241615271591080346751331129510155707954444981636591 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 25.53 hours. Scaled time: 19.99 units (timescale=0.783). Factorization parameters were as follows: name: 27779_153 n: 8014216405156462018926099823156586249159542824660379557516458721325017323013340800025073267558580653489159472339843971887 m: 5000000000000000000000000000000 c5: 8 c0: 11 skew: 1.07 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:175424, largePrimes:5471494 encountered Relations: rels:5387090, finalFF:488774 Max relations in full relation-set: 28 Initial matrix: 351791 x 488774 with sparse part having weight 42592876. Pruned matrix : 290759 x 292581 with weight 23002981. Total sieving time: 24.47 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.86 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 25.53 hours. --------- CPU info (if available) ----------
Sep 20, 2008 (2nd): By Jo Yeong Uk / GGNFS, GMP-ECM
(25·10¹⁴²+11)/9 = 2(7)₁₄₁9_<143> = 18679 · 2324149 · 21883871 · 2721872386127978805349_<22> · C104
C104 = P32 · P72
P32 = 17100579543785749444125700728983_<32>
P72 = 628169976582331219460679003133833163982380481247619650573495514275530357_<72>

Number: 27779_142 N=10742070651564186516675552053776763874950710443051540573202381782044493421278783011980786156993846236931 ( 104 digits) Divisors found: r1=17100579543785749444125700728983 (pp32) r2=628169976582331219460679003133833163982380481247619650573495514275530357 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.95 hours. Scaled time: 11.79 units (timescale=2.380). Factorization parameters were as follows: name: 27779_142 n: 10742070651564186516675552053776763874950710443051540573202381782044493421278783011980786156993846236931 skew: 25644.16 # norm 4.05e+14 c5: 4200 c4: 237417580 c3: -22938014228706 c2: -99292987080815543 c1: 3491001841126376848650 c0: -7512869258041779422968325 # alpha -6.19 Y1: 6826139641 Y0: -76132011157515595038 # Murphy_E 2.31e-09 # M 2345490416613929445046528387112026856772247017840236364780300929704505961959466593458521683729229215729 type: gnfs rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [800000, 1550001) Primes: RFBsize:121127, AFBsize:120508, largePrimes:4424323 encountered Relations: rels:4365416, finalFF:305834 Max relations in full relation-set: 28 Initial matrix: 241714 x 305834 with sparse part having weight 26506673. Pruned matrix : 208289 x 209561 with weight 15361234. Polynomial selection time: 0.39 hours. Total sieving time: 4.29 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.15 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1600000,1600000,26,26,49,49,2.6,2.6,50000 total time: 4.95 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343) Calibrating delay using timer specific routine.. 5344.63 BogoMIPS (lpj=2672318) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)
(25·10¹⁷¹+11)/9 = 2(7)₁₇₀9_<172> = 7 · 139 · 160019 · 16845041 · 26144659 · 65978131 · 31757213781199_<14> · 470300919484222862311_<21> · C107
C107 = P44 · P63
P44 = 47874100857762290609637818483054673407660177_<44>
P63 = 858695511971689614580328938461510753245623133163645463110819701_<63>

Number: 27779_171 N=41109275546240495062432283264051165658091623196993437906976151352389340190469170320769270885516502924747077 ( 107 digits) Divisors found: r1=47874100857762290609637818483054673407660177 (pp44) r2=858695511971689614580328938461510753245623133163645463110819701 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.77 hours. Scaled time: 22.77 units (timescale=2.331). Factorization parameters were as follows: name: 27779_171 n: 41109275546240495062432283264051165658091623196993437906976151352389340190469170320769270885516502924747077 skew: 12398.44 # norm 1.37e+15 c5: 159840 c4: -1028441856 c3: -137128844967686 c2: 134334849458104183 c1: 5984236747583308367232 c0: 6813532622585497995327780 # alpha -6.31 Y1: 102254484497 Y0: -191448147793948031093 # Murphy_E 1.43e-09 # M 17913856090839271483351743511826600163139299801714024344774155683648315054779271422721430516648895900507594 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1550001) Primes: RFBsize:148933, AFBsize:148910, largePrimes:4994109 encountered Relations: rels:5074616, finalFF:422065 Max relations in full relation-set: 28 Initial matrix: 297927 x 422065 with sparse part having weight 40159545. Pruned matrix : 222425 x 223978 with weight 20465865. Polynomial selection time: 0.54 hours. Total sieving time: 8.84 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.24 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,26,26,50,50,2.6,2.6,50000 total time: 9.77 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343) Calibrating delay using timer specific routine.. 5344.63 BogoMIPS (lpj=2672318) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)
(25·10¹⁸⁷+11)/9 = 2(7)₁₈₆9_<188> = C188
C188 = P37 · C151
P37 = 3467294206652453951666199350752110791_<37>
C151 = [8011370285360413276920870842742682043675772489490261688319864518192193944560646037656706933240715383931249954780125806286441085989770305439253452225269_<151>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 (188 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3112568619 Step 1 took 18665ms Step 2 took 7928ms ********** Factor found in step 2: 3467294206652453951666199350752110791 Found probable prime factor of 37 digits: 3467294206652453951666199350752110791 Composite cofactor 8011370285360413276920870842742682043675772489490261688319864518192193944560646037656706933240715383931249954780125806286441085989770305439253452225269 has 151 digits
Sep 20, 2008: By Thomas Womack / ggnfs lattice siever, msieve
(16·10¹⁷⁹-1)/3 = 5(3)₁₇₉_<180> = 59431787 · C172
C172 = P58 · P115
P58 = 1226638090264928115723655327333228728490191370449664758311_<58>
P115 = 7315828104216888973836157895081638072697654891738449634905084897704701381178005284947042277396339224057301618595369_<115>

prp58 factor: 1226638090264928115723655327333228728490191370449664758311 prp115 factor: 7315828104216888973836157895081638072697654891738449634905084897704701381178005284947042277396339224057301618595369 elapsed time 06:07:08 (that's the processing time, sieving was ~101 CPU-hours)
Sep 19, 2008 (8th): By Robert Backstrom / GGNFS, Msieve
(13·10¹⁷⁸+23)/9 = 1(4)₁₇₇7_<179> = 277 · C176
C176 = P64 · P113
P64 = 4761758900615140831294272937064147828242820480788864164772892249_<64>
P113 = 10950997291772328108097594654307473313103101691401224343725196196487050663817487869687697193902016189467940704539_<113>

Number: n N=52146008824709185720016044925792218210990774167669474528680304853590052146008824709185720016044925792218210990774167669474528680304853590052146008824709185720016044925792218211 ( 176 digits) SNFS difficulty: 179 digits. Divisors found: Sat Sep 20 00:18:31 2008 prp64 factor: 4761758900615140831294272937064147828242820480788864164772892249 Sat Sep 20 00:18:31 2008 prp113 factor: 10950997291772328108097594654307473313103101691401224343725196196487050663817487869687697193902016189467940704539 Sat Sep 20 00:18:31 2008 elapsed time 04:43:43 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 55.55 hours. Scaled time: 113.93 units (timescale=2.051). Factorization parameters were as follows: name: KA_1_4_177_7 n: 52146008824709185720016044925792218210990774167669474528680304853590052146008824709185720016044925792218210990774167669474528680304853590052146008824709185720016044925792218211 type: snfs skew: 0.28 deg: 5 c5: 13000 c0: 23 m: 100000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 11400001) Primes: RFBsize:539777, AFBsize:540425, largePrimes:15635665 encountered Relations: rels:16290338, finalFF:1677740 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 54.95 hours. Total relation processing time: 0.60 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,179,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000 total time: 55.55 hours. --------- CPU info (if available) ----------
Sep 19, 2008 (7th): By Sinkiti Sibata / Msieve, GGNFS
(25·10¹⁰⁴+11)/9 = 2(7)₁₀₃9_<105> = 3 · 157 · 491248811 · C94
C94 = P45 · P49
P45 = 252854036142891231851223614578087693577960987_<45>
P49 = 4747939643331217537545944530363101682879932936157_<49>

Fri Sep 19 16:36:13 2008 Msieve v. 1.36 Fri Sep 19 16:36:13 2008 random seeds: 58339ecb c2f9e10e Fri Sep 19 16:36:13 2008 factoring 1200535702179137783553330569598159007986633480577939579822794144056580555474363458076107706959 (94 digits) Fri Sep 19 16:36:14 2008 no P-1/P+1/ECM available, skipping Fri Sep 19 16:36:14 2008 commencing quadratic sieve (94-digit input) Fri Sep 19 16:36:14 2008 using multiplier of 5 Fri Sep 19 16:36:14 2008 using 64kb Pentium 4 sieve core Fri Sep 19 16:36:14 2008 sieve interval: 18 blocks of size 65536 Fri Sep 19 16:36:14 2008 processing polynomials in batches of 6 Fri Sep 19 16:36:14 2008 using a sieve bound of 1991609 (73803 primes) Fri Sep 19 16:36:14 2008 using large prime bound of 256917561 (27 bits) Fri Sep 19 16:36:14 2008 using double large prime bound of 1372868018887893 (42-51 bits) Fri Sep 19 16:36:14 2008 using trial factoring cutoff of 51 bits Fri Sep 19 16:36:14 2008 polynomial 'A' values have 12 factors Fri Sep 19 21:37:50 2008 74067 relations (18463 full + 55604 combined from 1027184 partial), need 73899 Fri Sep 19 21:37:54 2008 begin with 1045647 relations Fri Sep 19 21:37:55 2008 reduce to 190511 relations in 10 passes Fri Sep 19 21:37:55 2008 attempting to read 190511 relations Fri Sep 19 21:38:01 2008 recovered 190511 relations Fri Sep 19 21:38:01 2008 recovered 173085 polynomials Fri Sep 19 21:38:01 2008 attempting to build 74067 cycles Fri Sep 19 21:38:01 2008 found 74067 cycles in 5 passes Fri Sep 19 21:38:01 2008 distribution of cycle lengths: Fri Sep 19 21:38:01 2008 length 1 : 18463 Fri Sep 19 21:38:01 2008 length 2 : 13069 Fri Sep 19 21:38:01 2008 length 3 : 12697 Fri Sep 19 21:38:01 2008 length 4 : 10086 Fri Sep 19 21:38:01 2008 length 5 : 7424 Fri Sep 19 21:38:01 2008 length 6 : 5078 Fri Sep 19 21:38:01 2008 length 7 : 3085 Fri Sep 19 21:38:01 2008 length 9+: 4165 Fri Sep 19 21:38:01 2008 largest cycle: 19 relations Fri Sep 19 21:38:02 2008 matrix is 73803 x 74067 (19.5 MB) with weight 4812420 (64.97/col) Fri Sep 19 21:38:02 2008 sparse part has weight 4812420 (64.97/col) Fri Sep 19 21:38:03 2008 filtering completed in 3 passes Fri Sep 19 21:38:03 2008 matrix is 69969 x 70033 (18.5 MB) with weight 4577242 (65.36/col) Fri Sep 19 21:38:03 2008 sparse part has weight 4577242 (65.36/col) Fri Sep 19 21:38:04 2008 saving the first 48 matrix rows for later Fri Sep 19 21:38:04 2008 matrix is 69921 x 70033 (11.8 MB) with weight 3620447 (51.70/col) Fri Sep 19 21:38:04 2008 sparse part has weight 2665595 (38.06/col) Fri Sep 19 21:38:04 2008 matrix includes 64 packed rows Fri Sep 19 21:38:04 2008 using block size 21845 for processor cache size 512 kB Fri Sep 19 21:38:05 2008 commencing Lanczos iteration Fri Sep 19 21:38:05 2008 memory use: 11.2 MB Fri Sep 19 21:38:59 2008 lanczos halted after 1107 iterations (dim = 69913) Fri Sep 19 21:38:59 2008 recovered 12 nontrivial dependencies Fri Sep 19 21:39:01 2008 prp45 factor: 252854036142891231851223614578087693577960987 Fri Sep 19 21:39:01 2008 prp49 factor: 4747939643331217537545944530363101682879932936157 Fri Sep 19 21:39:01 2008 elapsed time 05:02:48
(25·10¹³¹+11)/9 = 2(7)₁₃₀9_<132> = 3 · 474917 · 916760665887089_<15> · C111
C111 = P35 · P76
P35 = 94380226647732964091537890550890669_<35>
P76 = 2253313099465234579424830713654498806792655361016665349309311724347507836769_<76>

Number: 27779_131 N=212668201035834491692037209728328759241937969007540092694188106330944785211386193946770471207640858090417208461 ( 111 digits) SNFS difficulty: 132 digits. Divisors found: r1=94380226647732964091537890550890669 (pp35) r2=2253313099465234579424830713654498806792655361016665349309311724347507836769 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.15 hours. Scaled time: 4.02 units (timescale=0.781). Factorization parameters were as follows: name: 27779_131 n: 212668201035834491692037209728328759241937969007540092694188106330944785211386193946770471207640858090417208461 m: 100000000000000000000000000 c5: 250 c0: 11 skew: 0.54 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:64024, largePrimes:1524370 encountered Relations: rels:1534771, finalFF:177835 Max relations in full relation-set: 28 Initial matrix: 128041 x 177835 with sparse part having weight 14394177. Pruned matrix : 114549 x 115253 with weight 7529044. Total sieving time: 5.01 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.15 hours. --------- CPU info (if available) ----------
Sep 19, 2008 (6th): By Jo Yeong Uk / GGNFS
(25·10¹²⁶+11)/9 = 2(7)₁₂₅9_<127> = 4079 · 80877693697_<11> · C112
C112 = P34 · P79
P34 = 5921234966250715563066349802636897_<34>
P79 = 1422010294334862352761456402011079915700506602156564668923988341467060275943389_<79>

Number: 27779_126 N=8420057077184058787598473132349406192030301923297927628502389558208977776558965593828185370809262511926494623933 ( 112 digits) SNFS difficulty: 128 digits. Divisors found: r1=5921234966250715563066349802636897 (pp34) r2=1422010294334862352761456402011079915700506602156564668923988341467060275943389 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.76 hours. Scaled time: 4.04 units (timescale=2.292). Factorization parameters were as follows: n: 8420057077184058787598473132349406192030301923297927628502389558208977776558965593828185370809262511926494623933 m: 50000000000000000000000000 c5: 2 c0: 275 skew: 2.68 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78707, largePrimes:1558651 encountered Relations: rels:1609975, finalFF:224099 Max relations in full relation-set: 28 Initial matrix: 157270 x 224099 with sparse part having weight 11295137. Pruned matrix : 125906 x 126756 with weight 5116173. Total sieving time: 1.70 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 1.76 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673813) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.29 BogoMIPS (lpj=2672145) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(25·10¹²⁸+11)/9 = 2(7)₁₂₇9_<129> = 3³ · 463 · 3053293 · 106459341671_<12> · C107
C107 = P41 · P66
P41 = 88835349405043160784533804171443167335437_<41>
P66 = 769510713970792550300555952851855989341577812582377543694990208889_<66>

Number: 27779_128 N=68359753146519583856843073026007483494688797670717179829285121834152207820493624762386763326338142162099493 ( 107 digits) SNFS difficulty: 130 digits. Divisors found: r1=88835349405043160784533804171443167335437 (pp41) r2=769510713970792550300555952851855989341577812582377543694990208889 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.51 hours. Scaled time: 3.57 units (timescale=2.354). Factorization parameters were as follows: n: 68359753146519583856843073026007483494688797670717179829285121834152207820493624762386763326338142162099493 m: 100000000000000000000000000 c5: 1 c0: 44 skew: 2.13 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 850001) Primes: RFBsize:78498, AFBsize:78087, largePrimes:1507905 encountered Relations: rels:1540170, finalFF:207011 Max relations in full relation-set: 28 Initial matrix: 156649 x 207011 with sparse part having weight 9809048. Pruned matrix : 130030 x 130877 with weight 4819028. Total sieving time: 1.46 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 1.51 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673813) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.29 BogoMIPS (lpj=2672145) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Sep 19, 2008 (5th): By anonymous / GMP-ECM
(25·10¹⁶⁴+11)/9 = 2(7)₁₆₃9_<165> = 3² · 2729 · 2336093 · 21024053473_<11> · C144
C144 = P31 · P113
P31 = 2530290505519396636552217573611_<31>
P113 = 91006934911632667105331373545676803276176580669962007769491107333139904850733355058121735195657525624018987256541_<113>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 230273983343325847520474402702127170340777004798958820095817677549008342383184157970938223756549950521498102500948013368207088201076600608739551 (144 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=808694177 Step 1 took 4610ms Step 2 took 2619ms ********** Factor found in step 2: 2530290505519396636552217573611 Found probable prime factor of 31 digits: 2530290505519396636552217573611 Probable prime cofactor 91006934911632667105331373545676803276176580669962007769491107333139904850733355058121735195657525624018987256541 has 113 digits
Sep 19, 2008 (4th): By Serge Batalov / Msieve-1.37 QS, GMP-ECM 6.2.1, GMP-ECM 6.2.1 [P-1!]
(25·10¹³⁴+11)/9 = 2(7)₁₃₃9_<135> = 3 · 5569 · 6501367 · 325527911 · 1641755237_<10> · 35864341695964682465531767_<26> · C81
C81 = P37 · P44
P37 = 7464496412545245228296694969557118343_<37>
P44 = 17874517414703582293209008808015497997711773_<44>

Thu Sep 18 21:24:45 2008 Msieve v. 1.37 Thu Sep 18 21:24:45 2008 random seeds: 8396dfb3 39287007 Thu Sep 18 21:24:45 2008 factoring 133424271118032401399678682893589251520170031584126003417413899923975037765352139 (81 digits) Thu Sep 18 21:24:46 2008 searching for 15-digit factors Thu Sep 18 21:24:46 2008 commencing quadratic sieve (81-digit input) Thu Sep 18 21:24:46 2008 using multiplier of 3 Thu Sep 18 21:24:46 2008 using 64kb Opteron sieve core Thu Sep 18 21:24:46 2008 sieve interval: 6 blocks of size 65536 Thu Sep 18 21:24:46 2008 processing polynomials in batches of 17 Thu Sep 18 21:24:46 2008 using a sieve bound of 1309421 (50122 primes) Thu Sep 18 21:24:46 2008 using large prime bound of 129632679 (26 bits) Thu Sep 18 21:24:46 2008 using trial factoring cutoff of 27 bits Thu Sep 18 21:24:46 2008 polynomial 'A' values have 10 factors Thu Sep 18 21:36:25 2008 50241 relations (25847 full + 24394 combined from 272444 partial), need 50218 Thu Sep 18 21:36:25 2008 begin with 298291 relations Thu Sep 18 21:36:25 2008 reduce to 71651 relations in 2 passes Thu Sep 18 21:36:25 2008 attempting to read 71651 relations Thu Sep 18 21:36:26 2008 recovered 71651 relations Thu Sep 18 21:36:26 2008 recovered 61361 polynomials Thu Sep 18 21:36:26 2008 attempting to build 50241 cycles Thu Sep 18 21:36:26 2008 found 50241 cycles in 1 passes Thu Sep 18 21:36:26 2008 distribution of cycle lengths: Thu Sep 18 21:36:26 2008 length 1 : 25847 Thu Sep 18 21:36:26 2008 length 2 : 24394 Thu Sep 18 21:36:26 2008 largest cycle: 2 relations Thu Sep 18 21:36:26 2008 matrix is 50122 x 50241 (7.4 MB) with weight 1528596 (30.43/col) Thu Sep 18 21:36:26 2008 sparse part has weight 1528596 (30.43/col) Thu Sep 18 21:36:26 2008 filtering completed in 3 passes Thu Sep 18 21:36:26 2008 matrix is 35603 x 35667 (5.7 MB) with weight 1215903 (34.09/col) Thu Sep 18 21:36:26 2008 sparse part has weight 1215903 (34.09/col) Thu Sep 18 21:36:26 2008 saving the first 48 matrix rows for later Thu Sep 18 21:36:26 2008 matrix is 35555 x 35667 (4.1 MB) with weight 931931 (26.13/col) Thu Sep 18 21:36:26 2008 sparse part has weight 707670 (19.84/col) Thu Sep 18 21:36:26 2008 matrix includes 64 packed rows Thu Sep 18 21:36:26 2008 using block size 14266 for processor cache size 1024 kB Thu Sep 18 21:36:27 2008 commencing Lanczos iteration Thu Sep 18 21:36:27 2008 memory use: 4.0 MB Thu Sep 18 21:36:31 2008 lanczos halted after 564 iterations (dim = 35553) Thu Sep 18 21:36:31 2008 recovered 16 nontrivial dependencies Thu Sep 18 21:36:31 2008 prp37 factor: 7464496412545245228296694969557118343 Thu Sep 18 21:36:31 2008 prp44 factor: 17874517414703582293209008808015497997711773 Thu Sep 18 21:36:31 2008 elapsed time 00:11:46
(25·10¹⁶²+11)/9 = 2(7)₁₆₁9_<163> = C163
C163 = P36 · C127
P36 = 956996067485339718144137108196685667_<36>
C127 = [2902601036884961627173699119809625917037467027349604362385456802139104947986390088924478788941052925770284265498185067416124337_<127>]

Using B1=3000000, B2=23415979870, polynomial Dickson(12), sigma=3570635795 Step 1 took 21809ms Step 2 took 19409ms ********** Factor found in step 2: 956996067485339718144137108196685667 Found probable prime factor of 36 digits: 956996067485339718144137108196685667 Composite cofactor 2902601036884961627173699119809625917037467027349604362385456802139104947986390088924478788941052925770284265498185067416124337 has 127 digits
(25·10¹²¹+11)/9 = 2(7)₁₂₀9_<122> = C122
C122 = P41 · P81
P41 = 28281986806699176262127343626160011389591_<41>
P81 = 982172078914838963908547772788255008357011466169123485822865552044233331522856069_<81>

Number: 27779_121 N=27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 122 digits) SNFS difficulty: 122 digits. Divisors found: r1=28281986806699176262127343626160011389591 r2=982172078914838963908547772788255008357011466169123485822865552044233331522856069 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.728). Factorization parameters were as follows: n: 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 Y1: 1 Y0: -1000000000000000000000000 c5: 250 c0: 11 skew: 0.54 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 121099 x 121346 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.80 hours.
(25·10¹²⁴+11)/9 = 2(7)₁₂₃9_<125> = C125
C125 = P47 · P78
P47 = 27794149819268048962266606788818980074038015727_<47>
P78 = 999410953686414922780705848621382863777285842485662131420022280753390278988477_<78>

Number: 27779_124 N=27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 125 digits) SNFS difficulty: 125 digits. Divisors found: r1=27794149819268048962266606788818980074038015727 r2=999410953686414922780705848621382863777285842485662131420022280753390278988477 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.180). Factorization parameters were as follows: n: 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 Y1: 1 Y0: -10000000000000000000000000 c5: 5 c0: 22 skew: 1.34 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 127050 x 127270 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.20 hours.
(25·10¹⁹¹+11)/9 = 2(7)₁₉₀9_<192> = 3² · 19 · 33419237 · 25138963259580059_<17> · 3389122341921446988947_<22> · C144
C144 = P31 · P114
P31 = 2526416268926009103666694532857_<31>
P114 = 225821526905109989428395988313810618602302745969461692647476062511113200159315648162004578240008559799312133924557_<114>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [P-1] Input number is 570519179446782359339252890837934249143440005001801732527646024358610926299288672350376351755659176142334448475296192648854650039135351195669349 (144 digits) Using B1=30000000, B2=756268978042, polynomial x^1, x0=3676457812 Step 1 took 18456ms ********** Factor found in step 1: 2526416268926009103666694532857 Found probable prime factor of 31 digits: 2526416268926009103666694532857 Probable prime cofactor 225821526905109989428395988313810618602302745969461692647476062511113200159315648162004578240008559799312133924557 has 114 digits
(25·10¹³⁶+11)/9 = 2(7)₁₃₅9_<137> = C137
C137 = P68 · P69
P68 = 49939563665725420108333887821126316151365501830209825661485480290103_<68>
P69 = 556227883041001713698169637988173699800671023277860382280971907619493_<69>

Number: 27779_136 N=27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 137 digits) SNFS difficulty: 137 digits. Divisors found: r1=49939563665725420108333887821126316151365501830209825661485480290103 r2=556227883041001713698169637988173699800671023277860382280971907619493 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.731). Factorization parameters were as follows: n: 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 Y1: 1 Y0: -1000000000000000000000000000 c5: 250 c0: 11 skew: 0.54 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 1550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 142483 x 142700 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 4.00 hours.
Sep 19, 2008 (3rd): By Sinkiti Sibata / GGNFS, Msieve
(25·10¹⁷³-43)/9 = 2(7)₁₇₂3_<174> = 3 · 33037 · C169
C169 = P77 · P92
P77 = 46558850779493096424492483442855753081279943870049563681536791783611326923121_<77>
P92 = 60196797774643852813248874227286977777238841940686534272161886935039204136300928460553097083_<92>

Number: 27773_173 N=2802693724992965238750267657250736828180300650561267445367091218712128601041032557211387008281399418609213687459290873644477179907152362278433047570681133050597590356043 ( 169 digits) SNFS difficulty: 174 digits. Divisors found: r1=46558850779493096424492483442855753081279943870049563681536791783611326923121 (pp77) r2=60196797774643852813248874227286977777238841940686534272161886935039204136300928460553097083 (pp92) Version: GGNFS-0.77.1-20050930-nocona Total time: 262.57 hours. Scaled time: 265.45 units (timescale=1.011). Factorization parameters were as follows: name: 27773_173 n: 2802693724992965238750267657250736828180300650561267445367091218712128601041032557211387008281399418609213687459290873644477179907152362278433047570681133050597590356043 m: 50000000000000000000000000000000000 c5: 8 c0: -43 skew: 1.4 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 11000001) Primes: RFBsize:501962, AFBsize:502386, largePrimes:6593939 encountered Relations: rels:7149050, finalFF:1223519 Max relations in full relation-set: 28 Initial matrix: 1004413 x 1223519 with sparse part having weight 75368111. Pruned matrix : 812967 x 818053 with weight 54796900. Total sieving time: 255.78 hours. Total relation processing time: 0.19 hours. Matrix solve time: 6.48 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,174,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 262.57 hours. --------- CPU info (if available) ----------
(25·10¹⁰⁸+11)/9 = 2(7)₁₀₇9_<109> = 47 · 97² · 1489717 · 22665857 · C90
C90 = P33 · P57
P33 = 853359707941802590369203380773573_<33>
P57 = 217995797342499960244508687999226483457599274315394828629_<57>

