News and updates, October 2008

Since June 16, 2000

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News and updates, October 2008	2008-11-01(Sat) 01:14

September October November

News and updates, October 2008

Oct 31, 2008 (4th): By Jo Yeong Uk / GMP-ECM
(8·10²²⁵+1)/9 = (8)₂₂₄9_<225> = 7² · 43 · 8228029 · 24020107 · 14857882856581287529_<20> · 3258352894056569900803_<22> · 5000236399743388811370403_<25> · 320247123017961326534531395337587_<33> · C110
C110 = P32 · P78
P32 = 50532169039234753564210908503389_<32>
P78 = 544895758886235998604351913304690160474307653093573978373738315850473064776483_<78>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 27534764596801380073444030684382856370143345530480298090729657481328086634802851751249267898435076081333000887 (110 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3291085960 Step 1 took 3256ms Step 2 took 2058ms ********** Factor found in step 2: 50532169039234753564210908503389 Found probable prime factor of 32 digits: 50532169039234753564210908503389 Probable prime cofactor 544895758886235998604351913304690160474307653093573978373738315850473064776483 has 78 digits
Oct 31, 2008 (3rd): Factorizations of 899...99, Factorizations of 88...889, Factorizations of 533...33 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Oct 31, 2008 (2nd): By matsui / GMP-ECM
(7·10¹⁹⁰-61)/9 = (7)₁₈₉1_<190> = 23² · C188
C188 = P31 · C157
P31 = 2688905664266052337484729565917_<31>
C157 = [5467946951863048473626887020863645023766677773365149383086724143142152008359250701849934634922233312157204345407319371930536542980234660828386982636456713847_<157>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 14702793530770846460827557235874816215080865364419239655534551564797311489182944759504305818105440033606385213190506196177273681999579920184835118672547784078975005250997689561016593152699 =2688905664266052337484729565917* 5467946951863048473626887020863645023766677773365149383086724143142152008359250701849934634922233312157204345407319371930536542980234660828386982636456713847
Oct 31, 2008: By Serge Batalov / GMP-ECM 6.2.1
6·10¹⁶⁸-1 = 5(9)₁₆₈_<169> = 4799 · 2017177 · 4202161651613_<13> · 10503821362051_<14> · C134
C134 = P34 · P100
P34 = 6720571008125216270124997913782507_<34>
P100 = 2089441596792376491620750374295583364339925722989928143182632024080598639760461288200867439741680893_<100>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3109165435 Step 1 took 12077ms Step 2 took 9621ms ********** Factor found in step 2: 6720571008125216270124997913782507 Found probable prime factor of 34 digits: 6720571008125216270124997913782507 Probable prime cofactor 2089441596792376491620750374295583364339925722989928143182632024080598639760461288200867439741680893 has 100 digits
Oct 30, 2008 (7th): By Jo Yeong Uk / GGNFS
(26·10¹⁵⁹+1)/9 = 2(8)₁₅₈9_<160> = 3 · 19 · 2897 · 47530117865256101258279_<23> · C132
C132 = P53 · P79
P53 = 63372486529335247949657526960405508372415068972242089_<53>
P79 = 5808150331783600012048251978464509513167533255570748146548143492258533560391311_<79>

Number: 28889_159 N=368076928661310242796685223052351194474178929325136743683341593384751145819507087501554444508127876795316137199592189505603864088679 ( 132 digits) SNFS difficulty: 161 digits. Divisors found: r1=63372486529335247949657526960405508372415068972242089 (pp53) r2=5808150331783600012048251978464509513167533255570748146548143492258533560391311 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.36 hours. Scaled time: 57.78 units (timescale=2.372). Factorization parameters were as follows: n: 368076928661310242796685223052351194474178929325136743683341593384751145819507087501554444508127876795316137199592189505603864088679 m: 100000000000000000000000000000000 deg: 5 c5: 13 c0: 5 skew: 0.83 type: snfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1500000, 3100001) Primes: RFBsize:216816, AFBsize:217321, largePrimes:9125240 encountered Relations: rels:9381690, finalFF:582288 Max relations in full relation-set: 28 Initial matrix: 434202 x 582288 with sparse part having weight 65760285. Pruned matrix : 383610 x 385845 with weight 43352181. Total sieving time: 23.04 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.15 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,51,51,2.5,2.5,100000 total time: 24.36 hours. --------- CPU info (if available) ----------
Oct 30, 2008 (6th): By matsui / GMP-ECM
5·10¹⁷⁷-3 = 4(9)₁₇₆7_<178> = 29 · 71 · 647 · 11597 · 32257 · 11155845410727571_<17> · C147
C147 = P31 · P117
P31 = 4116890636843482409367503214379_<31>
P117 = 218457987170696445427188464234004646047913220813017808820800049784287693771198669963461651749956944384214219693687749_<117>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 899367641926713799141991352700853887454818241078024680408131394423372550185069563049583638222675661519098771870475781201357007143856873533832942871 =4116890636843482409367503214379* 218457987170696445427188464234004646047913220813017808820800049784287693771198669963461651749956944384214219693687749
Oct 30, 2008 (5th): By Wataru Sakai / GGNFS
(4·10¹⁸⁷+17)/3 = 1(3)₁₈₆9_<188> = 227 · C185
C185 = P62 · P123
P62 = 68965476147814636902426765565516035764069141667886618893443389_<62>
P123 = 851689200583090792929308232980079439143509638878237547282829962931049006405070726814731704503101259053470178580894789150813_<123>

Number: 13339_187 N=58737151248164464023494860499265785609397944199706314243759177679882525697503671071953010279001468428781204111600587371512481644640234948604992657856093979441997063142437591776798825257 ( 185 digits) SNFS difficulty: 187 digits. Divisors found: r1=68965476147814636902426765565516035764069141667886618893443389 (pp62) r2=851689200583090792929308232980079439143509638878237547282829962931049006405070726814731704503101259053470178580894789150813 (pp123) Version: GGNFS-0.77.1-20060722-nocona Total time: 1042.92 hours. Scaled time: 2087.93 units (timescale=2.002). Factorization parameters were as follows: n: 58737151248164464023494860499265785609397944199706314243759177679882525697503671071953010279001468428781204111600587371512481644640234948604992657856093979441997063142437591776798825257 m: 20000000000000000000000000000000000000 c5: 25 c0: 34 skew: 1.06 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, 18500001) Primes: RFBsize:501962, AFBsize:503361, largePrimes:7202596 encountered Relations: rels:7831073, finalFF:1219969 Max relations in full relation-set: 32 Initial matrix: 1005387 x 1219969 with sparse part having weight 139107803. Pruned matrix : 846533 x 851623 with weight 122408733. Total sieving time: 1030.97 hours. Total relation processing time: 0.16 hours. Matrix solve time: 11.53 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1042.92 hours. --------- CPU info (if available) ----------
2·10¹⁹⁰+9 = 2(0)₁₈₉9_<191> = 11 · 2267 · C186
C186 = P43 · P144
P43 = 3598257171209322387124035246065550912037121_<43>
P144 = 222891543042545298957116640948488621345212099759851442244790596744882493938600415976943482712976628381818095574564453234501990920912116689990817_<144>

Number: 20009_190 N=802021093154749969924209006696876127842162248867145205918915667482054778040662469422945823475157396639531619681597626017564261940089024341340177246661587199743353250190480009624253117857 ( 186 digits) SNFS difficulty: 190 digits. Divisors found: r1=3598257171209322387124035246065550912037121 (pp43) r2=222891543042545298957116640948488621345212099759851442244790596744882493938600415976943482712976628381818095574564453234501990920912116689990817 (pp144) Version: GGNFS-0.77.1-20060722-nocona Total time: 868.84 hours. Scaled time: 1750.70 units (timescale=2.015). Factorization parameters were as follows: n: 802021093154749969924209006696876127842162248867145205918915667482054778040662469422945823475157396639531619681597626017564261940089024341340177246661587199743353250190480009624253117857 m: 100000000000000000000000000000000000000 c5: 2 c0: 9 skew: 1.35 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, 15700001) Primes: RFBsize:501962, AFBsize:502156, largePrimes:6947303 encountered Relations: rels:7503487, finalFF:1184004 Max relations in full relation-set: 32 Initial matrix: 1004183 x 1184004 with sparse part having weight 117312846. Pruned matrix : 866921 x 872005 with weight 96822749. Total sieving time: 860.03 hours. Total relation processing time: 0.13 hours. Matrix solve time: 8.42 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 868.84 hours. --------- CPU info (if available) ----------
Oct 30, 2008 (4th): By Sinkiti Sibata / GGNFS
(26·10¹⁷⁹-17)/9 = 2(8)₁₇₈7_<180> = 577 · 2011439 · 27778159 · 98699849 · 1653903478537_<13> · C143
C143 = P49 · P94
P49 = 5568917968267078138899173830351221759908557861721_<49>
P94 = 9857056137728383106952550168939175812236563857884385884810595206543334545507467963339269590847_<94>

Number: 28887_179 N=54893137039612879596184897392530603975543294236018838293195344236899356693945768816826702494078297548438412058402012173090931238202908873267687 ( 143 digits) SNFS difficulty: 181 digits. Divisors found: r1=5568917968267078138899173830351221759908557861721 (pp49) r2=9857056137728383106952550168939175812236563857884385884810595206543334545507467963339269590847 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 548.54 hours. Scaled time: 553.48 units (timescale=1.009). Factorization parameters were as follows: name: 28887_179 n: 54893137039612879596184897392530603975543294236018838293195344236899356693945768816826702494078297548438412058402012173090931238202908873267687 m: 1000000000000000000000000000000000000 c5: 13 c0: -85 skew: 1.46 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:501546, largePrimes:6747299 encountered Relations: rels:7249285, finalFF:1172045 Max relations in full relation-set: 28 Initial matrix: 1003573 x 1172045 with sparse part having weight 87126144. Pruned matrix : 865254 x 870335 with weight 67813684. Total sieving time: 540.27 hours. Total relation processing time: 0.16 hours. Matrix solve time: 7.96 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 548.54 hours. --------- CPU info (if available) ----------
Oct 30, 2008 (3rd): By Serge Batalov / GMP-ECM 6.2.1
(28·10¹⁹⁰+17)/9 = 3(1)₁₈₉3_<191> = 3 · 53 · 2324869405289_<13> · C176
C176 = P30 · P147
P30 = 189344953281801099289844032523_<30>
P147 = 444494202776565721977201120940522199860059753010149064714369456018500463217163672442226792310654799092430889759491584962078996666281704027405100381_<147>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=732919934 Step 1 took 22026ms Step 2 took 16557ms ********** Factor found in step 2: 189344953281801099289844032523 Found probable prime factor of 30 digits: 189344953281801099289844032523 Probable prime cofactor 444494202776565721977201120940522199860059753010149064714369456018500463217163672442226792310654799092430889759491584962078996666281704027405100381 has 147 digits
(10¹⁹⁵-7)/3 = (3)₁₉₄1_<195> = 181 · 269 · 8124997885001_<13> · 74717295626884435829_<20> · 326293390169303271462521_<24> · C134
C134 = P38 · P97
P38 = 29260605544995388086468822651950635609_<38>
P97 = 1181168628435656755332100955486268041776709445145430749775935359970677708462298380422465750774959_<97>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3346586215 Step 1 took 11984ms Step 2 took 11253ms ********** Factor found in step 2: 29260605544995388086468822651950635609 Found probable prime factor of 38 digits: 29260605544995388086468822651950635609 Probable prime cofactor 1181168628435656755332100955486268041776709445145430749775935359970677708462298380422465750774959 has 97 digits
(2·10²⁰⁰-17)/3 = (6)₁₉₉1_<200> = 273765949 · 189134477377_<12> · C181
C181 = P33 · C148
P33 = 522353457577022509514639952407329_<33>
C148 = [2464870651612724961793238428217840495900981675124347834528712637053912675622666484609096621861583916321050830926456254813740600462323677340559278633_<148>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3352591208 Step 1 took 22005ms Step 2 took 16481ms ********** Factor found in step 2: 522353457577022509514639952407329 Found probable prime factor of 33 digits: 522353457577022509514639952407329 Composite cofactor 2464870651612724961793238428217840495900981675124347834528712637053912675622666484609096621861583916321050830926456254813740600462323677340559278633 has 148 digits
Oct 30, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve
(28·10¹⁷¹+17)/9 = 3(1)₁₇₀3_<172> = 11 · 98671529155359905029_<20> · C151
C151 = P30 · P121
P30 = 568989076397229877436168709083_<30>
P121 = 5037639078551312735260150274259076408128833763875038399879050906215408406462219863760359907480071781960561895317179882669_<121>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3387344901 Step 1 took 16665ms Step 2 took 13201ms ********** Factor found in step 2: 568989076397229877436168709083 Found probable prime factor of 30 digits: 568989076397229877436168709083 Probable prime cofactor 5037639078551312735260150274259076408128833763875038399879050906215408406462219863760359907480071781960561895317179882669 has 121 digits
(28·10¹⁸¹+17)/9 = 3(1)₁₈₀3_<182> = 3 · 11 · 59 · 1013 · 14321 · 25444583528418949967_<20> · C152
C152 = P33 · P35 · P35 · P50
P33 = 487786121583417478031377245240619_<33>
P35 = 23713943396205054814260936625106267_<35>
P35 = 74651041133013577781884111541307929_<35>
P50 = 50130535731281299048808262966371781007594617903457_<50>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=80191738 Step 1 took 14481ms Step 2 took 12853ms ********** Factor found in step 2: 23713943396205054814260936625106267 Found probable prime factor of 35 digits: 23713943396205054814260936625106267 Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=392881417 Step 1 took 15425ms Step 2 took 12941ms ********** Factor found in step 2: 487786121583417478031377245240619 Found probable prime factor of 33 digits: 487786121583417478031377245240619 Wed Oct 29 19:41:35 2008 Msieve v. 1.36 Wed Oct 29 19:41:35 2008 random seeds: 6270e78e 23782657 Wed Oct 29 19:41:35 2008 factoring 3742296684895887151566152410872755963617683239627020475047963724780736160593630610553 (85 digits) Wed Oct 29 19:41:35 2008 no P-1/P+1/ECM available, skipping Wed Oct 29 19:41:35 2008 commencing quadratic sieve (85-digit input) Wed Oct 29 19:41:35 2008 using multiplier of 3 Wed Oct 29 19:41:35 2008 using 64kb Opteron sieve core Wed Oct 29 19:41:35 2008 sieve interval: 6 blocks of size 65536 Wed Oct 29 19:41:35 2008 processing polynomials in batches of 17 Wed Oct 29 19:41:35 2008 using a sieve bound of 1426129 (54330 primes) Wed Oct 29 19:41:35 2008 using large prime bound of 116942578 (26 bits) Wed Oct 29 19:41:35 2008 using double large prime bound of 332928269126164 (41-49 bits) Wed Oct 29 19:41:35 2008 using trial factoring cutoff of 49 bits Wed Oct 29 19:41:35 2008 polynomial 'A' values have 11 factors Wed Oct 29 20:07:14 2008 54749 relations (16077 full + 38672 combined from 569767 partial), need 54426 Wed Oct 29 20:07:14 2008 begin with 585844 relations Wed Oct 29 20:07:14 2008 reduce to 128305 relations in 9 passes Wed Oct 29 20:07:14 2008 attempting to read 128305 relations Wed Oct 29 20:07:15 2008 recovered 128305 relations Wed Oct 29 20:07:15 2008 recovered 107033 polynomials Wed Oct 29 20:07:15 2008 attempting to build 54749 cycles Wed Oct 29 20:07:15 2008 found 54749 cycles in 6 passes Wed Oct 29 20:07:15 2008 distribution of cycle lengths: Wed Oct 29 20:07:15 2008 length 1 : 16077 Wed Oct 29 20:07:15 2008 length 2 : 11191 Wed Oct 29 20:07:15 2008 length 3 : 9634 Wed Oct 29 20:07:15 2008 length 4 : 7021 Wed Oct 29 20:07:15 2008 length 5 : 4652 Wed Oct 29 20:07:15 2008 length 6 : 2817 Wed Oct 29 20:07:15 2008 length 7 : 1583 Wed Oct 29 20:07:15 2008 length 9+: 1774 Wed Oct 29 20:07:15 2008 largest cycle: 17 relations Wed Oct 29 20:07:15 2008 matrix is 54330 x 54749 (12.7 MB) with weight 2892970 (52.84/col) Wed Oct 29 20:07:16 2008 sparse part has weight 2892970 (52.84/col) Wed Oct 29 20:07:16 2008 filtering completed in 4 passes Wed Oct 29 20:07:16 2008 matrix is 48985 x 49049 (11.5 MB) with weight 2610556 (53.22/col) Wed Oct 29 20:07:16 2008 sparse part has weight 2610556 (53.22/col) Wed Oct 29 20:07:16 2008 saving the first 48 matrix rows for later Wed Oct 29 20:07:16 2008 matrix is 48937 x 49049 (6.8 MB) with weight 1947250 (39.70/col) Wed Oct 29 20:07:16 2008 sparse part has weight 1294865 (26.40/col) Wed Oct 29 20:07:16 2008 matrix includes 64 packed rows Wed Oct 29 20:07:16 2008 using block size 19619 for processor cache size 1024 kB Wed Oct 29 20:07:17 2008 commencing Lanczos iteration Wed Oct 29 20:07:17 2008 memory use: 6.5 MB Wed Oct 29 20:07:27 2008 lanczos halted after 775 iterations (dim = 48935) Wed Oct 29 20:07:27 2008 recovered 18 nontrivial dependencies Wed Oct 29 20:07:28 2008 prp35 factor: 74651041133013577781884111541307929 Wed Oct 29 20:07:28 2008 prp50 factor: 50130535731281299048808262966371781007594617903457 Wed Oct 29 20:07:28 2008 elapsed time 00:25:53
Oct 30, 2008: By Robert Backstrom / GGNFS, Msieve
(14·10²⁰⁰-23)/9 = 1(5)₁₉₉3_<201> = 3² · C200
C200 = P52 · P65 · P84
P52 = 3033496037622857307870842268067364837548775059726949_<52>
P65 = 12252998283212933037938412743529586470315179061764978083771647637_<65>
P84 = 465004560406171829084976708697089017173510355031372707962704278582642195060480525009_<84>

Number: n N=17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617 ( 200 digits) SNFS difficulty: 201 digits. Divisors found: Thu Oct 30 08:57:29 2008 prp52 factor: 3033496037622857307870842268067364837548775059726949 Thu Oct 30 08:57:29 2008 prp65 factor: 12252998283212933037938412743529586470315179061764978083771647637 Thu Oct 30 08:57:29 2008 prp84 factor: 465004560406171829084976708697089017173510355031372707962704278582642195060480525009 Thu Oct 30 08:57:30 2008 elapsed time 26:37:36 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 83.40 hours. Scaled time: 170.54 units (timescale=2.045). Factorization parameters were as follows: name: KA_1_5_199_3 n: 17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617 type: snfs skew: 1.10 deg: 5 c5: 14 c0: -23 m: 10000000000000000000000000000000000000000 rlim: 9600000 alim: 9600000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9600000/9600000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 13300001) Primes: RFBsize:639851, AFBsize:640823, largePrimes:35380027 encountered Relations: rels:26823768, finalFF:263116 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 81.43 hours. Total relation processing time: 1.97 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,9600000,9600000,29,29,58,58,2.5,2.5,100000 total time: 83.40 hours. --------- CPU info (if available) ----------
Oct 29, 2008 (5th): By Jo Yeong Uk / GGNFS
(26·10¹⁸³-17)/9 = 2(8)₁₈₂7_<184> = C184
C184 = P90 · P94
P90 = 571191356051002418872131436996090915923457383067405912592086693050165007850808002169422749_<90>
P94 = 5057655124302924926840820612415887462963794902802707794326442625485636705143562806846593819363_<94>

Number: 28887_183 N=2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 ( 184 digits) SNFS difficulty: 186 digits. Divisors found: r1=571191356051002418872131436996090915923457383067405912592086693050165007850808002169422749 (pp90) r2=5057655124302924926840820612415887462963794902802707794326442625485636705143562806846593819363 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 296.85 hours. Scaled time: 704.43 units (timescale=2.373). Factorization parameters were as follows: n: 2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 m: 10000000000000000000000000000000000000 c5: 13 c0: -850 skew: 2.31 type: snfs Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 51/51 Sieved algebraic special-q in [6000000, 11300001) Primes: RFBsize:788060, AFBsize:788454, largePrimes:12608406 encountered Relations: rels:13159127, finalFF:1768281 Max relations in full relation-set: 28 Initial matrix: 1576580 x 1768281 with sparse part having weight 117863959. Pruned matrix : 1406297 x 1414243 with weight 86507487. Total sieving time: 280.09 hours. Total relation processing time: 0.24 hours. Matrix solve time: 16.38 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,51,51,2.6,2.6,100000 total time: 296.85 hours. --------- CPU info (if available) ----------
Oct 29, 2008 (4th): By Justin Card / GGNFS for sieving, msieve for linear algebra
(10¹⁷⁹+17)/9 = (1)₁₇₈3_<179> = 19 · 1439 · 11791673 · 350355007 · 41417257495760776071419_<23> · C136
C136 = P56 · P80
P56 = 64359895320324138046847817077342166028615808217898933063_<56>
P80 = 36903084954015880064848993395715905165599046095682487205693219081526100375034279_<80>

Tue Oct 28 18:11:06 2008 Msieve v. 1.38 Tue Oct 28 18:11:06 2008 random seeds: d81d15f7 8c4cc99f Tue Oct 28 18:11:06 2008 factoring 2375078684637490748471009799403460903791906373419845536550774278476483193823770338103403225837841896931094354587473006789445556151466577 (136 digits) Tue Oct 28 18:11:07 2008 no P-1/P+1/ECM available, skipping Tue Oct 28 18:11:07 2008 commencing number field sieve (136-digit input) Tue Oct 28 18:11:07 2008 R0: -1000000000000000000000000000000000000 Tue Oct 28 18:11:07 2008 R1: 1 Tue Oct 28 18:11:07 2008 A0: 170 Tue Oct 28 18:11:07 2008 A1: 0 Tue Oct 28 18:11:07 2008 A2: 0 Tue Oct 28 18:11:07 2008 A3: 0 Tue Oct 28 18:11:07 2008 A4: 0 Tue Oct 28 18:11:07 2008 A5: 1 Tue Oct 28 18:11:07 2008 size score = 2.613876e-12, Murphy alpha = 0.851423, combined = 1.968017e-12 Tue Oct 28 18:11:07 2008 Tue Oct 28 18:11:07 2008 commencing relation filtering Tue Oct 28 18:11:07 2008 commencing duplicate removal, pass 1 Tue Oct 28 18:14:06 2008 error -9 reading relation 16302560 Tue Oct 28 18:14:58 2008 error -15 reading relation 21041764 Tue Oct 28 18:15:19 2008 found 1848518 hash collisions in 22933637 relations Tue Oct 28 18:16:47 2008 added 721562 free relations Tue Oct 28 18:16:47 2008 commencing duplicate removal, pass 2 Tue Oct 28 18:17:06 2008 found 1107318 duplicates and 22547881 unique relations Tue Oct 28 18:17:06 2008 memory use: 94.6 MB Tue Oct 28 18:17:06 2008 reading rational ideals above 18415616 Tue Oct 28 18:17:06 2008 reading algebraic ideals above 18415616 Tue Oct 28 18:17:06 2008 commencing singleton removal, pass 1 Tue Oct 28 18:21:41 2008 relations with 0 large ideals: 922249 Tue Oct 28 18:21:41 2008 relations with 1 large ideals: 4236483 Tue Oct 28 18:21:41 2008 relations with 2 large ideals: 7900596 Tue Oct 28 18:21:41 2008 relations with 3 large ideals: 6655370 Tue Oct 28 18:21:41 2008 relations with 4 large ideals: 2152524 Tue Oct 28 18:21:41 2008 relations with 5 large ideals: 17717 Tue Oct 28 18:21:41 2008 relations with 6 large ideals: 662941 Tue Oct 28 18:21:41 2008 relations with 7+ large ideals: 1 Tue Oct 28 18:21:41 2008 22547881 relations and about 18723100 large ideals Tue Oct 28 18:21:41 2008 commencing singleton removal, pass 2 Tue Oct 28 18:26:16 2008 found 6186686 singletons Tue Oct 28 18:26:16 2008 current dataset: 16361195 relations and about 11312019 large ideals Tue Oct 28 18:26:16 2008 commencing singleton removal, pass 3 Tue Oct 28 18:29:28 2008 found 1867860 singletons Tue Oct 28 18:29:28 2008 current dataset: 14493335 relations and about 9370319 large ideals Tue Oct 28 18:29:28 2008 commencing singleton removal, pass 4 Tue Oct 28 18:32:18 2008 found 423643 singletons Tue Oct 28 18:32:18 2008 current dataset: 14069692 relations and about 8941622 large ideals Tue Oct 28 18:32:18 2008 commencing singleton removal, final pass Tue Oct 28 18:35:28 2008 memory use: 218.4 MB Tue Oct 28 18:35:28 2008 commencing in-memory singleton removal Tue Oct 28 18:35:30 2008 begin with 14069692 relations and 9950674 unique ideals Tue Oct 28 18:35:54 2008 reduce to 12261335 relations and 8095900 ideals in 14 passes Tue Oct 28 18:35:54 2008 max relations containing the same ideal: 64 Tue Oct 28 18:35:57 2008 reading rational ideals above 720000 Tue Oct 28 18:35:57 2008 reading algebraic ideals above 720000 Tue Oct 28 18:35:57 2008 commencing singleton removal, final pass Tue Oct 28 18:39:45 2008 keeping 9433782 ideals with weight <= 20, new excess is 1020107 Tue Oct 28 18:39:55 2008 memory use: 348.3 MB Tue Oct 28 18:39:56 2008 commencing in-memory singleton removal Tue Oct 28 18:39:58 2008 begin with 12262644 relations and 9433782 unique ideals Tue Oct 28 18:40:25 2008 reduce to 12250914 relations and 9415970 ideals in 11 passes Tue Oct 28 18:40:25 2008 max relations containing the same ideal: 20 Tue Oct 28 18:40:37 2008 removing 2080308 relations and 1680308 ideals in 400000 cliques Tue Oct 28 18:40:38 2008 commencing in-memory singleton removal Tue Oct 28 18:40:39 2008 begin with 10170606 relations and 9415970 unique ideals Tue Oct 28 18:40:55 2008 reduce to 9954338 relations and 7510988 ideals in 8 passes Tue Oct 28 18:40:55 2008 max relations containing the same ideal: 20 Tue Oct 28 18:41:05 2008 removing 1568488 relations and 1168488 ideals in 400000 cliques Tue Oct 28 18:41:05 2008 commencing in-memory singleton removal Tue Oct 28 18:41:07 2008 begin with 8385850 relations and 7510988 unique ideals Tue Oct 28 18:41:18 2008 reduce to 8228753 relations and 6179332 ideals in 7 passes Tue Oct 28 18:41:18 2008 max relations containing the same ideal: 20 Tue Oct 28 18:41:25 2008 removing 1410938 relations and 1010938 ideals in 400000 cliques Tue Oct 28 18:41:26 2008 commencing in-memory singleton removal Tue Oct 28 18:41:27 2008 begin with 6817815 relations and 6179332 unique ideals Tue Oct 28 18:41:36 2008 reduce to 6663133 relations and 5006972 ideals in 7 passes Tue Oct 28 18:41:36 2008 max relations containing the same ideal: 19 Tue Oct 28 18:41:42 2008 removing 1327964 relations and 927964 ideals in 400000 cliques Tue Oct 28 18:41:42 2008 commencing in-memory singleton removal Tue Oct 28 18:41:43 2008 begin with 5335169 relations and 5006972 unique ideals Tue Oct 28 18:41:51 2008 reduce to 5164439 relations and 3899279 ideals in 9 passes Tue Oct 28 18:41:51 2008 max relations containing the same ideal: 19 Tue Oct 28 18:41:56 2008 removing 377053 relations and 295218 ideals in 81835 cliques Tue Oct 28 18:41:56 2008 commencing in-memory singleton removal Tue Oct 28 18:41:57 2008 begin with 4787386 relations and 3899279 unique ideals Tue Oct 28 18:42:02 2008 reduce to 4769762 relations and 3586176 ideals in 6 passes Tue Oct 28 18:42:02 2008 max relations containing the same ideal: 18 Tue Oct 28 18:42:07 2008 relations with 0 large ideals: 142358 Tue Oct 28 18:42:07 2008 relations with 1 large ideals: 686352 Tue Oct 28 18:42:07 2008 relations with 2 large ideals: 1396880 Tue Oct 28 18:42:07 2008 relations with 3 large ideals: 1417942 Tue Oct 28 18:42:07 2008 relations with 4 large ideals: 792619 Tue Oct 28 18:42:07 2008 relations with 5 large ideals: 262925 Tue Oct 28 18:42:07 2008 relations with 6 large ideals: 65802 Tue Oct 28 18:42:07 2008 relations with 7+ large ideals: 4884 Tue Oct 28 18:42:07 2008 commencing 2-way merge Tue Oct 28 18:42:12 2008 reduce to 3246628 relation sets and 2063042 unique ideals Tue Oct 28 18:42:12 2008 commencing full merge Tue Oct 28 18:42:58 2008 memory use: 188.1 MB Tue Oct 28 18:42:59 2008 found 1609067 cycles, need 1449242 Tue Oct 28 18:43:00 2008 weight of 1449242 cycles is about 101702624 (70.18/cycle) Tue Oct 28 18:43:00 2008 distribution of cycle lengths: Tue Oct 28 18:43:00 2008 1 relations: 183967 Tue Oct 28 18:43:00 2008 2 relations: 144810 Tue Oct 28 18:43:00 2008 3 relations: 147743 Tue Oct 28 18:43:00 2008 4 relations: 142868 Tue Oct 28 18:43:00 2008 5 relations: 138666 Tue Oct 28 18:43:00 2008 6 relations: 127732 Tue Oct 28 18:43:00 2008 7 relations: 116050 Tue Oct 28 18:43:00 2008 8 relations: 102946 Tue Oct 28 18:43:00 2008 9 relations: 90027 Tue Oct 28 18:43:00 2008 10+ relations: 254433 Tue Oct 28 18:43:00 2008 heaviest cycle: 17 relations Tue Oct 28 18:43:00 2008 commencing cycle optimization Tue Oct 28 18:43:04 2008 start with 8311173 relations Tue Oct 28 18:43:28 2008 pruned 344021 relations Tue Oct 28 18:43:28 2008 memory use: 259.1 MB Tue Oct 28 18:43:28 2008 distribution of cycle lengths: Tue Oct 28 18:43:28 2008 1 relations: 183967 Tue Oct 28 18:43:28 2008 2 relations: 150111 Tue Oct 28 18:43:28 2008 3 relations: 156291 Tue Oct 28 18:43:28 2008 4 relations: 150605 Tue Oct 28 18:43:28 2008 5 relations: 147049 Tue Oct 28 18:43:28 2008 6 relations: 134232 Tue Oct 28 18:43:28 2008 7 relations: 121130 Tue Oct 28 18:43:28 2008 8 relations: 105413 Tue Oct 28 18:43:28 2008 9 relations: 89711 Tue Oct 28 18:43:28 2008 10+ relations: 210733 Tue Oct 28 18:43:28 2008 heaviest cycle: 16 relations Tue Oct 28 18:43:30 2008 elapsed time 00:32:24 Tue Oct 28 18:49:39 2008 commencing linear algebra Tue Oct 28 18:49:39 2008 read 1449242 cycles Tue Oct 28 18:49:45 2008 cycles contain 4205356 unique relations Tue Oct 28 18:50:50 2008 read 4205356 relations Tue Oct 28 18:51:02 2008 using 32 quadratic characters above 268434108 Tue Oct 28 18:52:08 2008 building initial matrix Tue Oct 28 18:53:21 2008 memory use: 535.9 MB Tue Oct 28 18:53:22 2008 read 1449242 cycles Tue Oct 28 18:53:24 2008 matrix is 1448913 x 1449242 (426.1 MB) with weight 135761514 (93.68/col) Tue Oct 28 18:53:24 2008 sparse part has weight 95768962 (66.08/col) Tue Oct 28 18:54:31 2008 filtering completed in 3 passes Tue Oct 28 18:54:31 2008 matrix is 1445023 x 1445223 (425.4 MB) with weight 135504932 (93.76/col) Tue Oct 28 18:54:31 2008 sparse part has weight 95625280 (66.17/col) Tue Oct 28 18:54:54 2008 read 1445223 cycles Tue Oct 28 18:54:56 2008 matrix is 1445023 x 1445223 (425.4 MB) with weight 135504932 (93.76/col) Tue Oct 28 18:54:56 2008 sparse part has weight 95625280 (66.17/col) Tue Oct 28 18:54:56 2008 saving the first 48 matrix rows for later Tue Oct 28 18:54:57 2008 matrix is 1444975 x 1445223 (407.0 MB) with weight 103303242 (71.48/col) Tue Oct 28 18:54:57 2008 sparse part has weight 92233447 (63.82/col) Tue Oct 28 18:54:57 2008 matrix includes 64 packed rows Tue Oct 28 18:54:57 2008 using block size 10922 for processor cache size 256 kB Tue Oct 28 18:55:08 2008 commencing Lanczos iteration (2 threads) Tue Oct 28 18:55:08 2008 memory use: 401.3 MB Wed Oct 29 05:44:13 2008 lanczos halted after 22851 iterations (dim = 1444972) Wed Oct 29 05:44:18 2008 recovered 49 nontrivial dependencies Wed Oct 29 05:44:18 2008 elapsed time 10:54:41 Wed Oct 29 06:58:26 2008 commencing square root phase Wed Oct 29 06:58:26 2008 reading relations for dependency 1 Wed Oct 29 06:58:26 2008 read 722524 cycles Wed Oct 29 06:58:28 2008 cycles contain 2614791 unique relations Wed Oct 29 06:59:15 2008 read 2614791 relations Wed Oct 29 06:59:34 2008 multiplying 2100892 relations Wed Oct 29 07:03:48 2008 multiply complete, coefficients have about 49.51 million bits Wed Oct 29 07:03:49 2008 initial square root is modulo 12816931 Wed Oct 29 07:10:19 2008 prp56 factor: 64359895320324138046847817077342166028615808217898933063 Wed Oct 29 07:10:19 2008 prp80 factor: 36903084954015880064848993395715905165599046095682487205693219081526100375034279 Wed Oct 29 07:10:19 2008 elapsed time 00:11:55
Oct 29, 2008 (3rd): By Sinkiti Sibata / GGNFS
(26·10¹⁵⁶+1)/9 = 2(8)₁₅₅9_<157> = 3² · 223 · 233769517 · 134568092601416937915213119_<27> · C119
C119 = P52 · P67
P52 = 4694190438486921544482209313363107731432206332676001_<52>
P67 = 9747489708959753624184848714122459667180630977918143237919612742549_<67>

Number: 28889_156 N=45756572991048541133395486566429369623153492393720523352242534418823215640644591834205930308998136427613459753843866549 ( 119 digits) SNFS difficulty: 157 digits. Divisors found: r1=4694190438486921544482209313363107731432206332676001 (pp52) r2=9747489708959753624184848714122459667180630977918143237919612742549 (pp67) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 48.37 hours. Scaled time: 22.88 units (timescale=0.473). Factorization parameters were as follows: name: 28889_156 n: 45756572991048541133395486566429369623153492393720523352242534418823215640644591834205930308998136427613459753843866549 m: 10000000000000000000000000000000 c5: 260 c0: 1 skew: 0.33 type: snfs lss: 1 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved rational special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:217216, largePrimes:5794216 encountered Relations: rels:5821754, finalFF:597590 Max relations in full relation-set: 28 Initial matrix: 434099 x 597590 with sparse part having weight 50890701. Pruned matrix : 346420 x 348654 with weight 28861073. Total sieving time: 43.83 hours. Total relation processing time: 0.32 hours. Matrix solve time: 4.10 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 48.37 hours. --------- CPU info (if available) ----------
Oct 29, 2008 (2nd): By Markus Tervooren / GGNFS
(5·10¹⁶⁹-11)/3 = 1(6)₁₆₈3_<170> = 13 · 89 · 22391 · 23029 · 461413 · 1819826843737381_<16> · 4550168374230307_<16> · C121
C121 = P60 · P62
P60 = 342855645862195973177653413327612398418129301253722970119969_<60>
P62 = 21325938610287432927341056805305788973239926323324136910316219_<62>

Number: 16663_169 N=7311718455847639845721422994958497742937731902430134270627579900735868508985975918296890634287583350087847104844156477211 ( 121 digits) SNFS difficulty: 170 digits. Divisors found: r1=342855645862195973177653413327612398418129301253722970119969 (pp60) r2=21325938610287432927341056805305788973239926323324136910316219 (pp62) Version: GGNFS-0.77.1-20060722-nocona Total time: 93.56 hours. Scaled time: 188.44 units (timescale=2.014). Factorization parameters were as follows: n: 7311718455847639845721422994958497742937731902430134270627579900735868508985975918296890634287583350087847104844156477211 m: 10000000000000000000000000000000000 c5: 1 c0: -22 skew: 1.86 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, 7000001) Primes: RFBsize:412849, AFBsize:413702, largePrimes:6022667 encountered Relations: rels:6293835, finalFF:938359 Max relations in full relation-set: 32 Initial matrix: 826615 x 938359 with sparse part having weight 53816742. Pruned matrix : 732721 x 736918 with weight 39211480. Total sieving time: 89.30 hours. Total relation processing time: 0.14 hours. Matrix solve time: 4.04 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 93.56 hours. --------- CPU info (if available) ----------
Oct 29, 2008: By Markus Tervooren / GGNFS
(26·10¹⁶⁶+1)/9 = 2(8)₁₆₅9_<167> = 7 · 1667 · C163
C163 = P31 · P132
P31 = 6479340028054522941348709917163_<31>
P132 = 382090664543561576649417393525054205485383414004188396956282953099429824152707303462083388779904441883425715160662357958463678303487_<132>

Number: 28889_166 N=2475695337123051580160158444501575875301130250140448100856019272336008988678454785233429504575275421106254939488292817626950800316127250740328124851220232144047381 ( 163 digits) SNFS difficulty: 167 digits. Divisors found: r1=6479340028054522941348709917163 (pp31) r2=382090664543561576649417393525054205485383414004188396956282953099429824152707303462083388779904441883425715160662357958463678303487 (pp132) Version: GGNFS-0.77.1-20060722-nocona Total time: 78.56 hours. Scaled time: 159.94 units (timescale=2.036). Factorization parameters were as follows: n: 2475695337123051580160158444501575875301130250140448100856019272336008988678454785233429504575275421106254939488292817626950800316127250740328124851220232144047381 m: 1000000000000000000000000000000000 c5: 260 c0: 1 skew: 0.33 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, 6150001) Primes: RFBsize:380800, AFBsize:380647, largePrimes:5982858 encountered Relations: rels:6228346, finalFF:897352 Max relations in full relation-set: 32 Initial matrix: 761514 x 897352 with sparse part having weight 55066587. Pruned matrix : 649767 x 653638 with weight 38510994. Total sieving time: 73.75 hours. Total relation processing time: 0.13 hours. Matrix solve time: 4.58 hours. Time per square root: 0.09 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: 78.56 hours. --------- CPU info (if available) ----------
Oct 28, 2008 (2nd): By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(64·10²⁴⁹-1)/9 = 7(1)₂₄₉_<250> = 13⁴ · 31 · 79 · 575149723 · 1750665933361_<13> · 133333333333333333333333333333333333333333333333333333333333333333333333333333333333_<84> · C138
C138 = P44 · P95
P44 = 27086436208081622110852425797559383058724969_<44>
P95 = 27957637508878218719963598621020965070748187141715745023108986130986591894311142081697805427129_<95>

SNFS difficulty: 168 digits. Divisors found: r1=27086436208081622110852425797559383058724969 r2=27957637508878218719963598621020965070748187141715745023108986130986591894311142081697805427129 Version: Msieve-1.38 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.953). Factorization parameters were as follows: n: 757272764912899866386887025526747705214803310378892063447463012260184658852997426333940202723454900300368209126720821842355792483182284001 m: 10000000000000000000000000000 c6: 4 c3: 10 c0: 25 skew: 1.36 type: snfs lss: 0 rlim: 4400000 alim: 4400000 lpbr: 27 lpba: 27 mfbr: 54 mfba: 54 rlambda: 2.6 alambda: 2.6 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved algebraic special-q in [2200000, 4600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 872724 x 872972 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,168,6,0,0,0,0,0,0,0,0,4400000,4400000,27,27,54,54,2.6,2.6,100000 total time: 40.00 hours.
(64·10²²⁹-1)/9 = 7(1)₂₂₉_<230> = C230
C230 = P40 · P191
P40 = 4034369654841644099524570966777671875083_<40>
P191 = 17626325100321612372043581868911704206480250854797206110017885233003976436117257470546278972236787342059112346427096034798397900124082888413527743045616320435222095135066126658177229500020917_<191>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=72303299 Step 1 took 111927ms Step 2 took 31142ms ********** Factor found in step 2: 4034369654841644099524570966777671875083 Found probable prime factor of 40 digits: 4034369654841644099524570966777671875083 Probable prime cofactor 17626325100321612372043581868911704206480250854797206110017885233003976436117257470546278972236787342059112346427096034798397900124082888413527743045616320435222095135066126658177229500020917 has 191 digits
Oct 28, 2008: By Jo Yeong Uk / msieve v1.32 for x86_64
(64·10²⁴³-1)/9 = 7(1)₂₄₃_<244> = 13 · 67 · 12373 · 380557 · 47182356220003_<14> · 6517738858382209_<16> · 54699974406060473236679_<23> · 11669402665120428032569628031827203_<35> · 24375392270487185471964198611176415474970434465429475617027_<59> · C87
C87 = P41 · P47
P41 = 17158834697255184376964105105887004062117_<41>
P47 = 21118975572183169191742372770186676720387518241_<47>

Mon Oct 27 20:54:49 2008 Mon Oct 27 20:54:49 2008 Mon Oct 27 20:54:49 2008 Msieve v. 1.32 Mon Oct 27 20:54:49 2008 random seeds: 115608e0 5cb23f87 Mon Oct 27 20:54:49 2008 factoring 362377010818461224190198188942329063958140704637401162426736098893805128375151434576197 (87 digits) Mon Oct 27 20:54:49 2008 no P-1/P+1/ECM available, skipping Mon Oct 27 20:54:49 2008 commencing quadratic sieve (87-digit input) Mon Oct 27 20:54:49 2008 using multiplier of 13 Mon Oct 27 20:54:49 2008 using VC8 32kb sieve core Mon Oct 27 20:54:49 2008 sieve interval: 20 blocks of size 32768 Mon Oct 27 20:54:49 2008 processing polynomials in batches of 11 Mon Oct 27 20:54:49 2008 using a sieve bound of 1489097 (56667 primes) Mon Oct 27 20:54:49 2008 using large prime bound of 119127760 (26 bits) Mon Oct 27 20:54:49 2008 using double large prime bound of 344209894043680 (42-49 bits) Mon Oct 27 20:54:49 2008 using trial factoring cutoff of 49 bits Mon Oct 27 20:54:49 2008 polynomial 'A' values have 11 factors Mon Oct 27 21:25:48 2008 56817 relations (16105 full + 40712 combined from 594294 partial), need 56763 Mon Oct 27 21:25:51 2008 begin with 610399 relations Mon Oct 27 21:25:51 2008 reduce to 135207 relations in 9 passes Mon Oct 27 21:25:51 2008 attempting to read 135207 relations Mon Oct 27 21:25:53 2008 recovered 135207 relations Mon Oct 27 21:25:53 2008 recovered 113112 polynomials Mon Oct 27 21:25:53 2008 attempting to build 56817 cycles Mon Oct 27 21:25:53 2008 found 56817 cycles in 6 passes Mon Oct 27 21:25:53 2008 distribution of cycle lengths: Mon Oct 27 21:25:53 2008 length 1 : 16105 Mon Oct 27 21:25:53 2008 length 2 : 11391 Mon Oct 27 21:25:53 2008 length 3 : 10003 Mon Oct 27 21:25:53 2008 length 4 : 7238 Mon Oct 27 21:25:53 2008 length 5 : 5067 Mon Oct 27 21:25:53 2008 length 6 : 3127 Mon Oct 27 21:25:53 2008 length 7 : 1795 Mon Oct 27 21:25:53 2008 length 9+: 2091 Mon Oct 27 21:25:53 2008 largest cycle: 19 relations Mon Oct 27 21:25:53 2008 matrix is 56667 x 56817 with weight 3227551 (avg 56.81/col) Mon Oct 27 21:25:53 2008 filtering completed in 3 passes Mon Oct 27 21:25:53 2008 matrix is 51992 x 52056 with weight 2991184 (avg 57.46/col) Mon Oct 27 21:25:53 2008 saving the first 48 matrix rows for later Mon Oct 27 21:25:53 2008 matrix is 51944 x 52056 with weight 2392846 (avg 45.97/col) Mon Oct 27 21:25:53 2008 matrix includes 64 packed rows Mon Oct 27 21:25:53 2008 using block size 20822 for processor cache size 4096 kB Mon Oct 27 21:25:54 2008 commencing Lanczos iteration Mon Oct 27 21:26:06 2008 lanczos halted after 823 iterations (dim = 51940) Mon Oct 27 21:26:06 2008 recovered 15 nontrivial dependencies Mon Oct 27 21:26:06 2008 prp41 factor: 17158834697255184376964105105887004062117 Mon Oct 27 21:26:06 2008 prp47 factor: 21118975572183169191742372770186676720387518241 Mon Oct 27 21:26:06 2008 elapsed time 00:31:17
Oct 27, 2008 (2nd): By Jo Yeong Uk / GMP-ECM, GGNFS
(64·10²⁴³-1)/9 = 7(1)₂₄₃_<244> = 13 · 67 · 12373 · 380557 · 47182356220003_<14> · 6517738858382209_<16> · 54699974406060473236679_<23> · 24375392270487185471964198611176415474970434465429475617027_<59> · C121
C121 = P35 · C87
P35 = 11669402665120428032569628031827203_<35>
C87 = [362377010818461224190198188942329063958140704637401162426736098893805128375151434576197_<87>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 4228723255823325591225591310871269787909747181710337388679437779965558548033222618556156136920285183366078808713840886991 (121 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1941427008 Step 1 took 3928ms Step 2 took 2305ms ********** Factor found in step 2: 11669402665120428032569628031827203 Found probable prime factor of 35 digits: 11669402665120428032569628031827203 Composite cofactor 362377010818461224190198188942329063958140704637401162426736098893805128375151434576197 has 87 digits
(64·10²¹³-1)/9 = 7(1)₂₁₃_<214> = 13 · 382523701896683_<15> · 4067453597354015437_<19> · 348562279075051256093224790444794552907778175157643567551_<57> · C124
C124 = P30 · P94
P30 = 567258301292899201186210025281_<30>
P94 = 1778082503370430610274480465861532259362412214947513681455173686500912615751057885081460445747_<94>

Number: 71111_213 N=1008632060420536186503070653401950661490631137612965301768555874785722944164613998799848275106831807902913290493950398929907 ( 124 digits) SNFS difficulty: 144 digits. Divisors found: r1=567258301292899201186210025281 (pp30) r2=1778082503370430610274480465861532259362412214947513681455173686500912615751057885081460445747 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.56 hours. Scaled time: 25.03 units (timescale=2.371). Factorization parameters were as follows: n: 1008632060420536186503070653401950661490631137612965301768555874785722944164613998799848275106831807902913290493950398929907 m: 1000000000000000000000000 c6: 4 c3: 10 c0: 25 skew: 1.36 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1550001) Primes: RFBsize:114155, AFBsize:113529, largePrimes:3493047 encountered Relations: rels:3529121, finalFF:303069 Max relations in full relation-set: 28 Initial matrix: 227750 x 303069 with sparse part having weight 30082344. Pruned matrix : 203350 x 204552 with weight 17555191. Total sieving time: 10.30 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.18 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,144,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 10.56 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Oct 27, 2008: By Sinkiti Sibata / GGNFS
(26·10¹⁶³+1)/9 = 2(8)₁₆₂9_<164> = 7457 · 18506641791872782624357_<23> · 40079919846728870051247378643_<29> · C109
C109 = P41 · P69
P41 = 28009093238970577101538416824495651053679_<41>
P69 = 186471808485408531378078405605085883074515478870902537239877522909513_<69>

Number: 28889_163 N=5222906270307272385287641264035510040058867306663010966297297185700537761242664898692400059453720580222748327 ( 109 digits) Divisors found: r1=28009093238970577101538416824495651053679 (pp41) r2=186471808485408531378078405605085883074515478870902537239877522909513 (pp69) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 28.21 hours. Scaled time: 13.34 units (timescale=0.473). Factorization parameters were as follows: name: 28889_163 n: 5222906270307272385287641264035510040058867306663010966297297185700537761242664898692400059453720580222748327 skew: 14112.08 # norm 1.79e+15 c5: 223200 c4: -6134129468 c3: -76619933374282 c2: 612536663203801749 c1: 11856328080881592151098 c0: 35073061741902416693402160 # alpha -6.38 Y1: 311615672159 Y0: -471894792419104682383 # Murphy_E 1.14e-09 # M 2569326901361743041309263714221806126383752657397438348950049127272982709113883339738467089251094412998729618 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, 3000001) Primes: RFBsize:230209, AFBsize:230072, largePrimes:7400735 encountered Relations: rels:7297161, finalFF:627508 Max relations in full relation-set: 28 Initial matrix: 460365 x 627508 with sparse part having weight 50506885. Pruned matrix : 330047 x 332412 with weight 27258385. Polynomial selection time: 1.35 hours. Total sieving time: 22.24 hours. Total relation processing time: 0.62 hours. Matrix solve time: 3.71 hours. Time per square root: 0.28 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: 28.21 hours. --------- CPU info (if available) ----------
(26·10¹⁵³+1)/9 = 2(8)₁₅₂9_<154> = 3 · 263 · 171697 · 217829018959_<12> · C134
C134 = P37 · P37 · P62
P37 = 1799406072605487269788642443251985797_<37>
P37 = 3155029794925095373974038518269034733_<37>
P62 = 17244187886143827169731047895923370766606567965331126953137387_<62>