Fri Sep 19 14:38:44 2008 Msieve v. 1.36 Fri Sep 19 14:38:44 2008 random seeds: e11317bc 9b0d859a Fri Sep 19 14:38:44 2008 factoring 186028829952736151348531947356431309694958639565062282660203345428934749304330489787021417 (90 digits) Fri Sep 19 14:38:45 2008 no P-1/P+1/ECM available, skipping Fri Sep 19 14:38:45 2008 commencing quadratic sieve (90-digit input) Fri Sep 19 14:38:46 2008 using multiplier of 1 Fri Sep 19 14:38:46 2008 using 64kb Pentium 4 sieve core Fri Sep 19 14:38:46 2008 sieve interval: 18 blocks of size 65536 Fri Sep 19 14:38:46 2008 processing polynomials in batches of 6 Fri Sep 19 14:38:46 2008 using a sieve bound of 1572443 (59667 primes) Fri Sep 19 14:38:46 2008 using large prime bound of 125795440 (26 bits) Fri Sep 19 14:38:46 2008 using double large prime bound of 379661707918720 (42-49 bits) Fri Sep 19 14:38:46 2008 using trial factoring cutoff of 49 bits Fri Sep 19 14:38:46 2008 polynomial 'A' values have 11 factors Fri Sep 19 16:27:20 2008 59783 relations (16226 full + 43557 combined from 632833 partial), need 59763 Fri Sep 19 16:27:22 2008 begin with 649059 relations Fri Sep 19 16:27:23 2008 reduce to 145005 relations in 9 passes Fri Sep 19 16:27:23 2008 attempting to read 145005 relations Fri Sep 19 16:27:26 2008 recovered 145005 relations Fri Sep 19 16:27:26 2008 recovered 120201 polynomials Fri Sep 19 16:27:27 2008 attempting to build 59783 cycles Fri Sep 19 16:27:27 2008 found 59783 cycles in 5 passes Fri Sep 19 16:27:27 2008 distribution of cycle lengths: Fri Sep 19 16:27:27 2008 length 1 : 16226 Fri Sep 19 16:27:27 2008 length 2 : 11495 Fri Sep 19 16:27:27 2008 length 3 : 10335 Fri Sep 19 16:27:27 2008 length 4 : 7992 Fri Sep 19 16:27:27 2008 length 5 : 5624 Fri Sep 19 16:27:27 2008 length 6 : 3481 Fri Sep 19 16:27:27 2008 length 7 : 2186 Fri Sep 19 16:27:27 2008 length 9+: 2444 Fri Sep 19 16:27:27 2008 largest cycle: 18 relations Fri Sep 19 16:27:27 2008 matrix is 59667 x 59783 (14.6 MB) with weight 3583703 (59.95/col) Fri Sep 19 16:27:27 2008 sparse part has weight 3583703 (59.95/col) Fri Sep 19 16:27:28 2008 filtering completed in 3 passes Fri Sep 19 16:27:28 2008 matrix is 55554 x 55618 (13.7 MB) with weight 3369862 (60.59/col) Fri Sep 19 16:27:28 2008 sparse part has weight 3369862 (60.59/col) Fri Sep 19 16:27:28 2008 saving the first 48 matrix rows for later Fri Sep 19 16:27:29 2008 matrix is 55506 x 55618 (10.1 MB) with weight 2804439 (50.42/col) Fri Sep 19 16:27:29 2008 sparse part has weight 2310918 (41.55/col) Fri Sep 19 16:27:29 2008 matrix includes 64 packed rows Fri Sep 19 16:27:29 2008 using block size 21845 for processor cache size 512 kB Fri Sep 19 16:27:29 2008 commencing Lanczos iteration Fri Sep 19 16:27:29 2008 memory use: 9.1 MB Fri Sep 19 16:28:04 2008 lanczos halted after 879 iterations (dim = 55506) Fri Sep 19 16:28:05 2008 recovered 17 nontrivial dependencies Fri Sep 19 16:28:06 2008 prp33 factor: 853359707941802590369203380773573 Fri Sep 19 16:28:06 2008 prp57 factor: 217995797342499960244508687999226483457599274315394828629 Fri Sep 19 16:28:06 2008 elapsed time 01:49:22
(25·10¹³⁷+11)/9 = 2(7)₁₃₆9_<138> = 3² · 19 · 31 · C134
C134 = P45 · P90
P45 = 161921640164388497483372857632347906673665639_<45>
P90 = 323619588033082331955512247873525202849766126106862528717344406156559958159975949812820961_<90>

Number: 27779_137 N=52401014483640403278207466096543629084659078999769435536271982225575887149175208032027500052401014483640403278207466096543629084659079 ( 134 digits) SNFS difficulty: 139 digits. Divisors found: r1=161921640164388497483372857632347906673665639 (pp45) r2=323619588033082331955512247873525202849766126106862528717344406156559958159975949812820961 (pp90) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.21 hours. Scaled time: 5.25 units (timescale=1.008). Factorization parameters were as follows: name: 27779_137 n: 52401014483640403278207466096543629084659078999769435536271982225575887149175208032027500052401014483640403278207466096543629084659079 m: 5000000000000000000000000000 c5: 4 c0: 55 skew: 1.69 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:63994, largePrimes:1557289 encountered Relations: rels:1578648, finalFF:193359 Max relations in full relation-set: 28 Initial matrix: 142556 x 193359 with sparse part having weight 14877974. Pruned matrix : 126678 x 127454 with weight 8126953. Total sieving time: 5.09 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.06 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.21 hours. --------- CPU info (if available) ----------
(25·10¹³⁹+11)/9 = 2(7)₁₃₈9_<140> = 1579 · 23677 · C132
C132 = P30 · P103
P30 = 209083018584969192252595113529_<30>
P103 = 3553611393113190589659808998064869756016200551109239594585632907970680199445429803699384634763303281397_<103>

Number: 27779_139 N=742999796950043490304314795675635378579661200235868554740897886188462070872331423725779198524157510524138893921226513631533448720013 ( 132 digits) SNFS difficulty: 140 digits. Divisors found: r1=209083018584969192252595113529 (pp30) r2=3553611393113190589659808998064869756016200551109239594585632907970680199445429803699384634763303281397 (pp103) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.10 hours. Scaled time: 10.19 units (timescale=1.009). Factorization parameters were as follows: name: 27779_137 n: 742999796950043490304314795675635378579661200235868554740897886188462070872331423725779198524157510524138893921226513631533448720013 m: 10000000000000000000000000000 c5: 5 c0: 22 skew: 1.34 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1950001) Primes: RFBsize:100021, AFBsize:100104, largePrimes:2894835 encountered Relations: rels:2976696, finalFF:348480 Max relations in full relation-set: 28 Initial matrix: 200190 x 348480 with sparse part having weight 35375015. Pruned matrix : 163148 x 164212 with weight 16176754. Total sieving time: 9.88 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.14 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 10.10 hours. --------- CPU info (if available) ----------
(25·10¹⁵⁵+11)/9 = 2(7)₁₅₄9_<156> = 3³ · 19 · 862257989 · 822143730045749087393_<21> · 182026023701860412223553_<24> · C100
C100 = P41 · P60
P41 = 18085812322923420183023124569529108930833_<41>
P60 = 232019056365966092443217013695946993609084795707320945808071_<60>

Number: 27779_155 N=4196253108776653175638038416478924297372907360500066045972590132987812392925813812223693780032153143 ( 100 digits) Divisors found: r1=18085812322923420183023124569529108930833 (pp41) r2=232019056365966092443217013695946993609084795707320945808071 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 7.29 hours. Scaled time: 5.71 units (timescale=0.784). Factorization parameters were as follows: name: 27779_155 n: 4196253108776653175638038416478924297372907360500066045972590132987812392925813812223693780032153143 skew: 2549.76 # norm 8.24e+13 c5: 708000 c4: 19166104 c3: -4074259275762 c2: -16901136602923433 c1: 32379437717701640298 c0: 46739428509995733823168 # alpha -6.81 Y1: 50409368801 Y0: -5682843064049718825 # Murphy_E 3.68e-09 # M 1027250211033138229216287220548871958441136017879058543953306680295155783875246280193616482926558222 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, 1400001) Primes: RFBsize:135072, AFBsize:135060, largePrimes:4208119 encountered Relations: rels:4572216, finalFF:675038 Max relations in full relation-set: 28 Initial matrix: 270217 x 675038 with sparse part having weight 54174360. Pruned matrix : 135288 x 136703 with weight 15301062. Total sieving time: 6.89 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.13 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 7.29 hours. --------- CPU info (if available) ----------
Sep 19, 2008 (2nd): Factorizations of 277...779 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Sep 19, 2008: By Serge Batalov / GMP-ECM 6.2.1
(7·10¹⁸⁹-61)/9 = (7)₁₈₈1_<189> = 3 · 1291 · 355909522613_<12> · C174
C174 = P40 · C134
P40 = 6586408395714765506229052421915313517957_<40>
C134 = [85668225182877184644786666541917164742621853107779269580528230063969136871950475692301384534838463105695144272049997293525583827839347_<134>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=272832663 Step 1 took 28102ms Step 2 took 18633ms ********** Factor found in step 2: 6586408395714765506229052421915313517957 Found probable prime factor of 40 digits: 6586408395714765506229052421915313517957 Composite cofactor 85668225182877184644786666541917164742621853107779269580528230063969136871950475692301384534838463105695144272049997293525583827839347 has 134 digits
Sep 18, 2008: By Serge Batalov / GMP-ECM 6.2.1
(5·10¹⁸⁰-23)/9 = (5)₁₇₉3_<180> = 617 · 19195003 · 108827351 · 1035425066346613909_<19> · C144
C144 = P42 · P102
P42 = 687803100970957788662415682330278575034733_<42>
P102 = 605247890592415863871110605761674126376482105290280241337087884763077147497213529971623886197755952749_<102>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1426785098 Step 1 took 67428ms Step 2 took 43125ms ********** Factor found in step 2: 687803100970957788662415682330278575034733 Found probable prime factor of 42 digits: 687803100970957788662415682330278575034733 Probable prime cofactor 605247890592415863871110605761674126376482105290280241337087884763077147497213529971623886197755952749 has 102 digits
3·10¹⁸⁹-7 = 2(9)₁₈₈3_<190> = 29 · 4139 · 116881 · 184949 · C175
C175 = P33 · P142
P33 = 349757439117349435285448300528377_<33>
P142 = 3305711616124445048311225343825846971474411661265757514018027000415495130450466308113753852376938088222883119475153546917208332615074442720531_<142>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3188158830 Step 1 took 29325ms Step 2 took 18759ms ********** Factor found in step 2: 349757439117349435285448300528377 Found probable prime factor of 33 digits: 349757439117349435285448300528377 Probable prime cofactor 3305711616124445048311225343825846971474411661265757514018027000415495130450466308113753852376938088222883119475153546917208332615074442720531 has 142 digits
(5·10¹⁸⁸-23)/9 = (5)₁₈₇3_<188> = 329994138355223_<15> · C174
C174 = P28 · C146
P28 = 6949099976695798019485329959_<28>
C146 = [24226613417251399107633278235282534498979801691191248382376457126126295340750015734646309207992878830271994380586380451824139683183787774912460129_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2395590199 Step 1 took 25942ms ********** Factor found in step 1: 6949099976695798019485329959 Found probable prime factor of 28 digits: 6949099976695798019485329959 Composite cofactor 24226613417251399107633278235282534498979801691191248382376457126126295340750015734646309207992878830271994380586380451824139683183787774912460129 has 146 digits
(8·10¹⁸¹-17)/9 = (8)₁₈₀7_<181> = 7 · 1709 · 4253 · C174
C174 = P28 · C146
P28 = 3983165093026307702402046217_<28>
C146 = [43861520701364732252769870687031534361057141753068471924374557286056504583720673640378144134184647090935167172927062385446263634692674481022068849_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2914738981 Step 1 took 25105ms Step 2 took 16411ms ********** Factor found in step 2: 3983165093026307702402046217 Found probable prime factor of 28 digits: 3983165093026307702402046217 Composite cofactor 43861520701364732252769870687031534361057141753068471924374557286056504583720673640378144134184647090935167172927062385446263634692674481022068849 has 146 digits
Sep 17, 2008 (2nd): By matsui / GMP-ECM
4·10¹⁸⁸+9 = 4(0)₁₈₇9_<189> = 337 · 1201 · 58693 · 876529 · C173
C173 = P37 · P136
P37 = 2430640727175969638994585027337101361_<37>
P136 = 7903395490385727731463723829241886338897947794113256415232279926080628572269461573229661036837524536596561491729907318379745124431713621_<136>

Input number is 19210314961910444414903654271569167794536732506063457824599929055888256292329337954197463698980821541562015442076418326664270192429185687422314470872745845677597780201338181 (173 digits) Using B1=88000000, B2=582207787990, polynomial Dickson(30), sigma=101061817 Step 1 took 1763944ms Step 2 took 402772ms ********** Factor found in step 2: 2430640727175969638994585027337101361 Found probable prime factor of 37 digits: 2430640727175969638994585027337101361 Probable prime cofactor 7903395490385727731463723829241886338897947794113256415232279926080628572269461573229661036837524536596561491729907318379745124431713621 has 136 digits
4·10¹⁹⁰+9 = 4(0)₁₈₉9_<191> = 2789 · 17155258129_<11> · C177
C177 = P34 · C144
P34 = 1411411376393248424585966404607993_<34>
C144 = [592325740845773596110618934810993533587964947739141920784957245331142523666993635952898907996987364689434079735407153529578722036865973825841773_<144>]

Input number is 836015289160283879500272797444715885812605958351520507116372858766515218453575577239195951346683064794135993251110322481581764211436292340215488177214241765662632022089309091589 (177 digits) Using B1=88000000, B2=582207787990, polynomial Dickson(30), sigma=2898798771 Step 1 took 1923663ms ********** Factor found in step 1: 1411411376393248424585966404607993 Found probable prime factor of 34 digits: 1411411376393248424585966404607993 Composite cofactor 592325740845773596110618934810993533587964947739141920784957245331142523666993635952898907996987364689434079735407153529578722036865973825841773 has 144 digits
4·10¹⁹²+9 = 4(0)₁₉₁9_<193> = 13 · 3084049 · 20054833 · C178
C178 = P33 · C146
P33 = 362793721871669762743297557966121_<33>
C146 = [13712497346156392212676019147625431370510365650834689585981115102219563918727772856984851299023907414810459127022107546442249298162322016417074149_<146>]

Input number is 4974807948367471887114396159851198874837557117234981819868633168970552843782088694722828194509779833777082181924438616285128530903647465329505197651600423635188354862434086906029 (178 digits) Using B1=88000000, B2=582207787990, polynomial Dickson(30), sigma=2110858031 Step 1 took 1929223ms Step 2 took 431804ms ********** Factor found in step 2: 362793721871669762743297557966121 Found probable prime factor of 33 digits: 362793721871669762743297557966121 Composite cofactor 13712497346156392212676019147625431370510365650834689585981115102219563918727772856984851299023907414810459127022107546442249298162322016417074149 has 146 digits
Sep 17, 2008: By Robert Backstrom / GGNFS, Msieve
9·10¹⁹³-1 = 8(9)₁₉₃_<194> = 43 · C193
C193 = P43 · P66 · P85
P43 = 1821585162697457488304296102273254935173081_<43>
P66 = 577907847913674910737796883693373565504125011795363899114213268519_<66>
P85 = 1988227065562338941228938824773608620242017418041162968604820660552549013425070142387_<85>

Number: n N=2093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093 ( 193 digits) SNFS difficulty: 193 digits. Divisors found: Wed Sep 17 08:14:24 2008 prp43 factor: 1821585162697457488304296102273254935173081 Wed Sep 17 08:14:24 2008 prp66 factor: 577907847913674910737796883693373565504125011795363899114213268519 Wed Sep 17 08:14:24 2008 prp85 factor: 1988227065562338941228938824773608620242017418041162968604820660552549013425070142387 Wed Sep 17 08:14:25 2008 elapsed time 09:59:33 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 161.42 hours. Scaled time: 330.10 units (timescale=2.045). Factorization parameters were as follows: name: KA_8_9_193 n: 2093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093023255813953488372093 type: snfs skew: 0.16 deg: 5 c5: 9000 c0: -1 m: 100000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 12100001) Primes: RFBsize:633578, AFBsize:634548, largePrimes:15156746 encountered Relations: rels:15251348, finalFF:1305201 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 160.82 hours. Total relation processing time: 0.59 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,193,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000 total time: 161.42 hours. --------- CPU info (if available) ----------
Sep 16, 2008: By Sinkiti Sibata / GGNFS
(25·10¹⁷⁰-43)/9 = 2(7)₁₆₉3_<171> = 3² · 7 · 13 · 331 · 78778604771093191_<17> · C149
C149 = P44 · P105
P44 = 17619764491236916651312474862954886430331357_<44>
P105 = 738205403106764575938062723471690111389545121101186209390350592296561164036335958186089930067485740613911_<105>

Number: 27773_170 N=13007005348899804709094980881302261626646867240510572909883953359395253502607313995996074802578303581068987576332763598695119953893377355680333707227 ( 149 digits) SNFS difficulty: 171 digits. Divisors found: r1=17619764491236916651312474862954886430331357 (pp44) r2=738205403106764575938062723471690111389545121101186209390350592296561164036335958186089930067485740613911 (pp105) Version: GGNFS-0.77.1-20050930-nocona Total time: 183.30 hours. Scaled time: 184.95 units (timescale=1.009). Factorization parameters were as follows: name: 27773_170 n: 13007005348899804709094980881302261626646867240510572909883953359395253502607313995996074802578303581068987576332763598695119953893377355680333707227 m: 10000000000000000000000000000000000 c5: 25 c0: -43 skew: 1.11 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, 8700001) Primes: RFBsize:412849, AFBsize:411971, largePrimes:6323654 encountered Relations: rels:6647667, finalFF:972289 Max relations in full relation-set: 28 Initial matrix: 824884 x 972289 with sparse part having weight 73248063. Pruned matrix : 707814 x 712002 with weight 55447414. Total sieving time: 178.63 hours. Total relation processing time: 0.14 hours. Matrix solve time: 4.40 hours. Time per square root: 0.11 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: 183.30 hours. --------- CPU info (if available) ----------
Sep 15, 2008 (4th): By Chris Monico / GGNFS-0.91.4
(16·10¹⁶⁹-1)/3 = 5(3)₁₆₉_<170> = 2477 · 2837 · 4254557 · 4055471607565486774482757_<25> · C132
C132 = P49 · P84
P49 = 2359339499068883240543885710901550432466257806573_<49>
P84 = 186434909099572698920884170268392055319140036876977757831249406175990968275589112521_<84>

N=439863245043938633275360032107760843619767204363929593692974356134399238277245461761858058337741355248435942840638766855441150400533 r1=2359339499068883240543885710901550432466257806573 (pp49) r2=186434909099572698920884170268392055319140036876977757831249406175990968275589112521 (pp84) Version: GGNFS-0.91.4
Sep 15, 2008 (3rd): By Sinkiti Sibata / Msieve
(25·10¹⁰⁸-43)/9 = 2(7)₁₀₇3_<109> = C109
C109 = P47 · P62
P47 = 98977571642142365276984929935548439173343598577_<47>
P62 = 28064719427760380820022102182615812657550236296462577237567549_<62>

Fri Sep 12 05:02:50 2008 Msieve v. 1.36 Fri Sep 12 05:02:50 2008 random seeds: 9881df76 48087ea0 Fri Sep 12 05:02:50 2008 factoring 2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773 (109 digits) Fri Sep 12 05:02:52 2008 no P-1/P+1/ECM available, skipping Fri Sep 12 05:02:52 2008 commencing quadratic sieve (109-digit input) Fri Sep 12 05:02:52 2008 using multiplier of 5 Fri Sep 12 05:02:52 2008 using 32kb Intel Core sieve core Fri Sep 12 05:02:52 2008 sieve interval: 50 blocks of size 32768 Fri Sep 12 05:02:52 2008 processing polynomials in batches of 5 Fri Sep 12 05:02:52 2008 using a sieve bound of 5812619 (200667 primes) Fri Sep 12 05:02:52 2008 using large prime bound of 871892850 (29 bits) Fri Sep 12 05:02:52 2008 using double large prime bound of 12383220374195100 (45-54 bits) Fri Sep 12 05:02:52 2008 using trial factoring cutoff of 54 bits Fri Sep 12 05:02:52 2008 polynomial 'A' values have 14 factors Mon Sep 15 10:59:05 2008 201065 relations (48104 full + 152961 combined from 2940810 partial), need 200763 Mon Sep 15 10:59:18 2008 begin with 2988914 relations Mon Sep 15 10:59:21 2008 reduce to 528487 relations in 12 passes Mon Sep 15 10:59:21 2008 attempting to read 528487 relations Mon Sep 15 10:59:38 2008 recovered 528487 relations Mon Sep 15 10:59:38 2008 recovered 519328 polynomials Mon Sep 15 10:59:39 2008 attempting to build 201065 cycles Mon Sep 15 10:59:39 2008 found 201065 cycles in 7 passes Mon Sep 15 10:59:39 2008 distribution of cycle lengths: Mon Sep 15 10:59:39 2008 length 1 : 48104 Mon Sep 15 10:59:39 2008 length 2 : 34121 Mon Sep 15 10:59:39 2008 length 3 : 33987 Mon Sep 15 10:59:39 2008 length 4 : 27116 Mon Sep 15 10:59:39 2008 length 5 : 21113 Mon Sep 15 10:59:39 2008 length 6 : 14366 Mon Sep 15 10:59:39 2008 length 7 : 9281 Mon Sep 15 10:59:39 2008 length 9+: 12977 Mon Sep 15 10:59:39 2008 largest cycle: 21 relations Mon Sep 15 10:59:40 2008 matrix is 200667 x 201065 (61.2 MB) with weight 15238112 (75.79/col) Mon Sep 15 10:59:40 2008 sparse part has weight 15238112 (75.79/col) Mon Sep 15 10:59:42 2008 filtering completed in 3 passes Mon Sep 15 10:59:42 2008 matrix is 192791 x 192855 (59.0 MB) with weight 14697710 (76.21/col) Mon Sep 15 10:59:42 2008 sparse part has weight 14697710 (76.21/col) Mon Sep 15 10:59:44 2008 saving the first 48 matrix rows for later Mon Sep 15 10:59:44 2008 matrix is 192743 x 192855 (40.9 MB) with weight 12213594 (63.33/col) Mon Sep 15 10:59:44 2008 sparse part has weight 9571959 (49.63/col) Mon Sep 15 10:59:44 2008 matrix includes 64 packed rows Mon Sep 15 10:59:44 2008 using block size 65536 for processor cache size 2048 kB Mon Sep 15 10:59:46 2008 commencing Lanczos iteration Mon Sep 15 10:59:46 2008 memory use: 36.9 MB Mon Sep 15 11:04:34 2008 lanczos halted after 3049 iterations (dim = 192738) Mon Sep 15 11:04:35 2008 recovered 15 nontrivial dependencies Mon Sep 15 11:04:38 2008 prp47 factor: 98977571642142365276984929935548439173343598577 Mon Sep 15 11:04:38 2008 prp62 factor: 28064719427760380820022102182615812657550236296462577237567549 Mon Sep 15 11:04:38 2008 elapsed time 78:01:48
Sep 15, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(16·10¹⁶⁶-7)/9 = 1(7)₁₆₆_<167> = 73867 · 261427 · 45020051 · 2159829807661_<13> · C136
C136 = P65 · P72
P65 = 11534998653303754286376078599436060408108912634496357909792199251_<65>
P72 = 820792749689864725133726681975155104671578537741228360509241468320423773_<72>

Number: n N=9467843262314075088114456690203792146385655753244537824265820827096598765879588060136679376473184972544225902520642437741750597973194023 ( 136 digits) SNFS difficulty: 167 digits. Divisors found: Mon Sep 15 00:12:37 2008 prp65 factor: 11534998653303754286376078599436060408108912634496357909792199251 Mon Sep 15 00:12:37 2008 prp72 factor: 820792749689864725133726681975155104671578537741228360509241468320423773 Mon Sep 15 00:12:37 2008 elapsed time 03:35:17 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 40.54 hours. Scaled time: 34.09 units (timescale=0.841). Factorization parameters were as follows: name: KA_1_7_166 n: 9467843262314075088114456690203792146385655753244537824265820827096598765879588060136679376473184972544225902520642437741750597973194023 type: snfs skew: 1.07 deg: 5 c5: 5 c0: -7 m: 2000000000000000000000000000000000 rlim: 5400000 alim: 5400000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 4700001) Primes: RFBsize:374362, AFBsize:373867, largePrimes:14071031 encountered Relations: rels:13318773, finalFF:814933 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 40.16 hours. Total relation processing time: 0.38 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,52,52,2.5,2.5,100000 total time: 40.54 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(29·10¹⁶⁶+7)/9 = 3(2)₁₆₅3_<167> = 3 · 2309 · 63281501 · 412394155289780003_<18> · C138
C138 = P53 · P85
P53 = 79353768896243354879317921547141159657539357186424707_<53>
P85 = 2246226099411522565081310175327100561059317639528459166402607843175730179074495466669_<85>