Number: 28889_153 N=97898354655912498577542654582672781408023360921519599642012823005388701296746551513056855209262153547431585837515028847674767970483787 ( 134 digits) SNFS difficulty: 154 digits. Divisors found: r1=1799406072605487269788642443251985797 (pp37) r2=3155029794925095373974038518269034733 (pp37) r3=17244187886143827169731047895923370766606567965331126953137387 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 37.34 hours. Scaled time: 29.20 units (timescale=0.782). Factorization parameters were as follows: name: 28889_153 n: 97898354655912498577542654582672781408023360921519599642012823005388701296746551513056855209262153547431585837515028847674767970483787 m: 2000000000000000000000000000000 c5: 1625 c0: 2 skew: 0.26 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:217126, largePrimes:5838600 encountered Relations: rels:5918466, finalFF:645652 Max relations in full relation-set: 28 Initial matrix: 434008 x 645652 with sparse part having weight 54622944. Pruned matrix : 325218 x 327452 with weight 33994766. Total sieving time: 35.64 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.43 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 37.34 hours. --------- CPU info (if available) ----------
Oct 26, 2008 (3rd): Factorizations of 711...11 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Oct 26, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1
4·10¹⁸⁷-9 = 3(9)₁₈₆1_<188> = 53 · 10684013423190202598370871_<26> · C161
C161 = P34 · C128
P34 = 1626349888286077666713489931346081_<34>
C128 = [43434588619417477329933277408700569125776242676471321059204704968470235596379158309505822359339758001320385530719040417854267197_<128>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1057010532 Step 1 took 19422ms Step 2 took 12488ms ********** Factor found in step 2: 1626349888286077666713489931346081 Found probable prime factor of 34 digits: 1626349888286077666713489931346081 Composite cofactor 43434588619417477329933277408700569125776242676471321059204704968470235596379158309505822359339758001320385530719040417854267197 has 128 digits
Oct 26, 2008: By Sinkiti Sibata / GGNFS
(26·10¹⁵⁰+1)/9 = 2(8)₁₄₉9_<151> = 3 · 71 · C149
C149 = P55 · P94
P55 = 3017003463910021527742494989600535726691290449142078503_<55>
P94 = 4495473338205509039310196795964079881302715548106765302223250101153564129630339087731808697251_<94>

Number: 28889_150 N=13562858633281168492436098069900886802295252999478351591027647365675534689619196661450182576943140323422013562858633281168492436098069900886802295253 ( 149 digits) SNFS difficulty: 151 digits. Divisors found: r1=3017003463910021527742494989600535726691290449142078503 (pp55) r2=4495473338205509039310196795964079881302715548106765302223250101153564129630339087731808697251 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 21.15 hours. Scaled time: 16.37 units (timescale=0.774). Factorization parameters were as follows: name: 28889_150 n: 13562858633281168492436098069900886802295252999478351591027647365675534689619196661450182576943140323422013562858633281168492436098069900886802295253 m: 1000000000000000000000000000000 c5: 26 c0: 1 skew: 0.52 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, 1900001) Primes: RFBsize:176302, AFBsize:176443, largePrimes:5632146 encountered Relations: rels:5707812, finalFF:631681 Max relations in full relation-set: 28 Initial matrix: 352813 x 631681 with sparse part having weight 54511948. Pruned matrix : 239959 x 241787 with weight 23574679. Total sieving time: 20.32 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.62 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 21.15 hours. --------- CPU info (if available) ----------
Oct 25, 2008 (4th): By Jo Yeong Uk / GMP-ECM
(26·10¹⁶¹+1)/9 = 2(8)₁₆₀9_<162> = 76423 · 220372643 · 1474229971_<10> · 147156782343257_<15> · C125
C125 = P35 · P91
P35 = 10361570462978943081240648695403377_<35>
P91 = 7630938828349621287861991098515099831174529504441192479176022590263801165241085184406853279_<91>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 79068510368626578914580689981349106518885530717911113165602486185883192699712154881358461884808530837102009408078304160123183 (125 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4091174184 Step 1 took 3914ms Step 2 took 2300ms ********** Factor found in step 2: 10361570462978943081240648695403377 Found probable prime factor of 35 digits: 10361570462978943081240648695403377 Probable prime cofactor 7630938828349621287861991098515099831174529504441192479176022590263801165241085184406853279 has 91 digits
Oct 25, 2008 (3rd): By Robert Backstrom / GMP-ECM
(13·10²⁰⁰-31)/9 = 1(4)₁₉₉1_<201> = 3 · C200
C200 = P42 · P159
P42 = 114479882131369179149234001603952546215491_<42>
P159 = 420581741103617402874421898652662038794499187212832147446391522348358265479791351017478571599457943977151584144697838957610036655579567326450207149555866212817_<159>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 48148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147 (200 digits) Using B1=5144000, B2=11416472350, polynomial Dickson(12), sigma=3111509481 Step 1 took 94705ms Step 2 took 35047ms ********** Factor found in step 2: 114479882131369179149234001603952546215491 Found probable prime factor of 42 digits: 114479882131369179149234001603952546215491 Probable prime cofactor 420581741103617402874421898652662038794499187212832147446391522348358265479791351017478571599457943977151584144697838957610036655579567326450207149555866212817 has 159 digits
Oct 25, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁴⁹+1)/9 = 2(8)₁₄₈9_<150> = 20179355711_<11> · 106315628013331801_<18> · C123
C123 = P38 · P85
P38 = 15750235873838074915509902031059707619_<38>
P85 = 8549473520716549201848743714153027681604986908351797552246043947706893694574847601621_<85>

Number: 28889_149 N=134656224548418501202256267790773535854432105692255442723175176680010180799465933023419580788851221043186204159831650450399 ( 123 digits) SNFS difficulty: 151 digits. Divisors found: r1=15750235873838074915509902031059707619 (pp38) r2=8549473520716549201848743714153027681604986908351797552246043947706893694574847601621 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.14 hours. Scaled time: 24.36 units (timescale=1.009). Factorization parameters were as follows: name: 28889_149 n: 134656224548418501202256267790773535854432105692255442723175176680010180799465933023419580788851221043186204159831650450399 m: 1000000000000000000000000000000 c5: 13 c0: 5 skew: 0.83 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:177028, largePrimes:5838819 encountered Relations: rels:6030865, finalFF:724886 Max relations in full relation-set: 28 Initial matrix: 353395 x 724886 with sparse part having weight 65294965. Pruned matrix : 231892 x 233722 with weight 29627846. Total sieving time: 23.59 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.42 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 24.14 hours. --------- CPU info (if available) ----------
(26·10¹⁴³+1)/9 = 2(8)₁₄₂9_<144> = 61 · 1187 · 117617 · 63544867 · 163152643 · 5008510873_<10> · C108
C108 = P51 · P58
P51 = 242354794037594091064567695394505940331886690503589_<51>
P58 = 2695537401622218909188582052352420335657517229979365604083_<58>

Number: 28889_143 N=653276411790784408103837393616365788765257143439082180152626896708423506902293078416685615987036100464553887 ( 108 digits) SNFS difficulty: 144 digits. Divisors found: r1=242354794037594091064567695394505940331886690503589 (pp51) r2=2695537401622218909188582052352420335657517229979365604083 (pp58) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.79 hours. Scaled time: 13.79 units (timescale=0.775). Factorization parameters were as follows: name: 28889_143 n: 653276411790784408103837393616365788765257143439082180152626896708423506902293078416685615987036100464553887 m: 20000000000000000000000000000 c5: 1625 c0: 2 skew: 0.26 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, 2750001) Primes: RFBsize:100021, AFBsize:99838, largePrimes:2898969 encountered Relations: rels:2922932, finalFF:246910 Max relations in full relation-set: 28 Initial matrix: 199925 x 246910 with sparse part having weight 29217163. Pruned matrix : 187821 x 188884 with weight 20844043. Total sieving time: 17.28 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.34 hours. Time per square root: 0.05 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: 17.79 hours. --------- CPU info (if available) ----------
(26·10¹²⁴+1)/9 = 2(8)₁₂₃9_<125> = 7 · 46359253 · 7190093831059_<13> · C104
C104 = P36 · P68
P36 = 773275929802648482592761218854738987_<36>
P68 = 16011326705494942557586789847113370037134298211097213575458840860723_<68>

Number: 28889_124 N=12381173545565578195482031153109208249880322714939240951946839415492096378310151279966671538102585107601 ( 104 digits) SNFS difficulty: 126 digits. Divisors found: r1=773275929802648482592761218854738987 (pp36) r2=16011326705494942557586789847113370037134298211097213575458840860723 (pp68) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.98 hours. Scaled time: 1.41 units (timescale=0.473). Factorization parameters were as follows: name: 28889_124 n: 12381173545565578195482031153109208249880322714939240951946839415492096378310151279966671538102585107601 m: 10000000000000000000000000 c5: 13 c0: 5 skew: 0.83 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:64323, largePrimes:2131178 encountered Relations: rels:2175070, finalFF:179780 Max relations in full relation-set: 28 Initial matrix: 113486 x 179780 with sparse part having weight 16502796. Pruned matrix : 98778 x 99409 with weight 6491834. Total sieving time: 2.75 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.13 hours. Time per square root: 0.03 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: 2.98 hours. --------- CPU info (if available) ----------
Oct 25, 2008: By matsui / GGNFS
9·10¹⁶⁹+1 = 9(0)₁₆₈1_<170> = 7 · 13 · 23 · 26680727 · 2783029903_<10> · C150
C150 = P59 · P92
P59 = 11273267512862863753557060067341695659241008487576093151619_<59>
P92 = 51369807273759613054098903544267959129913929401519425473243091409904983605073403539507467663_<92>

GGNFS-0.77.1-20060513-pentium-m 579105579481300680664203254199355666978495794312124657905662485914995879034725283343220643005997344743212838687825264828908375906570902705963398596397 = 11273267512862863753557060067341695659241008487576093151619* 51369807273759613054098903544267959129913929401519425473243091409904983605073403539507467663
Oct 24, 2008 (5th): By Jo Yeong Uk / GMP-ECM
(26·10¹⁵⁸+1)/9 = 2(8)₁₅₇9_<159> = 105188220778305713_<18> · 24222934745760446147_<20> · C123
C123 = P33 · P90
P33 = 417696229209318550390360676653337_<33>
P90 = 271441605526889400486767802727114167273548745703371791610999906296442521703183253981680827_<90>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 113380135079105024067914279723335761157532854479549372542241163306012886790982389958922970574426694448602106850588458469699 (123 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1028318472 Step 1 took 3951ms Step 2 took 2281ms ********** Factor found in step 2: 417696229209318550390360676653337 Found probable prime factor of 33 digits: 417696229209318550390360676653337 Probable prime cofactor 271441605526889400486767802727114167273548745703371791610999906296442521703183253981680827 has 90 digits
Oct 24, 2008 (4th): By Sinkiti Sibata / GGNFS
(26·10¹³²+1)/9 = 2(8)₁₃₁9_<133> = 3 · 229 · 2651273 · 36877893731033_<14> · C110
C110 = P55 · P56
P55 = 2726275397938340164900433126360846604110296672882596679_<55>
P56 = 15775524934216280471244052315246368790827525421860015377_<56>

Number: 28889_132 N=43008425517716697593767624874994058946918870477503849624665527408666408016173678755798405053073648918629132983 ( 110 digits) SNFS difficulty: 133 digits. Divisors found: r1=2726275397938340164900433126360846604110296672882596679 (pp55) r2=15775524934216280471244052315246368790827525421860015377 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.84 hours. Scaled time: 4.59 units (timescale=0.786). Factorization parameters were as follows: name: 28889_132 n: 43008425517716697593767624874994058946918870477503849624665527408666408016173678755798405053073648918629132983 m: 100000000000000000000000000 c5: 2600 c0: 1 skew: 0.21 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, 1150001) Primes: RFBsize:63951, AFBsize:64003, largePrimes:1522242 encountered Relations: rels:1518630, finalFF:162295 Max relations in full relation-set: 28 Initial matrix: 128021 x 162295 with sparse part having weight 14413076. Pruned matrix : 119236 x 119940 with weight 8876334. Total sieving time: 5.66 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,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.84 hours. --------- CPU info (if available) ----------
Oct 24, 2008 (3rd): By Sinkiti Sibata / Msieve, GGNFS
(26·10¹⁰⁹+1)/9 = 2(8)₁₀₈9_<110> = 107 · 2185727459_<10> · 3764215737119_<13> · C86
C86 = P40 · P47
P40 = 2352715497850448405626204828134063318937_<40>
P47 = 13947845666568227036142246713980273600953265951_<47>

Fri Oct 24 07:38:35 2008 Msieve v. 1.38 Fri Oct 24 07:38:35 2008 random seeds: 27520f42 5012447c Fri Oct 24 07:38:35 2008 factoring 32815312661361285664799561745417563767797352627553000827562716332375330588420695614087 (86 digits) Fri Oct 24 07:38:36 2008 searching for 15-digit factors Fri Oct 24 07:38:38 2008 commencing quadratic sieve (86-digit input) Fri Oct 24 07:38:38 2008 using multiplier of 7 Fri Oct 24 07:38:38 2008 using 64kb Pentium 4 sieve core Fri Oct 24 07:38:38 2008 sieve interval: 8 blocks of size 65536 Fri Oct 24 07:38:38 2008 processing polynomials in batches of 13 Fri Oct 24 07:38:38 2008 using a sieve bound of 1461403 (55577 primes) Fri Oct 24 07:38:38 2008 using large prime bound of 116912240 (26 bits) Fri Oct 24 07:38:38 2008 using double large prime bound of 332772803587280 (41-49 bits) Fri Oct 24 07:38:38 2008 using trial factoring cutoff of 49 bits Fri Oct 24 07:38:38 2008 polynomial 'A' values have 11 factors Fri Oct 24 08:44:54 2008 55888 relations (15735 full + 40153 combined from 584474 partial), need 55673 Fri Oct 24 08:44:57 2008 begin with 600209 relations Fri Oct 24 08:44:57 2008 reduce to 133634 relations in 11 passes Fri Oct 24 08:44:57 2008 attempting to read 133634 relations Fri Oct 24 08:45:01 2008 recovered 133634 relations Fri Oct 24 08:45:01 2008 recovered 114115 polynomials Fri Oct 24 08:45:01 2008 attempting to build 55888 cycles Fri Oct 24 08:45:01 2008 found 55887 cycles in 5 passes Fri Oct 24 08:45:01 2008 distribution of cycle lengths: Fri Oct 24 08:45:01 2008 length 1 : 15735 Fri Oct 24 08:45:01 2008 length 2 : 10950 Fri Oct 24 08:45:01 2008 length 3 : 9687 Fri Oct 24 08:45:01 2008 length 4 : 7328 Fri Oct 24 08:45:01 2008 length 5 : 5058 Fri Oct 24 08:45:01 2008 length 6 : 3109 Fri Oct 24 08:45:01 2008 length 7 : 1856 Fri Oct 24 08:45:01 2008 length 9+: 2164 Fri Oct 24 08:45:01 2008 largest cycle: 19 relations Fri Oct 24 08:45:01 2008 matrix is 55577 x 55887 (12.5 MB) with weight 3052144 (54.61/col) Fri Oct 24 08:45:01 2008 sparse part has weight 3052144 (54.61/col) Fri Oct 24 08:45:02 2008 filtering completed in 3 passes Fri Oct 24 08:45:02 2008 matrix is 51138 x 51202 (11.5 MB) with weight 2815779 (54.99/col) Fri Oct 24 08:45:02 2008 sparse part has weight 2815779 (54.99/col) Fri Oct 24 08:45:02 2008 saving the first 48 matrix rows for later Fri Oct 24 08:45:03 2008 matrix is 51090 x 51202 (6.9 MB) with weight 2162007 (42.23/col) Fri Oct 24 08:45:03 2008 sparse part has weight 1511643 (29.52/col) Fri Oct 24 08:45:03 2008 matrix includes 64 packed rows Fri Oct 24 08:45:03 2008 using block size 20480 for processor cache size 512 kB Fri Oct 24 08:45:03 2008 commencing Lanczos iteration Fri Oct 24 08:45:03 2008 memory use: 7.1 MB Fri Oct 24 08:45:30 2008 lanczos halted after 809 iterations (dim = 51090) Fri Oct 24 08:45:30 2008 recovered 18 nontrivial dependencies Fri Oct 24 08:45:30 2008 prp40 factor: 2352715497850448405626204828134063318937 Fri Oct 24 08:45:30 2008 prp47 factor: 13947845666568227036142246713980273600953265951 Fri Oct 24 08:45:30 2008 elapsed time 01:06:55
(26·10¹⁴⁰+1)/9 = 2(8)₁₃₉9_<141> = 31 · 4973 · 13349257 · 146756720381_<12> · C117
C117 = P41 · P77
P41 = 16946406410302077950728265839823308474681_<41>
P77 = 56444025048774398773331902576688228725404795527707944697772162262625763068639_<77>

Number: 28889_140 N=956523387909801529433876566582169079255855390436023481092130570669948064133375135303153768545553242649095876996629159 ( 117 digits) SNFS difficulty: 141 digits. Divisors found: r1=16946406410302077950728265839823308474681 (pp41) r2=56444025048774398773331902576688228725404795527707944697772162262625763068639 (pp77) Version: GGNFS-0.77.1-20050930-nocona Total time: 7.86 hours. Scaled time: 7.93 units (timescale=1.009). Factorization parameters were as follows: name: 28889_140 n: 956523387909801529433876566582169079255855390436023481092130570669948064133375135303153768545553242649095876996629159 m: 10000000000000000000000000000 c5: 26 c0: 1 skew: 0.52 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, 1550001) Primes: RFBsize:100021, AFBsize:100158, largePrimes:2845541 encountered Relations: rels:2958063, finalFF:396703 Max relations in full relation-set: 28 Initial matrix: 200247 x 396703 with sparse part having weight 33108599. Pruned matrix : 147491 x 148556 with weight 12955765. Total sieving time: 7.67 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.03 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: 7.86 hours. --------- CPU info (if available) ----------
(26·10¹¹⁸+1)/9 = 2(8)₁₁₇9_<119> = 7 · 43 · 347 · 18493 · 142596099014873898701_<21> · C90
C90 = P39 · P51
P39 = 310504758589188668868039465733010830759_<39>
P51 = 337793737293839609947074217344570551540349654109001_<51>

Fri Oct 24 08:55:48 2008 Msieve v. 1.38 Fri Oct 24 08:55:48 2008 random seeds: a74e622f fe874ab3 Fri Oct 24 08:55:48 2008 factoring 104886562851363485405548252303473041147564571797863156376514452609058806792242120949561759 (90 digits) Fri Oct 24 08:55:49 2008 searching for 15-digit factors Fri Oct 24 08:55:51 2008 commencing quadratic sieve (90-digit input) Fri Oct 24 08:55:51 2008 using multiplier of 41 Fri Oct 24 08:55:51 2008 using 64kb Pentium 4 sieve core Fri Oct 24 08:55:51 2008 sieve interval: 17 blocks of size 65536 Fri Oct 24 08:55:51 2008 processing polynomials in batches of 6 Fri Oct 24 08:55:51 2008 using a sieve bound of 1561267 (59333 primes) Fri Oct 24 08:55:51 2008 using large prime bound of 124901360 (26 bits) Fri Oct 24 08:55:51 2008 using double large prime bound of 374818364744400 (42-49 bits) Fri Oct 24 08:55:51 2008 using trial factoring cutoff of 49 bits Fri Oct 24 08:55:51 2008 polynomial 'A' values have 12 factors Fri Oct 24 11:06:35 2008 59936 relations (15999 full + 43937 combined from 627733 partial), need 59429 Fri Oct 24 11:06:37 2008 begin with 643732 relations Fri Oct 24 11:06:38 2008 reduce to 145799 relations in 9 passes Fri Oct 24 11:06:38 2008 attempting to read 145799 relations Fri Oct 24 11:06:42 2008 recovered 145799 relations Fri Oct 24 11:06:42 2008 recovered 126067 polynomials Fri Oct 24 11:06:42 2008 attempting to build 59936 cycles Fri Oct 24 11:06:42 2008 found 59936 cycles in 5 passes Fri Oct 24 11:06:42 2008 distribution of cycle lengths: Fri Oct 24 11:06:42 2008 length 1 : 15999 Fri Oct 24 11:06:42 2008 length 2 : 11788 Fri Oct 24 11:06:42 2008 length 3 : 10497 Fri Oct 24 11:06:42 2008 length 4 : 7907 Fri Oct 24 11:06:42 2008 length 5 : 5609 Fri Oct 24 11:06:42 2008 length 6 : 3532 Fri Oct 24 11:06:42 2008 length 7 : 2083 Fri Oct 24 11:06:42 2008 length 9+: 2521 Fri Oct 24 11:06:42 2008 largest cycle: 22 relations Fri Oct 24 11:06:42 2008 matrix is 59333 x 59936 (14.6 MB) with weight 3594607 (59.97/col) Fri Oct 24 11:06:42 2008 sparse part has weight 3594607 (59.97/col) Fri Oct 24 11:06:43 2008 filtering completed in 3 passes Fri Oct 24 11:06:43 2008 matrix is 55352 x 55416 (13.5 MB) with weight 3320978 (59.93/col) Fri Oct 24 11:06:43 2008 sparse part has weight 3320978 (59.93/col) Fri Oct 24 11:06:44 2008 saving the first 48 matrix rows for later Fri Oct 24 11:06:44 2008 matrix is 55304 x 55416 (8.4 MB) with weight 2564229 (46.27/col) Fri Oct 24 11:06:44 2008 sparse part has weight 1857421 (33.52/col) Fri Oct 24 11:06:44 2008 matrix includes 64 packed rows Fri Oct 24 11:06:44 2008 using block size 21845 for processor cache size 512 kB Fri Oct 24 11:06:44 2008 commencing Lanczos iteration Fri Oct 24 11:06:44 2008 memory use: 8.2 MB Fri Oct 24 11:07:15 2008 lanczos halted after 876 iterations (dim = 55304) Fri Oct 24 11:07:15 2008 recovered 19 nontrivial dependencies Fri Oct 24 11:07:16 2008 prp39 factor: 310504758589188668868039465733010830759 Fri Oct 24 11:07:16 2008 prp51 factor: 337793737293839609947074217344570551540349654109001 Fri Oct 24 11:07:16 2008 elapsed time 02:11:28
(26·10¹³⁵+1)/9 = 2(8)₁₃₄9_<136> = 3 · 3623 · 8298691 · C125
C125 = P55 · P71
P55 = 2984924145121567481231370167761731005911594902352492537_<55>
P71 = 10729966269440986387424384155216021254035129543325817268738099540010143_<71>

Number: 28889_135 N=32028135393994390893512870715772478008650433931356742226952684544130115555067978734842948059021629198081409882507694311802791 ( 125 digits) SNFS difficulty: 136 digits. Divisors found: r1=2984924145121567481231370167761731005911594902352492537 (pp55) r2=10729966269440986387424384155216021254035129543325817268738099540010143 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.86 hours. Scaled time: 4.26 units (timescale=0.728). Factorization parameters were as follows: name: 28889_135 n: 32028135393994390893512870715772478008650433931356742226952684544130115555067978734842948059021629198081409882507694311802791 m: 1000000000000000000000000000 c5: 26 c0: 1 skew: 0.52 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:63993, largePrimes:1584823 encountered Relations: rels:1636631, finalFF:222218 Max relations in full relation-set: 28 Initial matrix: 142559 x 222218 with sparse part having weight 16894199. Pruned matrix : 118197 x 118973 with weight 7602832. Total sieving time: 5.70 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,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.86 hours. --------- CPU info (if available) ----------
(26·10¹⁴⁴+1)/9 = 2(8)₁₄₃9_<145> = 3 · C144
C144 = P40 · P105
P40 = 3868456166380275987258850199506057417163_<40>
P105 = 248926941794460034322836458820266164478157735098297360503167305646685102364493278068850644610523325296601_<105>