Number: n N=178246506781412113310294463823584874541396179184968819439212220708712747355434245310443530401773459134403743276598581768969540379596590983 ( 138 digits) SNFS difficulty: 167 digits. Divisors found: Mon Sep 15 03:08:09 2008 prp53 factor: 79353768896243354879317921547141159657539357186424707 Mon Sep 15 03:08:09 2008 prp85 factor: 2246226099411522565081310175327100561059317639528459166402607843175730179074495466669 Mon Sep 15 03:08:09 2008 elapsed time 03:50:18 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 43.04 hours. Scaled time: 36.20 units (timescale=0.841). Factorization parameters were as follows: name: KA_3_2_165_3 n: 178246506781412113310294463823584874541396179184968819439212220708712747355434245310443530401773459134403743276598581768969540379596590983 type: snfs skew: 0.47 deg: 5 c5: 290 c0: 7 m: 1000000000000000000000000000000000 rlim: 5400000 alim: 5400000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 4900001) Primes: RFBsize:374362, AFBsize:374497, largePrimes:14043887 encountered Relations: rels:13214911, finalFF:755528 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 42.60 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,52,52,2.5,2.5,100000 total time: 43.04 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Sep 15, 2008: By Serge Batalov / Msieve-1.37
(25·10¹⁶⁹-43)/9 = 2(7)₁₆₈3_<170> = 6761 · C166
C166 = P79 · P88
P79 = 3080145577490737926404037860940972976068672736877912330103917098426035030034777_<79>
P88 = 1333875575134097511706641124139988902844113672229182918543377260872116052419579028419309_<88>

Number: 27773_169 N=4108530953672204966392216798961363374911666584496047593222567338822330687439399168433334976745714802215319890220052917878683297999967131752370622360268862265608309093 ( 166 digits) SNFS difficulty: 170 digits. Divisors found: r1=3080145577490737926404037860940972976068672736877912330103917098426035030034777 r2=1333875575134097511706641124139988902844113672229182918543377260872116052419579028419309 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.727). Factorization parameters were as follows: n: 4108530953672204966392216798961363374911666584496047593222567338822330687439399168433334976745714802215319890220052917878683297999967131752370622360268862265608309093 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 5 c0: -86 skew: 1.77 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [3000000, 5500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 996680 x 996928 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 42.50 hours.
Sep 14, 2008 (2nd): By Wataru Sakai / GGNFS
(25·10¹⁸⁴-61)/9 = 2(7)₁₈₃1_<185> = 3 · 269 · C182
C182 = P75 · P107
P75 = 509575232245114400105218066214409542599718583695395748663216501642189269183_<75>
P107 = 67548491293142657192636214891586037775613013390913300305025073464846830376816916705229553974495985164761891_<107>

Number: 27771_184 N=34421038138510257469365276056725870852264904309513974941484235164532562302079030703566019551149662673826242599476800220294644086465647803937766763045573454495387580889439625499105053 ( 182 digits) SNFS difficulty: 185 digits. Divisors found: r1=509575232245114400105218066214409542599718583695395748663216501642189269183 (pp75) r2=67548491293142657192636214891586037775613013390913300305025073464846830376816916705229553974495985164761891 (pp107) Version: GGNFS-0.77.1-20060722-nocona Total time: 835.22 hours. Scaled time: 1672.94 units (timescale=2.003). Factorization parameters were as follows: n: 34421038138510257469365276056725870852264904309513974941484235164532562302079030703566019551149662673826242599476800220294644086465647803937766763045573454495387580889439625499105053 m: 10000000000000000000000000000000000000 c5: 5 c0: -122 skew: 1.89 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 15000001) Primes: RFBsize:501962, AFBsize:500647, largePrimes:6989854 encountered Relations: rels:7537555, finalFF:1185130 Max relations in full relation-set: 32 Initial matrix: 1002674 x 1185130 with sparse part having weight 117077372. Pruned matrix : 861922 x 866999 with weight 96601519. Total sieving time: 826.03 hours. Total relation processing time: 0.12 hours. Matrix solve time: 8.80 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 835.22 hours. --------- CPU info (if available) ----------
Sep 14, 2008: By Sinkiti Sibata / GMP-ECM
(25·10¹⁶⁸-43)/9 = 2(7)₁₆₇3_<169> = 17 · 8971 · 10337 · 8615692218787_<13> · C147
C147 = P40 · P108
P40 = 1985140693063465171692545141141610284639_<40>
P108 = 103022417519537981589629426097797637160177611134278915004628187551244055578499294100173927259247731956871779_<108>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 204513993315809305228716749061373306143831113687280897005385595482580547491319916444125287840919440008825849540473546379899733573903628096216302781 Run 377 out of 2350: Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3964083566 Step 1 took 54756ms Step 2 took 18455ms ********** Factor found in step 2: 1985140693063465171692545141141610284639 Found probable prime factor of 40 digits: 1985140693063465171692545141141610284639 Probable prime cofactor 103022417519537981589629426097797637160177611134278915004628187551244055578499294100173927259247731956871779 has 108 digits
Sep 13, 2008 (2nd): By Sinkiti Sibata / GGNFS
(25·10¹⁶⁶-43)/9 = 2(7)₁₆₅3_<167> = 503 · 706751 · 2776343 · 2440785247913_<13> · C140
C140 = P47 · P93
P47 = 64438863979153398772474615309331228867392153447_<47>
P93 = 178942095075642967256744351697024985709989506953109244293032020741491038953890828802470902717_<93>

Number: 27773_166 N=11530825324724092380753939585475456118157613190482884095671427620741334156187743828513545625362299892188371422291850861036994978256673215499 ( 140 digits) SNFS difficulty: 167 digits. Divisors found: r1=64438863979153398772474615309331228867392153447 (pp47) r2=178942095075642967256744351697024985709989506953109244293032020741491038953890828802470902717 (pp93) Version: GGNFS-0.77.1-20050930-nocona Total time: 106.94 hours. Scaled time: 107.80 units (timescale=1.008). Factorization parameters were as follows: name: 27773_166 n: 11530825324724092380753939585475456118157613190482884095671427620741334156187743828513545625362299892188371422291850861036994978256673215499 m: 1000000000000000000000000000000000 c5: 250 c0: -43 skew: 0.7 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, 6450001) Primes: RFBsize:380800, AFBsize:381622, largePrimes:6131252 encountered Relations: rels:6442154, finalFF:949844 Max relations in full relation-set: 28 Initial matrix: 762488 x 949844 with sparse part having weight 61604041. Pruned matrix : 608545 x 612421 with weight 43738158. Total sieving time: 103.72 hours. Total relation processing time: 0.11 hours. Matrix solve time: 3.01 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 106.94 hours. --------- CPU info (if available) ----------
Sep 13, 2008: By Robert Backstrom / GGNFS
(25·10¹⁵⁰-43)/9 = 2(7)₁₄₉3_<151> = 4024156931_<10> · C141
C141 = P55 · P86
P55 = 7093738736322567193255076634889767778935410319128407547_<55>
P86 = 97307743410819327218171555923430401617608483828797046105780850465138527911441189609789_<86>

Number: n N=690275708777466108659015857296291355238347134374660344919281622761788307051929376602579065219307615957827509927638499885773410405245892677583 ( 141 digits) SNFS difficulty: 151 digits. Divisors found: r1=7093738736322567193255076634889767778935410319128407547 (pp55) r2=97307743410819327218171555923430401617608483828797046105780850465138527911441189609789 (pp86) Version: GGNFS-0.77.1-20051202-athlon Total time: 14.80 hours. Scaled time: 26.61 units (timescale=1.798). Factorization parameters were as follows: name: KA_2_7_149_3 n: 690275708777466108659015857296291355238347134374660344919281622761788307051929376602579065219307615957827509927638499885773410405245892677583 type: snfs skew: 1.11 deg: 5 c5: 25 c0: -43 m: 1000000000000000000000000000000 rlim: 1600000 alim: 1600000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved algebraic special-q in [100000, 960001) Primes: RFBsize:121127, AFBsize:120625, largePrimes:10273485 encountered Relations: rels:9213877, finalFF:294423 Max relations in full relation-set: 48 Initial matrix: 241816 x 294423 with sparse part having weight 47230275. Pruned matrix : 227056 x 228329 with weight 31481125. Total sieving time: 13.74 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.78 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,52,52,2.5,2.5,100000 total time: 14.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Sep 12, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
(13·10¹⁹³+41)/9 = 1(4)₁₉₂9_<194> = C194
C194 = P49 · P145
P49 = 1901287922333370738124450534127671428882960582469_<49>
P145 = 7597189397131069455903065721394056844398540195601305071590900567978034358366761385835754036511022197005546476527689112466320193426394369847525421_<145>

Number: n N=14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 ( 194 digits) SNFS difficulty: 194 digits. Divisors found: Fri Sep 12 22:18:39 2008 prp49 factor: 1901287922333370738124450534127671428882960582469 Fri Sep 12 22:18:39 2008 prp145 factor: 7597189397131069455903065721394056844398540195601305071590900567978034358366761385835754036511022197005546476527689112466320193426394369847525421 Fri Sep 12 22:18:39 2008 elapsed time 24:07:01 (Msieve 1.37) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 249.78 hours. Scaled time: 320.72 units (timescale=1.284). Factorization parameters were as follows: name: KA_1_4_192_9 n: 14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 type: snfs skew: 0.32 deg: 5 c5: 13000 c0: 41 m: 100000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 20100001) Primes: RFBsize:633578, AFBsize:632714, largePrimes:15887207 encountered Relations: rels:16490078, finalFF:1303499 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 248.58 hours. Total relation processing time: 1.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,194,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000 total time: 249.78 hours. --------- CPU info (if available) ----------
Sep 12, 2008 (3rd): By Jo Yeong Uk / GGNFS, GMP-ECM
(25·10¹⁵⁶-43)/9 = 2(7)₁₅₅3_<157> = C157
C157 = P39 · P50 · P69
P39 = 372185119464374581000505742262872837559_<39>
P50 = 27261215972898031404791163916223415134863840191709_<50>
P69 = 273774673963716145379187767741510557645709906000665535557462756307383_<69>

Number: 27773_156 N=2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773 ( 157 digits) SNFS difficulty: 158 digits. Divisors found: r1=372185119464374581000505742262872837559 (pp39) r2=27261215972898031404791163916223415134863840191709 (pp50) r3=273774673963716145379187767741510557645709906000665535557462756307383 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.15 hours. Scaled time: 57.46 units (timescale=2.379). Factorization parameters were as follows: n: 2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773 m: 50000000000000000000000000000000 c5: 2 c0: -1075 skew: 3.52 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:283717, largePrimes:5772871 encountered Relations: rels:5900578, finalFF:739057 Max relations in full relation-set: 28 Initial matrix: 566928 x 739057 with sparse part having weight 46097498. Pruned matrix : 429064 x 431962 with weight 29205104. Total sieving time: 23.11 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.93 hours. Time per square root: 0.04 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: 24.15 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(25·10¹⁸⁵-43)/9 = 2(7)₁₈₄3_<186> = 3 · 1106257 · 527014997 · 6161874197_<10> · 7380221741_<10> · 645660194219364791_<18> · 773333185615761311050817_<24> · C109
C109 = P36 · P74
P36 = 207427746518315298219866961491334487_<36>
P74 = 33719217843231569076697258173474898117809420616890018677139524636324971843_<74>

Number: 27773_185 N=6994301371581692181777843367355613443324859575717902716265870548989008052704863600572322946143570728769849541 ( 109 digits) Divisors found: r1=207427746518315298219866961491334487 (pp36) r2=33719217843231569076697258173474898117809420616890018677139524636324971843 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.43 hours. Scaled time: 27.16 units (timescale=2.377). Factorization parameters were as follows: name: 27773_185 n: 6994301371581692181777843367355613443324859575717902716265870548989008052704863600572322946143570728769849541 skew: 21151.42 # norm 1.25e+15 c5: 16560 c4: -2088178530 c3: -65952207601223 c2: 745789390304980316 c1: 6183343412064671125560 c0: -39578050847778957024291000 # alpha -6.06 Y1: 210305389327 Y0: -841665524867103496247 # Murphy_E 1.19e-09 # M 3656899472026595564392796563244510379395325061944130045086403262223357093135654178911921285543656665588495754 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1650001) Primes: RFBsize:148933, AFBsize:148957, largePrimes:4996228 encountered Relations: rels:5005800, finalFF:346194 Max relations in full relation-set: 28 Initial matrix: 297968 x 346194 with sparse part having weight 32876209. Pruned matrix : 268177 x 269730 with weight 22653877. Polynomial selection time: 0.68 hours. Total sieving time: 10.27 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.33 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,26,26,50,50,2.6,2.6,50000 total time: 11.43 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(23·10¹⁶⁷+31)/9 = 2(5)₁₆₆9_<168> = 37 · 89 · 42499349 · 111504861389_<12> · 186436563074621_<15> · C131
C131 = P38 · P94
P38 = 55483666228939118598781075378752414371_<38>
P94 = 1583147127896190823350447145282876632629418105166606868157240854518223554213826164611612094613_<94>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 87838806835495842387786872741538203556807416279684160572753784510959133212549527350596610907585322642508289465712809312178232883423 (131 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3374304280 Step 1 took 3886ms Step 2 took 2369ms ********** Factor found in step 2: 55483666228939118598781075378752414371 Found probable prime factor of 38 digits: 55483666228939118598781075378752414371 Probable prime cofactor 1583147127896190823350447145282876632629418105166606868157240854518223554213826164611612094613 has 94 digits
Sep 12, 2008 (2nd): By Sinkiti Sibata / GGNFS
(25·10¹³⁸-43)/9 = 2(7)₁₃₇3_<139> = 3461369355503102471_<19> · C120
C120 = P48 · P73
P48 = 790851346784577684398460172607720171516872020779_<48>
P73 = 1014739803995546828170875314780552789730502310354605465076404664637362497_<73>

Number: 27773_138 N=802508340625796592750740934904214903221912043435135793932312557736238617400120237419203039842903464308882342049139325163 ( 120 digits) SNFS difficulty: 139 digits. Divisors found: r1=790851346784577684398460172607720171516872020779 (pp48) r2=1014739803995546828170875314780552789730502310354605465076404664637362497 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.93 hours. Scaled time: 8.46 units (timescale=0.774). Factorization parameters were as follows: name: 27773_142 n: 802508340625796592750740934904214903221912043435135793932312557736238617400120237419203039842903464308882342049139325163 m: 5000000000000000000000000000 c5: 8 c0: -43 skew: 1.4 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1825001) Primes: RFBsize:78498, AFBsize:64453, largePrimes:1658794 encountered Relations: rels:1698186, finalFF:193639 Max relations in full relation-set: 28 Initial matrix: 143016 x 193639 with sparse part having weight 20004298. Pruned matrix : 130828 x 131607 with weight 12027837. Total sieving time: 10.71 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 10.93 hours. --------- CPU info (if available) ----------
(25·10¹⁵⁸-43)/9 = 2(7)₁₅₇3_<159> = 3 · 7 · 13 · 18731 · 43991 · 3802871 · 1406979953_<10> · 31936685952781180337671_<23> · C109
C109 = P52 · P58
P52 = 1060954734369655295158543412841251294725874914494979_<52>
P58 = 6811203372630868140845047043796262908156716759170685398043_<58>

Number: 27773_158 N=7226378464947282981654061338531266785619495339921092659976461093024228582184017894788462297005065080939926097 ( 109 digits) Divisors found: r1=1060954734369655295158543412841251294725874914494979 (pp52) r2=6811203372630868140845047043796262908156716759170685398043 (pp58) Version: GGNFS-0.77.1-20050930-nocona Total time: 21.60 hours. Scaled time: 21.65 units (timescale=1.002). Factorization parameters were as follows: name: 27773_158 n: 7226378464947282981654061338531266785619495339921092659976461093024228582184017894788462297005065080939926097 skew: 13387.42 # norm 4.83e+14 c5: 114000 c4: 25870285 c3: -58382673621146 c2: 61359297300806952 c1: 4190972551164436333248 c0: -10579597973151794333285760 # alpha -5.46 Y1: 423910963663 Y0: -575974366622446883713 # Murphy_E 1.16e-09 # M 4576898731503046020234271183227462729024026786633249131730637009994011599613654968105344173860276081349930103 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:230748, largePrimes:8157077 encountered Relations: rels:8862586, finalFF:1267055 Max relations in full relation-set: 28 Initial matrix: 461037 x 1267055 with sparse part having weight 112957061. Pruned matrix : 231027 x 233396 with weight 44419779. Total sieving time: 20.70 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.55 hours. Time per square root: 0.13 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: 21.60 hours. --------- CPU info (if available) ----------
(25·10¹⁵²-43)/9 = 2(7)₁₅₁3_<153> = 3³ · 7 · 13 · 17² · 71593 · 19123127327388755233_<20> · C123
C123 = P43 · P81
P43 = 1979428177393314368570122123308590554452839_<43>
P81 = 144352820453911733686418927078964022953285009748700229868308507688975473906555211_<81>

Number: 27773_152 N=285736040292670853957964209651635759654923438991468283221845678871226287254773670813818454574097166010637334422447449194029 ( 123 digits) SNFS difficulty: 154 digits. Divisors found: r1=1979428177393314368570122123308590554452839 (pp43) r2=144352820453911733686418927078964022953285009748700229868308507688975473906555211 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 31.41 hours. Scaled time: 31.60 units (timescale=1.006). Factorization parameters were as follows: name: 27773_152 n: 285736040292670853957964209651635759654923438991468283221845678871226287254773670813818454574097166010637334422447449194029 m: 5000000000000000000000000000000 c5: 4 c0: -215 skew: 2.22 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2500001) Primes: RFBsize:176302, AFBsize:176203, largePrimes:6287534 encountered Relations: rels:6809416, finalFF:1013312 Max relations in full relation-set: 28 Initial matrix: 352569 x 1013312 with sparse part having weight 97004807. Pruned matrix : 226092 x 227918 with weight 43662774. Total sieving time: 30.70 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.56 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 31.41 hours. --------- CPU info (if available) ----------
Sep 12, 2008: By Serge Batalov / GMP-ECM 6.2.1, Msieve 1.37
(25·10¹⁹⁷-43)/9 = 2(7)₁₉₆3_<198> = 3² · 557 · 69708090293108587957264033909_<29> · C165
C165 = P39 · C127
P39 = 295129451897746307965079731115042417503_<39>
C127 = [2693419861220489027602411855507083936235406613469644223236807794490616222429689028593525007468377268250369054863714727544458923_<127>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3572283450 Step 1 took 24483ms Step 2 took 20195ms ********** Factor found in step 2: 295129451897746307965079731115042417503 Found probable prime factor of 39 digits: 295129451897746307965079731115042417503 Composite cofactor 2693419861220489027602411855507083936235406613469644223236807794490616222429689028593525007468377268250369054863714727544458923 has 127 digits
(25·10¹⁵⁹-43)/9 = 2(7)₁₅₈3_<160> = 14804843 · C153
C153 = P52 · P101
P52 = 7089429201080214479664670394561412242126294491529591_<52>
P101 = 26465641374720917002970020698949335866709819281304228891957159307035545316434566546736730357665451121_<101>

Number: 27773_159 N=187626290787263179878218078893357921983892553117772189666434002561038828833090481120115747109089760545098504440592701846130876077360481146458478335621511 ( 153 digits) SNFS difficulty: 160 digits. Divisors found: r1=7089429201080214479664670394561412242126294491529591 r2=26465641374720917002970020698949335866709819281304228891957159307035545316434566546736730357665451121 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.726). Factorization parameters were as follows: n: 187626290787263179878218078893357921983892553117772189666434002561038828833090481120115747109089760545098504440592701846130876077360481146458478335621511 Y1: 1 Y0: -100000000000000000000000000000000 c5: 5 c0: -86 skew: 1.77 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2000000, 3200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 653896 x 654144 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.5,2.5,100000 total time: 18.00 hours.
Sep 11, 2008 (4th): By Robert Backstrom / GGNFS
(25·10¹²²-43)/9 = 2(7)₁₂₁3_<123> = 3 · 7² · 13 · 53 · 163 · 15187 · C112
C112 = P41 · P71
P41 = 12296099279101296181724216494604921968343_<41>
P71 = 90101907275351747216622783339526222453849108310187602759487276953447057_<71>

Number: n N=1107901997094104452594768197905015821872713125836258972221023391495310813044300088873487367827302532099280516551 ( 112 digits) SNFS difficulty: 124 digits. Divisors found: r1=12296099279101296181724216494604921968343 (pp41) r2=90101907275351747216622783339526222453849108310187602759487276953447057 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.58 hours. Scaled time: 2.87 units (timescale=1.813). Factorization parameters were as follows: name: KA_2_7_121_3 n: 1107901997094104452594768197905015821872713125836258972221023391495310813044300088873487367827302532099280516551 type: snfs skew: 2.22 deg: 5 c5: 4 c0: -215 m: 5000000000000000000000000 rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved algebraic special-q in [100000, 260001) Primes: RFBsize:49098, AFBsize:49151, largePrimes:4627065 encountered Relations: rels:3986750, finalFF:176484 Max relations in full relation-set: 48 Initial matrix: 98313 x 176484 with sparse part having weight 18651096. Pruned matrix : 80127 x 80682 with weight 4849535. Total sieving time: 1.44 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.03 hours. Total square root time: 0.05 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,600000,600000,28,28,52,52,2.5,2.5,50000 total time: 1.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Sep 11, 2008 (3rd): By Sinkiti Sibata / Msieve, GGNFS
(25·10¹¹¹-43)/9 = 2(7)₁₁₀3_<112> = 23 · 595207 · 4435129 · 6200659 · C91
C91 = P32 · P59
P32 = 80335719249839503097507848265209_<32>
P59 = 91843588104175473506416389257508387935075613929940942541007_<59>

Wed Sep 10 21:25:51 2008 Msieve v. 1.36 Wed Sep 10 21:25:51 2008 random seeds: e69762f8 0dfdb476 Wed Sep 10 21:25:51 2008 factoring 7378320708834939980942794923012846889957608886051853826338735120290578568531951753293925463 (91 digits) Wed Sep 10 21:25:53 2008 no P-1/P+1/ECM available, skipping Wed Sep 10 21:25:53 2008 commencing quadratic sieve (91-digit input) Wed Sep 10 21:25:53 2008 using multiplier of 15 Wed Sep 10 21:25:53 2008 using 64kb Pentium 4 sieve core Wed Sep 10 21:25:53 2008 sieve interval: 18 blocks of size 65536 Wed Sep 10 21:25:53 2008 processing polynomials in batches of 6 Wed Sep 10 21:25:53 2008 using a sieve bound of 1719863 (64695 primes) Wed Sep 10 21:25:53 2008 using large prime bound of 165106848 (27 bits) Wed Sep 10 21:25:53 2008 using double large prime bound of 619408411789728 (42-50 bits) Wed Sep 10 21:25:53 2008 using trial factoring cutoff of 50 bits Wed Sep 10 21:25:53 2008 polynomial 'A' values have 12 factors Thu Sep 11 00:35:10 2008 64893 relations (16878 full + 48015 combined from 766514 partial), need 64791 Thu Sep 11 00:35:13 2008 begin with 783392 relations Thu Sep 11 00:35:13 2008 reduce to 162113 relations in 11 passes Thu Sep 11 00:35:13 2008 attempting to read 162113 relations Thu Sep 11 00:35:18 2008 recovered 162113 relations Thu Sep 11 00:35:18 2008 recovered 143629 polynomials Thu Sep 11 00:35:18 2008 attempting to build 64893 cycles Thu Sep 11 00:35:18 2008 found 64893 cycles in 6 passes Thu Sep 11 00:35:18 2008 distribution of cycle lengths: Thu Sep 11 00:35:18 2008 length 1 : 16878 Thu Sep 11 00:35:18 2008 length 2 : 12100 Thu Sep 11 00:35:18 2008 length 3 : 11142 Thu Sep 11 00:35:18 2008 length 4 : 8604 Thu Sep 11 00:35:18 2008 length 5 : 6293 Thu Sep 11 00:35:18 2008 length 6 : 4176 Thu Sep 11 00:35:18 2008 length 7 : 2556 Thu Sep 11 00:35:18 2008 length 9+: 3144 Thu Sep 11 00:35:18 2008 largest cycle: 20 relations Thu Sep 11 00:35:19 2008 matrix is 64695 x 64893 (16.0 MB) with weight 3929052 (60.55/col) Thu Sep 11 00:35:19 2008 sparse part has weight 3929052 (60.55/col) Thu Sep 11 00:35:20 2008 filtering completed in 3 passes Thu Sep 11 00:35:20 2008 matrix is 60904 x 60968 (15.1 MB) with weight 3714849 (60.93/col) Thu Sep 11 00:35:20 2008 sparse part has weight 3714849 (60.93/col) Thu Sep 11 00:35:20 2008 saving the first 48 matrix rows for later Thu Sep 11 00:35:20 2008 matrix is 60856 x 60968 (8.8 MB) with weight 2835309 (46.50/col) Thu Sep 11 00:35:20 2008 sparse part has weight 1949848 (31.98/col) Thu Sep 11 00:35:20 2008 matrix includes 64 packed rows Thu Sep 11 00:35:20 2008 using block size 21845 for processor cache size 512 kB Thu Sep 11 00:35:21 2008 commencing Lanczos iteration Thu Sep 11 00:35:21 2008 memory use: 9.0 MB Thu Sep 11 00:35:58 2008 lanczos halted after 964 iterations (dim = 60856) Thu Sep 11 00:35:58 2008 recovered 19 nontrivial dependencies Thu Sep 11 00:35:59 2008 prp32 factor: 80335719249839503097507848265209 Thu Sep 11 00:35:59 2008 prp59 factor: 91843588104175473506416389257508387935075613929940942541007 Thu Sep 11 00:35:59 2008 elapsed time 03:10:08
(5·10¹⁶⁵+31)/9 = (5)₁₆₄9_<165> = 13² · 197 · 509 · 90527 · 272351681066590730815104119_<27> · C127
C127 = P60 · P67
P60 = 370716149467693053462676008244862500592389799729429922243563_<60>
P67 = 3586799392723596076389074822312062821586305721304049998960779310453_<67>

Number: 55559_165 N=1329684459783551319011438303306065173410835619674644634108352388375150231496077427760368587873116286526650932326829865857864039 ( 127 digits) SNFS difficulty: 165 digits. Divisors found: r1=370716149467693053462676008244862500592389799729429922243563 (pp60) r2=3586799392723596076389074822312062821586305721304049998960779310453 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 88.75 hours. Scaled time: 89.55 units (timescale=1.009). Factorization parameters were as follows: name: 55559_165 n: 1329684459783551319011438303306065173410835619674644634108352388375150231496077427760368587873116286526650932326829865857864039 m: 1000000000000000000000000000000000 c5: 5 c0: 31 skew: 1.44 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5400001) Primes: RFBsize:348513, AFBsize:348707, largePrimes:5990856 encountered Relations: rels:6232115, finalFF:871113 Max relations in full relation-set: 28 Initial matrix: 697285 x 871113 with sparse part having weight 55986264. Pruned matrix : 558153 x 561703 with weight 38940973. Total sieving time: 86.17 hours. Total relation processing time: 0.11 hours. Matrix solve time: 2.38 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 88.75 hours. --------- CPU info (if available) ----------
(25·10¹²³-43)/9 = 2(7)₁₂₂3_<124> = 9187 · 23567851 · 2954627142542967631_<19> · C94
C94 = P36 · P59
P36 = 197767387776465112016466741177603017_<36>
P59 = 21955657065213338757728221623461856918053744589286504372427_<59>

Thu Sep 11 05:57:41 2008 Msieve v. 1.36 Thu Sep 11 05:57:41 2008 random seeds: 19311b63 c69426e7 Thu Sep 11 05:57:41 2008 factoring 4342112944703132326197740951319412899341521838472865926258815265174619316324832004333726812259 (94 digits) Thu Sep 11 05:57:43 2008 no P-1/P+1/ECM available, skipping Thu Sep 11 05:57:43 2008 commencing quadratic sieve (94-digit input) Thu Sep 11 05:57:43 2008 using multiplier of 19 Thu Sep 11 05:57:43 2008 using 64kb Pentium 4 sieve core Thu Sep 11 05:57:43 2008 sieve interval: 18 blocks of size 65536 Thu Sep 11 05:57:43 2008 processing polynomials in batches of 6 Thu Sep 11 05:57:43 2008 using a sieve bound of 2058671 (76471 primes) Thu Sep 11 05:57:43 2008 using large prime bound of 284096598 (28 bits) Thu Sep 11 05:57:43 2008 using double large prime bound of 1645276127747088 (42-51 bits) Thu Sep 11 05:57:43 2008 using trial factoring cutoff of 51 bits Thu Sep 11 05:57:43 2008 polynomial 'A' values have 12 factors Thu Sep 11 10:30:36 2008 76676 relations (19493 full + 57183 combined from 1084674 partial), need 76567 Thu Sep 11 10:30:40 2008 begin with 1104167 relations Thu Sep 11 10:30:41 2008 reduce to 195866 relations in 10 passes Thu Sep 11 10:30:41 2008 attempting to read 195866 relations Thu Sep 11 10:30:47 2008 recovered 195866 relations Thu Sep 11 10:30:47 2008 recovered 176093 polynomials Thu Sep 11 10:30:48 2008 attempting to build 76676 cycles Thu Sep 11 10:30:48 2008 found 76676 cycles in 5 passes Thu Sep 11 10:30:48 2008 distribution of cycle lengths: Thu Sep 11 10:30:48 2008 length 1 : 19493 Thu Sep 11 10:30:48 2008 length 2 : 13874 Thu Sep 11 10:30:48 2008 length 3 : 13105 Thu Sep 11 10:30:48 2008 length 4 : 10291 Thu Sep 11 10:30:48 2008 length 5 : 7656 Thu Sep 11 10:30:48 2008 length 6 : 5026 Thu Sep 11 10:30:48 2008 length 7 : 3090 Thu Sep 11 10:30:48 2008 length 9+: 4141 Thu Sep 11 10:30:48 2008 largest cycle: 20 relations Thu Sep 11 10:30:48 2008 matrix is 76471 x 76676 (20.2 MB) with weight 4983164 (64.99/col) Thu Sep 11 10:30:48 2008 sparse part has weight 4983164 (64.99/col) Thu Sep 11 10:30:50 2008 filtering completed in 3 passes Thu Sep 11 10:30:50 2008 matrix is 72258 x 72322 (19.2 MB) with weight 4734465 (65.46/col) Thu Sep 11 10:30:50 2008 sparse part has weight 4734465 (65.46/col) Thu Sep 11 10:30:50 2008 saving the first 48 matrix rows for later Thu Sep 11 10:30:51 2008 matrix is 72210 x 72322 (12.7 MB) with weight 3804435 (52.60/col) Thu Sep 11 10:30:51 2008 sparse part has weight 2885271 (39.89/col) Thu Sep 11 10:30:51 2008 matrix includes 64 packed rows Thu Sep 11 10:30:51 2008 using block size 21845 for processor cache size 512 kB Thu Sep 11 10:30:51 2008 commencing Lanczos iteration Thu Sep 11 10:30:51 2008 memory use: 11.8 MB Thu Sep 11 10:31:50 2008 lanczos halted after 1143 iterations (dim = 72210) Thu Sep 11 10:31:50 2008 recovered 18 nontrivial dependencies Thu Sep 11 10:31:51 2008 prp36 factor: 197767387776465112016466741177603017 Thu Sep 11 10:31:51 2008 prp59 factor: 21955657065213338757728221623461856918053744589286504372427 Thu Sep 11 10:31:51 2008 elapsed time 04:34:10
(25·10¹³⁷-43)/9 = 2(7)₁₃₆3_<138> = 3 · 183078069497_<12> · C126
C126 = P37 · P41 · P49
P37 = 3450507775979522920422222278082125473_<37>
P41 = 18317658128532632830435818365348120635739_<41>
P49 = 8001786516984967398026373100632236071167857872549_<49>

Number: 27773_137 N=505754691684193538361759780341565552359166040090181804723821047319728569316991723580215967720444203699416467812879368361655303 ( 126 digits) SNFS difficulty: 139 digits. Divisors found: r1=3450507775979522920422222278082125473 (pp37) r2=18317658128532632830435818365348120635739 (pp41) r3=8001786516984967398026373100632236071167857872549 (pp49) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.32 hours. Scaled time: 8.37 units (timescale=1.005). Factorization parameters were as follows: name: 27773_137 n: 505754691684193538361759780341565552359166040090181804723821047319728569316991723580215967720444203699416467812879368361655303 m: 5000000000000000000000000000 c5: 4 c0: -215 skew: 2.22 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1675001) Primes: RFBsize:78498, AFBsize:64043, largePrimes:1675641 encountered Relations: rels:1732833, finalFF:212605 Max relations in full relation-set: 28 Initial matrix: 142605 x 212605 with sparse part having weight 21652651. Pruned matrix : 126227 x 127004 with weight 11457432. Total sieving time: 8.18 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 8.32 hours. --------- CPU info (if available) ----------
(25·10¹⁴⁵-43)/9 = 2(7)₁₄₄3_<146> = 47237 · 52957 · 4493917383401_<13> · C124
C124 = P61 · P63
P61 = 9361636002439421548832013290405714726713563748317735359487143_<61>
P63 = 263945937385059899912750880407649594646514339637183924419826979_<63>

Number: 27773_145 N=2470965790121598028563385922026799376277420920856636335118189769521140183570701413099038001314908717575196572384098235030997 ( 124 digits) SNFS difficulty: 146 digits. Divisors found: r1=9361636002439421548832013290405714726713563748317735359487143 (pp61) r2=263945937385059899912750880407649594646514339637183924419826979 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.36 hours. Scaled time: 18.96 units (timescale=0.778). Factorization parameters were as follows: name: 27773_145 n: 2470965790121598028563385922026799376277420920856636335118189769521140183570701413099038001314908717575196572384098235030997 m: 100000000000000000000000000000 c5: 25 c0: -43 skew: 1.11 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3450001) Primes: RFBsize:114155, AFBsize:113677, largePrimes:2999915 encountered Relations: rels:3045828, finalFF:292596 Max relations in full relation-set: 28 Initial matrix: 227896 x 292596 with sparse part having weight 34011955. Pruned matrix : 209927 x 211130 with weight 23189695. Total sieving time: 23.70 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.48 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 24.36 hours. --------- CPU info (if available) ----------
(25·10¹⁴²-43)/9 = 2(7)₁₄₁3_<143> = 19 · 109 · 59026157 · 18399994554796203751_<20> · C113
C113 = P34 · P79
P34 = 5428210099470840332597507186448961_<34>
P79 = 2275089826819532792479137350314839096344705558799489784040259764474500966858369_<79>

Number: 27773_142 N=12349665575145153005345838457224467517841859428044691619956472747422827816639099804751127362518567750321334204609 ( 113 digits) SNFS difficulty: 144 digits. Divisors found: r1=5428210099470840332597507186448961 (pp34) r2=2275089826819532792479137350314839096344705558799489784040259764474500966858369 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.10 hours. Scaled time: 10.21 units (timescale=1.011). Factorization parameters were as follows: name: 27773_142 n: 12349665575145153005345838457224467517841859428044691619956472747422827816639099804751127362518567750321334204609 m: 50000000000000000000000000000 c5: 4 c0: -215 skew: 2.22 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1950001) Primes: RFBsize:100021, AFBsize:100053, largePrimes:2707861 encountered Relations: rels:2659320, finalFF:231209 Max relations in full relation-set: 28 Initial matrix: 200138 x 231209 with sparse part having weight 23015066. Pruned matrix : 191293 x 192357 with weight 17221770. Total sieving time: 9.82 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.20 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 10.10 hours. --------- CPU info (if available) ----------
(25·10¹³⁵-43)/9 = 2(7)₁₃₄3_<136> = 29 · 53 · 238020656130017_<15> · C118
C118 = P43 · P76
P43 = 1364825535132809236399287376342620506894869_<43>
P76 = 5563291859982587204588404791822161196008037539326329882180989274171637224473_<76>

Number: 27773_135 N=7592922789900736215977182615340711041741161887250275039784231201917045291412141943209741657646425920334073674764929037 ( 118 digits) SNFS difficulty: 136 digits. Divisors found: r1=1364825535132809236399287376342620506894869 (pp43) r2=5563291859982587204588404791822161196008037539326329882180989274171637224473 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.93 hours. Scaled time: 6.95 units (timescale=0.778). Factorization parameters were as follows: name: 27773_135 n: 7592922789900736215977182615340711041741161887250275039784231201917045291412141943209741657646425920334073674764929037 m: 1000000000000000000000000000 c5: 25 c0: -43 skew: 1.11 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1525001) Primes: RFBsize:78498, AFBsize:63718, largePrimes:1599745 encountered Relations: rels:1612334, finalFF:178104 Max relations in full relation-set: 28 Initial matrix: 142280 x 178104 with sparse part having weight 16706176. Pruned matrix : 132155 x 132930 with weight 10824903. Total sieving time: 8.73 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 8.93 hours. --------- CPU info (if available) ----------
(25·10¹¹⁷-43)/9 = 2(7)₁₁₆3_<118> = 24535543 · C111
C111 = P54 · P57
P54 = 332379232893091453153280727133385117857511762001897881_<54>
P57 = 340618274207022680190491805403099427972738440448723209331_<57>

Number: 27773_117 N=113214440690298876930409804982827475135878499928767738206477752612924758900904609194007965414817914475248327611 ( 111 digits) SNFS difficulty: 119 digits. Divisors found: r1=332379232893091453153280727133385117857511762001897881 (pp54) r2=340618274207022680190491805403099427972738440448723209331 (pp57) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.08 hours. Scaled time: 0.98 units (timescale=0.473). Factorization parameters were as follows: name: 27773_117 n: 113214440690298876930409804982827475135878499928767738206477752612924758900904609194007965414817914475248327611 m: 500000000000000000000000 c5: 4 c0: -215 skew: 2.22 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64043, largePrimes:2098489 encountered Relations: rels:2176365, finalFF:225353 Max relations in full relation-set: 28 Initial matrix: 113205 x 225353 with sparse part having weight 18857668. Pruned matrix : 86361 x 86991 with weight 4764692. Total sieving time: 1.91 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.08 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,119,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.08 hours. --------- CPU info (if available) ----------
Sep 11, 2008 (2nd): By Serge Batalov / Msieve 1.37, GMP-ECM 6.2.1
(25·10¹²⁵-43)/9 = 2(7)₁₂₄3_<126> = 3³ · 1873255141_<10> · 71896123627953440059_<20> · C95
C95 = P33 · P63
P33 = 381306168368381458964149411069297_<33>
P63 = 200335306845756080003950949178160433159808858651862484975520193_<63>

Number: 27773_125 N=76389088242259230546878135267029828620090034029365369180195758708686390425923652120904945814321 ( 95 digits) SNFS difficulty: 126 digits. Divisors found: r1=381306168368381458964149411069297 r2=200335306845756080003950949178160433159808858651862484975520193 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: n: 76389088242259230546878135267029828620090034029365369180195758708686390425923652120904945814321 Y1: 1 Y0: -10000000000000000000000000 c5: 25 c0: -43 skew: 1.11 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 113348 x 113566 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.60 hours.
(25·10¹⁴³-43)/9 = 2(7)₁₄₂3_<144> = 3² · 1482743516013854857834034989178053_<34> · C110
C110 = P31 · P79
P31 = 8226588327582747533833817658727_<31>
P79 = 2530283545192651715467543393327713035545251849149594450020225834649504085392087_<79>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3216840893 Step 1 took 4375ms Step 2 took 4197ms ********** Factor found in step 2: 8226588327582747533833817658727 Found probable prime factor of 31 digits: 8226588327582747533833817658727 Probable prime cofactor 2530283545192651715467543393327713035545251849149594450020225834649504085392087 has 79 digits
(25·10¹⁸⁷-43)/9 = 2(7)₁₈₆3_<188> = 47 · 53 · 191 · 730757 · C176
C176 = P36 · C141
P36 = 408695703662735190084599512114819513_<36>
C141 = [195486759675827484517045324269925956580801061150249953622950500225372551296385452583893098093930134597595406548846078045518688710538357715613_<141>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=634280738 Step 1 took 9559ms Step 2 took 7056ms ********** Factor found in step 2: 408695703662735190084599512114819513 Found probable prime factor of 36 digits: 408695703662735190084599512114819513 Composite cofactor 195486759675827484517045324269925956580801061150249953622950500225372551296385452583893098093930134597595406548846078045518688710538357715613 has 141 digits
(25·10¹⁵⁵-43)/9 = 2(7)₁₅₄3_<156> = 3 · 23 · 548425147 · C145
C145 = P32 · P114
P32 = 34510830591104725201050200123389_<32>
P114 = 212703989838578957956596911663076383197629838071552664368933220525486296004406576502241258446128246382524518156199_<114>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4161596758 Step 1 took 6051ms Step 2 took 5277ms ********** Factor found in step 2: 34510830591104725201050200123389 Found probable prime factor of 32 digits: 34510830591104725201050200123389 Probable prime cofactor 212703989838578957956596911663076383197629838071552664368933220525486296004406576502241258446128246382524518156199 has 114 digits
(25·10¹⁷¹-43)/9 = 2(7)₁₇₀3_<172> = 233 · C170
C170 = P39 · P131
P39 = 308225110411339886828989718831887891927_<39>
P131 = 38678850732708674890175184503305789832974358219544817519426484893378186338847858514538120983978402786856331024910705786603696208803_<131>

Run 731 out of 940: Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1398058429 Step 1 took 9015ms Step 2 took 5397ms ********** Factor found in step 2: 308225110411339886828989718831887891927 Found probable prime factor of 39 digits: 308225110411339886828989718831887891927 Probable prime cofactor 38678850732708674890175184503305789832974358219544817519426484893378186338847858514538120983978402786856331024910705786603696208803 has 131 digits
(25·10¹⁸⁸-43)/9 = 2(7)₁₈₇3_<189> = 3² · 7 · 13 · 2501779210016117_<16> · C171
C171 = P32 · C139
P32 = 75595202411944051335860944001329_<32>
C139 = [1793371996900593249505181161038180873846675034251124827702447409512594054767965061858759389454185358822624969674213962033030690382324261619_<139>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1655319311 Step 1 took 24426ms Step 2 took 19927ms ********** Factor found in step 2: 75595202411944051335860944001329 Found probable prime factor of 32 digits: 75595202411944051335860944001329 Composite cofactor 1793371996900593249505181161038180873846675034251124827702447409512594054767965061858759389454185358822624969674213962033030690382324261619 has 139 digits
(25·10¹⁷⁹-43)/9 = 2(7)₁₇₈3_<180> = 3⁷ · 1321 · 2309 · 16398814309_<11> · C160
C160 = P36 · P125
P36 = 129908366675717436134275154951566843_<36>
P125 = 19546652628421566148393564324629980588172892836991090912732311730703259332008780061652120853995535520635416749547652215263653_<125>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2302857862 Step 1 took 24350ms Step 2 took 19295ms ********** Factor found in step 2: 129908366675717436134275154951566843 Found probable prime factor of 36 digits: 129908366675717436134275154951566843 Probable prime cofactor 19546652628421566148393564324629980588172892836991090912732311730703259332008780061652120853995535520635416749547652215263653 has 125 digits
(25·10¹⁶³-43)/9 = 2(7)₁₆₂3_<164> = 29 · 9689 · 2518933 · C152
C152 = P38 · P115
P38 = 25131004094841299841358281520343734889_<38>
P115 = 1561687335706147372245163522601054060771060260107529473974744099616485815066706249125187406434716123100749765802509_<115>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4270192938 Step 1 took 20946ms ********** Factor found in step 1: 25131004094841299841358281520343734889 Found probable prime factor of 38 digits: 25131004094841299841358281520343734889 Probable prime cofactor 1561687335706147372245163522601054060771060260107529473974744099616485815066706249125187406434716123100749765802509 has 115 digits
Sep 11, 2008: By Jo Yeong Uk / GGNFS, Msieve v1.32 for x86_64
(25·10¹³²-43)/9 = 2(7)₁₃₁3_<133> = C133
C133 = P50 · P83
P50 = 91185321297776872404938800679692229995674932806297_<50>
P83 = 30462992708076369935379615201255241888123967336490277389467361391384334239604056309_<83>

Number: 27773_132 N=2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773 ( 133 digits) SNFS difficulty: 134 digits. Divisors found: r1=91185321297776872404938800679692229995674932806297 (pp50) r2=30462992708076369935379615201255241888123967336490277389467361391384334239604056309 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.65 hours. Scaled time: 6.31 units (timescale=2.382). Factorization parameters were as follows: n: 2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773 m: 500000000000000000000000000 c5: 4 c0: -215 skew: 2.22 type: snfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved algebraic special-q in [600000, 1200001) Primes: RFBsize:92938, AFBsize:93049, largePrimes:2380853 encountered Relations: rels:2288460, finalFF:236025 Max relations in full relation-set: 28 Initial matrix: 186051 x 236025 with sparse part having weight 12189200. Pruned matrix : 164924 x 165918 with weight 6809779. Total sieving time: 2.54 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,46,46,2.2,2.2,50000 total time: 2.65 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(25·10¹⁵³-43)/9 = 2(7)₁₅₂3_<154> = 881 · 71577134882299548903547_<23> · 84565353734169392574360041_<26> · C102
C102 = P41 · P61
P41 = 80602305649128280728158724072025600598519_<41>
P61 = 6462601031553857846813389871404198724474243802915238445011241_<61>

Wed Sep 10 22:58:26 2008 Wed Sep 10 22:58:26 2008 Wed Sep 10 22:58:26 2008 Msieve v. 1.32 Wed Sep 10 22:58:26 2008 random seeds: 3e19a540 473eeb8a Wed Sep 10 22:58:26 2008 factoring 520900543633675770740076921288124839804013151855325091973855979598655668095461137038511238639282952079 (102 digits) Wed Sep 10 22:58:27 2008 no P-1/P+1/ECM available, skipping Wed Sep 10 22:58:27 2008 commencing quadratic sieve (102-digit input) Wed Sep 10 22:58:27 2008 using multiplier of 7 Wed Sep 10 22:58:27 2008 using VC8 32kb sieve core Wed Sep 10 22:58:27 2008 sieve interval: 36 blocks of size 32768 Wed Sep 10 22:58:27 2008 processing polynomials in batches of 6 Wed Sep 10 22:58:27 2008 using a sieve bound of 3198409 (114644 primes) Wed Sep 10 22:58:27 2008 using large prime bound of 479761350 (28 bits) Wed Sep 10 22:58:27 2008 using double large prime bound of 4225182407156700 (44-52 bits) Wed Sep 10 22:58:27 2008 using trial factoring cutoff of 52 bits Wed Sep 10 22:58:27 2008 polynomial 'A' values have 13 factors Thu Sep 11 15:38:50 2008 114820 relations (26751 full + 88069 combined from 1732378 partial), need 114740 Thu Sep 11 15:39:08 2008 begin with 1759129 relations Thu Sep 11 15:39:09 2008 reduce to 306160 relations in 10 passes Thu Sep 11 15:39:09 2008 attempting to read 306160 relations Thu Sep 11 15:39:14 2008 recovered 306160 relations Thu Sep 11 15:39:14 2008 recovered 298979 polynomials Thu Sep 11 15:39:14 2008 attempting to build 114820 cycles Thu Sep 11 15:39:14 2008 found 114820 cycles in 7 passes Thu Sep 11 15:39:14 2008 distribution of cycle lengths: Thu Sep 11 15:39:14 2008 length 1 : 26751 Thu Sep 11 15:39:14 2008 length 2 : 19192 Thu Sep 11 15:39:14 2008 length 3 : 19098 Thu Sep 11 15:39:14 2008 length 4 : 15690 Thu Sep 11 15:39:14 2008 length 5 : 12104 Thu Sep 11 15:39:14 2008 length 6 : 8269 Thu Sep 11 15:39:14 2008 length 7 : 5581 Thu Sep 11 15:39:14 2008 length 9+: 8135 Thu Sep 11 15:39:14 2008 largest cycle: 25 relations Thu Sep 11 15:39:15 2008 matrix is 114644 x 114820 with weight 8535738 (avg 74.34/col) Thu Sep 11 15:39:15 2008 filtering completed in 3 passes Thu Sep 11 15:39:15 2008 matrix is 110340 x 110404 with weight 8259057 (avg 74.81/col) Thu Sep 11 15:39:16 2008 saving the first 48 matrix rows for later Thu Sep 11 15:39:16 2008 matrix is 110292 x 110404 with weight 7008939 (avg 63.48/col) Thu Sep 11 15:39:16 2008 matrix includes 64 packed rows Thu Sep 11 15:39:16 2008 using block size 44161 for processor cache size 4096 kB Thu Sep 11 15:39:17 2008 commencing Lanczos iteration Thu Sep 11 15:40:34 2008 lanczos halted after 1746 iterations (dim = 110292) Thu Sep 11 15:40:34 2008 recovered 18 nontrivial dependencies Thu Sep 11 15:40:36 2008 prp41 factor: 80602305649128280728158724072025600598519 Thu Sep 11 15:40:36 2008 prp61 factor: 6462601031553857846813389871404198724474243802915238445011241 Thu Sep 11 15:40:36 2008 elapsed time 16:42:10
Sep 10, 2008 (4th): Factorizations of 277...773 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Sep 10, 2008 (3rd): By Serge Batalov / GMP-ECM 6.2.1
(22·10¹⁹⁹+41)/9 = 2(4)₁₉₈9_<200> = 41061733 · C192
C192 = P31 · C162
P31 = 1897620275559982337516555558951_<31>
C162 = [313713772035430533818551391590458721020856491086140653105242080969835209074220644870655195685240555478883046828465009236909425448182270062487091452141001532415403_<162>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=614666195 Step 1 took 7800ms Step 2 took 5917ms ********** Factor found in step 2: 1897620275559982337516555558951 Found probable prime factor of 31 digits: 1897620275559982337516555558951 Composite cofactor 313713772035430533818551391590458721020856491086140653105242080969835209074220644870655195685240555478883046828465009236909425448182270062487091452141001532415403 has 162 digits
(4·10²⁰⁰+17)/3 = 1(3)₁₉₉9_<201> = 4877 · 1293587 · C191
C191 = P33 · P158
P33 = 310858393336630686720841637998697_<33>
P158 = 67987291591061721286953508434298743969287676084869733019950591260403028836697158046529832913321391635730918226951318222021514833120320272626786443796812828213_<158>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4007235084 Step 1 took 7252ms Step 2 took 5488ms ********** Factor found in step 2: 310858393336630686720841637998697 Found probable prime factor of 33 digits: 310858393336630686720841637998697 Probable prime cofactor 67987291591061721286953508434298743969287676084869733019950591260403028836697158046529832913321391635730918226951318222021514833120320272626786443796812828213 has 158 digits
(23·10¹⁹⁹+1)/3 = 7(6)₁₉₈7_<200> = 7³ · 11 · 1733 · 10429 · C190
C190 = P29 · C161
P29 = 34568930457523287016666104607_<29>
C161 = [32523150062698802917720624652745100514767773266788406670334720522108075012188621040006096086302630721307928762888386196012800664896540679247928777489412633566121_<161>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=567802524 Step 1 took 29554ms Step 2 took 22544ms ********** Factor found in step 2: 34568930457523287016666104607 Found probable prime factor of 29 digits: 34568930457523287016666104607 Composite cofactor 32523150062698802917720624652745100514767773266788406670334720522108075012188621040006096086302630721307928762888386196012800664896540679247928777489412633566121 has 161 digits
7·10²⁰⁰-9 = 6(9)₁₉₉1_<201> = 15764641 · C194
C194 = P32 · P163
P32 = 11284635217137977617526487653933_<32>
P163 = 3934834132347528894029161821328170864341780603433105197044385991837432909415350859571119308115656096581344079723625343143220426630178141030835445756037523722590547_<163>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=13078247 Step 1 took 8353ms ********** Factor found in step 1: 11284635217137977617526487653933 Found probable prime factor of 32 digits: 11284635217137977617526487653933 Probable prime cofactor 3934834132347528894029161821328170864341780603433105197044385991837432909415350859571119308115656096581344079723625343143220426630178141030835445756037523722590547 has 163 digits
Sep 10, 2008 (2nd): By Serge Batalov / Msieve v. 1.37
(22·10²⁰³+41)/9 = 2(4)₂₀₂9_<204> = 3³ · C202
C202 = P80 · P123
P80 = 20334617025001623036456051797874969977087099512082033181887892745732650713921249_<80>
P123 = 445225888997833666251265091330295968315737344718479488559782320485075276157873543888006881723934397805015254789157876721363_<123>