Number: 28889_144 N=962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962963 ( 144 digits) SNFS difficulty: 146 digits. Divisors found: r1=3868456166380275987258850199506057417163 (pp40) r2=248926941794460034322836458820266164478157735098297360503167305646685102364493278068850644610523325296601 (pp105) Version: GGNFS-0.77.1-20050930-nocona Total time: 13.04 hours. Scaled time: 13.00 units (timescale=0.997). Factorization parameters were as follows: name: 28889_144 n: 962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962963 m: 100000000000000000000000000000 c5: 13 c0: 5 skew: 0.83 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, 2450001) Primes: RFBsize:114155, AFBsize:114927, largePrimes:2920308 encountered Relations: rels:2974362, finalFF:340461 Max relations in full relation-set: 28 Initial matrix: 229147 x 340461 with sparse part having weight 34112156. Pruned matrix : 196490 x 197699 with weight 18660001. Total sieving time: 12.72 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.22 hours. Time per square root: 0.04 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: 13.04 hours. --------- CPU info (if available) ----------
(26·10¹³⁶+1)/9 = 2(8)₁₃₅9_<137> = 7² · 1009163 · 92173330259_<11> · C118
C118 = P39 · P80
P39 = 109003884098615801826326739083592367603_<39>
P80 = 58146849261168928709085037160922928516795192130437343258069237123101709831491811_<80>

Number: 28889_136 N=6338232417564141772974103575750162136421796142704203282418999024391507789321722903633658782706570980626231650996199033 ( 118 digits) SNFS difficulty: 137 digits. Divisors found: r1=109003884098615801826326739083592367603 (pp39) r2=58146849261168928709085037160922928516795192130437343258069237123101709831491811 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.84 hours. Scaled time: 8.22 units (timescale=0.759). Factorization parameters were as follows: name: 28889_136 n: 6338232417564141772974103575750162136421796142704203282418999024391507789321722903633658782706570980626231650996199033 m: 1000000000000000000000000000 c5: 260 c0: 1 skew: 0.33 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, 1375001) Primes: RFBsize:78498, AFBsize:64178, largePrimes:1540035 encountered Relations: rels:1534558, finalFF:167204 Max relations in full relation-set: 28 Initial matrix: 142743 x 167204 with sparse part having weight 14162172. Pruned matrix : 135478 x 136255 with weight 9964494. Total sieving time: 10.56 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.12 hours. Time per square root: 0.05 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: 10.84 hours. --------- CPU info (if available) ----------
(26·10¹⁴⁶+1)/9 = 2(8)₁₄₅9_<147> = 17 · 1367 · 185599 · 5265763 · 20930509 · C123
C123 = P58 · P66
P58 = 1124073153303578585771807081716025889983932995108149151131_<58>
P66 = 540632434021785268234902288892949509330978466439075267476173783637_<66>

Number: 28889_146 N=607710404889057066896460732610797716908669403889768225367727440828283420463903579304033251169460502873600370283178007843447 ( 123 digits) SNFS difficulty: 147 digits. Divisors found: r1=1124073153303578585771807081716025889983932995108149151131 (pp58) r2=540632434021785268234902288892949509330978466439075267476173783637 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.54 hours. Scaled time: 15.59 units (timescale=1.003). Factorization parameters were as follows: name: 28889_146 n: 607710404889057066896460732610797716908669403889768225367727440828283420463903579304033251169460502873600370283178007843447 m: 100000000000000000000000000000 c5: 260 c0: 1 skew: 0.33 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:114352, largePrimes:2879800 encountered Relations: rels:2888648, finalFF:289991 Max relations in full relation-set: 28 Initial matrix: 228574 x 289991 with sparse part having weight 30172774. Pruned matrix : 209836 x 211042 with weight 20187694. Total sieving time: 15.18 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.27 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: 15.54 hours. --------- CPU info (if available) ----------
Oct 24, 2008 (2nd): By Jo Yeong Uk / GGNFS
(26·10¹²⁷+1)/9 = 2(8)₁₂₆9_<128> = C128
C128 = P33 · P46 · P49
P33 = 458085681516861371474360406126427_<33>
P46 = 7023583414196555680661945198122510555776461537_<46>
P49 = 8978946353297513072321536821597066798123200152411_<49>

Number: 28889_127 N=28888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 ( 128 digits) SNFS difficulty: 129 digits. Divisors found: r1=458085681516861371474360406126427 (pp33) r2=7023583414196555680661945198122510555776461537 (pp46) r3=8978946353297513072321536821597066798123200152411 (pp49) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.91 hours. Scaled time: 4.57 units (timescale=2.386). Factorization parameters were as follows: n: 28888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 m: 20000000000000000000000000 c5: 325 c0: 4 skew: 0.41 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, 950001) Primes: RFBsize:78498, AFBsize:78521, largePrimes:1556455 encountered Relations: rels:1594578, finalFF:212343 Max relations in full relation-set: 28 Initial matrix: 157086 x 212343 with sparse part having weight 10787721. Pruned matrix : 132986 x 133835 with weight 5333440. Total sieving time: 1.85 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,129,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 1.91 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Oct 24, 2008: By Serge Batalov / Msieve, GMP-ECM 6.2.1, Msieve-1.38
(26·10¹⁴⁵+1)/9 = 2(8)₁₄₄9_<146> = 23 · 16034479 · 187957327080463607012417_<24> · 588289017691633394319116788695937_<33> · C81
C81 = P32 · P50
P32 = 54896618346979991955469420943911_<32>
P50 = 12904837953364134191960473735409301929999830768343_<50>

Thu Oct 23 10:29:56 2008 Msieve v. 1.38 Thu Oct 23 10:29:56 2008 random seeds: bf8006ca f25a0719 Thu Oct 23 10:29:56 2008 factoring 708431963955453258881716546076869813358455186906357975700925723287910831437409473 (81 digits) Thu Oct 23 10:29:57 2008 searching for 15-digit factors Thu Oct 23 10:29:57 2008 commencing quadratic sieve (81-digit input) Thu Oct 23 10:29:57 2008 using multiplier of 29 Thu Oct 23 10:29:57 2008 using 64kb Opteron sieve core Thu Oct 23 10:29:57 2008 sieve interval: 6 blocks of size 65536 Thu Oct 23 10:29:57 2008 processing polynomials in batches of 17 Thu Oct 23 10:29:57 2008 using a sieve bound of 1319687 (50882 primes) Thu Oct 23 10:29:57 2008 using large prime bound of 126689952 (26 bits) Thu Oct 23 10:29:57 2008 using trial factoring cutoff of 27 bits Thu Oct 23 10:29:57 2008 polynomial 'A' values have 10 factors Thu Oct 23 10:42:21 2008 51080 relations (26277 full + 24803 combined from 272800 partial), need 50978 Thu Oct 23 10:42:21 2008 begin with 299077 relations Thu Oct 23 10:42:21 2008 reduce to 72762 relations in 2 passes Thu Oct 23 10:42:21 2008 attempting to read 72762 relations Thu Oct 23 10:42:22 2008 recovered 72762 relations Thu Oct 23 10:42:22 2008 recovered 63176 polynomials Thu Oct 23 10:42:22 2008 attempting to build 51080 cycles Thu Oct 23 10:42:22 2008 found 51080 cycles in 1 passes Thu Oct 23 10:42:22 2008 distribution of cycle lengths: Thu Oct 23 10:42:22 2008 length 1 : 26277 Thu Oct 23 10:42:22 2008 length 2 : 24803 Thu Oct 23 10:42:22 2008 largest cycle: 2 relations Thu Oct 23 10:42:22 2008 matrix is 50882 x 51080 (7.6 MB) with weight 1575931 (30.85/col) Thu Oct 23 10:42:22 2008 sparse part has weight 1575931 (30.85/col) Thu Oct 23 10:42:22 2008 filtering completed in 3 passes Thu Oct 23 10:42:22 2008 matrix is 36078 x 36141 (5.9 MB) with weight 1255285 (34.73/col) Thu Oct 23 10:42:22 2008 sparse part has weight 1255285 (34.73/col) Thu Oct 23 10:42:22 2008 saving the first 48 matrix rows for later Thu Oct 23 10:42:22 2008 matrix is 36030 x 36141 (4.6 MB) with weight 1016694 (28.13/col) Thu Oct 23 10:42:22 2008 sparse part has weight 840697 (23.26/col) Thu Oct 23 10:42:22 2008 matrix includes 64 packed rows Thu Oct 23 10:42:22 2008 using block size 14456 for processor cache size 1024 kB Thu Oct 23 10:42:22 2008 commencing Lanczos iteration Thu Oct 23 10:42:22 2008 memory use: 4.3 MB Thu Oct 23 10:42:27 2008 lanczos halted after 571 iterations (dim = 36030) Thu Oct 23 10:42:27 2008 recovered 18 nontrivial dependencies Thu Oct 23 10:42:27 2008 prp32 factor: 54896618346979991955469420943911 Thu Oct 23 10:42:27 2008 prp50 factor: 12904837953364134191960473735409301929999830768343 Thu Oct 23 10:42:27 2008 elapsed time 00:12:31
(26·10¹⁴¹+1)/9 = 2(8)₁₄₀9_<142> = 3 · 19 · 29 · 3296148577_<10> · 5839065893291_<13> · 35712359448084329_<17> · 144912971424315491_<18> · C83
C83 = P37 · P46
P37 = 7537297685684934579476791673851030409_<37>
P46 = 2327910906718027614464758526910877086171667909_<46>

Thu Oct 23 10:32:00 2008 Msieve v. 1.38 Thu Oct 23 10:32:00 2008 random seeds: f4ffedc8 bb9bb07a Thu Oct 23 10:32:00 2008 factoring 17546157489686507164223646012583316051508274916630319119035081251725924541808444781 (83 digits) Thu Oct 23 10:32:01 2008 searching for 15-digit factors Thu Oct 23 10:32:01 2008 commencing quadratic sieve (83-digit input) Thu Oct 23 10:32:01 2008 using multiplier of 69 Thu Oct 23 10:32:01 2008 using 64kb Opteron sieve core Thu Oct 23 10:32:01 2008 sieve interval: 6 blocks of size 65536 Thu Oct 23 10:32:01 2008 processing polynomials in batches of 17 Thu Oct 23 10:32:01 2008 using a sieve bound of 1367749 (52320 primes) Thu Oct 23 10:32:01 2008 using large prime bound of 124465159 (26 bits) Thu Oct 23 10:32:01 2008 using trial factoring cutoff of 27 bits Thu Oct 23 10:32:01 2008 polynomial 'A' values have 11 factors Thu Oct 23 10:49:00 2008 52549 relations (27310 full + 25239 combined from 272691 partial), need 52416 Thu Oct 23 10:49:01 2008 begin with 300001 relations Thu Oct 23 10:49:01 2008 reduce to 74599 relations in 2 passes Thu Oct 23 10:49:01 2008 attempting to read 74599 relations Thu Oct 23 10:49:01 2008 recovered 74599 relations Thu Oct 23 10:49:01 2008 recovered 67221 polynomials Thu Oct 23 10:49:01 2008 attempting to build 52549 cycles Thu Oct 23 10:49:01 2008 found 52549 cycles in 1 passes Thu Oct 23 10:49:01 2008 distribution of cycle lengths: Thu Oct 23 10:49:01 2008 length 1 : 27310 Thu Oct 23 10:49:01 2008 length 2 : 25239 Thu Oct 23 10:49:01 2008 largest cycle: 2 relations Thu Oct 23 10:49:01 2008 matrix is 52320 x 52549 (8.1 MB) with weight 1707055 (32.49/col) Thu Oct 23 10:49:01 2008 sparse part has weight 1707055 (32.49/col) Thu Oct 23 10:49:02 2008 filtering completed in 3 passes Thu Oct 23 10:49:02 2008 matrix is 37474 x 37538 (6.3 MB) with weight 1347017 (35.88/col) Thu Oct 23 10:49:02 2008 sparse part has weight 1347017 (35.88/col) Thu Oct 23 10:49:02 2008 saving the first 48 matrix rows for later Thu Oct 23 10:49:02 2008 matrix is 37426 x 37538 (4.0 MB) with weight 985377 (26.25/col) Thu Oct 23 10:49:02 2008 sparse part has weight 680625 (18.13/col) Thu Oct 23 10:49:02 2008 matrix includes 64 packed rows Thu Oct 23 10:49:02 2008 using block size 15015 for processor cache size 1024 kB Thu Oct 23 10:49:02 2008 commencing Lanczos iteration Thu Oct 23 10:49:02 2008 memory use: 4.1 MB Thu Oct 23 10:49:06 2008 lanczos halted after 593 iterations (dim = 37426) Thu Oct 23 10:49:06 2008 recovered 19 nontrivial dependencies Thu Oct 23 10:49:06 2008 prp37 factor: 7537297685684934579476791673851030409 Thu Oct 23 10:49:06 2008 prp46 factor: 2327910906718027614464758526910877086171667909 Thu Oct 23 10:49:06 2008 elapsed time 00:17:06
(26·10¹²³+1)/9 = 2(8)₁₂₂9_<124> = 3 · 19 · 23 · 293673451 · 14086235410802221_<17> · C96
C96 = P31 · P66
P31 = 2260206644216843897235550228849_<31>
P66 = 235678719982591680453016546251331940361325353146335698040419053881_<66>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1715797540 Step 1 took 8517ms Step 2 took 8480ms ********** Factor found in step 2: 2260206644216843897235550228849 Found probable prime factor of 31 digits: 2260206644216843897235550228849 Probable prime cofactor 235678719982591680453016546251331940361325353146335698040419053881 has 66 digits
(26·10¹⁶⁸+1)/9 = 2(8)₁₆₇9_<169> = 3 · 156641 · 21214442884961_<14> · 23964088941151470239380261199_<29> · C122
C122 = P35 · P87
P35 = 26698194639575122525661827534142287_<35>
P87 = 452928540577266887157236259134255076239219768187618558929062743927670190164498760454451_<87>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=274814543 Step 1 took 13361ms Step 2 took 10905ms ********** Factor found in step 2: 26698194639575122525661827534142287 Found probable prime factor of 35 digits: 26698194639575122525661827534142287 Probable prime cofactor 452928540577266887157236259134255076239219768187618558929062743927670190164498760454451 has 87 digits
(26·10¹⁵¹+1)/9 = 2(8)₁₅₀9_<152> = 367 · 11399 · 6075767 · 959734623010792392437077357_<27> · C112
C112 = P34 · P38 · P40
P34 = 7947880915750697011047998057190331_<34>
P38 = 51027845668162402739414306998386845861_<38>
P40 = 2920028986625899746912414355924945584277_<40>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1288646471 Step 1 took 11085ms Step 2 took 9828ms ********** Factor found in step 2: 7947880915750697011047998057190331 Found probable prime factor of 34 digits: 7947880915750697011047998057190331 # Thu Oct 23 11:52:40 2008 Msieve v. 1.38 Thu Oct 23 11:52:40 2008 random seeds: 55b14030 4ff574bf Thu Oct 23 11:52:40 2008 factoring 149002788476107069043684168199295287350958471236577922876144705896373784127497 (78 digits) Thu Oct 23 11:52:41 2008 searching for 15-digit factors Thu Oct 23 11:52:41 2008 commencing quadratic sieve (78-digit input) Thu Oct 23 11:52:41 2008 using multiplier of 5 Thu Oct 23 11:52:41 2008 using 64kb Opteron sieve core Thu Oct 23 11:52:41 2008 sieve interval: 6 blocks of size 65536 Thu Oct 23 11:52:41 2008 processing polynomials in batches of 17 Thu Oct 23 11:52:41 2008 using a sieve bound of 958687 (37824 primes) Thu Oct 23 11:52:41 2008 using large prime bound of 95868700 (26 bits) Thu Oct 23 11:52:41 2008 using trial factoring cutoff of 27 bits Thu Oct 23 11:52:41 2008 polynomial 'A' values have 10 factors Thu Oct 23 11:57:36 2008 38199 relations (20007 full + 18192 combined from 205677 partial), need 37920 Thu Oct 23 11:57:36 2008 begin with 225684 relations Thu Oct 23 11:57:37 2008 reduce to 54082 relations in 2 passes Thu Oct 23 11:57:37 2008 attempting to read 54082 relations Thu Oct 23 11:57:37 2008 recovered 54082 relations Thu Oct 23 11:57:37 2008 recovered 42175 polynomials Thu Oct 23 11:57:37 2008 attempting to build 38199 cycles Thu Oct 23 11:57:37 2008 found 38199 cycles in 1 passes Thu Oct 23 11:57:37 2008 distribution of cycle lengths: Thu Oct 23 11:57:37 2008 length 1 : 20007 Thu Oct 23 11:57:37 2008 length 2 : 18192 Thu Oct 23 11:57:37 2008 largest cycle: 2 relations Thu Oct 23 11:57:37 2008 matrix is 37824 x 38199 (5.5 MB) with weight 1141071 (29.87/col) Thu Oct 23 11:57:37 2008 sparse part has weight 1141071 (29.87/col) Thu Oct 23 11:57:37 2008 filtering completed in 4 passes Thu Oct 23 11:57:37 2008 matrix is 27598 x 27662 (4.3 MB) with weight 893917 (32.32/col) Thu Oct 23 11:57:37 2008 sparse part has weight 893917 (32.32/col) Thu Oct 23 11:57:37 2008 saving the first 48 matrix rows for later Thu Oct 23 11:57:37 2008 matrix is 27550 x 27662 (2.8 MB) with weight 652298 (23.58/col) Thu Oct 23 11:57:37 2008 sparse part has weight 456512 (16.50/col) Thu Oct 23 11:57:37 2008 matrix includes 64 packed rows Thu Oct 23 11:57:37 2008 commencing Lanczos iteration Thu Oct 23 11:57:37 2008 memory use: 3.9 MB Thu Oct 23 11:57:54 2008 lanczos halted after 437 iterations (dim = 27550) Thu Oct 23 11:57:54 2008 recovered 18 nontrivial dependencies Thu Oct 23 11:57:55 2008 prp38 factor: 51027845668162402739414306998386845861 Thu Oct 23 11:57:55 2008 prp40 factor: 2920028986625899746912414355924945584277 Thu Oct 23 11:57:55 2008 elapsed time 00:05:15
(26·10¹²²+1)/9 = 2(8)₁₂₁9_<123> = 74162267 · 237038273947153447_<18> · C98
C98 = P38 · P60
P38 = 46879667831372870430779365910146268011_<38>
P60 = 350545857881710086313544549379318576471907638151859610638951_<60>

Using B1=4000000, B2=14268967450, polynomial Dickson(12), sigma=2427505608 Step 1 took 13613ms Step 2 took 9084ms ********** Factor found in step 2: 46879667831372870430779365910146268011 Found probable prime factor of 38 digits: 46879667831372870430779365910146268011 Probable prime cofactor 350545857881710086313544549379318576471907638151859610638951 has 60 digits
10²³⁷-9 = (9)₂₃₆1_<237> = 107 · 7561 · 57235347277_<11> · 672331504409_<12> · 4675438610011439_<16> · C193
C193 = P33 · P161
P33 = 124195659693998352897446580594911_<33>
P161 = 55317229683125179811055047825566314237250570327459404598417890762364651604901335574716743377299431025304065892097911840931358872788401832572008373559390024256489_<161>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=1344070187 Step 1 took 16461ms Step 2 took 8449ms ********** Factor found in step 2: 124195659693998352897446580594911 Found probable prime factor of 33 digits: 124195659693998352897446580594911 Probable prime cofactor 55317229683125179811055047825566314237250570327459404598417890762364651604901335574716743377299431025304065892097911840931358872788401832572008373559390024256489 has 161 digits
10²⁰⁹-9 = (9)₂₀₈1_<209> = 6199 · 1098311 · 8749770522229013046664029725719_<31> · C169
C169 = P32 · P138
P32 = 11779221979625493750760591465889_<32>
P138 = 142508169351112330751625366154027236299106678544471738141095195169427914114649935286029433461028125436734063605464802185882769616072838209_<138>

Using B1=6000000, B2=35128842850, polynomial Dickson(12), sigma=2769882817 Step 1 took 40563ms ********** Factor found in step 1: 11779221979625493750760591465889 Found probable prime factor of 32 digits: 11779221979625493750760591465889 Probable prime cofactor 142508169351112330751625366154027236299106678544471738141095195169427914114649935286029433461028125436734063605464802185882769616072838209 has 138 digits
10²²⁷-9 = (9)₂₂₆1_<227> = 43 · 925733 · 1415114047290409_<16> · C205
C205 = P41 · P164
P41 = 17786640496933624840678534245662351596213_<41>
P164 = 99806868526225823221956954125006142277499588289181858360905874746351256925536418640176658497489042909882373987832308907586475427226873597370517730462039750438400917_<164>

Using B1=6000000, B2=35128842850, polynomial Dickson(12), sigma=1970878906 Step 1 took 50263ms Step 2 took 28402ms ********** Factor found in step 2: 17786640496933624840678534245662351596213 Found probable prime factor of 41 digits: 17786640496933624840678534245662351596213 Probable prime cofactor 99806868526225823221956954125006142277499588289181858360905874746351256925536418640176658497489042909882373987832308907586475427226873597370517730462039750438400917 has 164 digits
(26·10¹²⁸+1)/9 = 2(8)₁₂₇9_<129> = 47 · 587621 · C122
C122 = P36 · P86
P36 = 608854427798862595293365769991723889_<36>
P86 = 17179962200419555232686564654540718862779882714985860187643887329996349818496153104123_<86>

SNFS difficulty: 129 digits. Divisors found: r1=608854427798862595293365769991723889 r2=17179962200419555232686564654540718862779882714985860187643887329996349818496153104123 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 10460096055142536651261318814623454062675761044303483385382570148029227584304823806460897990475945755921230053547283494347 m: 20000000000000000000000000 c5: 1625 c0: 2 skew: 0.26 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [400000, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 111088 x 111310 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,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 2.00 hours.
Oct 23, 2008 (5th): Factorizations of 288...889 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Oct 23, 2008 (4th): The following PRPs were imported from Henri & Renaud Lifchitz's PRP Top records (www.primenumbers.net).
10²⁶⁹²⁷+3 = 1(0)₂₆₉₂₆3_<26928> is PRP. (Jason Earls / Dec 2007)
10²³⁶³⁶+7 = 1(0)₂₃₆₃₅7_<23637> is PRP. (Jason Earls / Nov 2007)
10³⁰²²¹+7 = 1(0)₃₀₂₂₀7_<30222> is PRP. (Jason Earls / Nov 2007)
10⁵⁰⁷¹¹+7 = 1(0)₅₀₇₁₀7_<50712> is PRP. (Jason Earls / Dec 2007)
10⁴³¹⁸⁶+9 = 1(0)₄₃₁₈₅9_<43187> is PRP. (Jason Earls / Dec 2007)
10⁴⁸¹⁰⁹+9 = 1(0)₄₈₁₀₈9_<48110> is PRP. (Jason Earls / Dec 2007)
(10²⁰⁰¹⁶+17)/9 = (1)₂₀₀₁₅3_<20016> is PRP. (Lelio R Paula / Oct 2008)
(10²²⁹⁷³+53)/9 = (1)₂₂₉₇₂7_<22973> is PRP. (Lelio R Paula / Oct 2008)
(10¹⁰⁶⁸³+11)/3 = (3)₁₀₆₈₂7_<10683> is PRP. (Lelio R Paula / Oct 2008)
(10¹²⁸⁹¹+11)/3 = (3)₁₂₈₉₀7_<12891> is PRP. (Lelio R Paula / Oct 2008)
(10¹⁴¹¹⁸+11)/3 = (3)₁₄₁₁₇7_<14118> is PRP. (Lelio R Paula / Oct 2008)
(61·10³⁰⁹⁷⁶-7)/9 = 6(7)₃₀₉₇₆_<30977> is PRP. (Maksym Voznyy / Jan 2008)
(61·10³¹⁶³¹-7)/9 = 6(7)₃₁₆₃₁_<31632> is PRP. (Maksym Voznyy / Jan 2008)
(61·10⁴³²⁷¹-7)/9 = 6(7)₄₃₂₇₁_<43272> is PRP. (Maksym Voznyy / Jan 2008)
10³⁵⁹²⁵-9 = (9)₃₅₉₂₄1_<35925> is PRP. (Jason Earls / Jan 2008)
10³⁷⁵⁹⁷-9 = (9)₃₇₅₉₆1_<37597> is PRP. (Jason Earls / Jan 2008)
Oct 23, 2008 (3rd): Factorizations of 99...991 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Oct 23, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(64·10¹⁹⁷-1)/9 = 7(1)₁₉₇_<198> = 3 · 79 · C196
C196 = P55 · P141
P55 = 3210403733699042628385928154786408307073629412536388653_<55>
P141 = 934607940975846911851800500250432186081148964077948364953109571678411737172955610971512851456158708210894860371172826511957783213489964794351_<141>