Number: 24449_203 N=905349...53497942387 ( 202 digits) SNFS difficulty: 205 digits. Divisors found: r1=20334617025001623036456051797874969977087099512082033181887892745732650713921249 r2=445225888997833666251265091330295968315737344718479488559782320485075276157873543888006881723934397805015254789157876721363 Version: Msieve v. 1.37 Scaled time: 0.00 units (timescale=2.512). Factorization parameters were as follows: Y0: -10000000000000000000000000000000000 Y1: 1 c0: 205 c6: 11 skew: 1.6 type: snfs lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 rlim: 15000000 alim: 15000000 Factor base limits: 15000000/15000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [7500000, 15100001) Primes: rational ideals reading, algebraic ideals reading, found 4443154 hash collisions in 25,677,752 relations found 4233772 duplicates and 22662229 unique relations Relations: 22,662,229 relations and about 20,667,937 large ideals Max relations in full relation-set: 19 found 2671198 cycles, need 2587737 building initial matrix memory use: 997.0 MB Pruned matrix : 2578133 x 2578381 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 17.90 hours. Time per square root: 3.50 hours. Prototype def-par.txt line would be: snfs,205,6,0,0,0,0,0,0,0,0,15000000,15000000,28,28,56,56,2.5,2.5,100000 total time: 24 CPU-days.
Sep 10, 2008: By Sinkiti Sibata / GGNFS
(23·10¹⁸⁴+13)/9 = 2(5)₁₈₃7_<185> = 3 · 7 · C184
C184 = P60 · P62 · P62
P60 = 142386499451271609105675459975554447296326441982772562419531_<60>
P62 = 89036746517664876241810609616253040552772136863324747726467631_<62>
P62 = 95990429887620748854364521660144618194288049254915390847010397_<62>

Number: 25557_184 N=1216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931217 ( 184 digits) SNFS difficulty: 186 digits. Divisors found: r1=142386499451271609105675459975554447296326441982772562419531 (pp60) r2=89036746517664876241810609616253040552772136863324747726467631 (pp62) r3=95990429887620748854364521660144618194288049254915390847010397 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 1200.97 hours. Scaled time: 922.35 units (timescale=0.768). Factorization parameters were as follows: name: 25557_184 n: 1216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931216931217 m: 10000000000000000000000000000000000000 c5: 23 c0: 130 skew: 1.41 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 17400001) Primes: RFBsize:501962, AFBsize:502146, largePrimes:7061627 encountered Relations: rels:7610234, finalFF:1155388 Max relations in full relation-set: 28 Initial matrix: 1004173 x 1155388 with sparse part having weight 119681935. Pruned matrix : 890697 x 895781 with weight 101009017. Total sieving time: 1183.49 hours. Total relation processing time: 1.03 hours. Matrix solve time: 16.19 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1200.97 hours. --------- CPU info (if available) ----------
Sep 9, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(64·10¹⁷⁷+53)/9 = 7(1)₁₇₆7_<178> = 11 · 239 · C175
C175 = P79 · P96
P79 = 2746163758092184047690455322356302856116462038401676834020608038326185212384119_<79>
P96 = 984964203168698675125288342788491918288490272600571711870157920520614551405691698408931673803167_<96>

Number: n N=2704872997760027048729977600270487299776002704872997760027048729977600270487299776002704872997760027048729977600270487299776002704872997760027048729977600270487299776002704873 ( 175 digits) SNFS difficulty: 178 digits. Divisors found: Tue Sep 09 18:31:04 2008 prp79 factor: 2746163758092184047690455322356302856116462038401676834020608038326185212384119 Tue Sep 09 18:31:04 2008 prp96 factor: 984964203168698675125288342788491918288490272600571711870157920520614551405691698408931673803167 Tue Sep 09 18:31:05 2008 elapsed time 04:42:39 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.10 hours. Scaled time: 49.11 units (timescale=2.038). Factorization parameters were as follows: name: KA_7_1_176_7 n: 2704872997760027048729977600270487299776002704872997760027048729977600270487299776002704872997760027048729977600270487299776002704872997760027048729977600270487299776002704873 type: snfs skew: 0.77 deg: 5 c5: 200 c0: 53 m: 200000000000000000000000000000000000 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 6100001) Primes: RFBsize:539777, AFBsize:539400, largePrimes:13853455 encountered Relations: rels:13478199, finalFF:1170101 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 23.78 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,178,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,52,52,2.5,2.5,100000 total time: 24.10 hours. --------- CPU info (if available) ----------
Sep 9, 2008: By Robert Backstrom / GGNFS, Msieve
(16·10¹⁷⁷+11)/9 = 1(7)₁₇₆9_<178> = 3³ · C176
C176 = P82 · P95
P82 = 2621531707625220519663585478246951504563621768505547944917351252820632944202250639_<82>
P95 = 25116469584425904701377272005029275086064055491074195222257361498430466934150973115235367370343_<95>

Number: n N=65843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399177 ( 176 digits) SNFS difficulty: 178 digits. Divisors found: Tue Sep 9 00:56:01 2008 prp82 factor: 2621531707625220519663585478246951504563621768505547944917351252820632944202250639 Tue Sep 9 00:56:01 2008 prp95 factor: 25116469584425904701377272005029275086064055491074195222257361498430466934150973115235367370343 Tue Sep 9 00:56:01 2008 elapsed time 06:39:00 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 69.76 hours. Scaled time: 58.46 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_7_176_9 n: 65843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399176954732510288065843621399177 type: snfs skew: 0.74 deg: 5 c5: 50 c0: 11 m: 200000000000000000000000000000000000 rlim: 8500000 alim: 8500000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 11050001) Primes: RFBsize:571119, AFBsize:570218, largePrimes:14534848 encountered Relations: rels:14277297, finalFF:1165292 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 69.27 hours. Total relation processing time: 0.49 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,178,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,52,52,2.5,2.5,100000 total time: 69.76 hours. --------- CPU info (if available) ----------
Sep 8, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(82·10¹⁹³-1)/9 = 9(1)₁₉₃_<194> = 7 · 13 · 569 · C190
C190 = P53 · P137
P53 = 39594545141939885526894322438648642768790356810813157_<53>
P137 = 44440846840731324443581573454499877887493864000996240378981166983107524169324621440113544908284126532200838021972350456511361678763879337_<137>

Number: n N=1759615116381372971882637963481548718807066785977155045696346223586996873464360283340951179264008789492093534272796135713534659053112480177506539545203868578209527242919158560634834800036909 ( 190 digits) SNFS difficulty: 195 digits. Divisors found: Mon Sep 08 12:03:07 2008 prp53 factor: 39594545141939885526894322438648642768790356810813157 Mon Sep 08 12:03:07 2008 prp137 factor: 44440846840731324443581573454499877887493864000996240378981166983107524169324621440113544908284126532200838021972350456511361678763879337 Mon Sep 08 12:03:07 2008 elapsed time 07:55:00 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 147.85 hours. Scaled time: 303.24 units (timescale=2.051). Factorization parameters were as follows: name: KA_9_1_193 n: 1759615116381372971882637963481548718807066785977155045696346223586996873464360283340951179264008789492093534272796135713534659053112480177506539545203868578209527242919158560634834800036909 type: snfs skew: 0.21 deg: 5 c5: 5125 c0: -2 m: 200000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 12100001) Primes: RFBsize:633578, AFBsize:633804, largePrimes:14961201 encountered Relations: rels:14978001, finalFF:1305987 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 147.24 hours. Total relation processing time: 0.61 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000 total time: 147.85 hours. --------- CPU info (if available) ----------
Sep 8, 2008 (2nd): By Jo Yeong Uk / GGNFS
(65·10¹⁶⁵+43)/9 = 7(2)₁₆₄7_<166> = 3² · 11 · 29 · 7639 · 2252567 · 12425239 · 72706584488576609_<17> · C129
C129 = P49 · P80
P49 = 2844021580936529047321181522766000025422187626149_<49>
P80 = 56899971005532573858733054130402004114671676641026019412601626011729833138572151_<80>

Number: 72227_165 N=161824745494397415085594949862446015318804831340450950581977528424876612513918227943180593176597511704495626812201425598050776499 ( 129 digits) SNFS difficulty: 166 digits. Divisors found: r1=2844021580936529047321181522766000025422187626149 (pp49) r2=56899971005532573858733054130402004114671676641026019412601626011729833138572151 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 45.38 hours. Scaled time: 108.18 units (timescale=2.384). Factorization parameters were as follows: n: 161824745494397415085594949862446015318804831340450950581977528424876612513918227943180593176597511704495626812201425598050776499 m: 1000000000000000000000000000000000 c5: 65 c0: 43 skew: 0.92 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [3000000, 5500001) Primes: RFBsize:412849, AFBsize:413366, largePrimes:6535631 encountered Relations: rels:6859270, finalFF:962155 Max relations in full relation-set: 28 Initial matrix: 826281 x 962155 with sparse part having weight 57220973. Pruned matrix : 707273 x 711468 with weight 37824375. Total sieving time: 42.55 hours. Total relation processing time: 0.10 hours. Matrix solve time: 2.66 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,49,49,2.6,2.6,100000 total time: 45.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Sep 8, 2008: By Serge Batalov / Msieve-1.37
3·10¹⁹⁸+1 = 3(0)₁₉₇1_<199> = C199
C199 = P82 · P118
P82 = 1833911383348466522566074446250134380140228731863510782284501695384966021186952971_<82>
P118 = 1635847853521917851052479217771526282232255683407487990801439756907074080101789715314755512178980013517705612191904931_<118>

Number: 30001_198 N=3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 ( 199 digits) SNFS difficulty: 198 digits. Divisors found: r1=1833911383348466522566074446250134380140228731863510782284501695384966021186952971 r2=1635847853521917851052479217771526282232255683407487990801439756907074080101789715314755512178980013517705612191904931 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 Y1: 1 Y0: -1000000000000000000000000000000000000000 c5: 3000 c0: 1 skew: 0.2 type: snfs lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 rlim: 10000000 alim: 10000000 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [5000000, 10100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1857143 x 1857391 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 11.00 hours. (4 threads) Time per square root: 0.55 hours. Prototype def-par.txt line would be: snfs,198,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,56,56,2.5,2.5,100000 total time: 20 CPU-days.
Sep 7, 2008 (2nd): By Wataru Sakai / GGNFS
(4·10¹⁸⁶+17)/3 = 1(3)₁₈₅9_<187> = 7 · 139 · C184
C184 = P70 · P114
P70 = 4683752657040481930352270796090095702982198572437623038900544234035807_<70>
P114 = 292571449844658244129724130403038430010264115229371023800613342811197195422433644669612330433068714444752149233049_<114>

Number: 13339_186 N=1370332305584104145255224391915039397053785542994176087701267557382665296334361082562521411442274751627269612881123672490578965399109284001370332305584104145255224391915039397053785543 ( 184 digits) SNFS difficulty: 186 digits. Divisors found: r1=4683752657040481930352270796090095702982198572437623038900544234035807 (pp70) r2=292571449844658244129724130403038430010264115229371023800613342811197195422433644669612330433068714444752149233049 (pp114) Version: GGNFS-0.77.1-20060722-nocona Total time: 739.89 hours. Scaled time: 1489.40 units (timescale=2.013). Factorization parameters were as follows: n: 1370332305584104145255224391915039397053785542994176087701267557382665296334361082562521411442274751627269612881123672490578965399109284001370332305584104145255224391915039397053785543 m: 10000000000000000000000000000000000000 c5: 40 c0: 17 skew: 0.84 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 13600001) Primes: RFBsize:501962, AFBsize:502686, largePrimes:6810292 encountered Relations: rels:7291905, finalFF:1137529 Max relations in full relation-set: 32 Initial matrix: 1004714 x 1137529 with sparse part having weight 102564823. Pruned matrix : 901497 x 906584 with weight 83116476. Total sieving time: 730.37 hours. Total relation processing time: 0.13 hours. Matrix solve time: 9.13 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 739.89 hours. --------- CPU info (if available) ----------
Sep 7, 2008: By Robert Backstrom / GMP-ECM, Msieve
(4·10¹⁶²+17)/3 = 1(3)₁₆₁9_<163> = 7 · 631789 · 1255021 · 4123529 · 219455932845923_<15> · C129
C129 = P39 · P41 · P51
P39 = 175477359310145651369576592622195539679_<39>
P41 = 11017383187107043445598825146216819497967_<41>
P51 = 137309858416434405546180978438036203884533672564143_<51>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 265461328902714720449135413796276012856770681128783935438114532587303104386318078788477129357372613085202661101773298430470012799 (129 digits) Using B1=2842000, B2=4281592780, polynomial Dickson(6), sigma=4034181669 Step 1 took 27125ms Step 2 took 11531ms ********** Factor found in step 2: 11017383187107043445598825146216819497967 Found probable prime factor of 41 digits: 11017383187107043445598825146216819497967 Composite cofactor 24094771362165887160008178046242774179489161331528524488085284544470775942950829629130097 has 89 digits Sun Sep 07 03:19:16 2008 Sun Sep 07 03:19:16 2008 Sun Sep 07 03:19:16 2008 Msieve v. 1.37 Sun Sep 07 03:19:16 2008 random seeds: f938b800 08bc6fd4 Sun Sep 07 03:19:16 2008 factoring 24094771362165887160008178046242774179489161331528524488085284544470775942950829629130097 (89 digits) Sun Sep 07 03:19:16 2008 searching for 15-digit factors Sun Sep 07 03:19:17 2008 commencing quadratic sieve (89-digit input) Sun Sep 07 03:19:17 2008 using multiplier of 17 Sun Sep 07 03:19:17 2008 using 64kb Opteron sieve core Sun Sep 07 03:19:17 2008 sieve interval: 15 blocks of size 65536 Sun Sep 07 03:19:17 2008 processing polynomials in batches of 7 Sun Sep 07 03:19:17 2008 using a sieve bound of 1546837 (58635 primes) Sun Sep 07 03:19:17 2008 using large prime bound of 123746960 (26 bits) Sun Sep 07 03:19:17 2008 using double large prime bound of 368605688486800 (42-49 bits) Sun Sep 07 03:19:17 2008 using trial factoring cutoff of 49 bits Sun Sep 07 03:19:17 2008 polynomial 'A' values have 11 factors Sun Sep 07 04:22:05 2008 58762 relations (16144 full + 42618 combined from 616952 partial), need 58731 Sun Sep 07 04:22:07 2008 begin with 633096 relations Sun Sep 07 04:22:07 2008 reduce to 141733 relations in 11 passes Sun Sep 07 04:22:07 2008 attempting to read 141733 relations Sun Sep 07 04:22:10 2008 recovered 141733 relations Sun Sep 07 04:22:10 2008 recovered 119607 polynomials Sun Sep 07 04:22:10 2008 attempting to build 58762 cycles Sun Sep 07 04:22:10 2008 found 58762 cycles in 5 passes Sun Sep 07 04:22:11 2008 distribution of cycle lengths: Sun Sep 07 04:22:11 2008 length 1 : 16144 Sun Sep 07 04:22:11 2008 length 2 : 11470 Sun Sep 07 04:22:11 2008 length 3 : 10451 Sun Sep 07 04:22:11 2008 length 4 : 7660 Sun Sep 07 04:22:11 2008 length 5 : 5338 Sun Sep 07 04:22:11 2008 length 6 : 3372 Sun Sep 07 04:22:11 2008 length 7 : 1977 Sun Sep 07 04:22:11 2008 length 9+: 2350 Sun Sep 07 04:22:11 2008 largest cycle: 19 relations Sun Sep 07 04:22:11 2008 matrix is 58635 x 58762 (14.3 MB) with weight 3516020 (59.83/col) Sun Sep 07 04:22:11 2008 sparse part has weight 3516020 (59.83/col) Sun Sep 07 04:22:12 2008 filtering completed in 4 passes Sun Sep 07 04:22:12 2008 matrix is 54458 x 54522 (13.4 MB) with weight 3300382 (60.53/col) Sun Sep 07 04:22:12 2008 sparse part has weight 3300382 (60.53/col) Sun Sep 07 04:22:13 2008 saving the first 48 matrix rows for later Sun Sep 07 04:22:13 2008 matrix is 54410 x 54522 (10.1 MB) with weight 2767191 (50.75/col) Sun Sep 07 04:22:13 2008 sparse part has weight 2308672 (42.34/col) Sun Sep 07 04:22:13 2008 matrix includes 64 packed rows Sun Sep 07 04:22:13 2008 using block size 21808 for processor cache size 1024 kB Sun Sep 07 04:22:14 2008 commencing Lanczos iteration Sun Sep 07 04:22:14 2008 memory use: 9.0 MB Sun Sep 07 04:22:56 2008 lanczos halted after 862 iterations (dim = 54409) Sun Sep 07 04:22:56 2008 recovered 17 nontrivial dependencies Sun Sep 07 04:22:56 2008 prp39 factor: 175477359310145651369576592622195539679 Sun Sep 07 04:22:56 2008 prp51 factor: 137309858416434405546180978438036203884533672564143 Sun Sep 07 04:22:56 2008 elapsed time 01:03:40
Sep 6, 2008 (5th): By Serge Batalov / GMP-ECM 6.2.1
(4·10²²⁹-1)/3 = 1(3)₂₂₉_<230> = 13 · 347 · C226
C226 = P49 · C177
P49 = 4246645545363041585151546344082603927473277793231_<49>
C177 = [696017078534428470457529048170257815534293367782109964021146339362857748163339563659802340252478769639355612562186287999935138147155138236220734436267484891688123677205851655813_<177>]

# ...and another nice factor; my personal 2nd best (my best is 56-digit) # Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=2062470196 Step 1 took 111731ms Step 2 took 57919ms ********** Factor found in step 2: 4246645545363041585151546344082603927473277793231 Found probable prime factor of 49 digits: 4246645545363041585151546344082603927473277793231 Composite cofactor 696017078534428470457529048170257815534293367782109964021146339362857748163339563659802340252478769639355612562186287999935138147155138236220734436267484891688123677205851655813 has 177 digits
Sep 6, 2008 (4th): By nuggetprime / GMP-ECM
(4·10¹⁶³+17)/3 = 1(3)₁₆₂9_<164> = 19 · 2797 · 5791 · 69661 · 720611 · 1560371 · 14857397 · 3514121576753_<13> · C119
C119 = P51 · P68
P51 = 495436223298434385356722609135189152207142936793249_<51>
P68 = 21383233343940664218943433891745463379743409952464040968535330972587_<68>

This is a nuggetprime's result posted on 21 Aug 2008 at: http://www.mersenneforum.org/showthread.php?p=139605#post139605 GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 10594028369831114716682888330845541566105401124620505895213725128397891350870967330967394277735211887867089454105665163 (119 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=861666340 Step 1 took 46698ms Step 2 took 25614ms ********** Factor found in step 2: 495436223298434385356722609135189152207142936793249 Found probable prime factor of 51 digits: 495436223298434385356722609135189152207142936793249 Probable prime cofactor 21383233343940664218943433891745463379743409952464040968535330972587 has 68 digits
Makoto Kamada posted.
Sep 6, 2008 (3rd): By Serge Batalov / Msieve-1.37, GMP-ECM 6.2.1
8·10¹⁷²-7 = 7(9)₁₇₁3_<173> = 190313 · C168
C168 = P60 · P109
P60 = 138161571992322355518249925361034781278945385532571294634897_<60>
P109 = 3042525772479980573421781698654833894292124178776206300829682839392738230075715174164879797011327208823658113_<109>

Number: 79993_172 N=420360143552989023345751472574127884064672408085627361241743864055529574963349849983973769527042293484943225108111374420034364441735456852658515182882934954522286969361 ( 168 digits) SNFS difficulty: 172 digits. Divisors found: r1=138161571992322355518249925361034781278945385532571294634897 r2=3042525772479980573421781698654833894292124178776206300829682839392738230075715174164879797011327208823658113 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.728). Factorization parameters were as follows: n: 420360143552989023345751472574127884064672408085627361241743864055529574963349849983973769527042293484943225108111374420034364441735456852658515182882934954522286969361 Y1: 1 Y0: -20000000000000000000000000000000000 c5: 25 c0: -7 skew: 0.78 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [4500000, 6800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1139892 x 1140140 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,52,52,2.6,2.6,100000 total time: 45.00 hours.
8·10²²⁹-1 = 7(9)₂₂₉_<230> = 4365541 · C224
C224 = P35 · P189
P35 = 22899378996803067916894382980974701_<35>
P189 = 800254657956886391196780894633531374565554844629496936038376921729764352514694201229462957643423367969876748771951592669068650319491433270363334538454741598932512755263816205496476120544639_<189>

# there goes a big number # Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=754930536 Step 1 took 37320ms Step 2 took 27701ms ********** Factor found in step 2: 22899378996803067916894382980974701 Found probable prime factor of 35 digits: 22899378996803067916894382980974701 Probable prime cofactor 800254657956886391196780894633531374565554844629496936038376921729764352514694201229462957643423367969876748771951592669068650319491433270363334538454741598932512755263816205496476120544639 has 189 digits
Sep 6, 2008 (2nd): By Sinkiti Sibata / GGNFS
(25·10¹⁷⁰-61)/9 = 2(7)₁₆₉1_<171> = 131909045573_<12> · 123310363949659_<15> · C146
C146 = P71 · P75
P71 = 51349565953817840490156245892197350453929733234153814020952530482561583_<71>
P75 = 332572675808658297792850706653907384324838226345820816882845634793838252691_<75>

Number: 27771_170 N=17077462550874378271150629056169128122565987071157482103253108951984884573035699470470382216719112388277895264154420547419468349410224094522969853 ( 146 digits) SNFS difficulty: 171 digits. Divisors found: r1=51349565953817840490156245892197350453929733234153814020952530482561583 (pp71) r2=332572675808658297792850706653907384324838226345820816882845634793838252691 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 170.65 hours. Scaled time: 172.53 units (timescale=1.011). Factorization parameters were as follows: name: 27771_170 n: 17077462550874378271150629056169128122565987071157482103253108951984884573035699470470382216719112388277895264154420547419468349410224094522969853 m: 10000000000000000000000000000000000 c5: 25 c0: -61 skew: 1.2 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, 7900001) Primes: RFBsize:412849, AFBsize:412112, largePrimes:6360126 encountered Relations: rels:6833798, finalFF:1111408 Max relations in full relation-set: 28 Initial matrix: 825025 x 1111408 with sparse part having weight 72010060. Pruned matrix : 587573 x 591762 with weight 55353352. Total sieving time: 166.78 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.59 hours. Time per square root: 0.10 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: 170.65 hours. --------- CPU info (if available) ----------
Sep 6, 2008: By Jo Yeong Uk / GMP-ECM, GGNFS
(43·10¹⁶⁵-7)/9 = 4(7)₁₆₅_<166> = 1344190880737392833_<19> · 2301204226992762281_<19> · C130
C130 = P42 · P88
P42 = 385071591629280252011363710960963257145127_<42>
P88 = 4011144968271534743653930349805245289947412403901164321780638693543548253701599315974287_<88>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 1544577977188098720238620993157952890934508035999346072911447051418801275216503660329923388280907102934899877127344967702159349449 (130 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3941855257 Step 1 took 11715ms Step 2 took 5580ms ********** Factor found in step 2: 385071591629280252011363710960963257145127 Found probable prime factor of 42 digits: 385071591629280252011363710960963257145127 Probable prime cofactor 4011144968271534743653930349805245289947412403901164321780638693543548253701599315974287 has 88 digits
5·10¹⁹⁴+9 = 5(0)₁₉₃9_<195> = C195
C195 = P88 · P108
P88 = 3403248951366474932718274863522798490198007146565255920384348350563174584990964183684189_<88>
P108 = 146918432105661751654501039168244531252281316834293602197361365522821831096719447512829008767795879133716381_<108>

Number: 50009_194 N=500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 ( 195 digits) SNFS difficulty: 195 digits. Divisors found: r1=3403248951366474932718274863522798490198007146565255920384348350563174584990964183684189 (pp88) r2=146918432105661751654501039168244531252281316834293602197361365522821831096719447512829008767795879133716381 (pp108) Version: GGNFS-0.77.1-20050930-nocona Total time: 482.37 hours. Scaled time: 1149.02 units (timescale=2.382). Factorization parameters were as follows: n: 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 m: 1000000000000000000000000000000000000000 c5: 1 c0: 18 skew: 1.78 type: snfs Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 53/53 Sieved algebraic special-q in [10000000, 17700001) Primes: RFBsize:1270607, AFBsize:1269885, largePrimes:23603955 encountered Relations: rels:24083724, finalFF:2909883 Max relations in full relation-set: 28 Initial matrix: 2540559 x 2909883 with sparse part having weight 199159428. Pruned matrix : 2192610 x 2205376 with weight 135726398. Total sieving time: 435.38 hours. Total relation processing time: 0.62 hours. Matrix solve time: 46.13 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,53,53,2.6,2.6,100000 total time: 482.37 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345) Calibrating delay using timer specific routine.. 5344.05 BogoMIPS (lpj=2672026) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Sep 5, 2008 (2nd): By Robert Backstrom / GMP-ECM
(73·10¹⁸⁷-1)/9 = 8(1)₁₈₇_<188> = 3 · C188
C188 = P43 · P146
P43 = 2013417203339758754699697149093409802311811_<43>
P146 = 13428432513733026611376469936844319340401408181621142465772463805980046207426301273004696887406182311284638034277950590963617673065257314162498767_<146>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 27037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037 (188 digits) Using B1=5764000, B2=11416947370, polynomial Dickson(12), sigma=2302872240 Step 1 took 98185ms Step 2 took 33267ms ********** Factor found in step 2: 2013417203339758754699697149093409802311811 Found probable prime factor of 43 digits: 2013417203339758754699697149093409802311811 Probable prime cofactor 13428432513733026611376469936844319340401408181621142465772463805980046207426301273004696887406182311284638034277950590963617673065257314162498767 has 146 digits
Sep 5, 2008: By Serge Batalov / GMP-ECM 6.2.1
(25·10¹⁹⁹-61)/9 = 2(7)₁₉₈1_<200> = 3 · 7 · 283 · 1391259626479767819093311_<25> · 4950310741210515424439214523_<28> · 21631834288992712007555427246085799_<35> · C110
C110 = P34 · P76
P34 = 8137130775905265500667125642011561_<34>
P76 = 3855551265441025333983640384610406523731030541038891638539125959121664278391_<76>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2054967644 Step 1 took 37534ms Step 2 took 21049ms ********** Factor found in step 2: 8137130775905265500667125642011561 Found probable prime factor of 34 digits: 8137130775905265500667125642011561 Probable prime cofactor 3855551265441025333983640384610406523731030541038891638539125959121664278391 has 76 digits
(25·10¹⁷⁷-61)/9 = 2(7)₁₇₆1_<178> = 271 · 419 · 66821 · 141356306265971_<15> · 127353589502138899_<18> · C137
C137 = P35 · P102
P35 = 71134251631905636534346663289671327_<35>
P102 = 285888094063953311988136712438838290992815309587898590647604791112176558836528871352247718253340599053_<102>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=1489180364 Step 1 took 60415ms Step 2 took 11865ms ********** Factor found in step 2: 71134251631905636534346663289671327 Found probable prime factor of 35 digits: 71134251631905636534346663289671327 Probable prime cofactor 285888094063953311988136712438838290992815309587898590647604791112176558836528871352247718253340599053 has 102 digits
Sep 4, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(25·10¹⁶¹-61)/9 = 2(7)₁₆₀1_<162> = 13 · 984211 · 17915596918681641487769_<23> · C133
C133 = P66 · P67
P66 = 253653749852508153250333883090711675749451709540031375104589078333_<66>
P67 = 4777419331469809285428949137256054363568169465244600000364285743961_<67>

Number: n N=1211810328045179737137835843378066173006313450989972138219571769921632974435429855162342174929531805158519800996508886585732210697013 ( 133 digits) SNFS difficulty: 162 digits. Divisors found: Thu Sep 4 16:02:43 2008 prp66 factor: 253653749852508153250333883090711675749451709540031375104589078333 Thu Sep 4 16:02:43 2008 prp67 factor: 4777419331469809285428949137256054363568169465244600000364285743961 Thu Sep 4 16:02:43 2008 elapsed time 01:45:45 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 15.24 hours. Scaled time: 12.77 units (timescale=0.838). Factorization parameters were as follows: name: KA_2_7_160_1 n: 1211810328045179737137835843378066173006313450989972138219571769921632974435429855162342174929531805158519800996508886585732210697013 type: snfs skew: 0.75 deg: 5 c5: 250 c0: -61 m: 100000000000000000000000000000000 rlim: 4400000 alim: 4400000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 2100001) Primes: RFBsize:309335, AFBsize:309449, largePrimes:12410612 encountered Relations: rels:11542233, finalFF:649714 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 14.97 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,52,52,2.5,2.5,100000 total time: 15.24 hours. --------- CPU info (if available) ----------
Sep 4, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1
(25·10¹⁷¹-61)/9 = 2(7)₁₇₀1_<172> = 1777 · 11110598531288144356616827185083_<32> · C138
C138 = P47 · P91
P47 = 44512398379504795249333730316447728566719025499_<47>
P91 = 3160760731055610510155798731208531392799859145056964147663316803202246756868891237027738419_<91>

# what a nice catch for B1=3e6! :-) Wow. # Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3132305148 Step 1 took 18363ms Step 2 took 16355ms ********** Factor found in step 2: 44512398379504795249333730316447728566719025499 Found probable prime factor of 47 digits: 44512398379504795249333730316447728566719025499 Probable prime cofactor 3160760731055610510155798731208531392799859145056964147663316803202246756868891237027738419 has 91 digits
(25·10¹⁹³-61)/9 = 2(7)₁₉₂1_<194> = 3 · 7 · 73883 · 26925317 · 19159973142181_<14> · 284017799510891_<15> · C153
C153 = P29 · C124
P29 = 80485311297327121853982640517_<29>
C124 = [1518153815704622240936737904859078621016147552740776785285576396386699185397561525934124104891750356941221401004594467058163_<124>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1712037598 Step 1 took 18241ms Step 2 took 16894ms ********** Factor found in step 2: 80485311297327121853982640517 Found probable prime factor of 29 digits: 80485311297327121853982640517 Composite cofactor 1518153815704622240936737904859078621016147552740776785285576396386699185397561525934124104891750356941221401004594467058163 has 124 digits
(25·10¹⁹⁹-61)/9 = 2(7)₁₉₈1_<200> = 3 · 7 · 283 · 1391259626479767819093311_<25> · 4950310741210515424439214523_<28> · C144
C144 = P35 · C110
P35 = 21631834288992712007555427246085799_<35>
C110 = [31373124860100658739370173152893372981358932607827628090607273537011259875274623530665824683543468162744478351_<110>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1435650970 Step 1 took 20513ms Step 2 took 16641ms ********** Factor found in step 2: 21631834288992712007555427246085799 Found probable prime factor of 35 digits: 21631834288992712007555427246085799 Composite cofactor 31373124860100658739370173152893372981358932607827628090607273537011259875274623530665824683543468162744478351 has 110 digits
(25·10¹⁸⁹-61)/9 = 2(7)₁₈₈1_<190> = 59 · 1447 · 1549 · 55837 · 18626559023_<11> · 1680493671035288368696859_<25> · C143
C143 = P40 · P103
P40 = 2016363122734122769308758804969621922733_<40>
P103 = 5960259958234267822953007523507500830294029263387822644819553059732204123759026007056155922498545778959_<103>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2931673241 Step 1 took 18370ms Step 2 took 16498ms ********** Factor found in step 2: 2016363122734122769308758804969621922733 Found probable prime factor of 40 digits: 2016363122734122769308758804969621922733 Probable prime cofactor 5960259958234267822953007523507500830294029263387822644819553059732204123759026007056155922498545778959 has 103 digits
Sep 4, 2008: By Sinkiti Sibata / Msieve, GGNFS
(25·10¹⁷²-61)/9 = 2(7)₁₇₁1_<173> = 3 · 47 · 271 · 57935341 · 12956265741884479104103362197_<29> · 323491665334534849464472655197_<30> · C103
C103 = P46 · P58
P46 = 1419307810265852610333835137969799236391677581_<46>
P58 = 2109337107130584539479018932845314440549663990721314805649_<58>

Msieve v. 1.36 Tue Sep 2 13:53:04 2008 random seeds: 331ffe7b d5a5e8c8 factoring 2993798630634018102752511257355121413329191653523966592393572962544732 016371065178595419712380085455069 (103 digits) no P-1/P+1/ECM available, skipping commencing quadratic sieve (103-digit input) using multiplier of 1 using 64kb Pentium 4 sieve core sieve interval: 18 blocks of size 65536 processing polynomials in batches of 6 using a sieve bound of 3418799 (122500 primes) using large prime bound of 512819850 (28 bits) using double large prime bound of 4763615381480700 (44-53 bits) using trial factoring cutoff of 53 bits polynomial 'A' values have 13 factors sieving in progress (press Ctrl-C to pause) 100039 relations (27689 full + 72350 combined from 1685255 partial), need 122596 100275 relations (27714 full + 72561 combined from 1686837 partial), need 122596 100506 relations (27736 full + 72770 combined from 1688414 partial), need 122596 100749 relations (27755 full + 72994 combined from 1690053 partial), need 122596 101012 relations (27781 full + 73231 combined from 1691734 partial), need 122596 101272 relations (27809 full + 73463 combined from 1693393 partial), need 122596 101524 relations (27834 full + 73690 combined from 1695033 partial), need 122596 101785 relations (27857 full + 73928 combined from 1696615 partial), need 122596 102024 relations (27882 full + 74142 combined from 1698192 partial), need 122596 102312 relations (27902 full + 74410 combined from 1699740 partial), need 122596 102557 relations (27936 full + 74621 combined from 1701299 partial), need 122596 102792 relations (27961 full + 74831 combined from 1702802 partial), need 122596 103045 relations (27997 full + 75048 combined from 1704372 partial), need 122596 103324 relations (28032 full + 75292 combined from 1706045 partial), need 122596 103582 relations (28060 full + 75522 combined from 1707634 partial), need 122596 103834 relations (28093 full + 75741 combined from 1709201 partial), need 122596 104069 relations (28118 full + 75951 combined from 1710735 partial), need 122596 104304 relations (28156 full + 76148 combined from 1712299 partial), need 122596 104536 relations (28183 full + 76353 combined from 1713828 partial), need 122596 104784 relations (28212 full + 76572 combined from 1715370 partial), need 122596 105055 relations (28236 full + 76819 combined from 1716949 partial), need 122596 105312 relations (28269 full + 77043 combined from 1718490 partial), need 122596 105545 relations (28303 full + 77242 combined from 1720109 partial), need 122596 105798 relations (28327 full + 77471 combined from 1721726 partial), need 122596 106066 relations (28358 full + 77708 combined from 1723336 partial), need 122596 106315 relations (28382 full + 77933 combined from 1724913 partial), need 122596 106540 relations (28405 full + 78135 combined from 1726523 partial), need 122596 106795 relations (28430 full + 78365 combined from 1728052 partial), need 122596 107071 relations (28456 full + 78615 combined from 1729635 partial), need 122596 107349 relations (28486 full + 78863 combined from 1731297 partial), need 122596 107612 relations (28505 full + 79107 combined from 1732891 partial), need 122596 107878 relations (28531 full + 79347 combined from 1734576 partial), need 122596 108119 relations (28560 full + 79559 combined from 1736178 partial), need 122596 108348 relations (28582 full + 79766 combined from 1737692 partial), need 122596 108579 relations (28603 full + 79976 combined from 1739206 partial), need 122596 108835 relations (28630 full + 80205 combined from 1740789 partial), need 122596 109089 relations (28658 full + 80431 combined from 1742365 partial), need 122596 109343 relations (28687 full + 80656 combined from 1743914 partial), need 122596 109578 relations (28712 full + 80866 combined from 1745500 partial), need 122596 109836 relations (28739 full + 81097 combined from 1747133 partial), need 122596 110093 relations (28764 full + 81329 combined from 1748667 partial), need 122596 110348 relations (28789 full + 81559 combined from 1750171 partial), need 122596 110618 relations (28818 full + 81800 combined from 1751812 partial), need 122596 110880 relations (28833 full + 82047 combined from 1753432 partial), need 122596 111115 relations (28862 full + 82253 combined from 1754973 partial), need 122596 111382 relations (28887 full + 82495 combined from 1756580 partial), need 122596 111634 relations (28915 full + 82719 combined from 1758168 partial), need 122596 111902 relations (28944 full + 82958 combined from 1759681 partial), need 122596 112141 relations (28969 full + 83172 combined from 1761279 partial), need 122596 112406 relations (28996 full + 83410 combined from 1762883 partial), need 122596 112641 relations (29019 full + 83622 combined from 1764483 partial), need 122596 112900 relations (29044 full + 83856 combined from 1765994 partial), need 122596 113157 relations (29063 full + 84094 combined from 1767612 partial), need 122596 113431 relations (29094 full + 84337 combined from 1769187 partial), need 122596 113699 relations (29115 full + 84584 combined from 1770789 partial), need 122596 113976 relations (29152 full + 84824 combined from 1772445 partial), need 122596 114260 relations (29181 full + 85079 combined from 1774007 partial), need 122596 114504 relations (29203 full + 85301 combined from 1775586 partial), need 122596 114784 relations (29225 full + 85559 combined from 1777186 partial), need 122596 115057 relations (29259 full + 85798 combined from 1778770 partial), need 122596 115325 relations (29282 full + 86043 combined from 1780307 partial), need 122596 115605 relations (29305 full + 86300 combined from 1781882 partial), need 122596 115862 relations (29330 full + 86532 combined from 1783480 partial), need 122596 116094 relations (29347 full + 86747 combined from 1785041 partial), need 122596 116349 relations (29365 full + 86984 combined from 1786621 partial), need 122596 116608 relations (29392 full + 87216 combined from 1788221 partial), need 122596 116875 relations (29411 full + 87464 combined from 1789818 partial), need 122596 117163 relations (29438 full + 87725 combined from 1791426 partial), need 122596 117465 relations (29464 full + 88001 combined from 1793037 partial), need 122596 117754 relations (29493 full + 88261 combined from 1794667 partial), need 122596 118013 relations (29511 full + 88502 combined from 1796239 partial), need 122596 118293 relations (29539 full + 88754 combined from 1797859 partial), need 122596 118590 relations (29576 full + 89014 combined from 1799475 partial), need 122596 118867 relations (29595 full + 89272 combined from 1801040 partial), need 122596 119128 relations (29618 full + 89510 combined from 1802617 partial), need 122596 119375 relations (29645 full + 89730 combined from 1804194 partial), need 122596 119642 relations (29675 full + 89967 combined from 1805758 partial), need 122596 119923 relations (29704 full + 90219 combined from 1807401 partial), need 122596 120225 relations (29745 full + 90480 combined from 1809005 partial), need 122596 120505 relations (29768 full + 90737 combined from 1810656 partial), need 122596 120771 relations (29787 full + 90984 combined from 1812243 partial), need 122596 121035 relations (29810 full + 91225 combined from 1813821 partial), need 122596 121305 relations (29831 full + 91474 combined from 1815435 partial), need 122596 121600 relations (29860 full + 91740 combined from 1816956 partial), need 122596 121881 relations (29884 full + 91997 combined from 1818562 partial), need 122596 122151 relations (29908 full + 92243 combined from 1820182 partial), need 122596 122423 relations (29927 full + 92496 combined from 1821756 partial), need 122596 122710 relations (29950 full + 92760 combined from 1823402 partial), need 122596 122710 relations (29950 full + 92760 combined from 1823402 partial), need 122596 sieving complete, commencing postprocessing begin with 1853352 relations reduce to 320739 relations in 10 passes attempting to read 320739 relations recovered 320739 relations recovered 310067 polynomials attempting to build 122710 cycles found 122709 cycles in 5 passes distribution of cycle lengths: length 1 : 29950 length 2 : 21063 length 3 : 20688 length 4 : 16492 length 5 : 12620 length 6 : 8658 length 7 : 5521 length 9+: 7717 largest cycle: 19 relations matrix is 122500 x 122709 (35.8 MB) with weight 8892811 (72.47/col) sparse part has weight 8892811 (72.47/col) filtering completed in 3 passes matrix is 116994 x 117058 (34.4 MB) with weight 8538750 (72.94/col) sparse part has weight 8538750 (72.94/col) saving the first 48 matrix rows for later matrix is 116946 x 117058 (24.7 MB) with weight 7163227 (61.19/col) sparse part has weight 5785677 (49.43/col) matrix includes 64 packed rows using block size 21845 for processor cache size 512 kB commencing Lanczos iteration memory use: 21.9 MB linear algebra completed 115406 out of 117058 dimensions (98.6%) lanczos halted after 1850 iterations (dim = 116945) recovered 16 nontrivial dependencies prp46 factor: 1419307810265852610333835137969799236391677581 prp58 factor: 2109337107130584539479018932845314440549663990721314805649 elapsed time 34:58:42
(25·10¹⁵⁷-61)/9 = 2(7)₁₅₆1_<158> = 3 · 7 · 271 · 3096349 · 23837571371_<11> · 53476976743_<11> · C127
C127 = P42 · P85
P42 = 251111527431617622010853018800610054904163_<42>
P85 = 4924515457609151256111451286897140203112085825934235152907008026879826815789247413971_<85>

Number: 27771_157 N=1236602598420845392465064144285320486196111595543875173246683943577905648456176531599471021910006680459702992441135973992261273 ( 127 digits) SNFS difficulty: 159 digits. Divisors found: r1=251111527431617622010853018800610054904163 (pp42) r2=4924515457609151256111451286897140203112085825934235152907008026879826815789247413971 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 43.89 hours. Scaled time: 44.02 units (timescale=1.003). Factorization parameters were as follows: name: 27771_157 n: 1236602598420845392465064144285320486196111595543875173246683943577905648456176531599471021910006680459702992441135973992261273 m: 50000000000000000000000000000000 c5: 4 c0: -305 skew: 2.38 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, 3700001) Primes: RFBsize:283146, AFBsize:282638, largePrimes:6156179 encountered Relations: rels:6587926, finalFF:1001963 Max relations in full relation-set: 28 Initial matrix: 565848 x 1001963 with sparse part having weight 66147813. Pruned matrix : 326559 x 329452 with weight 53505394. Total sieving time: 42.50 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.22 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 43.89 hours. --------- CPU info (if available) ----------
Sep 3, 2008 (2nd): By Sinkiti Sibata / GGNFS
(25·10¹⁴⁹-61)/9 = 2(7)₁₄₈1_<150> = 13 · 181 · 197 · 1690007339_<10> · C135
C135 = P39 · P96
P39 = 470636525232146442959347571682077326597_<39>
P96 = 753416498702436697593695957452689801144133736876627078063382917767291118360831661478156933806457_<96>

Number: 27771_149 N=354585323001884776628629511894083866932645350523269087652602074338492850583139742796679407422397312103865993638601297787473881576436829 ( 135 digits) SNFS difficulty: 150 digits. Divisors found: r1=470636525232146442959347571682077326597 (pp39) r2=753416498702436697593695957452689801144133736876627078063382917767291118360831661478156933806457 (pp96) Version: GGNFS-0.77.1-20050930-nocona Total time: 29.16 hours. Scaled time: 29.54 units (timescale=1.013). Factorization parameters were as follows: name: 27771_149 n: 354585323001884776628629511894083866932645350523269087652602074338492850583139742796679407422397312103865993638601297787473881576436829 m: 1000000000000000000000000000000 c5: 5 c0: -122 skew: 1.89 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:175719, largePrimes:5507544 encountered Relations: rels:5398019, finalFF:462635 Max relations in full relation-set: 28 Initial matrix: 352086 x 462635 with sparse part having weight 40929944. Pruned matrix : 302640 x 304464 with weight 23597003. Total sieving time: 28.49 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.52 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 29.16 hours. --------- CPU info (if available) ----------
(25·10¹³⁰-61)/9 = 2(7)₁₂₉1_<131> = 3 · 58495944249857_<14> · C117
C117 = P38 · P79
P38 = 72325146532934744296452924098623296259_<38>
P79 = 2188573651977845386131277387482593882061834489364029224669677420951255801033939_<79>

Number: 27771_130 N=158288910077417795908138195479665635472032771658895991675636236713434628266715780232941527665528194251098524510734201 ( 117 digits) SNFS difficulty: 131 digits. Divisors found: r1=72325146532934744296452924098623296259 (pp38) r2=2188573651977845386131277387482593882061834489364029224669677420951255801033939 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.74 hours. Scaled time: 2.93 units (timescale=0.783). Factorization parameters were as follows: name: 27771_130 n: 158288910077417795908138195479665635472032771658895991675636236713434628266715780232941527665528194251098524510734201 m: 100000000000000000000000000 c5: 25 c0: -61 skew: 1.2 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 850001) Primes: RFBsize:63951, AFBsize:63799, largePrimes:1454614 encountered Relations: rels:1449393, finalFF:168881 Max relations in full relation-set: 28 Initial matrix: 127814 x 168881 with sparse part having weight 10444584. Pruned matrix : 114673 x 115376 with weight 5503834. Total sieving time: 3.62 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.05 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 3.74 hours. --------- CPU info (if available) ----------
(25·10¹⁵⁴-61)/9 = 2(7)₁₅₃1_<155> = 3 · 293 · 26557 · 49256293730178799051846621_<26> · C122
C122 = P40 · P82
P40 = 5301064110976528276021825235523818767679_<40>
P82 = 4557270671561061255123982087138571971565022174347192982395270017827900110497448323_<82>

Number: 27771_154 N=24158384001018243165313643924362406754822830761328446656124480605992670616305009456597905435143480920734912217227845152317 ( 122 digits) SNFS difficulty: 155 digits. Divisors found: r1=5301064110976528276021825235523818767679 (pp40) r2=4557270671561061255123982087138571971565022174347192982395270017827900110497448323 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 32.40 hours. Scaled time: 32.60 units (timescale=1.006). Factorization parameters were as follows: name: 27771_154 n: 24158384001018243165313643924362406754822830761328446656124480605992670616305009456597905435143480920734912217227845152317 m: 10000000000000000000000000000000 c5: 5 c0: -122 skew: 1.89 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:216067, largePrimes:6039660 encountered Relations: rels:6273316, finalFF:769405 Max relations in full relation-set: 28 Initial matrix: 432948 x 769405 with sparse part having weight 68934654. Pruned matrix : 305773 x 308001 with weight 39508435. Total sieving time: 31.36 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.88 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 32.40 hours. --------- CPU info (if available) ----------
(25·10¹⁵²-61)/9 = 2(7)₁₅₁1_<153> = 271 · 251197 · 23650616473873_<14> · C132
C132 = P37 · P41 · P55
P37 = 1649194932995458194552098353071508753_<37>
P41 = 40462912832676719001557694003003432413533_<41>
P55 = 2585485814085485481752663875511265877142630193494391229_<55>

Number: 27771_152 N=172532650636111904860054938051259144514788546119627239692446419141078903561074468627544423576489365555172803898817679618101016804921 ( 132 digits) SNFS difficulty: 154 digits. Divisors found: r1=1649194932995458194552098353071508753 (pp37) r2=40462912832676719001557694003003432413533 (pp41) r3=2585485814085485481752663875511265877142630193494391229 (pp55) Version: GGNFS-0.77.1-20050930-nocona Total time: 30.42 hours. Scaled time: 23.91 units (timescale=0.786). Factorization parameters were as follows: name: 27771_152 n: 172532650636111904860054938051259144514788546119627239692446419141078903561074468627544423576489365555172803898817679618101016804921 m: 5000000000000000000000000000000 c5: 4 c0: -305 skew: 2.38 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:175969, largePrimes:5737118 encountered Relations: rels:5759844, finalFF:564149 Max relations in full relation-set: 28 Initial matrix: 352335 x 564149 with sparse part having weight 53178188. Pruned matrix : 277777 x 279602 with weight 28211723. Total sieving time: 29.27 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.94 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 30.42 hours. --------- CPU info (if available) ----------
Sep 3, 2008: By Serge Batalov / Msieve 1.37, GMP-ECM 6.2.1+Msieve 1.37/QS
(25·10¹⁵³-61)/9 = 2(7)₁₅₂1_<154> = C154
C154 = P51 · P104
P51 = 109597476817915399648783767470638342286678753105441_<51>
P104 = 25345271245548484326118620469718080997667197757537826608184756610171014468393711341782508146039235365131_<104>