Number: n N=3000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203 ( 196 digits) SNFS difficulty: 199 digits. Divisors found: Thu Oct 23 20:51:46 2008 prp55 factor: 3210403733699042628385928154786408307073629412536388653 Thu Oct 23 20:51:46 2008 prp141 factor: 934607940975846911851800500250432186081148964077948364953109571678411737172955610971512851456158708210894860371172826511957783213489964794351 Thu Oct 23 20:51:47 2008 elapsed time 11:12:22 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 84.04 hours. Scaled time: 171.86 units (timescale=2.045). Factorization parameters were as follows: name: KA_7_1_197 n: 3000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203000468823253633380215658696671354899203 type: snfs skew: 0.69 deg: 5 c5: 25 c0: -4 m: 4000000000000000000000000000000000000000 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, 15500001) Primes: RFBsize:633578, AFBsize:632788, largePrimes:15523414 encountered Relations: rels:15938365, finalFF:1374724 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 83.45 hours. Total relation processing time: 0.58 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,199,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,52,52,2.5,2.5,100000 total time: 84.04 hours. --------- CPU info (if available) ----------
Oct 23, 2008: By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38
(25·10²⁴¹-1)/3 = 8(3)₂₄₁_<242> = 2203 · 3533 · 3139573 · 1058961517_<10> · 2936784733_<10> · 59760373009_<11> · 119276608278517969_<18> · 166630678549184691608467541279_<30> · 372622263768407797404826574707693_<33> · C121
C121 = P41 · P80
P41 = 54171639063846133845831310427219878076359_<41>
P80 = 45737605300666532796752786676494483427340987650457306599587100372839171400797483_<80>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3548948731 Step 1 took 14409ms Step 2 took 5545ms ********** Factor found in step 2: 54171639063846133845831310427219878076359 Found probable prime factor of 41 digits: 54171639063846133845831310427219878076359 Probable prime cofactor 45737605300666532796752786676494483427340987650457306599587100372839171400797483 has 80 digits
6·10¹⁹⁴+7 = 6(0)₁₉₃7_<195> = 4880807929_<10> · C186
C186 = P33 · P153
P33 = 126110244771031557278809682152871_<33>
P153 = 974785733093042308010396782144898734663233985206820852016727149290684723767326775717208198754930119035872196205293376228506927605092858346962533362269673_<153>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1132209484 Step 1 took 21881ms Step 2 took 14389ms ********** Factor found in step 2: 126110244771031557278809682152871 Found probable prime factor of 33 digits: 126110244771031557278809682152871 Probable prime cofactor 974785733093042308010396782144898734663233985206820852016727149290684723767326775717208198754930119035872196205293376228506927605092858346962533362269673 has 153 digits
(82·10¹⁹⁴+71)/9 = 9(1)₁₉₃9_<195> = 157 · 35401 · 439303 · C183
C183 = P32 · P152
P32 = 22467877310459119267034990240771_<32>
P152 = 16608482289955078759929672168069305816166331355355992549338772775044676696047614498320631904769235512996939922475775859447478409033448005589419459522359_<152>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=93914341 Step 1 took 21998ms Step 2 took 14025ms ********** Factor found in step 2: 22467877310459119267034990240771 Found probable prime factor of 32 digits: 22467877310459119267034990240771 Probable prime cofactor 16608482289955078759929672168069305816166331355355992549338772775044676696047614498320631904769235512996939922475775859447478409033448005589419459522359 has 152 digits
(4·10¹⁹⁵-7)/3 = 1(3)₁₉₄1_<196> = 11 · 1657 · 23283583928233049_<17> · C175
C175 = P34 · P142
P34 = 2194943961380131549337327265014227_<34>
P142 = 1431364613322065902729609803616244522630895563591548703486827349517993939479808043205791458209999060733306207315449033301346771404634709812211_<142>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3766808131 Step 1 took 22026ms Step 2 took 10516ms ********** Factor found in step 2: 2194943961380131549337327265014227 Found probable prime factor of 34 digits: 2194943961380131549337327265014227 Probable prime cofactor 1431364613322065902729609803616244522630895563591548703486827349517993939479808043205791458209999060733306207315449033301346771404634709812211 has 142 digits
(8·10¹⁷²-71)/9 = (8)₁₇₁1_<172> = 179 · 286168242716791_<15> · C156
C156 = P42 · P47 · P67
P42 = 859892965727862593870368712758282269775693_<42>
P47 = 96055266805913240015249975071088706895776783497_<47>
P67 = 2100909916748059669934740832392497068778405503990060382377373126649_<67>

SNFS difficulty: 172 digits. Divisors found: r1=859892965727862593870368712758282269775693 r2=96055266805913240015249975071088706895776783497 r3=2100909916748059669934740832392497068778405503990060382377373126649 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.738). Factorization parameters were as follows: n: 173529377939311546112233330859262908774776885502244844273521228100899743749862292880170396230641247365799626515772661387843469000681651927737996523449881229 m: 20000000000000000000000000000000000 c5: 25 c0: -71 skew: 1.23 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 7800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1228674 x 1228922 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,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 80.00 hours.
Oct 22, 2008 (5th): By Sinkiti Sibata / GMP-ECM
(25·10²⁰³-1)/3 = 8(3)₂₀₃_<204> = 900569 · 2432695777627_<13> · C186
C186 = P33 · C153
P33 = 486546315175897598205259424750039_<33>
C153 = [781789388846407183224231919023102419829059677554399166273755190513515221233686096508806523349056395051660115861262590344318823595148958539349778964632369_<153>]

Input number is 380376746386836391787720513595455266505544842024516623969328880579839730067674651069153627908565521628498123510335067429803810807786576517269219113340039622848742338852787297549353412391 Run 179 out of 904: Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2772300172 Step 1 took 34118ms Step 2 took 12776ms Run 180 out of 904: Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3515028684 Step 1 took 34117ms Step 2 took 12761ms ********** Factor found in step 2: 486546315175897598205259424750039 Found probable prime factor of 33 digits: 486546315175897598205259424750039 Composite cofactor 781789388846407183224231919023102419829059677554399166273755190513515221233686096508806523349056395051660115861262590344318823595148958539349778964632369 has 153 digits
Oct 22, 2008 (4th): By Serge Batalov / GMP-ECM 6.2.1
(25·10²¹⁷-1)/3 = 8(3)₂₁₇_<218> = 24083 · 50159 · 682397437 · C201
C201 = P32 · C169
P32 = 53312541175672655088375062336039_<32>
C169 = [1896236612999935992014192963454630164995472234248038672300325066098629976525511506392351915195618799007084787069826889009159795113041528626213108925327088233124191280523_<169>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4157420674 Step 1 took 25198ms Step 2 took 15601ms ********** Factor found in step 2: 53312541175672655088375062336039 Found probable prime factor of 32 digits: 53312541175672655088375062336039 Composite cofactor 1896236612999935992014192963454630164995472234248038672300325066098629976525511506392351915195618799007084787069826889009159795113041528626213108925327088233124191280523 has 169 digits
3·10¹⁹⁵-7 = 2(9)₁₉₄3_<196> = 73 · 367 · 1013 · 919621 · C183
C183 = P37 · C146
P37 = 3410320049990177024859778486328134861_<37>
C146 = [35246732830663562403369748164068680908724548385265603739345073793139596507744308018070883299760651207926080099361321383824319522570619998407671491_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3556153323 Step 1 took 29388ms ********** Factor found in step 1: 3410320049990177024859778486328134861 Found probable prime factor of 37 digits: 3410320049990177024859778486328134861 Composite cofactor 35246732830663562403369748164068680908724548385265603739345073793139596507744308018070883299760651207926080099361321383824319522570619998407671491 has 146 digits
Oct 22, 2008 (3rd): Factorizations of 833...33 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Oct 22, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁷⁵-17)/9 = 2(8)₁₇₄7_<176> = 3 · 368227817 · 45998168948410733_<17> · 4452792496021608493_<19> · C132
C132 = P42 · P90
P42 = 333421341979068916546519038846193733716819_<42>
P90 = 382936350699197296494228208288801846939571547135265957954115629647469996359944562538119167_<90>

Number: 28887_175 N=127679151942693728206021113439808513462081475775475615214415429600954901928788362016440862567483214318764393846123460096592454169773 ( 132 digits) SNFS difficulty: 176 digits. Divisors found: r1=333421341979068916546519038846193733716819 (pp42) r2=382936350699197296494228208288801846939571547135265957954115629647469996359944562538119167 (pp90) Version: GGNFS-0.77.1-20050930-nocona Total time: 309.56 hours. Scaled time: 312.35 units (timescale=1.009). Factorization parameters were as follows: name: 28887_175 n: 127679151942693728206021113439808513462081475775475615214415429600954901928788362016440862567483214318764393846123460096592454169773 m: 100000000000000000000000000000000000 c5: 26 c0: -17 skew: 0.92 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, 15000001) Primes: RFBsize:501962, AFBsize:501686, largePrimes:6831540 encountered Relations: rels:7367937, finalFF:1178170 Max relations in full relation-set: 28 Initial matrix: 1003714 x 1178170 with sparse part having weight 96796142. Pruned matrix : 860913 x 865995 with weight 75896054. Total sieving time: 301.51 hours. Total relation processing time: 0.15 hours. Matrix solve time: 7.74 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 309.56 hours. --------- CPU info (if available) ----------
(22·10¹⁹⁵-31)/9 = 2(4)₁₉₄1_<196> = 18307 · 61409 · 226017649145596719973_<21> · C166
C166 = P32 · C135
P32 = 52333261226040013874068864421239_<32>
C135 = [183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681_<135>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1438106012 Step 1 took 21034ms Step 2 took 12889ms ********** Factor found in step 2: 52333261226040013874068864421239 Found probable prime factor of 32 digits: 52333261226040013874068864421239 Composite cofactor 183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681 has 135 digits
(26·10¹⁷⁴-71)/9 = 2(8)₁₇₃1_<175> = 61 · 70388459 · C165
C165 = P38 · C128
P38 = 22644944916809299781937983566931675591_<38>
C128 = [29711753102043529863724139334764046191153540703972565269144764438568718925369069665849357714992411887439678409638011808886202809_<128>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4142602450 Step 1 took 27291ms Step 2 took 20090ms ********** Factor found in step 2: 22644944916809299781937983566931675591 Found probable prime factor of 38 digits: 22644944916809299781937983566931675591 Composite cofactor 29711753102043529863724139334764046191153540703972565269144764438568718925369069665849357714992411887439678409638011808886202809 has 128 digits
Oct 22, 2008: By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38
5·10¹⁹⁷-9 = 4(9)₁₉₆1_<198> = 823 · 3257 · 34031 · 6940928766071_<13> · 76433656928038861510273_<23> · C152
C152 = P43 · P109
P43 = 2168632766838689918632576115783405377195649_<43>
P109 = 4764194222655886177034856326166901781481228840032171605198783310162696238849016167824739197316648246761058353_<109>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3644175409 Step 1 took 18528ms Step 2 took 14609ms ********** Factor found in step 2: 2168632766838689918632576115783405377195649 Found probable prime factor of 43 digits: 2168632766838689918632576115783405377195649 Probable prime cofactor 4764194222655886177034856326166901781481228840032171605198783310162696238849016167824739197316648246761058353 has 109 digits
5·10¹⁹⁹+9 = 5(0)₁₉₈9_<200> = 17 · 163 · C197
C197 = P37 · C161
P37 = 1593430546178302621526623328857130497_<37>
C161 = [11324012502583584716566772960189801921788975775190511695521026198515623091804565348455568883549293387605458234997823194604094623522025069708549012210465528813107_<161>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1420271003 Step 1 took 29385ms Step 2 took 17514ms ********** Factor found in step 2: 1593430546178302621526623328857130497 Found probable prime factor of 37 digits: 1593430546178302621526623328857130497 Composite cofactor 11324012502583584716566772960189801921788975775190511695521026198515623091804565348455568883549293387605458234997823194604094623522025069708549012210465528813107 has 161 digits
(7·10¹⁹⁶-61)/9 = (7)₁₉₅1_<196> = 131 · 1249 · 4051 · 127852841 · 1197242672028108617231_<22> · C158
C158 = P39 · P120
P39 = 484157287113548064449100693247493210791_<39>
P120 = 158336306549811414521395276193314134816000853211628844174230012646700094764773236328445359419394774791738633126133192019_<120>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1582530103 Step 1 took 24888ms Step 2 took 16469ms ********** Factor found in step 2: 484157287113548064449100693247493210791 Found probable prime factor of 39 digits: 484157287113548064449100693247493210791 Probable prime cofactor 158336306549811414521395276193314134816000853211628844174230012646700094764773236328445359419394774791738633126133192019 has 120 digits
(4·10¹⁷⁷-13)/9 = (4)₁₇₆3_<177> = 19 · 14431 · 23473 · 628267 · C162
C162 = P57 · P105
P57 = 320789733615284478790758170913537296973917782547673504923_<57>
P105 = 342636910756108034586766060914046263261456091001097853168240096906715579872630546306091053981879958965759_<105>

SNFS difficulty: 177 digits. Divisors found: r1=320789733615284478790758170913537296973917782547673504923 r2=342636910756108034586766060914046263261456091001097853168240096906715579872630546306091053981879958965759 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.281). Factorization parameters were as follows: n: 109914403328215897583290904223367841286661632871483804427109630525156921629961980459222248722455169313801745457689541853647747810604369591678411685966649674931557 m: 200000000000000000000000000000000000 c5: 25 c0: -26 skew: 1.01 type: snfs Factor base limits: 11400000/11400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [5700000, 10100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1424965 x 1425213 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,177,5,0,0,0,0,0,0,0,0,11400000,11400000,27,27,54,54,2.6,2.6,100000 total time: 110.00 hours.
(34·10¹⁹³-7)/9 = 3(7)₁₉₃_<194> = 37 · 22901 · C188
C188 = P30 · P158
P30 = 946117454127035503341112357253_<30>
P158 = 47123244252065994014385015090264019377616545139384926670539844445909827517900655076093584087367694433369681889961469872752436905117920097107236907128765203957_<158>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3439099762 Step 1 took 28025ms Step 2 took 19251ms ********** Factor found in step 2: 946117454127035503341112357253 Found probable prime factor of 30 digits: 946117454127035503341112357253 Probable prime cofactor 47123244252065994014385015090264019377616545139384926670539844445909827517900655076093584087367694433369681889961469872752436905117920097107236907128765203957 has 158 digits
(4·10¹⁹⁶+17)/3 = 1(3)₁₉₅9_<197> = 107 · C195
C195 = P30 · P165
P30 = 641296994832521105786533002959_<30>
P165 = 194310269507585008333310325816908802409995304643133352971273908773477838968564150543240097299719754825793275239136337188618271630275071223132887746105578377626129503_<165>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1275197237 Step 1 took 27673ms Step 2 took 15717ms ********** Factor found in step 2: 641296994832521105786533002959 Found probable prime factor of 30 digits: 641296994832521105786533002959 Probable prime cofactor 194310269507585008333310325816908802409995304643133352971273908773477838968564150543240097299719754825793275239136337188618271630275071223132887746105578377626129503 has 165 digits
(5·10¹⁹³+13)/9 = (5)₁₉₂7_<193> = 7 · 47 · 15649 · 1023815540327_<13> · C175
C175 = P35 · C140
P35 = 96202913674607842378594019111136319_<35>
C140 = [10955572152743952498130226545991213873754319162826343738038102711428932017005877244725536758158221707727384194996333763864519351564276702309_<140>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1846112973 Step 1 took 28376ms Step 2 took 18626ms ********** Factor found in step 2: 96202913674607842378594019111136319 Found probable prime factor of 35 digits: 96202913674607842378594019111136319 Composite cofactor 10955572152743952498130226545991213873754319162826343738038102711428932017005877244725536758158221707727384194996333763864519351564276702309 has 140 digits
(14·10¹⁹⁵+13)/9 = 1(5)₁₉₄7_<196> = 3 · C195
C195 = P31 · C165
P31 = 1415892518921261163610086153683_<31>
C165 = [366213191742524998189471571564403867788336481566277323078309497974979063250048045513244983636839391531554468834937850896594871724072212797942208215172448975244422093_<165>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1098833014 Step 1 took 35065ms Step 2 took 20938ms ********** Factor found in step 2: 1415892518921261163610086153683 Found probable prime factor of 31 digits: 1415892518921261163610086153683 Composite cofactor 366213191742524998189471571564403867788336481566277323078309497974979063250048045513244983636839391531554468834937850896594871724072212797942208215172448975244422093 has 165 digits
(88·10¹⁹⁵-7)/9 = 9(7)₁₉₅_<196> = 3 · 1373153 · 23721061919_<11> · 998739769839937_<15> · 229945776953320669_<18> · C147
C147 = P32 · P116
P32 = 17709857971448705875752495584023_<32>
P116 = 24602145954927762256766162278883504969116012969682193397520906584714252423186238558577964843369251118649923063873823_<116>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3297299414 Step 1 took 15977ms Step 2 took 10901ms ********** Factor found in step 2: 17709857971448705875752495584023 Found probable prime factor of 32 digits: 17709857971448705875752495584023 Probable prime cofactor 24602145954927762256766162278883504969116012969682193397520906584714252423186238558577964843369251118649923063873823 has 116 digits
Oct 21, 2008 (2nd): By matsui /
9·10¹⁹⁵-7 = 8(9)₁₉₄3_<196> = 17 · 439 · 119183 · 1271399 · 242885213 · C173
C173 = P36 · C137
P36 = 461827684596426570878380861037770727_<36>
C137 = [70949910236655858413737617479417459261252133160753837106470160640665889525424116417039764845206841627192033768547036282598220368986487733_<137>]

32766632766919078662825942812534767317385600913749182215022623020157389542005326478182856310139863849914763447191777621051072856816588852757981045807466834521306007851991891 = 461827684596426570878380861037770727* 70949910236655858413737617479417459261252133160753837106470160640665889525424116417039764845206841627192033768547036282598220368986487733
Oct 21, 2008: By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(14·10¹⁷⁶+31)/9 = 1(5)₁₇₅9_<177> = 3 · 566207205049711_<15> · C161
C161 = P59 · P103
P59 = 56152629625366819992137469300041576546741213872597735252417_<59>
P103 = 1630867885921653385652101326198882104756613516393727742204108998674895216128979500226008716085217882819_<103>

SNFS difficulty: 177 digits. Divisors found: r1=56152629625366819992137469300041576546741213872597735252417 r2=1630867885921653385652101326198882104756613516393727742204108998674895216128979500226008716085217882819 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.310). Factorization parameters were as follows: n: 91577520366063589277240766947306748041354023568047146249685501908499620499316018448070354842587752733157064074686017179232354084676531620519553064437257292523523 Y1: 1 Y0: -100000000000000000000000000000000000 c5: 140 c0: 31 skew: 0.74 type: snfs Factor base limits: 11400000/11400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [5700000, 10200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1465262 x 1465510 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,177,5,0,0,0,0,0,0,0,0,11400000,11400000,27,27,54,54,2.6,2.6,100000 total time: 150.00 hours.
2·10¹⁸²+9 = 2(0)₁₈₁9_<183> = 11² · 19 · C179
C179 = P46 · P134
P46 = 4792421492537717215974620350584419014570035427_<46>
P134 = 18152482101795525258673725492310366645321546282550812322674378256610903698310179167802038160476302016480186262806948758018518330672633_<134>

SNFS difficulty: 182 digits. Divisors found: r1=4792421492537717215974620350584419014570035427 r2=18152482101795525258673725492310366645321546282550812322674378256610903698310179167802038160476302016480186262806948758018518330672633 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: n: 86994345367551109177903436276642018268812527185732927359721618094823836450630709003914745541539799913005654632448890822096563723357981731187472814267072640278381905176163549369291 m: 1000000000000000000000000000000000000 c5: 200 c0: 9 skew: 0.54 type: snfs Factor base limits: 15000000/15000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 49/49 Sieved rational special-q in [7500000, 10300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1054356 x 1054581 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,182,5,0,0,0,0,0,0,0,0,15000000,15000000,28,28,49,49,2.6,2.6,100000 total time: 220.00 hours.
(14·10²⁰⁰+13)/9 = 1(5)₁₉₉7_<201> = 149 · 82234460157247_<14> · 801797680026694996283_<21> · C164
C164 = P28 · P31 · P32 · P74
P28 = 6459280719655949148659797177_<28>
P31 = 3406177645914414016513634539813_<31>
P32 = 29650943696340059768408884079497_<32>
P74 = 24271166126560128989106147319544463210746453787159176905895443038471222169_<74>