Number: 27771_153 N=2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771 ( 154 digits) SNFS difficulty: 154 digits. Divisors found: r1=109597476817915399648783767470638342286678753105441 r2=25345271245548484326118620469718080997667197757537826608184756610171014468393711341782508146039235365131 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.716). Factorization parameters were as follows: n: 2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771 Y1: 1 Y0: -5000000000000000000000000000000 c5: 8 c0: -61 skew: 1.5 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1200000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 472490 x 472732 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,52,52,2.5,2.5,100000 total time: 11.50 hours.
(25·10¹⁶⁵-61)/9 = 2(7)₁₆₄1_<166> = 139 · 163 · 1399 · 17783920837_<11> · 5046891031387_<13> · 28368734240391359_<17> · C119
C119 = P32 · P37 · P51
P32 = 80362373512148298738695020240543_<32>
P37 = 1311733054597632858229417944775231493_<37>
P51 = 326503438371259342587167097723316440052457045232143_<51>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4222096588 Step 1 took 3912ms ********** Factor found in step 1: 80362373512148298738695020240543 Found probable prime factor of 32 digits: 80362373512148298738695020240543 Composite cofactor 428285352551361986373445292067672882719692682241289020565800346753478523267674749479499 has 87 digits Tue Sep 2 09:21:10 2008 Msieve v. 1.37 Tue Sep 2 09:21:10 2008 random seeds: a88b20fd 0f1ad02c Tue Sep 2 09:21:10 2008 factoring 428285352551361986373445292067672882719692682241289020565800346753478523267674749479499 (87 digits) Tue Sep 2 09:21:11 2008 no P-1/P+1/ECM available, skipping Tue Sep 2 09:21:11 2008 commencing quadratic sieve (87-digit input) Tue Sep 2 09:21:11 2008 using multiplier of 3 Tue Sep 2 09:21:11 2008 using 64kb Opteron sieve core Tue Sep 2 09:21:11 2008 sieve interval: 10 blocks of size 65536 Tue Sep 2 09:21:11 2008 processing polynomials in batches of 11 Tue Sep 2 09:21:11 2008 using a sieve bound of 1484177 (56667 primes) Tue Sep 2 09:21:11 2008 using large prime bound of 118734160 (26 bits) Tue Sep 2 09:21:11 2008 using double large prime bound of 342165490136480 (42-49 bits) Tue Sep 2 09:21:11 2008 using trial factoring cutoff of 49 bits Tue Sep 2 09:21:11 2008 polynomial 'A' values have 11 factors Tue Sep 2 10:02:32 2008 56852 relations (15434 full + 41418 combined from 599869 partial), need 56763 Tue Sep 2 10:02:33 2008 begin with 615303 relations Tue Sep 2 10:02:33 2008 reduce to 138044 relations in 11 passes Tue Sep 2 10:02:33 2008 attempting to read 138044 relations Tue Sep 2 10:02:34 2008 recovered 138044 relations Tue Sep 2 10:02:34 2008 recovered 118769 polynomials Tue Sep 2 10:02:34 2008 attempting to build 56852 cycles Tue Sep 2 10:02:34 2008 found 56852 cycles in 5 passes Tue Sep 2 10:02:34 2008 distribution of cycle lengths: Tue Sep 2 10:02:34 2008 length 1 : 15434 Tue Sep 2 10:02:34 2008 length 2 : 11111 Tue Sep 2 10:02:34 2008 length 3 : 10050 Tue Sep 2 10:02:34 2008 length 4 : 7450 Tue Sep 2 10:02:34 2008 length 5 : 5195 Tue Sep 2 10:02:34 2008 length 6 : 3284 Tue Sep 2 10:02:34 2008 length 7 : 2019 Tue Sep 2 10:02:34 2008 length 9+: 2309 Tue Sep 2 10:02:34 2008 largest cycle: 17 relations Tue Sep 2 10:02:34 2008 matrix is 56667 x 56852 (14.0 MB) with weight 3220880 (56.65/col) Tue Sep 2 10:02:34 2008 sparse part has weight 3220880 (56.65/col) Tue Sep 2 10:02:35 2008 filtering completed in 3 passes Tue Sep 2 10:02:35 2008 matrix is 52655 x 52719 (13.1 MB) with weight 3016772 (57.22/col) Tue Sep 2 10:02:35 2008 sparse part has weight 3016772 (57.22/col) Tue Sep 2 10:02:35 2008 saving the first 48 matrix rows for later Tue Sep 2 10:02:35 2008 matrix is 52607 x 52719 (8.5 MB) with weight 2347485 (44.53/col) Tue Sep 2 10:02:35 2008 sparse part has weight 1706392 (32.37/col) Tue Sep 2 10:02:35 2008 matrix includes 64 packed rows Tue Sep 2 10:02:35 2008 using block size 21087 for processor cache size 1024 kB Tue Sep 2 10:02:35 2008 commencing Lanczos iteration Tue Sep 2 10:02:35 2008 memory use: 7.7 MB Tue Sep 2 10:02:50 2008 lanczos halted after 834 iterations (dim = 52604) Tue Sep 2 10:02:50 2008 recovered 15 nontrivial dependencies Tue Sep 2 10:02:50 2008 prp37 factor: 1311733054597632858229417944775231493 Tue Sep 2 10:02:50 2008 prp51 factor: 326503438371259342587167097723316440052457045232143 Tue Sep 2 10:02:50 2008 elapsed time 00:41:40
(25·10¹⁶⁴-61)/9 = 2(7)₁₆₃1_<165> = 3299 · C161
C161 = P33 · P48 · P81
P33 = 659829942255417221379291150281179_<33>
P48 = 248570702244139474826035756339690768851787296439_<48>
P81 = 513373237714119628900245111388942430675374787557277953916106237311225424401827709_<81>

Number: 27771_164 N=84200599508268498871711966589202115119059647704691657404600720757131790778350341854434003570105419150584352160587383382169681048129062678926273955070560102387929 ( 161 digits) SNFS difficulty: 165 digits. Divisors found: r1=659829942255417221379291150281179 r2=248570702244139474826035756339690768851787296439 r3=513373237714119628900245111388942430675374787557277953916106237311225424401827709 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.725). Factorization parameters were as follows: n: 84200599508268498871711966589202115119059647704691657404600720757131790778350341854434003570105419150584352160587383382169681048129062678926273955070560102387929 Y1: 1 Y0: -1000000000000000000000000000000000 c5: 5 c0: -122 skew: 1.89 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 4500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 827994 x 828242 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000 total time: 31.00 hours. # I knew about 3 factors, because of ECM results (but GNFS was still useless): Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3546418022 Step 1 took 19842ms Step 2 took 14809ms ********** Factor found in step 2: 659829942255417221379291150281179 Found probable prime factor of 33 digits: 659829942255417221379291150281179 Composite cofactor 127609546211946264112980194582537324356226142070695470718473719517438302591875232733472700792167849318979451951203715019387228251 has 129 digits
Sep 2, 2008 (5th): By Wataru Sakai / GGNFS
(8·10¹⁷⁹-11)/3 = 2(6)₁₇₈3_<180> = C180
C180 = P40 · P140
P40 = 4682209735745219226761500789554699502777_<40>
P140 = 56953165645456519175499917759107331724155107752653509943265611671232250463973830108138400277147620488064312051591440159053383107906533210719_<140>

Number: 26663_179 N=266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 180 digits) SNFS difficulty: 180 digits. Divisors found: r1=4682209735745219226761500789554699502777 (pp40) r2=56953165645456519175499917759107331724155107752653509943265611671232250463973830108138400277147620488064312051591440159053383107906533210719 (pp140) Version: GGNFS-0.77.1-20060722-nocona Total time: 340.53 hours. Scaled time: 686.16 units (timescale=2.015). Factorization parameters were as follows: n: 266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 m: 1000000000000000000000000000000000000 c5: 4 c0: -55 skew: 1.69 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 7800001) Primes: RFBsize:501962, AFBsize:500697, largePrimes:6409304 encountered Relations: rels:6929357, finalFF:1194527 Max relations in full relation-set: 32 Initial matrix: 1002723 x 1194527 with sparse part having weight 57740419. Pruned matrix : 833652 x 838729 with weight 41052163. Total sieving time: 336.37 hours. Total relation processing time: 0.09 hours. Matrix solve time: 3.89 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 340.53 hours. --------- CPU info (if available) ----------
Sep 2, 2008 (4th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(8·10¹⁶⁶-11)/3 = 2(6)₁₆₅3_<167> = 7 · 13² · 3343 · C160
C160 = P78 · P83
P78 = 651701029217118246663040446269232348044819826548758806571194117322481623985581_<78>
P83 = 10346636798875123657678542081026145261494185181631514140254760838629797607664649267_<83>

Number: n N=6742913850762627770842409927524633339309240733571712195242419131602039630296147933461263266366927288715640955683294439363377903151022642957570130307653030219127 ( 160 digits) SNFS difficulty: 167 digits. Divisors found: Tue Sep 2 13:14:52 2008 prp78 factor: 651701029217118246663040446269232348044819826548758806571194117322481623985581 Tue Sep 2 13:14:52 2008 prp83 factor: 10346636798875123657678542081026145261494185181631514140254760838629797607664649267 Tue Sep 2 13:14:52 2008 elapsed time 01:26:16 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 22.59 hours. Scaled time: 18.93 units (timescale=0.838). Factorization parameters were as follows: name: KA_2_6_165_3 n: 6742913850762627770842409927524633339309240733571712195242419131602039630296147933461263266366927288715640955683294439363377903151022642957570130307653030219127 type: snfs skew: 1.34 deg: 5 c5: 5 c0: -22 m: 2000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 2600001) Primes: RFBsize:348513, AFBsize:348587, largePrimes:13964706 encountered Relations: rels:13838473, finalFF:1133567 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Loading matrix into RAM... Matrix scanned: it should be 697165 x 1133567. Found 6 dense blocks. Re-reading matrix... The dense blocks consist of the following sets of rows: [697101, 697164] [0, 63] [64, 127] [128, 191] [348513, 348576] [348577, 348640] Matrix loaded: it is 697165 x 1133567. Warning: column 121076 is all zero! checkMat() did not like something about the matrix: This is probably a sign that something has gone horribly wrong in the matrix construction (matbuild). However, the number of bad columns is only 1, so we will delete them and attempt to continue. checkMat() returned some error! Terminating... Return value 65280. Terminating... Total sieving time: 22.25 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,52,52,2.5,2.5,100000 total time: 22.59 hours. --------- CPU info (if available) ----------
(52·10¹⁶⁷-7)/9 = 5(7)₁₆₇_<168> = 6469 · 14737 · 59029 · 158560488000179_<15> · C141
C141 = P39 · P50 · P53
P39 = 134423132005673053281516895507169533951_<39>
P50 = 92767036161728595441434580385004989605003143823259_<50>
P53 = 51926195999481557111023152924214215900076403618583911_<53>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 647521509972609978778474895181437790066412069595365135629283038763004668109673455943367523705566963333241654425358525680208523021452673454499 (141 digits) Using B1=4860000, B2=11416155670, polynomial Dickson(12), sigma=3081001015 Step 1 took 51375ms Step 2 took 24656ms ********** Factor found in step 2: 134423132005673053281516895507169533951 Found probable prime factor of 39 digits: 134423132005673053281516895507169533951 Composite cofactor 4817039302024912335467132326152784905075738362859412701896443731750706099437308147192818330864044985949 has 103 digits Number: n N=4817039302024912335467132326152784905075738362859412701896443731750706099437308147192818330864044985949 ( 103 digits) Divisors found: r1=92767036161728595441434580385004989605003143823259 (pp50) r2=51926195999481557111023152924214215900076403618583911 (pp53) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.65 hours. Scaled time: 12.17 units (timescale=1.829). Factorization parameters were as follows: name: KA_5_7_167 n: 4817039302024912335467132326152784905075738362859412701896443731750706099437308147192818330864044985949 skew: 3985.52 # norm 3.59e+13 c5: 93600 c4: -601932860 c3: -2428712294883 c2: 21750733387237273 c1: 13248076622685588363 c0: -19810988854558364477813 # alpha -4.55 Y1: 81379529627 Y0: -34857976460207414076 # Murphy_E 2.31e-09 # M 4281574460791113755516230351221977994129597477696987288901441868558155807652878845341700823494448725006 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:169511, AFBsize:169363, largePrimes:4077544 encountered Relations: rels:4035675, finalFF:430083 Max relations in full relation-set: 48 Initial matrix: 338952 x 430083 with sparse part having weight 26429719. Pruned matrix : 252628 x 254386 with weight 10673012. Total sieving time: 6.20 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.28 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 6.65 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Sep 2, 2008 (3rd): By Sinkiti Sibata / GGNFS, GMP-ECM, Msieve
(25·10¹²⁹-61)/9 = 2(7)₁₂₈1_<130> = 153151 · 4673772755787217_<16> · C109
C109 = P38 · P72
P38 = 20453259670836204190673329947267817129_<38>
P72 = 189735037545599924396551452154414396763586188577807393187978065955851197_<72>

Number: 27771_129 N=3880699991576011953128227159099334239837445535573922171440035776758693606702134517293709663755165267331753413 ( 109 digits) SNFS difficulty: 130 digits. Divisors found: r1=20453259670836204190673329947267817129 (pp38) r2=189735037545599924396551452154414396763586188577807393187978065955851197 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.11 hours. Scaled time: 4.01 units (timescale=0.785). Factorization parameters were as follows: name: 27771_129 n: 3880699991576011953128227159099334239837445535573922171440035776758693606702134517293709663755165267331753413 m: 100000000000000000000000000 c5: 5 c0: -122 skew: 1.89 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:63784, largePrimes:1545512 encountered Relations: rels:1563329, finalFF:183787 Max relations in full relation-set: 28 Initial matrix: 127800 x 183787 with sparse part having weight 14621739. Pruned matrix : 113248 x 113951 with weight 7290682. Total sieving time: 4.97 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.11 hours. --------- CPU info (if available) ----------
(25·10¹⁴⁷-61)/9 = 2(7)₁₄₆1_<148> = 17 · 271 · 3309855891091_<13> · C132
C132 = P34 · P98
P34 = 9229490189668026616203266998176737_<34>
P98 = 19737515731549627398346041144166461110062712518326895924348032317964415590287193972630324247892759_<98>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 182167207812755629686046229168270893227835379964737052055815747768780391916854905259389815243129008035784843900450078564467304547383 Run 334 out of 904: Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4055225039 Step 1 took 14680ms Step 2 took 6957ms ********** Factor found in step 2: 9229490189668026616203266998176737 Found probable prime factor of 34 digits: 9229490189668026616203266998176737 Probable prime cofactor 19737515731549627398346041144166461110062712518326895924348032317964415590287193972630324247892759 has 98 digits
(25·10¹²⁴-61)/9 = 2(7)₁₂₃1_<125> = 3² · 502027579 · 7574678889386110163953_<22> · C93
C93 = P41 · P53
P41 = 70362686316521436307034813012932569418787_<41>
P53 = 11535084375410612732158710144999540847723947258858451_<53>

Msieve v. 1.36 Tue Sep 2 06:30:15 2008 random seeds: fac47258 aa7b8a3d factoring 8116395235416245391682881300129730356859284926250012455520665659765342 50127979479486173118937 (93 digits) no P-1/P+1/ECM available, skipping commencing quadratic sieve (93-digit input) using multiplier of 57 using 64kb Pentium 4 sieve core sieve interval: 18 blocks of size 65536 processing polynomials in batches of 6 using a sieve bound of 1956883 (72856 primes) using large prime bound of 244610375 (27 bits) using double large prime bound of 1256766767596625 (42-51 bits) using trial factoring cutoff of 51 bits polynomial 'A' values have 12 factors sieving in progress (press Ctrl-C to pause) 73048 relations (18356 full + 54692 combined from 993590 partial), need 72952 73048 relations (18356 full + 54692 combined from 993590 partial), need 72952 sieving complete, commencing postprocessing begin with 1011946 relations reduce to 187410 relations in 10 passes attempting to read 187410 relations recovered 187410 relations recovered 170694 polynomials attempting to build 73048 cycles found 73048 cycles in 6 passes distribution of cycle lengths: length 1 : 18356 length 2 : 12889 length 3 : 12517 length 4 : 9860 length 5 : 7391 length 6 : 4737 length 7 : 3122 length 9+: 4176 largest cycle: 23 relations matrix is 72856 x 73048 (19.3 MB) with weight 4773964 (65.35/col) sparse part has weight 4773964 (65.35/col) filtering completed in 3 passes matrix is 69230 x 69294 (18.5 MB) with weight 4561561 (65.83/col) sparse part has weight 4561561 (65.83/col) saving the first 48 matrix rows for later matrix is 69182 x 69294 (11.9 MB) with weight 3618831 (52.22/col) sparse part has weight 2700647 (38.97/col) matrix includes 64 packed rows using block size 21845 for processor cache size 512 kB commencing Lanczos iteration memory use: 11.2 MB linear algebra completed 64229 out of 69294 dimensions (92.7%) lanczos halted after 1096 iterations (dim = 69181) recovered 18 nontrivial dependencies prp41 factor: 70362686316521436307034813012932569418787 prp53 factor: 11535084375410612732158710144999540847723947258858451 elapsed time 04:50:14
(25·10¹⁴³-61)/9 = 2(7)₁₄₂1_<144> = 13 · 2171111317_<10> · 9299223345239532250199_<22> · C112
C112 = P34 · P39 · P40
P34 = 1309143485309777583241846470683317_<34>
P39 = 484378549302141911629687706665230167387_<39>
P40 = 1668988046339800108673532942790290417931_<40>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 1058340406055840797247159275511465608167592959514093349104328096492970348022598919601596788146797957174561417149 Run 100 out of 904: Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2624782773 Step 1 took 11606ms Step 2 took 5928ms ********** Factor found in step 2: 1309143485309777583241846470683317 Found probable prime factor of 34 digits: 1309143485309777583241846470683317 Composite cofactor 808422008688688376397533217076481426744848381871723328550796245844581316216297 has 78 digits Tue Sep 2 11:39:26 2008 Msieve v. 1.36 Tue Sep 2 11:39:26 2008 random seeds: 5ccc56ec cd254687 Tue Sep 2 11:39:26 2008 factoring 808422008688688376397533217076481426744848381871723328550796245844581316216297 (78 digits) Tue Sep 2 11:39:27 2008 no P-1/P+1/ECM available, skipping Tue Sep 2 11:39:27 2008 commencing quadratic sieve (78-digit input) Tue Sep 2 11:39:27 2008 using multiplier of 5 Tue Sep 2 11:39:27 2008 using 32kb Intel Core sieve core Tue Sep 2 11:39:27 2008 sieve interval: 12 blocks of size 32768 Tue Sep 2 11:39:27 2008 processing polynomials in batches of 17 Tue Sep 2 11:39:27 2008 using a sieve bound of 1032511 (40529 primes) Tue Sep 2 11:39:27 2008 using large prime bound of 103251100 (26 bits) Tue Sep 2 11:39:27 2008 using trial factoring cutoff of 27 bits Tue Sep 2 11:39:27 2008 polynomial 'A' values have 10 factors Tue Sep 2 11:46:12 2008 40779 relations (20784 full + 19995 combined from 222822 partial), need 40625 Tue Sep 2 11:46:12 2008 begin with 243606 relations Tue Sep 2 11:46:12 2008 reduce to 58257 relations in 2 passes Tue Sep 2 11:46:12 2008 attempting to read 58257 relations Tue Sep 2 11:46:12 2008 recovered 58257 relations Tue Sep 2 11:46:12 2008 recovered 47947 polynomials Tue Sep 2 11:46:13 2008 attempting to build 40779 cycles Tue Sep 2 11:46:13 2008 found 40779 cycles in 1 passes Tue Sep 2 11:46:13 2008 distribution of cycle lengths: Tue Sep 2 11:46:13 2008 length 1 : 20784 Tue Sep 2 11:46:13 2008 length 2 : 19995 Tue Sep 2 11:46:13 2008 largest cycle: 2 relations Tue Sep 2 11:46:13 2008 matrix is 40529 x 40779 (5.3 MB) with weight 1219217 (29.90/col) Tue Sep 2 11:46:13 2008 sparse part has weight 1219217 (29.90/col) Tue Sep 2 11:46:13 2008 filtering completed in 3 passes Tue Sep 2 11:46:13 2008 matrix is 29746 x 29810 (4.1 MB) with weight 967944 (32.47/col) Tue Sep 2 11:46:13 2008 sparse part has weight 967944 (32.47/col) Tue Sep 2 11:46:13 2008 saving the first 48 matrix rows for later Tue Sep 2 11:46:13 2008 matrix is 29698 x 29810 (2.3 MB) with weight 682503 (22.90/col) Tue Sep 2 11:46:13 2008 sparse part has weight 436808 (14.65/col) Tue Sep 2 11:46:13 2008 matrix includes 64 packed rows Tue Sep 2 11:46:13 2008 commencing Lanczos iteration Tue Sep 2 11:46:13 2008 memory use: 3.5 MB Tue Sep 2 11:46:25 2008 lanczos halted after 471 iterations (dim = 29698) Tue Sep 2 11:46:25 2008 recovered 18 nontrivial dependencies Tue Sep 2 11:46:25 2008 prp39 factor: 484378549302141911629687706665230167387 Tue Sep 2 11:46:25 2008 prp40 factor: 1668988046339800108673532942790290417931 Tue Sep 2 11:46:25 2008 elapsed time 00:06:59
(25·10¹²¹-61)/9 = 2(7)₁₂₀1_<122> = 3 · 7 · 49627 · C116
C116 = P51 · P66
P51 = 151751901518049889837708613154968992021300406120197_<51>
P66 = 175641056329064573758109081077588831777126235148165732731308152329_<66>

Number: 27771_121 N=26653864282574460501798442838602429147898348132091860304325293141864766182174044829454183233376011500822591559488813 ( 116 digits) SNFS difficulty: 122 digits. Divisors found: r1=151751901518049889837708613154968992021300406120197 (pp51) r2=175641056329064573758109081077588831777126235148165732731308152329 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.43 hours. Scaled time: 1.90 units (timescale=0.781). Factorization parameters were as follows: name: 27771_121 n: 26653864282574460501798442838602429147898348132091860304325293141864766182174044829454183233376011500822591559488813 m: 1000000000000000000000000 c5: 250 c0: -61 skew: 0.75 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:64054, largePrimes:2215166 encountered Relations: rels:2352484, finalFF:253562 Max relations in full relation-set: 28 Initial matrix: 113218 x 253562 with sparse part having weight 24450133. Pruned matrix : 87484 x 88114 with weight 6169356. Total sieving time: 2.31 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.04 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.43 hours. --------- CPU info (if available) ----------
(25·10¹²⁰-61)/9 = 2(7)₁₁₉1_<121> = 19 · 731683 · 1060777 · C108
C108 = P34 · P74
P34 = 2077909526098467227127095357094899_<34>
P74 = 90650500191125839001849566503209300133757025311439466547532183753689765801_<74>

Number: 27771_120 N=188363537892731304918189934923172037561952148759302117343469768319278002963865656881762961384765891041749099 ( 108 digits) SNFS difficulty: 121 digits. Divisors found: r1=2077909526098467227127095357094899 (pp34) r2=90650500191125839001849566503209300133757025311439466547532183753689765801 (pp74) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.05 hours. Scaled time: 0.97 units (timescale=0.473). Factorization parameters were as follows: name: 27771_120 n: 188363537892731304918189934923172037561952148759302117343469768319278002963865656881762961384765891041749099 m: 1000000000000000000000000 c5: 25 c0: -61 skew: 1.2 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63799, largePrimes:2043190 encountered Relations: rels:2063781, finalFF:182037 Max relations in full relation-set: 28 Initial matrix: 112961 x 182037 with sparse part having weight 14502213. Pruned matrix : 92717 x 93345 with weight 4989049. Total sieving time: 1.87 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.09 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.05 hours. --------- CPU info (if available) ----------
(25·10¹⁴²-61)/9 = 2(7)₁₄₁1_<143> = 3² · 271 · 13907 · 8197537 · 4493806896529693_<16> · C113
C113 = P46 · P67
P46 = 2901173421641272627502030357866773367220862841_<46>
P67 = 7662681283468009442196894266756698463559266727460022585926879778867_<67>

Number: 27771_142 N=22230767278105423457838826207878695530231315713506366491222875197108426865608784560893162769503742321415017381147 ( 113 digits) SNFS difficulty: 144 digits. Divisors found: r1=2901173421641272627502030357866773367220862841 (pp46) r2=7662681283468009442196894266756698463559266727460022585926879778867 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.27 hours. Scaled time: 16.45 units (timescale=1.011). Factorization parameters were as follows: name: 27771_142 n: 22230767278105423457838826207878695530231315713506366491222875197108426865608784560893162769503742321415017381147 m: 50000000000000000000000000000 c5: 4 c0: -305 skew: 2.38 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2350001) Primes: RFBsize:100021, AFBsize:99834, largePrimes:3010808 encountered Relations: rels:3140551, finalFF:366900 Max relations in full relation-set: 28 Initial matrix: 199919 x 366900 with sparse part having weight 41430559. Pruned matrix : 163905 x 164968 with weight 19507651. Total sieving time: 15.88 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.27 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 16.27 hours. --------- CPU info (if available) ----------
(25·10¹³⁹-61)/9 = 2(7)₁₃₈1_<140> = 3 · 7 · 80084639981_<11> · C128
C128 = P52 · P76
P52 = 6190455589244173649468957716997216405600058094976893_<52>
P76 = 2668126182700760482119033930880089627186177930718096494876239686787844595447_<76>

Number: 27771_139 N=16516916640508643948357831885991140837451264045925620296168380208470962412813488436668742365820180095732542134692365768398006171 ( 128 digits) SNFS difficulty: 140 digits. Divisors found: r1=6190455589244173649468957716997216405600058094976893 (pp52) r2=2668126182700760482119033930880089627186177930718096494876239686787844595447 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.63 hours. Scaled time: 13.07 units (timescale=0.786). Factorization parameters were as follows: name: 27771_139 n: 16516916640508643948357831885991140837451264045925620296168380208470962412813488436668742365820180095732542134692365768398006171 m: 10000000000000000000000000000 c5: 5 c0: -122 skew: 1.89 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1950001) Primes: RFBsize:100021, AFBsize:99699, largePrimes:2732880 encountered Relations: rels:2707703, finalFF:256474 Max relations in full relation-set: 28 Initial matrix: 199785 x 256474 with sparse part having weight 24432411. Pruned matrix : 182795 x 183857 with weight 15345607. Total sieving time: 16.20 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.26 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 16.63 hours. --------- CPU info (if available) ----------
Sep 2, 2008 (2nd): By Serge Batalov / Msieve v. 1.36/QS, Msieve v. 1.37/QS, Msieve-1.37 snfs, GMP-ECM 6.2.1, Msieve-1.37; 64-bit sievers (Childers)
(25·10¹³⁴-61)/9 = 2(7)₁₃₃1_<135> = 154682376054408611_<18> · 4819569705512101509596789_<25> · C93
C93 = P34 · P60
P34 = 2285341270841103220316892131357527_<34>
P60 = 163041189884638045718398236420560827643537175317697019375987_<60>