# 3 ECM factors! Yes, 3! # Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3727128160 Step 1 took 19634ms ********** Factor found in step 1: 6459280719655949148659797177 Found probable prime factor of 28 digits: 6459280719655949148659797177 # Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=520959377 Step 1 took 24794ms Step 2 took 16513ms ********** Factor found in step 2: 3406177645914414016513634539813 Found probable prime factor of 31 digits: 3406177645914414016513634539813 # Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=249960142 Step 1 took 24944ms Step 2 took 16634ms ********** Factor found in step 2: 29650943696340059768408884079497 Found probable prime factor of 32 digits: 29650943696340059768408884079497
(19·10²⁰⁰+17)/9 = 2(1)₁₉₉3_<201> = 3 · 126544763 · 2943578385629665516163_<22> · C171
C171 = P27 · P144
P27 = 898447831098242238266148503_<27>
P144 = 210269939678342336529513921152874898053927458055258874398493904056791369753272627555998930381253413935650920678917164241827912150245681803371653_<144>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2082085495 Step 1 took 19441ms Step 2 took 12897ms ********** Factor found in step 2: 898447831098242238266148503 Found probable prime factor of 27 digits: 898447831098242238266148503 Probable prime cofactor 210269939678342336529513921152874898053927458055258874398493904056791369753272627555998930381253413935650920678917164241827912150245681803371653 has 144 digits
2·10²⁰⁰-1 = 1(9)₂₀₀_<201> = 47 · 199 · 8832847 · 26986789362889673_<17> · C173
C173 = P32 · C142
P32 = 22887618087703883422612434497873_<32>
C142 = [3919462703564142473698047873878421629698357069094950750629640809045036371942703314337013367544634521328393484746001349161465007919976067433841_<142>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2533383244 Step 1 took 20761ms Step 2 took 12781ms ********** Factor found in step 2: 22887618087703883422612434497873 Found probable prime factor of 32 digits: 22887618087703883422612434497873 Composite cofactor 3919462703564142473698047873878421629698357069094950750629640809045036371942703314337013367544634521328393484746001349161465007919976067433841 has 142 digits
8·10²⁰⁰+3 = 8(0)₁₉₉3_<201> = 11 · 607472219 · 147010366511382569644373_<24> · C168
C168 = P37 · C132
P37 = 7546527715304377195290179372975899421_<37>
C132 = [107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499_<132>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4043050459 Step 1 took 24875ms Step 2 took 17112ms ********** Factor found in step 2: 7546527715304377195290179372975899421 Found probable prime factor of 37 digits: 7546527715304377195290179372975899421 Composite cofactor 107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499 has 132 digits
(82·10²⁰⁰-1)/9 = 9(1)₂₀₀_<201> = 402883508155939_<15> · C187
C187 = P33 · P155
P33 = 102407901890348689567844185695023_<33>
P155 = 22083015858137772409667015245738789158555690527213028648393927531768748273294785668401228006283649881036393732744822021725553670861667592092248276044786563_<155>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3874257449 Step 1 took 29631ms Step 2 took 19525ms ********** Factor found in step 2: 102407901890348689567844185695023 Found probable prime factor of 33 digits: 102407901890348689567844185695023 Probable prime cofactor 22083015858137772409667015245738789158555690527213028648393927531768748273294785668401228006283649881036393732744822021725553670861667592092248276044786563 has 155 digits
6·10¹⁹⁸-7 = 5(9)₁₉₇3_<199> = 167 · 265447401151_<12> · C186
C186 = P31 · C155
P31 = 1599529266754550409912307759727_<31>
C155 = [84618263884039984680979205479242373328854046385994102543980925758836773562467373965067601568858438800912633777084401273137347795319481939335873583645268527_<155>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1986207576 Step 1 took 23769ms ********** Factor found in step 1: 1599529266754550409912307759727 Found probable prime factor of 31 digits: 1599529266754550409912307759727 Composite cofactor 84618263884039984680979205479242373328854046385994102543980925758836773562467373965067601568858438800912633777084401273137347795319481939335873583645268527 has 155 digits
(22·10¹⁹⁹+23)/9 = 2(4)₁₉₈7_<200> = 3² · 619 · 128173 · 742789 · 149620828199987785329497659_<27> · C159
C159 = P32 · P127
P32 = 43482312117488028224282836493909_<32>
P127 = 7084028770911422344248461958410720572198835237947535379552273443567806999719918274887993804124122573096734631865106103730841651_<127>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=329097599 Step 1 took 19390ms Step 2 took 12444ms ********** Factor found in step 2: 43482312117488028224282836493909 Found probable prime factor of 32 digits: 43482312117488028224282836493909 Probable prime cofactor 7084028770911422344248461958410720572198835237947535379552273443567806999719918274887993804124122573096734631865106103730841651 has 127 digits
(4·10¹⁹⁸-7)/3 = 1(3)₁₉₇1_<199> = 35433614694519093943915021_<26> · C173
C173 = P29 · C144
P29 = 53080170921181623484835211569_<29>
C144 = [708909776366544417055494111166661177395346300454696028653520045734998051049191473489799475703118236101317585796307759176426123229836426451112719_<144>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1091327796 Step 1 took 20217ms Step 2 took 12849ms ********** Factor found in step 2: 53080170921181623484835211569 Found probable prime factor of 29 digits: 53080170921181623484835211569 Composite cofactor 708909776366544417055494111166661177395346300454696028653520045734998051049191473489799475703118236101317585796307759176426123229836426451112719 has 144 digits
(8·10¹⁹⁸-71)/9 = (8)₁₉₇1_<198> = 7 · 181 · 246151 · 26571308869211899069_<20> · C171
C171 = P31 · C140
P31 = 2181736485124043717540785640249_<31>
C140 = [49164770484616078662130837495285105615980477313414831637996342826393591225258796960761072524813073625782737476138348702108473214785930571753_<140>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2812342345 Step 1 took 24849ms Step 2 took 16942ms ********** Factor found in step 2: 2181736485124043717540785640249 Found probable prime factor of 31 digits: 2181736485124043717540785640249 Composite cofactor 49164770484616078662130837495285105615980477313414831637996342826393591225258796960761072524813073625782737476138348702108473214785930571753 has 140 digits
(14·10¹⁹⁹-41)/9 = 1(5)₁₉₈1_<200> = 11 · 9905209 · 49424550329263117_<17> · C175
C175 = P29 · C146
P29 = 93342682385042014936376105033_<29>
C146 = [30946119177002457256257679064752877429329252807104046662651498568475129246685538584195558365545659808057878297832367685917174350969470564322807409_<146>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3253425714 Step 1 took 28821ms Step 2 took 18723ms ********** Factor found in step 2: 93342682385042014936376105033 Found probable prime factor of 29 digits: 93342682385042014936376105033 Composite cofactor 30946119177002457256257679064752877429329252807104046662651498568475129246685538584195558365545659808057878297832367685917174350969470564322807409 has 146 digits
(19·10¹⁹⁷+17)/9 = 2(1)₁₉₆3_<198> = 3 · 7 · 90017 · 189037603483_<12> · 1167987135194728007608387_<25> · C156
C156 = P33 · C124
P33 = 130987118004416341717932217759037_<33>
C124 = [3861467755350303484159223919449335539186556972805576020551599415949486879617583193229971628069176142786276497779467927144217_<124>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3671506003 Step 1 took 19437ms Step 2 took 12449ms ********** Factor found in step 2: 130987118004416341717932217759037 Found probable prime factor of 33 digits: 130987118004416341717932217759037 Composite cofactor 3861467755350303484159223919449335539186556972805576020551599415949486879617583193229971628069176142786276497779467927144217 has 124 digits
(88·10¹⁹⁷-7)/9 = 9(7)₁₉₇_<198> = 47 · 61 · 12150092320841_<14> · 39579394802884247_<17> · C165
C165 = P36 · C130
P36 = 120780957158617319735656378500678509_<36>
C130 = [5871719163515225280922211088120438405575691242148159445644927132369821177548971534618963281375524980385790625213433048301365617017_<130>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3923837933 Step 1 took 21101ms Step 2 took 12849ms ********** Factor found in step 2: 120780957158617319735656378500678509 Found probable prime factor of 36 digits: 120780957158617319735656378500678509 Composite cofactor 5871719163515225280922211088120438405575691242148159445644927132369821177548971534618963281375524980385790625213433048301365617017 has 130 digits
(25·10¹⁹⁷+11)/9 = 2(7)₁₉₆9_<198> = 3 · 29 · 31 · 131 · 167 · 11973221894137871_<17> · C174
C174 = P36 · P138
P36 = 859405617629884678518292762614354083_<36>
P138 = 457529990349271379357800820089302302513147819742197174361744364096811170650975745897790665507102867916025781272624748791884073929721978187_<138>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3634545673 Step 1 took 22749ms Step 2 took 14193ms ********** Factor found in step 2: 859405617629884678518292762614354083 Found probable prime factor of 36 digits: 859405617629884678518292762614354083 Probable prime cofactor 457529990349271379357800820089302302513147819742197174361744364096811170650975745897790665507102867916025781272624748791884073929721978187 has 138 digits
3·10¹⁹⁷+7 = 3(0)₁₉₆7_<198> = 2357 · 8929 · 1802680774763383_<16> · C175
C175 = P29 · P146
P29 = 97148865973080265245073984193_<29>
P146 = 81395854489413446318803739695291383680562514323245286068600107617125030508665056235124237334794958273834035260731457900762605517868916643151494701_<146>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1336248685 Step 1 took 21957ms Step 2 took 14189ms ********** Factor found in step 2: 97148865973080265245073984193 Found probable prime factor of 29 digits: 97148865973080265245073984193 Probable prime cofactor 81395854489413446318803739695291383680562514323245286068600107617125030508665056235124237334794958273834035260731457900762605517868916643151494701 has 146 digits
(19·10¹⁹⁷-1)/9 = 2(1)₁₉₇_<198> = 217409 · 148309607497483921_<18> · C175
C175 = P29 · C147
P29 = 39352703424498545120297305189_<29>
C147 = [166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091_<147>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2585434931 Step 1 took 22001ms Step 2 took 2841ms ********** Factor found in step 2: 39352703424498545120297305189 Found probable prime factor of 29 digits: 39352703424498545120297305189 Composite cofactor 166375630748703395463164557225749379129853263886867234344540086253317490155678563790257803512283631412627990637610456181042880430192706837121126091 has 147 digits
(4·10¹⁹⁷+11)/3 = 1(3)₁₉₆7_<198> = 19 · 1511 · 19347313 · 434677339 · C177
C177 = P33 · C145
P33 = 145143707113728537226153436432311_<33>
C145 = [3804826017512159968793268569143505668827839952767829974171836729047124862981119444455807733568534433006902687070212949433801193366615213429833609_<145>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1442437893 Step 1 took 21958ms Step 2 took 14017ms ********** Factor found in step 2: 145143707113728537226153436432311 Found probable prime factor of 33 digits: 145143707113728537226153436432311 Composite cofactor 3804826017512159968793268569143505668827839952767829974171836729047124862981119444455807733568534433006902687070212949433801193366615213429833609 has 145 digits
7·10¹⁹⁸-9 = 6(9)₁₉₇1_<199> = 113 · 557 · 14669 · 1011899197_<10> · C181
C181 = P33 · P149
P33 = 264988857469403991211956741757711_<33>
P149 = 28274766614610714157255420998775798591008627434112116606543963199796112209476723290238538742147137438714006318672046665431077283855690553184035469237_<149>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3404709547 Step 1 took 29350ms Step 2 took 18701ms ********** Factor found in step 2: 264988857469403991211956741757711 Found probable prime factor of 33 digits: 264988857469403991211956741757711 Probable prime cofactor 28274766614610714157255420998775798591008627434112116606543963199796112209476723290238538742147137438714006318672046665431077283855690553184035469237 has 149 digits
Oct 20, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁷²-17)/9 = 2(8)₁₇₁7_<173> = 3² · 41 · 83 · 131 · 527623 · 371470216724616829_<18> · 1322759690532757068064807_<25> · C119
C119 = P32 · P36 · P51
P32 = 79595740428624758405274066235447_<32>
P36 = 605333788407412819438944577230313913_<36>
P51 = 576423491058992736416957914655421765461285925809189_<51>

Number: 28887_172 N=27773231513010531676806997508834162293990971944311745383468612502175567406803821638563467475456350783538064197649005979 ( 119 digits) Divisors found: r1=79595740428624758405274066235447 (pp32) r2=605333788407412819438944577230313913 (pp36) r3=576423491058992736416957914655421765461285925809189 (pp51) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 94.00 hours. Scaled time: 44.46 units (timescale=0.473). Factorization parameters were as follows: name: 28887_172 n: 27773231513010531676806997508834162293990971944311745383468612502175567406803821638563467475456350783538064197649005979 skew: 37008.98 # norm 3.26e+16 c5: 55440 c4: 3164058222 c3: 1264562398005151 c2: -4105551205117045627 c1: -550046594059784674117371 c0: -1001973857328021287339465895 # alpha -6.55 Y1: 524543343403 Y0: -54949100966099077885304 # Murphy_E 3.50e-10 # M 6977594599683708295921293182066515609590231586712473955854354315894030466074015681292072989429107770858219365562363712 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, 4170001) Primes: RFBsize:315948, AFBsize:315849, largePrimes:7625017 encountered Relations: rels:7651561, finalFF:714486 Max relations in full relation-set: 28 Initial matrix: 631882 x 714486 with sparse part having weight 61493390. Pruned matrix : 563522 x 566745 with weight 43154206. Total sieving time: 77.23 hours. Total relation processing time: 0.94 hours. Matrix solve time: 15.34 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 94.00 hours. --------- CPU info (if available) ----------
Oct 20, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(86·10¹⁸⁷+31)/9 = 9(5)₁₈₆9_<188> = 3 · 11 · 17 · C186
C186 = P41 · P64 · P82
P41 = 82497070342294097847760872671048101547273_<41>
P64 = 1137506622062276258802403675541190635066970154120153739009283317_<64>
P82 = 1815100267956222784484327964833504354369950932271791040395824755849419204499493059_<82>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 170330758566052683699742523271935036640918993860170330758566052683699742523271935036640918993860170330758566052683699742523271935036640918993860170330758566052683699742523271935036640919 (186 digits) Using B1=6498000, B2=14271500890, polynomial Dickson(12), sigma=3182954353 Step 1 took 110706ms Step 2 took 38266ms ********** Factor found in step 2: 82497070342294097847760872671048101547273 Found probable prime factor of 41 digits: 82497070342294097847760872671048101547273 Composite cofactor 2064688574507215477497755904533791903970653712003879148874388035763738505270729759860310938616946784208098286504015093167178563384654221405996703 has 145 digits Number: n N=2064688574507215477497755904533791903970653712003879148874388035763738505270729759860310938616946784208098286504015093167178563384654221405996703 ( 145 digits) SNFS difficulty: 188 digits. Divisors found: Mon Oct 20 06:06:17 2008 prp64 factor: 1137506622062276258802403675541190635066970154120153739009283317 Mon Oct 20 06:06:17 2008 prp82 factor: 1815100267956222784484327964833504354369950932271791040395824755849419204499493059 Mon Oct 20 06:06:17 2008 elapsed time 14:04:55 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 73.18 hours. Scaled time: 95.50 units (timescale=1.305). Factorization parameters were as follows: name: KA_9_5_186_9 n: 2064688574507215477497755904533791903970653712003879148874388035763738505270729759860310938616946784208098286504015093167178563384654221405996703 # n: 170330758566052683699742523271935036640918993860170330758566052683699742523271935036640918993860170330758566052683699742523271935036640918993860170330758566052683699742523271935036640919 type: snfs skew: 0.32 deg: 5 c5: 8600 c0: 31 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 4600001) Primes: RFBsize:602489, AFBsize:602751, largePrimes:14634264 encountered Relations: rels:14608986, finalFF:1232635 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 72.49 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,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 73.18 hours. --------- CPU info (if available) ----------
Oct 19, 2008 (2nd): By Serge Batalov / Msieve-1.38
(5·10¹⁷⁵-11)/3 = 1(6)₁₇₄3_<176> = 13 · 79 · 2089896749_<10> · C163
C163 = P60 · P104
P60 = 144047157479044276664515263647763869136494387420848021424177_<60>
P104 = 53907449282249810484152355599174717398503110311207169164812814056689715236474601082663524167528740888753_<104>

SNFS difficulty: 175 digits. Divisors found: r1=144047157479044276664515263647763869136494387420848021424177 r2=53907449282249810484152355599174717398503110311207169164812814056689715236474601082663524167528740888753 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.289). Factorization parameters were as follows: n: 7765214836053830812275343365804816217160142233644828115751473920601722240369883569064895059784125043523570290124022191806025184608151076080284683874319931781581281 m: 100000000000000000000000000000000000 c5: 5 c0: -11 skew: 1.17 type: snfs Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [5000000, 8100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1275006 x 1275254 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,175,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000 total time: 60.00 hours.
Oct 19, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(67·10¹⁷²+23)/9 = 7(4)₁₇₁7_<173> = 97 · 113 · 1589431 · 1851763 · 15393406299013_<14> · 6244601986384031_<16> · C128
C128 = P48 · P80
P48 = 372451441498190701496064087171739015353189667169_<48>
P80 = 64453407041615178803320844206373593795836632906817191842652742276875476360294537_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 24005764362119208380643126639474468236589502434740487688631317708317255847326760429726029271573224998580272635211810049838955753 (128 digits) Using B1=7600000, B2=17126054410, polynomial Dickson(12), sigma=3670869563 Step 1 took 75402ms Step 2 took 28669ms ********** Factor found in step 2: 372451441498190701496064087171739015353189667169 Found probable prime factor of 48 digits: 372451441498190701496064087171739015353189667169 Probable prime cofactor 64453407041615178803320844206373593795836632906817191842652742276875476360294537 has 80 digits
(26·10¹⁷⁵-53)/9 = 2(8)₁₇₄3_<176> = 19 · C175
C175 = P44 · P52 · P80
P44 = 19864097753703704521827520997023829831149889_<44>
P52 = 1054510268817082005325406588880925137752766424226059_<52>
P80 = 72586788244848406664760136158312476684344733516938432662645506456827825620239107_<80>

Number: n N=1520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257 ( 175 digits) SNFS difficulty: 176 digits. Divisors found: Sun Oct 19 19:49:27 2008 prp44 factor: 19864097753703704521827520997023829831149889 Sun Oct 19 19:49:28 2008 prp52 factor: 1054510268817082005325406588880925137752766424226059 Sun Oct 19 19:49:28 2008 prp80 factor: 72586788244848406664760136158312476684344733516938432662645506456827825620239107 Sun Oct 19 19:49:28 2008 elapsed time 03:39:37 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.77 hours. Scaled time: 58.83 units (timescale=2.045). Factorization parameters were as follows: name: KA_2_8_174_3 n: 1520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257309941520467836257 type: snfs skew: 1.15 deg: 5 c5: 26 c0: -53 m: 100000000000000000000000000000000000 rlim: 7500000 alim: 7500000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7500000/7500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 5400001) Primes: RFBsize:508261, AFBsize:507306, largePrimes:15130815 encountered Relations: rels:15517541, finalFF:1644503 Max relations in full relation-set: 28 Initial matrix: 1015633 x 1644502 with sparse part having weight 201628258. Pruned matrix : Total sieving time: 28.36 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,52,52,2.5,2.5,100000 total time: 28.77 hours. --------- CPU info (if available) ----------
Oct 18, 2008 (4th): By Wataru Sakai / GGNFS
7·10¹⁸⁸+9 = 7(0)₁₈₇9_<189> = 29 · 281 · C185
C185 = P48 · P138
P48 = 390755155423951786421642709723832482956478913627_<48>
P138 = 219831035497922940488479509910463429809878109532808903912313282503371748866596450007079463861910551465289953658044366335149641788862040383_<138>

Number: 70009_188 N=85900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110442999141 ( 185 digits) SNFS difficulty: 188 digits. Divisors found: r1=390755155423951786421642709723832482956478913627 (pp48) r2=219831035497922940488479509910463429809878109532808903912313282503371748866596450007079463861910551465289953658044366335149641788862040383 (pp138) Version: GGNFS-0.77.1-20060722-nocona Total time: 1450.14 hours. Scaled time: 2891.58 units (timescale=1.994). Factorization parameters were as follows: n: 85900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110442999140998895570008590011044299914099889557000859001104429991409988955700085900110442999141 m: 10000000000000000000000000000000000000 c5: 7000 c0: 9 skew: 0.26 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, 24600001) Primes: RFBsize:501962, AFBsize:501336, largePrimes:7487189 encountered Relations: rels:8168947, finalFF:1186873 Max relations in full relation-set: 32 Initial matrix: 1003366 x 1186873 with sparse part having weight 161157006. Pruned matrix : 876731 x 881811 with weight 145912668. Total sieving time: 1436.68 hours. Total relation processing time: 0.20 hours. Matrix solve time: 12.95 hours. Time per square root: 0.31 hours. Prototype def-par.txt line would be: snfs,188,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1450.14 hours. --------- CPU info (if available) ----------
5·10¹⁹⁴-9 = 4(9)₁₉₃1_<195> = 311 · C193
C193 = P36 · P60 · P98
P36 = 568077914109210905300509346220531359_<36>
P60 = 132431729646308774647525574567728230397013165316585384835709_<60>
P98 = 21370252768992179896389372845940321522055761100150580614076984207751248231030310254841786517307851_<98>

Number: 49991_194 N=1607717041800643086816720257234726688102893890675241157556270096463022508038585209003215434083601286173633440514469453376205787781350482315112540192926045016077170418006430868167202572347266881 ( 193 digits) SNFS difficulty: 195 digits. Divisors found: r1=568077914109210905300509346220531359 (pp36) r2=132431729646308774647525574567728230397013165316585384835709 (pp60) r3=21370252768992179896389372845940321522055761100150580614076984207751248231030310254841786517307851 (pp98) Version: GGNFS-0.77.1-20060722-nocona Total time: 2068.37 hours. Scaled time: 4157.43 units (timescale=2.010). Factorization parameters were as follows: n: 1607717041800643086816720257234726688102893890675241157556270096463022508038585209003215434083601286173633440514469453376205787781350482315112540192926045016077170418006430868167202572347266881 m: 1000000000000000000000000000000000000000 c5: 1 c0: -18 skew: 1.78 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, 3700000) Primes: RFBsize:501962, AFBsize:502056, largePrimes:7770161 encountered Relations: rels:8548694, finalFF:1151262 Max relations in full relation-set: 32 Initial matrix: 1004085 x 1151262 with sparse part having weight 177304272. Pruned matrix : 910075 x 915159 with weight 160568505. Total sieving time: 2049.99 hours. Total relation processing time: 0.31 hours. Matrix solve time: 17.74 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 2068.37 hours. --------- CPU info (if available) ----------
Oct 18, 2008 (3rd): By Sinkiti Sibata / GGNFS
(26·10¹⁷¹-53)/9 = 2(8)₁₇₀3_<172> = 3 · 211 · 122719 · C164
C164 = P75 · P90
P75 = 180794175688461612300191133500389304146671181730293708035199997373677168279_<75>
P90 = 205698386608080360118607066964350163888517864066216726017377451689667747458205138175489651_<90>

Number: 28883_171 N=37189070247254379933093515608867117606170787003243257385914198810335088069575624062314246404907190505731062435395522633044302883104269186116325126035940349949980629 ( 164 digits) SNFS difficulty: 172 digits. Divisors found: r1=180794175688461612300191133500389304146671181730293708035199997373677168279 (pp75) r2=205698386608080360118607066964350163888517864066216726017377451689667747458205138175489651 (pp90) Version: GGNFS-0.77.1-20050930-nocona Total time: 221.55 hours. Scaled time: 223.54 units (timescale=1.009). Factorization parameters were as follows: name: 28883_171 n: 37189070247254379933093515608867117606170787003243257385914198810335088069575624062314246404907190505731062435395522633044302883104269186116325126035940349949980629 m: 10000000000000000000000000000000000 c5: 260 c0: -53 skew: 0.73 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, 11500001) Primes: RFBsize:412849, AFBsize:413441, largePrimes:6524908 encountered Relations: rels:6877907, finalFF:969004 Max relations in full relation-set: 28 Initial matrix: 826357 x 969004 with sparse part having weight 93418054. Pruned matrix : 719756 x 723951 with weight 75272991. Total sieving time: 215.51 hours. Total relation processing time: 0.16 hours. Matrix solve time: 5.74 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 221.55 hours. --------- CPU info (if available) ----------
Oct 18, 2008 (2nd): By Serge Batalov / Msieve-1.38
(17·10¹⁶⁹+1)/9 = 1(8)₁₆₈9_<170> = 2286095969_<10> · 61583159712948473_<17> · C144
C144 = P40 · P50 · P54
P40 = 2904146275484962375815593435366057290811_<40>
P50 = 67503164136279247648768712027109846191861011687973_<50>
P54 = 684395851991037539017805425656538836579993071788064599_<54>

SNFS difficulty: 171 digits. Divisors found: r1=2904146275484962375815593435366057290811 r2=67503164136279247648768712027109846191861011687973 r3=684395851991037539017805425656538836579993071788064599 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.313). Factorization parameters were as follows: n: 134168321346815434942285506994673592803638268962020611376419262011341845173814146151104444227872039130130466930338638784045925621136206412137697 m: 10000000000000000000000000000000000 c5: 17 c0: 10 skew: 0.9 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, 5200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 959749 x 959997 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,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 40.00 hours.
(13·10¹⁶⁷+23)/9 = 1(4)₁₆₆7_<168> = 3 · 571 · 1120864826830189595009_<22> · C143
C143 = P52 · P92
P52 = 2196722081660400619860435665895112903415321030329429_<52>
P92 = 34246415634863136312265358406712864250373833913675284562837241961141882980145948561830479379_<92>

SNFS difficulty: 168 digits. Divisors found: r1=2196722081660400619860435665895112903415321030329429 r2=34246415634863136312265358406712864250373833913675284562837241961141882980145948561830479379 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.310). Factorization parameters were as follows: n: 75229857442823839063327954585610815916921620664868103784648473223197175129674845956583458783493459542969045721078101701111280306855293361344591 m: 1000000000000000000000000000000000 c5: 1300 c0: 23 skew: 0.45 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, 5450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 972189 x 972437 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,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,54,54,2.6,2.6,100000 total time: 40.00 hours.
Oct 18, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(8·10¹⁸⁶-71)/9 = (8)₁₈₅1_<186> = 7 · 6247 · C182
C182 = P45 · P49 · P89
P45 = 987895103890722668057692699475951929826842691_<45>
P49 = 1518369038049027997383307706026952156843005415743_<49>
P89 = 13551574573816468594611225834346709335102626184834964057831450659712303002693008791158453_<89>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 20327217381803583180243977426625097507120878339063067732829218342264604470463282693153030915156735550524569253559168718445171142465843922543138166637446291680324015845065949115893089 (182 digits) Using B1=6016000, B2=14270867530, polynomial Dickson(12), sigma=513170549 Step 1 took 93488ms Step 2 took 36334ms ********** Factor found in step 2: 987895103890722668057692699475951929826842691 Found probable prime factor of 45 digits: 987895103890722668057692699475951929826842691 Composite cofactor 20576291249695377971301832017847716213382725784697613948242181117163577126798867943121419615352806546244832708544699170564753533853725579 has 137 digits Number: n N=20576291249695377971301832017847716213382725784697613948242181117163577126798867943121419615352806546244832708544699170564753533853725579 ( 137 digits) SNFS difficulty: 187 digits. Divisors found: Sat Oct 18 02:11:00 2008 prp49 factor: 1518369038049027997383307706026952156843005415743 Sat Oct 18 02:11:00 2008 prp89 factor: 13551574573816468594611225834346709335102626184834964057831450659712303002693008791158453 Sat Oct 18 02:11:00 2008 elapsed time 07:20:02 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 82.38 hours. Scaled time: 167.89 units (timescale=2.038). Factorization parameters were as follows: name: KA_8_185_1 n: 20576291249695377971301832017847716213382725784697613948242181117163577126798867943121419615352806546244832708544699170564753533853725579 type: snfs skew: 1.95 deg: 5 c5: 5 c0: -142 m: 20000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 6500001) Primes: RFBsize:602489, AFBsize:600661, largePrimes:14480275 encountered Relations: rels:14249707, finalFF:1207021 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 81.94 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,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 82.38 hours. --------- CPU info (if available) ----------
6·10¹⁷¹-7 = 5(9)₁₇₀3_<172> = 13 · 347 · 280561 · 3619261 · C157
C157 = P63 · P95
P63 = 104668478321136247869629778050319602787493232821426679133681787_<63>
P95 = 12514552052547785247649358827497335463132200483914345373302430877998388248495950980295389454969_<95>

Number: n N=1309879120210828994066681132598393425452886882387371219479021676852192760494238995653573474587735850307389375209623160606880841799831258125095168152211949603 ( 157 digits) SNFS difficulty: 171 digits. Divisors found: Sat Oct 18 08:27:22 2008 prp63 factor: 104668478321136247869629778050319602787493232821426679133681787 Sat Oct 18 08:27:22 2008 prp95 factor: 12514552052547785247649358827497335463132200483914345373302430877998388248495950980295389454969 Sat Oct 18 08:27:23 2008 elapsed time 02:57:46 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.18 hours. Scaled time: 14.01 units (timescale=1.951). Factorization parameters were as follows: name: KA_5_9_170_3 n: 1309879120210828994066681132598393425452886882387371219479021676852192760494238995653573474587735850307389375209623160606880841799831258125095168152211949603 type: snfs skew: 0.65 deg: 5 c5: 60 c0: -7 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, 2100001) Primes: RFBsize:425648, AFBsize:426177, largePrimes:13318679 encountered Relations: rels:12554588, finalFF:860203 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 6.87 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,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000 total time: 7.18 hours. --------- CPU info (if available) ----------
Oct 17, 2008 (6th): By Tyler Cadigan / GGNFS, Msieve
(10¹⁸⁰+53)/9 = (1)₁₇₉7_<180> = 3 · 263 · 1847 · 62191 · 121590592499_<12> · 5868575487559_<13> · C145
C145 = P56 · P89
P56 = 81793764274037836798450374935577510454727483448973394983_<56>
P89 = 21005507864120051654894845196111841280466161257529202703568230197334018456832678768309963_<89>

Number: 11117_180 N=1718119558694283508664575042321785026498137677843135605871188922547889529147024841393023704163871626361079396990446562395410058599515961373115629 ( 145 digits) SNFS difficulty: 180 digits. Divisors found: r1=81793764274037836798450374935577510454727483448973394983 r2=21005507864120051654894845196111841280466161257529202703568230197334018456832678768309963 Version: Total time: 370.11 hours. Scaled time: 954.51 units (timescale=2.579). Factorization parameters were as follows: n: 1718119558694283508664575042321785026498137677843135605871188922547889529147024841393023704163871626361079396990446562395410058599515961373115629 m: 1000000000000000000000000000000000000 c5: 1 c0: 53 skew: 2.21 type: snfs Y0: 1000000000000000000000000000000000000 Y1: -1 rlambda: 2.6 alambda: 2.6 rlim: 20000000 alim: 20000000 qintsize: 1000000Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [10000000, 15000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1009060 x 1009286 Total sieving time: 370.11 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,180,5,0,0,0,0,0,0,0,0,20000000,20000000,27,27,48,48,2.6,2.6,100000 total time: 370.11 hours. --------- CPU info (if available) ----------
Oct 17, 2008 (5th): By Sinkiti Sibata / GGNFS, Msieve
(26·10¹⁵⁷-17)/9 = 2(8)₁₅₆7_<158> = 3 · 41 · 82013 · 52965943 · 84856973371799_<14> · C129
C129 = P52 · P78
P52 = 3677069971699943402973240503427918915132808241897783_<52>
P78 = 173283371006799030478413179782103712024486470011088345019793475092290392389823_<78>

Number: 28887_157 N=637175080124041304185260340865104028285702638816685146476778755934657374983610403654286401198601947444535960325318924282255462409 ( 129 digits) SNFS difficulty: 158 digits. Divisors found: r1=3677069971699943402973240503427918915132808241897783 (pp52) r2=173283371006799030478413179782103712024486470011088345019793475092290392389823 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 58.34 hours. Scaled time: 44.57 units (timescale=0.764). Factorization parameters were as follows: name: 28887_157 n: 637175080124041304185260340865104028285702638816685146476778755934657374983610403654286401198601947444535960325318924282255462409 m: 10000000000000000000000000000000 c5: 2600 c0: -17 skew: 0.37 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:282132, largePrimes:5804981 encountered Relations: rels:5920382, finalFF:725994 Max relations in full relation-set: 28 Initial matrix: 565345 x 725994 with sparse part having weight 47524292. Pruned matrix : 442217 x 445107 with weight 31339304. Total sieving time: 53.79 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.22 hours. Time per square root: 0.11 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: 58.34 hours. --------- CPU info (if available) ----------
(26·10¹⁵⁹-17)/9 = 2(8)₁₅₈7_<160> = 8837 · 5635633 · 1139822240018422481622821_<25> · 145680615773863178153918657_<27> · C99
C99 = P48 · P51
P48 = 457172000486643298781203262917205228548147422071_<48>
P51 = 764125619267224024718139398079281672269351217374681_<51>

Fri Oct 17 07:48:19 2008 Msieve v. 1.38 Fri Oct 17 07:48:19 2008 random seeds: 0af0844d 10432bce Fri Oct 17 07:48:19 2008 factoring 349336837983491953871872894642555708833828354422395239433937378913519331683566606179884934655984351 (99 digits) Fri Oct 17 07:48:22 2008 searching for 15-digit factors Fri Oct 17 07:48:25 2008 commencing quadratic sieve (99-digit input) Fri Oct 17 07:48:26 2008 using multiplier of 5 Fri Oct 17 07:48:26 2008 using 32kb Intel Core sieve core Fri Oct 17 07:48:26 2008 sieve interval: 36 blocks of size 32768 Fri Oct 17 07:48:26 2008 processing polynomials in batches of 6 Fri Oct 17 07:48:26 2008 using a sieve bound of 2605289 (95294 primes) Fri Oct 17 07:48:26 2008 using large prime bound of 390793350 (28 bits) Fri Oct 17 07:48:26 2008 using double large prime bound of 2920820370574650 (43-52 bits) Fri Oct 17 07:48:26 2008 using trial factoring cutoff of 52 bits Fri Oct 17 07:48:26 2008 polynomial 'A' values have 13 factors Fri Oct 17 12:43:25 2008 15126 relations (9655 full + 5471 combined from 615376 partial), need 95390 Fri Oct 17 12:43:25 2008 elapsed time 04:55:06 Fri Oct 17 14:25:55 2008 Fri Oct 17 14:25:55 2008 Fri Oct 17 14:25:55 2008 Msieve v. 1.38 Fri Oct 17 14:25:55 2008 random seeds: 741f743b 867902a2 Fri Oct 17 14:25:55 2008 factoring 349336837983491953871872894642555708833828354422395239433937378913519331683566606179884934655984351 (99 digits) Fri Oct 17 14:25:56 2008 searching for 15-digit factors Fri Oct 17 14:25:58 2008 commencing quadratic sieve (99-digit input) Fri Oct 17 14:25:58 2008 using multiplier of 5 Fri Oct 17 14:25:58 2008 using 32kb Intel Core sieve core Fri Oct 17 14:25:58 2008 sieve interval: 36 blocks of size 32768 Fri Oct 17 14:25:58 2008 processing polynomials in batches of 6 Fri Oct 17 14:25:58 2008 using a sieve bound of 2605289 (95294 primes) Fri Oct 17 14:25:58 2008 using large prime bound of 390793350 (28 bits) Fri Oct 17 14:25:58 2008 using double large prime bound of 2920820370574650 (43-52 bits) Fri Oct 17 14:25:58 2008 using trial factoring cutoff of 52 bits Fri Oct 17 14:25:58 2008 polynomial 'A' values have 13 factors Fri Oct 17 14:26:01 2008 restarting with 9655 full and 615376 partial relations Fri Oct 17 19:59:18 2008 95480 relations (22688 full + 72792 combined from 1444752 partial), need 95390 Fri Oct 17 19:59:22 2008 begin with 1467440 relations Fri Oct 17 19:59:23 2008 reduce to 252468 relations in 11 passes Fri Oct 17 19:59:23 2008 attempting to read 252468 relations Fri Oct 17 19:59:30 2008 recovered 252468 relations Fri Oct 17 19:59:30 2008 recovered 242508 polynomials Fri Oct 17 19:59:30 2008 attempting to build 95480 cycles Fri Oct 17 19:59:30 2008 found 95480 cycles in 6 passes Fri Oct 17 19:59:30 2008 distribution of cycle lengths: Fri Oct 17 19:59:30 2008 length 1 : 22688 Fri Oct 17 19:59:30 2008 length 2 : 16361 Fri Oct 17 19:59:30 2008 length 3 : 15836 Fri Oct 17 19:59:30 2008 length 4 : 12998 Fri Oct 17 19:59:30 2008 length 5 : 9880 Fri Oct 17 19:59:30 2008 length 6 : 6778 Fri Oct 17 19:59:30 2008 length 7 : 4489 Fri Oct 17 19:59:30 2008 length 9+: 6450 Fri Oct 17 19:59:30 2008 largest cycle: 19 relations Fri Oct 17 19:59:31 2008 matrix is 95294 x 95480 (25.1 MB) with weight 6205758 (65.00/col) Fri Oct 17 19:59:31 2008 sparse part has weight 6205758 (65.00/col) Fri Oct 17 19:59:31 2008 filtering completed in 3 passes Fri Oct 17 19:59:31 2008 matrix is 91462 x 91526 (24.2 MB) with weight 5981686 (65.36/col) Fri Oct 17 19:59:31 2008 sparse part has weight 5981686 (65.36/col) Fri Oct 17 19:59:32 2008 saving the first 48 matrix rows for later Fri Oct 17 19:59:32 2008 matrix is 91414 x 91526 (13.5 MB) with weight 4495303 (49.12/col) Fri Oct 17 19:59:32 2008 sparse part has weight 2988757 (32.65/col) Fri Oct 17 19:59:32 2008 matrix includes 64 packed rows Fri Oct 17 19:59:32 2008 using block size 36610 for processor cache size 2048 kB Fri Oct 17 19:59:33 2008 commencing Lanczos iteration Fri Oct 17 19:59:33 2008 memory use: 14.1 MB Fri Oct 17 20:00:21 2008 lanczos halted after 1448 iterations (dim = 91412) Fri Oct 17 20:00:22 2008 recovered 17 nontrivial dependencies Fri Oct 17 20:00:22 2008 prp48 factor: 457172000486643298781203262917205228548147422071 Fri Oct 17 20:00:22 2008 prp51 factor: 764125619267224024718139398079281672269351217374681 Fri Oct 17 20:00:22 2008 elapsed time 05:34:27
Oct 17, 2008 (4th): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38/gnfs
(26·10¹⁹⁶-17)/9 = 2(8)₁₉₅7_<197> = 3 · 287771327 · 810857563 · 185726128967846339_<18> · 671758004937985886076476237_<27> · C135
C135 = P32 · P104
P32 = 31939879173910580438400878878759_<32>
P104 = 10356150813844787900834823060533787167148150203266154500522047784924543502448871053345793359278564043017_<104>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=847032883 Step 1 took 10326ms Step 2 took 4807ms ********** Factor found in step 2: 31939879173910580438400878878759 Found probable prime factor of 32 digits: 31939879173910580438400878878759 Probable prime cofactor 10356150813844787900834823060533787167148150203266154500522047784924543502448871053345793359278564043017 has 104 digits
(26·10¹⁹²-17)/9 = 2(8)₁₉₁7_<193> = 41 · 79272414103_<11> · 82042192357926772102610496389810561633_<38> · C143
C143 = P33 · P41 · P69
P33 = 646339692493393337747248290139367_<33>
P41 = 23347548471027891222391051218682713727291_<41>
P69 = 717935663614141323476198407218450614415097949778852880550482361549069_<69>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2198108180 Step 1 took 7098ms Step 2 took 3284ms ********** Factor found in step 2: 646339692493393337747248290139367 Found probable prime factor of 33 digits: 646339692493393337747248290139367 Composite cofactor 16762037705310739694160961481530313246498654277376477496854405204777871932916995964594549612157158757580942079 has 110 digits Number: 28883_192 N=16762037705310739694160961481530313246498654277376477496854405204777871932916995964594549612157158757580942079 ( 110 digits) Divisors found: r1=23347548471027891222391051218682713727291 r2=717935663614141323476198407218450614415097949778852880550482361549069 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.729). Factorization parameters were as follows: name: 28883_192 n: 16762037705310739694160961481530313246498654277376477496854405204777871932916995964594549612157158757580942079 skew: 19634.27 # norm 1.15e+15 c5: 23760 c4: -732510172 c3: -74628572677882 c2: 291776264655235985 c1: 6237779486097660130452 c0: -18038503918973282230456943 # alpha -5.40 Y1: 313275396047 Y0: -932603358146879780640 # Murphy_E 1.05e-09 # M 5809571181138759701044419189937894699342167502695450717956767491143381064004365373882245868097473045576903676 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, 3000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 406475 x 406723 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: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 10.00 hours.
Oct 17, 2008 (3rd): By Serge Batalov / PFGW
(86·10¹³⁷⁴¹+13)/9 = 9(5)₁₃₇₄₀7_<13742> is PRP.
Oct 17, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁶⁸-17)/9 = 2(8)₁₆₇7_<169> = 1151 · 53189 · 3845297 · C155
C155 = P30 · P60 · P65
P30 = 691786150359227305260342651851_<30>
P60 = 946812596364691311451086016834132866784096017745846067579369_<60>
P65 = 18735613134758722493314686248856404802936412322699495052983347031_<65>

Number: 28887_168 N=12271673742223879146119302921287351987225723768693572415492792094221612528875452222509963796606702569982599797468379627090212002056147005375530500792715589 ( 155 digits) SNFS difficulty: 169 digits. Divisors found: r1=691786150359227305260342651851 (pp30) r2=946812596364691311451086016834132866784096017745846067579369 (pp60) r3=18735613134758722493314686248856404802936412322699495052983347031 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 138.68 hours. Scaled time: 139.93 units (timescale=1.009). Factorization parameters were as follows: name: 28887_168 n: 12271673742223879146119302921287351987225723768693572415492792094221612528875452222509963796606702569982599797468379627090212002056147005375530500792715589 m: 2000000000000000000000000000000000 c5: 1625 c0: -34 skew: 0.46 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:412476, largePrimes:6178678 encountered Relations: rels:6457589, finalFF:939587 Max relations in full relation-set: 28 Initial matrix: 825391 x 939587 with sparse part having weight 63700451. Pruned matrix : 733378 x 737568 with weight 48023686. Total sieving time: 134.15 hours. Total relation processing time: 0.13 hours. Matrix solve time: 4.29 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 138.68 hours. --------- CPU info (if available) ----------
Oct 17, 2008: By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(26·10²⁰²-17)/9 = 2(8)₂₀₁7_<203> = 3 · 41 · 2333 · C198
C198 = P39 · C159
P39 = 129797485565316576138335938787553938939_<39>
C159 = [775612337868844507616271572284373761381973575256362313544270876107000293028543916178363902529711692579369109164356752919211141934170017178762799324790822743387_<159>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1776639700 Step 1 took 25697ms Step 2 took 8377ms ********** Factor found in step 2: 129797485565316576138335938787553938939 Found probable prime factor of 39 digits: 129797485565316576138335938787553938939 Composite cofactor 775612337868844507616271572284373761381973575256362313544270876107000293028543916178363902529711692579369109164356752919211141934170017178762799324790822743387 has 159 digits
(26·10¹⁶¹-17)/9 = 2(8)₁₆₀7_<162> = 491 · 30557 · 12184547 · C148
C148 = P69 · P79
P69 = 265985593868700211361992135555305954314323409649102462483859930225459_<69>
P79 = 5941158371782505498596768539671106948764441091331681031338463367290089728487537_<79>

SNFS difficulty: 162 digits. Divisors found: r1=265985593868700211361992135555305954314323409649102462483859930225459 r2=5941158371782505498596768539671106948764441091331681031338463367290089728487537 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: n: 1580262537786569725372553727321669981525482758855547985590946005188563140610837578431188916339843319915956447890498719664890521061648998787481604483 m: 100000000000000000000000000000000 c5: 260 c0: -17 skew: 0.58 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [2250000, 3750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 805162 x 805410 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,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,54,54,2.5,2.5,100000 total time: 20.00 hours.
(26·10¹⁷¹-17)/9 = 2(8)₁₇₀7_<172> = 71 · 2014690833579469_<16> · 1891416654878237659147193_<25> · C131
C131 = P35 · P96
P35 = 48109016865913520195095540051309093_<35>
P96 = 221947566920328070216344062694348500510850700259673035094854433728769797473984579418247370694137_<96>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2805974126 Step 1 took 5226ms Step 2 took 3003ms ********** Factor found in step 2: 48109016865913520195095540051309093 Found probable prime factor of 35 digits: 48109016865913520195095540051309093 Probable prime cofactor 221947566920328070216344062694348500510850700259673035094854433728769797473984579418247370694137 has 96 digits
(26·10¹⁹²-17)/9 = 2(8)₁₉₁7_<193> = 41 · 79272414103_<11> · C180
C180 = P38 · C143
P38 = 82042192357926772102610496389810561633_<38>
C143 = [10833970296013207989084662536581651616879108714184793508692814128673265107095600617603313406072713756279265813854583416619917872689578064723993_<143>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=652635297 Step 1 took 9334ms Step 2 took 4332ms ********** Factor found in step 2: 82042192357926772102610496389810561633 Found probable prime factor of 38 digits: 82042192357926772102610496389810561633 Composite cofactor 10833970296013207989084662536581651616879108714184793508692814128673265107095600617603313406072713756279265813854583416619917872689578064723993 has 143 digits
Oct 16, 2008 (7th): By Serge Batalov / PFGW
(86·10¹⁰⁰⁰³+13)/9 = 9(5)₁₀₀₀₂7_<10004> is PRP.
Oct 16, 2008 (6th): By Jo Yeong Uk / GGNFS
4·10¹⁷³+1 = 4(0)₁₇₂1_<174> = 7 · 19 · 19081 · 1380947158352491_<16> · C153
C153 = P49 · P49 · P56
P49 = 1031387844700915926546275570854626898299232457527_<49>
P49 = 4950984722498265333902822196208270860948138231881_<49>
P56 = 22352008973784616122462526641600512964655392476154917761_<56>

Number: 40001_173 N=114137973672119360672572150898106796661330101454417637896259526429919025856550052603359765770360708093834065329551585587198631771640340154306807238895407 ( 153 digits) SNFS difficulty: 175 digits. Divisors found: r1=1031387844700915926546275570854626898299232457527 (pp49) r2=4950984722498265333902822196208270860948138231881 (pp49) r3=22352008973784616122462526641600512964655392476154917761 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 92.56 hours. Scaled time: 220.01 units (timescale=2.377). Factorization parameters were as follows: n: 114137973672119360672572150898106796661330101454417637896259526429919025856550052603359765770360708093834065329551585587198631771640340154306807238895407 m: 100000000000000000000000000000000000 c5: 1 c0: 25 skew: 1.9 type: snfs Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [4000000, 5700001) Primes: RFBsize:539777, AFBsize:538970, largePrimes:10773912 encountered Relations: rels:10964419, finalFF:1364486 Max relations in full relation-set: 28 Initial matrix: 1078811 x 1364486 with sparse part having weight 86737254. Pruned matrix : 813086 x 818544 with weight 49578617. Total sieving time: 87.82 hours. Total relation processing time: 0.14 hours. Matrix solve time: 4.52 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,50,50,2.6,2.6,100000 total time: 92.56 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Oct 16, 2008 (5th): By Serge Batalov / Msieve-1.38
(26·10¹⁶⁶-17)/9 = 2(8)₁₆₅7_<167> = 3 · 293 · C164
C164 = P52 · P113
P52 = 1471197411837404676000587813206308006550640281066939_<52>
P113 = 22339374628322814429464629999793314774821231845019922359202585861305762667563370954938494467079355549589396537627_<113>

SNFS difficulty: 167 digits. Divisors found: r1=1471197411837404676000587813206308006550640281066939 r2=22339374628322814429464629999793314774821231845019922359202585861305762667563370954938494467079355549589396537627 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.953). Factorization parameters were as follows: n: 32865630135254708633548223991909998735937302490203514094299077234230817848565288838326380988497029452660851978258121602831500442421944128428770066995322968019213753 m: 1000000000000000000000000000000000 c5: 260 c0: -17 skew: 0.58 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, 4950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 951798 x 952046 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,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,54,54,2.6,2.6,100000 total time: 40.00 hours.
Oct 16, 2008 (4th): By Sinkiti Sibata / GGNFS, Msieve
(26·10¹²⁴-17)/9 = 2(8)₁₂₃7_<125> = 3 · 2089 · 67324333 · 83861369 · C105
C105 = P43 · P63
P43 = 1824903596618491254551411008086026120234261_<43>
P63 = 447401266840912389986722883683744380837849073077673223449077613_<63>

Number: 28887_124 N=816464180989650351224051488844692798792324458135191337497018777767584167746285873004029875623655930698993 ( 105 digits) Divisors found: r1=1824903596618491254551411008086026120234261 (pp43) r2=447401266840912389986722883683744380837849073077673223449077613 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.15 hours. Scaled time: 12.43 units (timescale=0.770). Factorization parameters were as follows: name: 28887_124 n: 816464180989650351224051488844692798792324458135191337497018777767584167746285873004029875623655930698993 skew: 5714.03 # norm 3.50e+14 c5: 401040 c4: 6493525469 c3: -27978259045032 c2: -159309783903663376 c1: 580710657569380116552 c0: -5182581195961543252333 # alpha -5.78 Y1: 154008731899 Y0: -72735580824209398380 # Murphy_E 1.78e-09 # M 447983274830461864379146476925871244975907299446442034552756791959963487336853989126526061321897454429511 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:183110, largePrimes:4631329 encountered Relations: rels:4993380, finalFF:682858 Max relations in full relation-set: 28 Initial matrix: 366260 x 682858 with sparse part having weight 52516455. Pruned matrix : 195355 x 197250 with weight 26985107. Total sieving time: 15.41 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.42 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 16.15 hours. --------- CPU info (if available) ----------
(26·10¹²⁵-17)/9 = 2(8)₁₂₄7_<126> = 367 · 829 · 107823286243_<12> · 7310071877663_<13> · C97
C97 = P31 · P66
P31 = 3042549675264553555477312649387_<31>
P66 = 395948183335808890825034372088476100294521230559806139712454179923_<66>

Wed Oct 15 16:15:04 2008 Msieve v. 1.38 Wed Oct 15 16:15:04 2008 random seeds: 96667591 d41288e4 Wed Oct 15 16:15:04 2008 factoring 1204692016629955256328089887937976301517969093592680868815711272508092143797499855243889513657201 (97 digits) Wed Oct 15 16:15:06 2008 searching for 15-digit factors Wed Oct 15 16:15:07 2008 commencing quadratic sieve (97-digit input) Wed Oct 15 16:15:08 2008 using multiplier of 1 Wed Oct 15 16:15:08 2008 using 64kb Pentium 4 sieve core Wed Oct 15 16:15:08 2008 sieve interval: 18 blocks of size 65536 Wed Oct 15 16:15:08 2008 processing polynomials in batches of 6 Wed Oct 15 16:15:08 2008 using a sieve bound of 2333549 (85882 primes) Wed Oct 15 16:15:08 2008 using large prime bound of 350032350 (28 bits) Wed Oct 15 16:15:08 2008 using double large prime bound of 2395491891430500 (43-52 bits) Wed Oct 15 16:15:08 2008 using trial factoring cutoff of 52 bits Wed Oct 15 16:15:08 2008 polynomial 'A' values have 12 factors Wed Oct 15 23:33:55 2008 86273 relations (21010 full + 65263 combined from 1288906 partial), need 85978 Wed Oct 15 23:34:00 2008 begin with 1309916 relations Wed Oct 15 23:34:02 2008 reduce to 225209 relations in 11 passes Wed Oct 15 23:34:02 2008 attempting to read 225209 relations Wed Oct 15 23:34:09 2008 recovered 225209 relations Wed Oct 15 23:34:09 2008 recovered 208543 polynomials Wed Oct 15 23:34:10 2008 attempting to build 86273 cycles Wed Oct 15 23:34:10 2008 found 86273 cycles in 6 passes Wed Oct 15 23:34:10 2008 distribution of cycle lengths: Wed Oct 15 23:34:10 2008 length 1 : 21010 Wed Oct 15 23:34:10 2008 length 2 : 15212 Wed Oct 15 23:34:10 2008 length 3 : 14481 Wed Oct 15 23:34:10 2008 length 4 : 11709 Wed Oct 15 23:34:10 2008 length 5 : 8783 Wed Oct 15 23:34:10 2008 length 6 : 5987 Wed Oct 15 23:34:10 2008 length 7 : 3793 Wed Oct 15 23:34:10 2008 length 9+: 5298 Wed Oct 15 23:34:10 2008 largest cycle: 22 relations Wed Oct 15 23:34:10 2008 matrix is 85882 x 86273 (23.5 MB) with weight 5811120 (67.36/col) Wed Oct 15 23:34:10 2008 sparse part has weight 5811120 (67.36/col) Wed Oct 15 23:34:12 2008 filtering completed in 4 passes Wed Oct 15 23:34:12 2008 matrix is 81786 x 81850 (22.3 MB) with weight 5526947 (67.53/col) Wed Oct 15 23:34:12 2008 sparse part has weight 5526947 (67.53/col) Wed Oct 15 23:34:13 2008 saving the first 48 matrix rows for later Wed Oct 15 23:34:13 2008 matrix is 81738 x 81850 (15.7 MB) with weight 4521233 (55.24/col) Wed Oct 15 23:34:13 2008 sparse part has weight 3616544 (44.19/col) Wed Oct 15 23:34:13 2008 matrix includes 64 packed rows Wed Oct 15 23:34:13 2008 using block size 21845 for processor cache size 512 kB Wed Oct 15 23:34:14 2008 commencing Lanczos iteration Wed Oct 15 23:34:14 2008 memory use: 14.2 MB Wed Oct 15 23:35:33 2008 lanczos halted after 1294 iterations (dim = 81736) Wed Oct 15 23:35:34 2008 recovered 16 nontrivial dependencies Wed Oct 15 23:35:35 2008 prp31 factor: 3042549675264553555477312649387 Wed Oct 15 23:35:35 2008 prp66 factor: 395948183335808890825034372088476100294521230559806139712454179923 Wed Oct 15 23:35:35 2008 elapsed time 07:20:31
Oct 16, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(34·10¹⁸⁶-43)/9 = 3(7)₁₈₅3_<187> = 2549 · C184
C184 = P72 · P112
P72 = 546343618539092922731973753936839243091501383544493873477842943394088769_<72>
P112 = 2712693316518363022366031105781560682107270534818253728649490721133162710749555853025070780629498066137114271833_<112>