Mon Sep 1 10:51:50 2008 Msieve v. 1.36 Mon Sep 1 10:51:50 2008 random seeds: 6c6c726c 4abd9356 Mon Sep 1 10:51:50 2008 factoring 372604760090404334748669246936986927822050971487117589245170278954091582540355072904735504149 (93 digits) Mon Sep 1 10:51:50 2008 no P-1/P+1/ECM available, skipping Mon Sep 1 10:51:50 2008 commencing quadratic sieve (93-digit input) Mon Sep 1 10:51:51 2008 using multiplier of 1 Mon Sep 1 10:51:51 2008 using 64kb Opteron sieve core Mon Sep 1 10:51:51 2008 sieve interval: 18 blocks of size 65536 Mon Sep 1 10:51:51 2008 processing polynomials in batches of 6 Mon Sep 1 10:51:51 2008 using a sieve bound of 1923133 (71747 primes) Mon Sep 1 10:51:51 2008 using large prime bound of 232699093 (27 bits) Mon Sep 1 10:51:51 2008 using double large prime bound of 1148762820023984 (42-51 bits) Mon Sep 1 10:51:51 2008 using trial factoring cutoff of 51 bits Mon Sep 1 10:51:51 2008 polynomial 'A' values have 12 factors Mon Sep 1 13:09:44 2008 72146 relations (17299 full + 54847 combined from 977711 partial), need 71843 Mon Sep 1 13:09:45 2008 begin with 995010 relations Mon Sep 1 13:09:45 2008 reduce to 187321 relations in 9 passes Mon Sep 1 13:09:45 2008 attempting to read 187321 relations Mon Sep 1 13:09:47 2008 recovered 187321 relations Mon Sep 1 13:09:47 2008 recovered 171042 polynomials Mon Sep 1 13:09:47 2008 attempting to build 72146 cycles Mon Sep 1 13:09:47 2008 found 72146 cycles in 6 passes Mon Sep 1 13:09:47 2008 distribution of cycle lengths: Mon Sep 1 13:09:47 2008 length 1 : 17299 Mon Sep 1 13:09:47 2008 length 2 : 12778 Mon Sep 1 13:09:47 2008 length 3 : 12307 Mon Sep 1 13:09:47 2008 length 4 : 9774 Mon Sep 1 13:09:47 2008 length 5 : 7552 Mon Sep 1 13:09:47 2008 length 6 : 4913 Mon Sep 1 13:09:47 2008 length 7 : 3199 Mon Sep 1 13:09:47 2008 length 9+: 4324 Mon Sep 1 13:09:47 2008 largest cycle: 20 relations Mon Sep 1 13:09:47 2008 matrix is 71747 x 72146 (18.8 MB) with weight 4351494 (60.32/col) Mon Sep 1 13:09:47 2008 sparse part has weight 4351494 (60.32/col) Mon Sep 1 13:09:48 2008 filtering completed in 3 passes Mon Sep 1 13:09:48 2008 matrix is 68402 x 68465 (17.9 MB) with weight 4139994 (60.47/col) Mon Sep 1 13:09:48 2008 sparse part has weight 4139994 (60.47/col) Mon Sep 1 13:09:48 2008 saving the first 48 matrix rows for later Mon Sep 1 13:09:48 2008 matrix is 68354 x 68465 (10.6 MB) with weight 3144332 (45.93/col) Mon Sep 1 13:09:48 2008 sparse part has weight 2085056 (30.45/col) Mon Sep 1 13:09:48 2008 matrix includes 64 packed rows Mon Sep 1 13:09:48 2008 using block size 27386 for processor cache size 1024 kB Mon Sep 1 13:09:48 2008 commencing Lanczos iteration Mon Sep 1 13:09:48 2008 memory use: 10.0 MB Mon Sep 1 13:10:13 2008 lanczos halted after 1082 iterations (dim = 68350) Mon Sep 1 13:10:13 2008 recovered 13 nontrivial dependencies Mon Sep 1 13:10:14 2008 prp34 factor: 2285341270841103220316892131357527 Mon Sep 1 13:10:14 2008 prp60 factor: 163041189884638045718398236420560827643537175317697019375987 Mon Sep 1 13:10:14 2008 elapsed time 02:18:24
(25·10¹¹⁷-61)/9 = 2(7)₁₁₆1_<118> = 271 · 39064037 · 35586743578678280759909_<23> · C85
C85 = P42 · P44
P42 = 619747506717711772232144970127654889620759_<42>
P44 = 11897290019020184431574871639392025782656283_<44>

Mon Sep 1 11:02:19 2008 Msieve v. 1.37 Mon Sep 1 11:02:19 2008 random seeds: 714daeb2 a296f0bc Mon Sep 1 11:02:19 2008 factoring 7373315825985276969439340659001240598496120288389807384293268160113990464333518578797 (85 digits) Mon Sep 1 11:02:20 2008 no P-1/P+1/ECM available, skipping Mon Sep 1 11:02:20 2008 commencing quadratic sieve (85-digit input) Mon Sep 1 11:02:20 2008 using multiplier of 2 Mon Sep 1 11:02:20 2008 using 64kb Opteron sieve core Mon Sep 1 11:02:20 2008 sieve interval: 6 blocks of size 65536 Mon Sep 1 11:02:20 2008 processing polynomials in batches of 17 Mon Sep 1 11:02:20 2008 using a sieve bound of 1434241 (54705 primes) Mon Sep 1 11:02:20 2008 using large prime bound of 116173521 (26 bits) Mon Sep 1 11:02:20 2008 using double large prime bound of 328997602795950 (41-49 bits) Mon Sep 1 11:02:20 2008 using trial factoring cutoff of 49 bits Mon Sep 1 11:02:20 2008 polynomial 'A' values have 11 factors Mon Sep 1 11:31:50 2008 54866 relations (16358 full + 38508 combined from 570198 partial), need 54801 Mon Sep 1 11:31:50 2008 begin with 586556 relations Mon Sep 1 11:31:51 2008 reduce to 128079 relations in 8 passes Mon Sep 1 11:31:51 2008 attempting to read 128079 relations Mon Sep 1 11:31:51 2008 recovered 128079 relations Mon Sep 1 11:31:51 2008 recovered 107644 polynomials Mon Sep 1 11:31:52 2008 attempting to build 54866 cycles Mon Sep 1 11:31:52 2008 found 54866 cycles in 5 passes Mon Sep 1 11:31:52 2008 distribution of cycle lengths: Mon Sep 1 11:31:52 2008 length 1 : 16358 Mon Sep 1 11:31:52 2008 length 2 : 11052 Mon Sep 1 11:31:52 2008 length 3 : 9697 Mon Sep 1 11:31:52 2008 length 4 : 7070 Mon Sep 1 11:31:52 2008 length 5 : 4547 Mon Sep 1 11:31:52 2008 length 6 : 2753 Mon Sep 1 11:31:52 2008 length 7 : 1601 Mon Sep 1 11:31:52 2008 length 9+: 1788 Mon Sep 1 11:31:52 2008 largest cycle: 18 relations Mon Sep 1 11:31:52 2008 matrix is 54705 x 54866 (12.5 MB) with weight 2844525 (51.84/col) Mon Sep 1 11:31:52 2008 sparse part has weight 2844525 (51.84/col) Mon Sep 1 11:31:52 2008 filtering completed in 4 passes Mon Sep 1 11:31:52 2008 matrix is 49391 x 49455 (11.4 MB) with weight 2593007 (52.43/col) Mon Sep 1 11:31:52 2008 sparse part has weight 2593007 (52.43/col) Mon Sep 1 11:31:52 2008 saving the first 48 matrix rows for later Mon Sep 1 11:31:52 2008 matrix is 49343 x 49455 (6.7 MB) with weight 1918802 (38.80/col) Mon Sep 1 11:31:52 2008 sparse part has weight 1248764 (25.25/col) Mon Sep 1 11:31:52 2008 matrix includes 64 packed rows Mon Sep 1 11:31:52 2008 using block size 19782 for processor cache size 1024 kB Mon Sep 1 11:31:53 2008 commencing Lanczos iteration Mon Sep 1 11:31:53 2008 memory use: 6.4 MB Mon Sep 1 11:32:03 2008 lanczos halted after 781 iterations (dim = 49337) Mon Sep 1 11:32:03 2008 recovered 14 nontrivial dependencies Mon Sep 1 11:32:04 2008 prp42 factor: 619747506717711772232144970127654889620759 Mon Sep 1 11:32:04 2008 prp44 factor: 11897290019020184431574871639392025782656283 Mon Sep 1 11:32:04 2008 elapsed time 00:29:45
(25·10¹⁶²-61)/9 = 2(7)₁₆₁1_<163> = 271 · 563 · 1879 · 1373431 · 1359263813985643_<16> · 151483474336947757_<18> · 23620461886232346133505839_<26> · C91
C91 = P30 · P61
P30 = 518359647652198152916575830119_<30>
P61 = 2798321461530763710270557913472221025759214843794041462439153_<61>

Mon Sep 1 10:49:29 2008 Msieve v. 1.37 Mon Sep 1 10:49:29 2008 random seeds: dc3a699f 068f696d Mon Sep 1 10:49:29 2008 factoring 1450536926816670844973433674050011398591359995388009351598663646137374467946327419502249207 (91 digits) Mon Sep 1 10:49:29 2008 no P-1/P+1/ECM available, skipping Mon Sep 1 10:49:29 2008 commencing quadratic sieve (91-digit input) Mon Sep 1 10:49:29 2008 using multiplier of 7 Mon Sep 1 10:49:30 2008 using 64kb Opteron sieve core Mon Sep 1 10:49:30 2008 sieve interval: 18 blocks of size 65536 Mon Sep 1 10:49:30 2008 processing polynomials in batches of 6 Mon Sep 1 10:49:30 2008 using a sieve bound of 1648379 (62353 primes) Mon Sep 1 10:49:30 2008 using large prime bound of 145057352 (27 bits) Mon Sep 1 10:49:30 2008 using double large prime bound of 490649675444456 (42-49 bits) Mon Sep 1 10:49:30 2008 using trial factoring cutoff of 49 bits Mon Sep 1 10:49:30 2008 polynomial 'A' values have 12 factors Mon Sep 1 12:30:08 2008 62716 relations (16467 full + 46249 combined from 697522 partial), need 62449 Mon Sep 1 12:30:08 2008 begin with 713989 relations Mon Sep 1 12:30:09 2008 reduce to 154131 relations in 12 passes Mon Sep 1 12:30:09 2008 attempting to read 154131 relations Mon Sep 1 12:30:11 2008 recovered 154131 relations Mon Sep 1 12:30:11 2008 recovered 134673 polynomials Mon Sep 1 12:30:11 2008 attempting to build 62716 cycles Mon Sep 1 12:30:11 2008 found 62716 cycles in 6 passes Mon Sep 1 12:30:11 2008 distribution of cycle lengths: Mon Sep 1 12:30:11 2008 length 1 : 16467 Mon Sep 1 12:30:11 2008 length 2 : 11946 Mon Sep 1 12:30:11 2008 length 3 : 11000 Mon Sep 1 12:30:11 2008 length 4 : 8364 Mon Sep 1 12:30:11 2008 length 5 : 5902 Mon Sep 1 12:30:11 2008 length 6 : 3907 Mon Sep 1 12:30:11 2008 length 7 : 2351 Mon Sep 1 12:30:11 2008 length 9+: 2779 Mon Sep 1 12:30:11 2008 largest cycle: 19 relations Mon Sep 1 12:30:11 2008 matrix is 62353 x 62716 (16.4 MB) with weight 3807249 (60.71/col) Mon Sep 1 12:30:11 2008 sparse part has weight 3807249 (60.71/col) Mon Sep 1 12:30:12 2008 filtering completed in 3 passes Mon Sep 1 12:30:12 2008 matrix is 58563 x 58627 (15.4 MB) with weight 3568812 (60.87/col) Mon Sep 1 12:30:12 2008 sparse part has weight 3568812 (60.87/col) Mon Sep 1 12:30:12 2008 saving the first 48 matrix rows for later Mon Sep 1 12:30:12 2008 matrix is 58515 x 58627 (10.2 MB) with weight 2824552 (48.18/col) Mon Sep 1 12:30:12 2008 sparse part has weight 2093163 (35.70/col) Mon Sep 1 12:30:12 2008 matrix includes 64 packed rows Mon Sep 1 12:30:12 2008 using block size 23450 for processor cache size 1024 kB Mon Sep 1 12:30:13 2008 commencing Lanczos iteration Mon Sep 1 12:30:13 2008 memory use: 9.0 MB Mon Sep 1 12:30:39 2008 lanczos halted after 927 iterations (dim = 58513) Mon Sep 1 12:30:40 2008 recovered 17 nontrivial dependencies Mon Sep 1 12:30:40 2008 prp30 factor: 518359647652198152916575830119 Mon Sep 1 12:30:40 2008 prp61 factor: 2798321461530763710270557913472221025759214843794041462439153 Mon Sep 1 12:30:40 2008 elapsed time 01:41:11
(25·10¹⁰¹-61)/9 = 2(7)₁₀₀1_<102> = 13 · 317 · 517601989 · C90
C90 = P40 · P51
P40 = 1220440232504536752439016607144455724019_<40>
P51 = 106704425575836651096236897680730256801192448458461_<51>

Number: 27771_101 N=130226373959037120408897782242685193121360604141675290599021813285783982746449324201474759 ( 90 digits) SNFS difficulty: 102 digits. Divisors found: r1=1220440232504536752439016607144455724019 r2=106704425575836651096236897680730256801192448458461 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.944). Factorization parameters were as follows: n: 130226373959037120408897782242685193121360604141675290599021813285783982746449324201474759 Y1: 1 Y0: -100000000000000000000 c5: 250 c0: -61 skew: 0.75 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [225000, 285001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 42339 x 42554 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 0.30 hours.
(25·10¹⁹⁰-61)/9 = 2(7)₁₈₉1_<191> = 3 · 619 · 2858827 · 3617101 · 220477529829865223482993_<24> · 26459747372041207956272582179_<29> · C123
C123 = P37 · P86
P37 = 2976504347692375718574208936493265731_<37>
P86 = 83306815908902703939279567118759249527571709871356299315811741626793814308282721962477_<86>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2641304095 Step 1 took 5033ms Step 2 took 2858ms ********** Factor found in step 2: 2976504347692375718574208936493265731 Found probable prime factor of 37 digits: 2976504347692375718574208936493265731 Probable prime cofactor 83306815908902703939279567118759249527571709871356299315811741626793814308282721962477 has 86 digits
(25·10¹⁴⁵-61)/9 = 2(7)₁₄₄1_<146> = 3 · 7² · C144
C144 = P40 · P47 · P57
P40 = 9828296418549422058299450666557398619289_<40>
P47 = 87046340760163089105257888142997578027021705923_<47>
P57 = 220877459896081835011433334820685258323697425657910538619_<57>

Number: 27771_145 N=188964474678760393046107331821617535903250188964474678760393046107331821617535903250188964474678760393046107331821617535903250188964474678760393 ( 144 digits) SNFS difficulty: 146 digits. Divisors found: r1=9828296418549422058299450666557398619289 r2=87046340760163089105257888142997578027021705923 r3=220877459896081835011433334820685258323697425657910538619 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.731). Factorization parameters were as follows: n: 188964474678760393046107331821617535903250188964474678760393046107331821617535903250188964474678760393046107331821617535903250188964474678760393 Y1: 1 Y0: -100000000000000000000000000000 c5: 25 c0: -61 skew: 1.2 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved rational special-q in [750000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 224466 x 224712 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 5.00 hours.
(25·10¹³⁶-61)/9 = 2(7)₁₃₅1_<137> = 3 · C136
C136 = P40 · P97
P40 = 1901077818633176986641273760618004825731_<40>
P97 = 4870531426176132915928552436849317829157610124238343115163233836263288860176292922476799468932947_<97>

Number: 27771_136 N=9259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257 ( 136 digits) SNFS difficulty: 137 digits. Divisors found: r1=1901077818633176986641273760618004825731 r2=4870531426176132915928552436849317829157610124238343115163233836263288860176292922476799468932947 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.291). Factorization parameters were as follows: n: 9259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257 Y1: 1 Y0: -1000000000000000000000000000 c5: 250 c0: -61 skew: 0.75 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 154199 x 154447 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.10 hours.
(25·10¹⁵⁹-61)/9 = 2(7)₁₅₈1_<160> = 23 · 29 · 1448387 · 439692763 · 961430228377_<12> · C130
C130 = P35 · P96
P35 = 40938435274311943365251489605994903_<35>
P96 = 166145551502820974033100434453141488073658394935290823556214125540250731272635492119584942449183_<96>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=232563863 Step 1 took 4581ms Step 2 took 3756ms ********** Factor found in step 2: 40938435274311943365251489605994903 Found probable prime factor of 35 digits: 40938435274311943365251489605994903 Probable prime cofactor 166145551502820974033100434453141488073658394935290823556214125540250731272635492119584942449183 has 96 digits
(25·10¹⁶³-61)/9 = 2(7)₁₆₂1_<164> = 3 · 7 · 17 · 739 · 11492161 · 4402226051_<10> · C142
C142 = P33 · P109
P33 = 343669074489795639277832878263307_<33>
P109 = 6055783638574069034440712866051481024164387943862544584024154281615135516630551624273818820529570512643159301_<109>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1462551368 Step 1 took 5520ms Step 2 took 4013ms ********** Factor found in step 2: 343669074489795639277832878263307 Found probable prime factor of 33 digits: 343669074489795639277832878263307 Probable prime cofactor 6055783638574069034440712866051481024164387943862544584024154281615135516630551624273818820529570512643159301 has 109 digits
10¹⁹³-9 = (9)₁₉₂1_<193> = 31 · 71 · 397 · 31039 · 7333825763352817867_<19> · C164
C164 = P66 · P99
P66 = 114623516402068263048374107148074526153902078826891749923032115067_<66>
P99 = 438608874285502256844751510885066987832289149361752461518587566928513572528389208388687896598390093_<99>

# the Labor day weekend (idle computers) motivated me to finish the 99991 series. # 1 day on 20cpu + 7 hrs Lanczos # Number: 99991_193 N=50274891495756964747055055496890986637122321939508209584006709525221053605515373965266365474014162871727873923935469195773083682555289322275596819198059208928831231 ( 164 digits) SNFS difficulty: 193 digits. Divisors found: r1=114623516402068263048374107148074526153902078826891749923032115067 r2=438608874285502256844751510885066987832289149361752461518587566928513572528389208388687896598390093 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 50274891495756964747055055496890986637122321939508209584006709525221053605515373965266365474014162871727873923935469195773083682555289322275596819198059208928831231 Y1: 1 Y0: -100000000000000000000000000000000000000 c5: 1000 c0: -9 skew: 0.39 type: snfs rlim: 15000000 alim: 15000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 #qintsize: 100000 Factor base limits: 15000000/15000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved rational special-q in [7500000, 15100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 63000000 relations (had to throw away 10000000) => 53000000 Max relations in full relation-set: Initial matrix: Pruned matrix : 1729622 x 1729870 Total sieving time: 380.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 7.30 hours. Time per square root: 0.40 hours * (4 sqrts) Prototype def-par.txt line would be: snfs,193,5,0,0,0,0,0,0,0,0,15000000,15000000,29,29,58,58,2.5,2.5,100000 total time: 389.00 hours.
Sep 2, 2008: Factorizations of 277...771 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Sep 1, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
(68·10¹⁹²+13)/9 = 7(5)₁₉₁7_<193> = 3 · C193
C193 = P92 · P102
P92 = 10084827411252959360121233502972739996691984935274651940807752390233804581909806438612395447_<92>
P102 = 249733427833209956994171060959372869772921006108776325921841891154070929004420634528685716659200605377_<102>

Number: n N=2518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519 ( 193 digits) SNFS difficulty: 194 digits. Divisors found: Mon Sep 01 20:42:16 2008 prp92 factor: 10084827411252959360121233502972739996691984935274651940807752390233804581909806438612395447 Mon Sep 01 20:42:16 2008 prp102 factor: 249733427833209956994171060959372869772921006108776325921841891154070929004420634528685716659200605377 Mon Sep 01 20:42:17 2008 elapsed time 06:18:29 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 160.26 hours. Scaled time: 327.72 units (timescale=2.045). Factorization parameters were as follows: name: KA_7_5_191_7 n: 2518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519 type: snfs skew: 0.57 deg: 5 c5: 425 c0: 26 m: 200000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 12500001) Primes: RFBsize:633578, AFBsize:634283, largePrimes:11118249 encountered Relations: rels:11173345, finalFF:1300777 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 159.88 hours. Total relation processing time: 0.38 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,194,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000 total time: 160.26 hours. --------- CPU info (if available) ----------
Sep 1, 2008 (3rd): By suberi / GMP-ECM 6.2.1
4·10¹⁶⁷+3 = 4(0)₁₆₆3_<168> = 31 · 28775130387762169_<17> · 6041416682842093129_<19> · C131
C131 = P40 · P91
P40 = 9040172761574724472563661611963885082577_<40>
P91 = 8210421944564469678826128815336450569971653908303104793893829949559207978039441352980000269_<91>

Run 691 out of 904: Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4208089882 Step 1 took 18313ms Step 2 took 9062ms ********** Factor found in step 2: 9040172761574724472563661611963885082577 Found probable prime factor of 40 digits: 9040172761574724472563661611963885082577 Probable prime cofactor 8210421944564469678826128815336450569971653908303104793893829949559207978039441352980000269 has 91 digits
Sep 1, 2008 (2nd): By Sinkiti Sibata / GGNFS
(8·10¹⁶⁸-11)/3 = 2(6)₁₆₇3_<169> = 10147737487_<11> · 16342775944014823_<17> · 7182282825305090787823969_<25> · C118
C118 = P52 · P66
P52 = 8673076109373383322045834079530356383323130570903067_<52>
P66 = 258129726574229822024593324520497107330628067659816506194390087581_<66>

Number: 26663_168 N=2238778764670036419303891122295571160842294590325316161112993170253842339716470732568621665558861692124847724391510927 ( 118 digits) Divisors found: r1=8673076109373383322045834079530356383323130570903067 (pp52) r2=258129726574229822024593324520497107330628067659816506194390087581 (pp66) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 82.55 hours. Scaled time: 38.96 units (timescale=0.472). Factorization parameters were as follows: name: 26663_168 n: 2238778764670036419303891122295571160842294590325316161112993170253842339716470732568621665558861692124847724391510927 skew: 87948.71 # norm 6.50e+15 c5: 3300 c4: -2150396930 c3: -27162499434620 c2: 11425700944262902017 c1: -153744611732049114131170 c0: -9212687014339136827415685337 # alpha -5.65 Y1: 3149785904737 Y0: -58385163583490247768414 # Murphy_E 4.08e-10 # M 75257000721508686292250693276166591660463930381830897805141574721611218468907349199283468006029506246273595166527328 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3810001) Primes: RFBsize:315948, AFBsize:315291, largePrimes:7527907 encountered Relations: rels:7516576, finalFF:709664 Max relations in full relation-set: 28 Initial matrix: 631318 x 709664 with sparse part having weight 55983557. Pruned matrix : 563555 x 566775 with weight 38359589. Polynomial selection time: 3.98 hours. Total sieving time: 63.38 hours. Total relation processing time: 0.72 hours. Matrix solve time: 14.05 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 82.55 hours. --------- CPU info (if available) ----------
Sep 1, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
3·10¹⁹²+1 = 3(0)₁₉₁1_<193> = 151 · C191
C191 = P48 · P71 · P72
P48 = 791442937966190685229637395742267041720820331589_<48>
P71 = 95011290548333356448178869786693410025075222062601524884381341878748749_<71>
P72 = 264210140483694895177251228728197166603387493603667452462313902636578791_<72>

Number: n N=19867549668874172185430463576158940397350993377483443708609271523178807947019867549668874172185430463576158940397350993377483443708609271523178807947019867549668874172185430463576158940397351 ( 191 digits) SNFS difficulty: 192 digits. Divisors found: Mon Sep 01 05:42:01 2008 prp48 factor: 791442937966190685229637395742267041720820331589 Mon Sep 01 05:42:01 2008 prp71 factor: 95011290548333356448178869786693410025075222062601524884381341878748749 Mon Sep 01 05:42:01 2008 prp72 factor: 264210140483694895177251228728197166603387493603667452462313902636578791 Mon Sep 01 05:42:01 2008 elapsed time 14:25:58 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 179.21 hours. Scaled time: 103.23 units (timescale=0.576). Factorization parameters were as follows: name: KA_3_0_191_1 n: 19867549668874172185430463576158940397350993377483443708609271523178807947019867549668874172185430463576158940397350993377483443708609271523178807947019867549668874172185430463576158940397351 type: snfs skew: 0.32 deg: 5 c5: 300 c0: 1 m: 100000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 14600001) Primes: RFBsize:633578, AFBsize:633363, largePrimes:11219211 encountered Relations: rels:11288392, finalFF:1313629 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 178.52 hours. Total relation processing time: 0.69 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,192,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000 total time: 179.21 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(8·10¹⁶⁵-11)/3 = 2(6)₁₆₄3_<166> = 1553 · 1190821 · C157
C157 = P33 · P57 · P67
P33 = 892943739843446667190715388245117_<33>
P57 = 392527646794798165127898569877809173341146158091463648461_<57>
P67 = 4113925703226251734064538448395755445011135196921757070023860615523_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 1441951960246082360764268417591729632910128417810088023130093284906523100277052882542186121907079037104833973273686096487538783909255696393232530195633467051 (157 digits) Using B1=2610000, B2=3568033570, polynomial Dickson(6), sigma=2799032758 Step 1 took 31469ms Step 2 took 12031ms ********** Factor found in step 2: 892943739843446667190715388245117 Found probable prime factor of 33 digits: 892943739843446667190715388245117 Composite cofactor 1614829575376035798972495961314039512335349400212716937196026101586056506417632008295855000696288207767290358854258751660103 has 124 digits Number: n N=1614829575376035798972495961314039512335349400212716937196026101586056506417632008295855000696288207767290358854258751660103 ( 124 digits) SNFS difficulty: 166 digits. Divisors found: Mon Sep 1 12:19:26 2008 prp57 factor: 392527646794798165127898569877809173341146158091463648461 Mon Sep 1 12:19:26 2008 prp67 factor: 4113925703226251734064538448395755445011135196921757070023860615523 Mon Sep 1 12:19:26 2008 elapsed time 01:21:42 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 12.27 hours. Scaled time: 10.29 units (timescale=0.839). Factorization parameters were as follows: name: KA_2_6_164_3 n: 1614829575376035798972495961314039512335349400212716937196026101586056506417632008295855000696288207767290358854258751660103 type: snfs skew: 2.13 deg: 5 c5: 1 c0: -44 m: 2000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 1400001) Primes: RFBsize:348513, AFBsize:347567, largePrimes:11994991 encountered Relations: rels:11300458, finalFF:810381 Max relations in full relation-set: 28 Initial matrix: 696143 x 810381 with sparse part having weight 59295126. Pruned matrix : Total sieving time: 12.01 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,52,52,2.5,2.5,100000 total time: 12.27 hours. --------- CPU info (if available) ----------

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