Number: n N=1482062682533455385554247853188614271391831219214506778257268645656248637810034436162329453816311407523647617802188221960681748833965389477354954012466762564840242360838673117998343577 ( 184 digits) SNFS difficulty: 187 digits. Divisors found: Thu Oct 16 05:34:52 2008 prp72 factor: 546343618539092922731973753936839243091501383544493873477842943394088769 Thu Oct 16 05:34:52 2008 prp112 factor: 2712693316518363022366031105781560682107270534818253728649490721133162710749555853025070780629498066137114271833 Thu Oct 16 05:34:52 2008 elapsed time 18:52:41 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 58.62 hours. Scaled time: 76.43 units (timescale=1.304). Factorization parameters were as follows: name: KA_3_7_185_3 n: 1482062682533455385554247853188614271391831219214506778257268645656248637810034436162329453816311407523647617802188221960681748833965389477354954012466762564840242360838673117998343577 type: snfs skew: 0.66 deg: 5 c5: 340 c0: -43 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 5600001) Primes: RFBsize:602489, AFBsize:603165, largePrimes:14394823 encountered Relations: rels:14154498, finalFF:1206761 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 58.03 hours. Total relation processing time: 0.58 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 58.62 hours. --------- CPU info (if available) ----------
(5·10¹⁷¹-23)/9 = (5)₁₇₀3_<171> = 7 · 53 · 131 · C167
C167 = P82 · P85
P82 = 6027739170558698373176408401461180267513269261549301064477211046506440175172858341_<82>
P85 = 1896390793053781284969080421438636485505504937000715539338204658483363752598306704533_<85>

Number: n N=11430949065977151819006924868944168958571954395085606377555102889972542860343522881330745366464796106161510165543004373481112642858285952049454858039043549629751559753 ( 167 digits) SNFS difficulty: 171 digits. Divisors found: Thu Oct 16 12:30:45 2008 prp82 factor: 6027739170558698373176408401461180267513269261549301064477211046506440175172858341 Thu Oct 16 12:30:45 2008 prp85 factor: 1896390793053781284969080421438636485505504937000715539338204658483363752598306704533 Thu Oct 16 12:30:45 2008 elapsed time 04:44:35 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 12.01 hours. Scaled time: 15.58 units (timescale=1.297). Factorization parameters were as follows: name: KA_5_170_3 n: 11430949065977151819006924868944168958571954395085606377555102889972542860343522881330745366464796106161510165543004373481112642858285952049454858039043549629751559753 type: snfs skew: 0.86 deg: 5 c5: 50 c0: -23 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, 1100001) Primes: RFBsize:425648, AFBsize:426017, largePrimes:13787792 encountered Relations: rels:13296250, finalFF:939569 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 11.29 hours. Total relation processing time: 0.72 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000 total time: 12.01 hours. --------- CPU info (if available) ----------
Oct 16, 2008 (2nd): By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(26·10¹⁶²-17)/9 = 2(8)₁₆₁7_<163> = 29 · 41 · 61 · 995377 · C152
C152 = P40 · P47 · P66
P40 = 5501286498405655905342717694686972908197_<40>
P47 = 10125694884984205676521560253483207273265641799_<47>
P66 = 718360506293268421227792773673534536293455189801295656412695055613_<66>

SNFS difficulty: 163 digits. Divisors found: r1=5501286498405655905342717694686972908197 r2=10125694884984205676521560253483207273265641799 r3=718360506293268421227792773673534536293455189801295656412695055613 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.927). Factorization parameters were as follows: n: 40015804032673956426793177377995556955910649250570011850509081244438492540540333850676610741645571858036088889078135323086736656603072425792048061050039 m: 100000000000000000000000000000000 c5: 2600 c0: -17 skew: 0.37 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [2250000, 3750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 854525 x 854773 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,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,54,54,2.5,2.5,100000 total time: 20.00 hours.
(26·10¹⁵⁴-17)/9 = 2(8)₁₅₃7_<155> = 3² · 33349 · C149
C149 = P58 · P92
P58 = 1655806187784170081376129355024512400874595061215829462877_<58>
P92 = 58129423001915900497455256477363673668965485263795199277948640370085158428885797129195181391_<92>

SNFS difficulty: 156 digits. Divisors found: r1=1655806187784170081376129355024512400874595061215829462877 r2=58129423001915900497455256477363673668965485263795199277948640370085158428885797129195181391 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: n: 96251058298895815263122628660825708213435981385045324993549328112083616996308031521481200132234146247559943123028472914026703745535894425916115721907 m: 10000000000000000000000000000000 c5: 13 c0: -85 skew: 1.46 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [1500000, 2500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 620058 x 620306 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,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,54,54,2.5,2.5,100000 total time: 15.00 hours.
(26·10¹⁶⁵-17)/9 = 2(8)₁₆₄7_<166> = 263957 · 4058137 · 7818152593406970277472416624103_<31> · C123
C123 = P32 · P92
P32 = 12764119228429224522971656618663_<32>
P92 = 27025638012775141945475448077100614364122822615878345459713349089216440618643727446116152387_<92>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=660598922 Step 1 took 12213ms ********** Factor found in step 1: 12764119228429224522971656618663 Found probable prime factor of 32 digits: 12764119228429224522971656618663 Probable prime cofactor 27025638012775141945475448077100614364122822615878345459713349089216440618643727446116152387 has 92 digits
(26·10¹⁸⁴-17)/9 = 2(8)₁₈₃7_<185> = 3 · 347 · 773 · C179
C179 = P37 · C143
P37 = 1320609859565989645500044320598167223_<37>
C143 = [27184796089295598978415391289548696133680825116303565800551982812921189048358167264993631889810511264157528029387662330821692327090836318455933_<143>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1909449008 Step 1 took 24466ms Step 2 took 16501ms ********** Factor found in step 2: 1320609859565989645500044320598167223 Found probable prime factor of 37 digits: 1320609859565989645500044320598167223 Composite cofactor 27184796089295598978415391289548696133680825116303565800551982812921189048358167264993631889810511264157528029387662330821692327090836318455933 has 143 digits
Oct 16, 2008: By Serge Batalov / PFGW
(14·10¹³⁰²⁴-23)/9 = 1(5)₁₃₀₂₃3_<13025> is PRP.
Oct 15, 2008 (9th): By Robert Backstrom / GGNFS, Msieve
4·10¹⁹³+9 = 4(0)₁₉₂9_<194> = 7 · 11437 · 13853895929_<11> · 284374155722383_<15> · 1455040861595700679822195920931_<31> · 40774884715492908428204364418823_<32> · C103
C103 = P46 · P57
P46 = 9456466122140544011470454984220083014832730601_<46>
P57 = 226042958165565708353120714503974059356275405880402226161_<57>

Number: n N=2137567576041104372111455292736110616642012466158171115994587987948441933469530773750128809166787452761 ( 103 digits) Divisors found: Wed Oct 15 22:27:48 2008 prp46 factor: 9456466122140544011470454984220083014832730601 Wed Oct 15 22:27:48 2008 prp57 factor: 226042958165565708353120714503974059356275405880402226161 Wed Oct 15 22:27:48 2008 elapsed time 00:36:40 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 5.56 hours. Scaled time: 4.66 units (timescale=0.838). Factorization parameters were as follows: name: n n: 2137567576041104372111455292736110616642012466158171115994587987948441933469530773750128809166787452761 skew: 9441.31 # norm 1.14e+14 c5: 44400 c4: -428088886 c3: -15435140099909 c2: 26020273585723447 c1: 570016691238045740745 c0: -1047976788238775541382005 # alpha -5.67 Y1: 15416468573 Y0: -34395985086804511558 # Murphy_E 2.49e-09 # M 454570796391432565790902417114729285898493548317986804335761562880391700012618568074746351559767174829 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 special-q in [100000, 1950001) Primes: RFBsize:169511, AFBsize:169709, largePrimes:4205201 encountered Relations: rels:4098356, finalFF:370203 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 5.48 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. 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: 5.56 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 Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Oct 15, 2008 (8th): By Serge Batalov / Msieve-1.38
(26·10¹⁴⁹-17)/9 = 2(8)₁₄₈7_<150> = C150
C150 = P69 · P82
P69 = 134971906566222676263728404267505511206402426126592403563178725170953_<69>
P82 = 2140363103985260191659544710319723616409514346738105611022769933803701494623081279_<82>

SNFS difficulty: 151 digits. Divisors found: r1=134971906566222676263728404267505511206402426126592403563178725170953 r2=2140363103985260191659544710319723616409514346738105611022769933803701494623081279 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.946). Factorization parameters were as follows: n: 288888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 m: 1000000000000000000000000000000 c5: 13 c0: -85 skew: 1.46 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, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 506341 x 506589 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,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,54,54,2.5,2.5,100000 total time: 10.00 hours.
7·10¹⁷²-9 = 6(9)₁₇₁1_<173> = 10598698069_<11> · C163
C163 = P75 · P89
P75 = 223245829680143568677436140783698003000608237638667397220569703726322445019_<75>
P89 = 29584359061808698085356769885290337868193171920464425723391688951441403237695049377138881_<89>

SNFS difficulty: 172 digits. Divisors found: r1=223245829680143568677436140783698003000608237638667397220569703726322445019 r2=29584359061808698085356769885290337868193171920464425723391688951441403237695049377138881 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.731). Factorization parameters were as follows: n: 6604584784308756592809399333404107371973103803302616752748256819882053383173887637991171460740665429743736952188103699060096321723041245359586061437788090649683739 m: 10000000000000000000000000000000000 c5: 700 c0: -9 skew: 0.42 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 7600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1249370 x 1249618 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,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 34.00 hours.
Oct 15, 2008 (7th): By Sinkiti Sibata / GMP-ECM, Msieve, GGNFS
(26·10¹¹⁸-17)/9 = 2(8)₁₁₇7_<119> = 3² · 31 · 4817 · C113
C113 = P33 · P34 · P46
P33 = 339145835876930553447588298468823_<33>
P34 = 6925540496049346647691472035885723_<34>
P46 = 9151869670383651567843410263648963919135064821_<46>

Factor28887_118 Inputnumber is 21495620639334323620041094666134567380379144717364418646392658683358512145893753595865962238643222881393696673809 Run 216 out of 904: Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=334309867 Step 1 took 15101ms Step 2 took 7317ms ********** Factor found in step 2: 339145835876930553447588298468823 Found probable prime factor of 33 digits: 339145835876930553447588298468823 Composite cofactor 63381644016807764877796119529273285908378065539823990280799855167981847753450583 has 80 digits Wed Oct 15 13:45:35 2008 Wed Oct 15 13:45:35 2008 Msieve v. 1.38 Wed Oct 15 13:45:35 2008 random seeds: 6e94724d 3e8b164c Wed Oct 15 13:45:35 2008 factoring 80 (2 digits) Wed Oct 15 13:45:35 2008 p1 factor: 2 Wed Oct 15 13:45:35 2008 p1 factor: 2 Wed Oct 15 13:45:35 2008 p1 factor: 2 Wed Oct 15 13:45:35 2008 p1 factor: 2 Wed Oct 15 13:45:35 2008 p1 factor: 5 Wed Oct 15 13:45:35 2008 elapsed time 00:00:00 Wed Oct 15 13:51:54 2008 Wed Oct 15 13:51:54 2008 Wed Oct 15 13:51:54 2008 Msieve v. 1.38 Wed Oct 15 13:51:54 2008 random seeds: c1fb0222 03cd8c81 Wed Oct 15 13:51:54 2008 factoring 63381644016807764877796119529273285908378065539823990280799855167981847753450583 (80 digits) Wed Oct 15 13:51:55 2008 searching for 15-digit factors Wed Oct 15 13:51:57 2008 commencing quadratic sieve (80-digit input) Wed Oct 15 13:51:57 2008 using multiplier of 47 Wed Oct 15 13:51:57 2008 using 32kb Intel Core sieve core Wed Oct 15 13:51:57 2008 sieve interval: 12 blocks of size 32768 Wed Oct 15 13:51:57 2008 processing polynomials in batches of 17 Wed Oct 15 13:51:57 2008 using a sieve bound of 1301023 (49967 primes) Wed Oct 15 13:51:57 2008 using large prime bound of 130102300 (26 bits) Wed Oct 15 13:51:57 2008 using trial factoring cutoff of 27 bits Wed Oct 15 13:51:57 2008 polynomial 'A' values have 10 factors Wed Oct 15 14:04:14 2008 50098 relations (26281 full + 23817 combined from 265003 partial), need 50063 Wed Oct 15 14:04:15 2008 begin with 291284 relations Wed Oct 15 14:04:15 2008 reduce to 70947 relations in 2 passes Wed Oct 15 14:04:15 2008 attempting to read 70947 relations Wed Oct 15 14:04:16 2008 recovered 70947 relations Wed Oct 15 14:04:16 2008 recovered 58432 polynomials Wed Oct 15 14:04:16 2008 attempting to build 50098 cycles Wed Oct 15 14:04:16 2008 found 50098 cycles in 1 passes Wed Oct 15 14:04:16 2008 distribution of cycle lengths: Wed Oct 15 14:04:16 2008 length 1 : 26281 Wed Oct 15 14:04:16 2008 length 2 : 23817 Wed Oct 15 14:04:16 2008 largest cycle: 2 relations Wed Oct 15 14:04:16 2008 matrix is 49967 x 50098 (6.6 MB) with weight 1541394 (30.77/col) Wed Oct 15 14:04:16 2008 sparse part has weight 1541394 (30.77/col) Wed Oct 15 14:04:17 2008 filtering completed in 3 passes Wed Oct 15 14:04:17 2008 matrix is 34614 x 34677 (5.1 MB) with weight 1207990 (34.84/col) Wed Oct 15 14:04:17 2008 sparse part has weight 1207990 (34.84/col) Wed Oct 15 14:04:17 2008 saving the first 48 matrix rows for later Wed Oct 15 14:04:17 2008 matrix is 34566 x 34677 (3.8 MB) with weight 961386 (27.72/col) Wed Oct 15 14:04:17 2008 sparse part has weight 792580 (22.86/col) Wed Oct 15 14:04:17 2008 matrix includes 64 packed rows Wed Oct 15 14:04:17 2008 using block size 13870 for processor cache size 2048 kB Wed Oct 15 14:04:17 2008 commencing Lanczos iteration Wed Oct 15 14:04:17 2008 memory use: 4.1 MB Wed Oct 15 14:04:23 2008 lanczos halted after 548 iterations (dim = 34564) Wed Oct 15 14:04:23 2008 recovered 17 nontrivial dependencies Wed Oct 15 14:04:23 2008 prp34 factor: 6925540496049346647691472035885723 Wed Oct 15 14:04:23 2008 prp46 factor: 9151869670383651567843410263648963919135064821 Wed Oct 15 14:04:23 2008 elapsed time 00:12:29
(26·10¹⁵³-17)/9 = 2(8)₁₅₂7_<154> = 191 · 13691 · 29404942766701_<14> · 2690568143184441439_<19> · 24008502534823630793_<20> · C96
C96 = P36 · P61
P36 = 144033299950349239793375411134290953_<36>
P61 = 4038034105758540631100193593028886436502038569222778774393017_<61>

Wed Oct 15 07:31:11 2008 Msieve v. 1.38 Wed Oct 15 07:31:11 2008 random seeds: 4a2e2996 99e36ae2 Wed Oct 15 07:31:11 2008 factoring 581611377564460147190254458089733717901553248586056816556993159064446199463882568826397249475201 (96 digits) Wed Oct 15 07:31:13 2008 searching for 15-digit factors Wed Oct 15 07:31:15 2008 commencing quadratic sieve (96-digit input) Wed Oct 15 07:31:15 2008 using multiplier of 5 Wed Oct 15 07:31:15 2008 using 64kb Pentium 4 sieve core Wed Oct 15 07:31:15 2008 sieve interval: 18 blocks of size 65536 Wed Oct 15 07:31:15 2008 processing polynomials in batches of 6 Wed Oct 15 07:31:15 2008 using a sieve bound of 2296873 (84706 primes) Wed Oct 15 07:31:15 2008 using large prime bound of 344530950 (28 bits) Wed Oct 15 07:31:15 2008 using double large prime bound of 2328149289953700 (43-52 bits) Wed Oct 15 07:31:15 2008 using trial factoring cutoff of 52 bits Wed Oct 15 07:31:15 2008 polynomial 'A' values have 12 factors Wed Oct 15 16:02:07 2008 85039 relations (20512 full + 64527 combined from 1285560 partial), need 84802 Wed Oct 15 16:02:12 2008 begin with 1306072 relations Wed Oct 15 16:02:14 2008 reduce to 223844 relations in 12 passes Wed Oct 15 16:02:14 2008 attempting to read 223844 relations Wed Oct 15 16:02:21 2008 recovered 223844 relations Wed Oct 15 16:02:21 2008 recovered 210027 polynomials Wed Oct 15 16:02:21 2008 attempting to build 85039 cycles Wed Oct 15 16:02:21 2008 found 85039 cycles in 6 passes Wed Oct 15 16:02:21 2008 distribution of cycle lengths: Wed Oct 15 16:02:21 2008 length 1 : 20512 Wed Oct 15 16:02:21 2008 length 2 : 14602 Wed Oct 15 16:02:21 2008 length 3 : 13960 Wed Oct 15 16:02:21 2008 length 4 : 11605 Wed Oct 15 16:02:21 2008 length 5 : 8985 Wed Oct 15 16:02:21 2008 length 6 : 6035 Wed Oct 15 16:02:21 2008 length 7 : 3886 Wed Oct 15 16:02:21 2008 length 9+: 5454 Wed Oct 15 16:02:21 2008 largest cycle: 20 relations Wed Oct 15 16:02:22 2008 matrix is 84706 x 85039 (23.8 MB) with weight 5898680 (69.36/col) Wed Oct 15 16:02:22 2008 sparse part has weight 5898680 (69.36/col) Wed Oct 15 16:02:24 2008 filtering completed in 3 passes Wed Oct 15 16:02:24 2008 matrix is 80977 x 81040 (22.8 MB) with weight 5643742 (69.64/col) Wed Oct 15 16:02:24 2008 sparse part has weight 5643742 (69.64/col) Wed Oct 15 16:02:24 2008 saving the first 48 matrix rows for later Wed Oct 15 16:02:25 2008 matrix is 80929 x 81040 (16.7 MB) with weight 4727767 (58.34/col) Wed Oct 15 16:02:25 2008 sparse part has weight 3887127 (47.97/col) Wed Oct 15 16:02:25 2008 matrix includes 64 packed rows Wed Oct 15 16:02:25 2008 using block size 21845 for processor cache size 512 kB Wed Oct 15 16:02:26 2008 commencing Lanczos iteration Wed Oct 15 16:02:26 2008 memory use: 14.7 MB Wed Oct 15 16:03:47 2008 lanczos halted after 1282 iterations (dim = 80929) Wed Oct 15 16:03:47 2008 recovered 18 nontrivial dependencies Wed Oct 15 16:03:50 2008 prp36 factor: 144033299950349239793375411134290953 Wed Oct 15 16:03:50 2008 prp61 factor: 4038034105758540631100193593028886436502038569222778774393017 Wed Oct 15 16:03:50 2008 elapsed time 08:32:39
(26·10¹⁴⁴-17)/9 = 2(8)₁₄₃7_<145> = 193 · C143
C143 = P37 · P41 · P66
P37 = 1782151055743702442344825007074171523_<37>
P41 = 16521095534080175058325500493943837954429_<41>
P66 = 508382011054035835676406114546052839485630855313152746851685502977_<66>

Number: 28887_144 N=14968336211859527921704087507196315486470926885434657455382843983880253310305123776626367299942429476108232584916522740356937248128957973517559 ( 143 digits) SNFS difficulty: 146 digits. Divisors found: r1=1782151055743702442344825007074171523 (pp37) r2=16521095534080175058325500493943837954429 (pp41) r3=508382011054035835676406114546052839485630855313152746851685502977 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 19.60 hours. Scaled time: 19.78 units (timescale=1.009). Factorization parameters were as follows: name: 28887_144 n: 14968336211859527921704087507196315486470926885434657455382843983880253310305123776626367299942429476108232584916522740356937248128957973517559 m: 100000000000000000000000000000 c5: 13 c0: -85 skew: 1.46 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, 3250001) Primes: RFBsize:114155, AFBsize:114742, largePrimes:2972820 encountered Relations: rels:2998620, finalFF:273682 Max relations in full relation-set: 28 Initial matrix: 228962 x 273682 with sparse part having weight 31732339. Pruned matrix : 216250 x 217458 with weight 23641325. Total sieving time: 19.18 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.32 hours. Time per square root: 0.04 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: 19.60 hours. --------- CPU info (if available) ----------
Oct 15, 2008 (6th): By Serge Batalov / PFGW
(67·10²⁶¹⁹⁴-13)/9 = 7(4)₂₆₁₉₃3_<26195> is PRP.
Oct 15, 2008 (5th): By Sinkiti Sibata / Msieve, GGNFS
(26·10¹¹⁰-17)/9 = 2(8)₁₀₉7_<111> = 7 · 67 · 1367 · 43744265513290879_<17> · C89
C89 = P40 · P49
P40 = 6001131512745860146554482788707579097961_<40>
P49 = 1716466010916447043435880068391731173711732687851_<49>

Wed Oct 15 05:27:12 2008 Msieve v. 1.38 Wed Oct 15 05:27:12 2008 random seeds: dba802fa 24726388 Wed Oct 15 05:27:12 2008 factoring 10300738268667869941900222275951412419627031093089343147466513267202507820099968563571811 (89 digits) Wed Oct 15 05:27:13 2008 searching for 15-digit factors Wed Oct 15 05:27:15 2008 commencing quadratic sieve (89-digit input) Wed Oct 15 05:27:15 2008 using multiplier of 11 Wed Oct 15 05:27:15 2008 using 64kb Pentium 4 sieve core Wed Oct 15 05:27:15 2008 sieve interval: 14 blocks of size 65536 Wed Oct 15 05:27:15 2008 processing polynomials in batches of 8 Wed Oct 15 05:27:15 2008 using a sieve bound of 1537147 (58224 primes) Wed Oct 15 05:27:15 2008 using large prime bound of 122971760 (26 bits) Wed Oct 15 05:27:15 2008 using double large prime bound of 364459767191680 (42-49 bits) Wed Oct 15 05:27:15 2008 using trial factoring cutoff of 49 bits Wed Oct 15 05:27:15 2008 polynomial 'A' values have 11 factors Wed Oct 15 06:57:24 2008 58395 relations (16414 full + 41981 combined from 610832 partial), need 58320 Wed Oct 15 06:57:26 2008 begin with 627246 relations Wed Oct 15 06:57:27 2008 reduce to 139598 relations in 11 passes Wed Oct 15 06:57:27 2008 attempting to read 139598 relations Wed Oct 15 06:57:30 2008 recovered 139598 relations Wed Oct 15 06:57:30 2008 recovered 115984 polynomials Wed Oct 15 06:57:30 2008 attempting to build 58395 cycles Wed Oct 15 06:57:31 2008 found 58395 cycles in 6 passes Wed Oct 15 06:57:31 2008 distribution of cycle lengths: Wed Oct 15 06:57:31 2008 length 1 : 16414 Wed Oct 15 06:57:31 2008 length 2 : 11404 Wed Oct 15 06:57:31 2008 length 3 : 10538 Wed Oct 15 06:57:31 2008 length 4 : 7465 Wed Oct 15 06:57:31 2008 length 5 : 5335 Wed Oct 15 06:57:31 2008 length 6 : 3216 Wed Oct 15 06:57:31 2008 length 7 : 1855 Wed Oct 15 06:57:31 2008 length 9+: 2168 Wed Oct 15 06:57:31 2008 largest cycle: 20 relations Wed Oct 15 06:57:31 2008 matrix is 58224 x 58395 (14.0 MB) with weight 3437825 (58.87/col) Wed Oct 15 06:57:31 2008 sparse part has weight 3437825 (58.87/col) Wed Oct 15 06:57:32 2008 filtering completed in 3 passes Wed Oct 15 06:57:32 2008 matrix is 53593 x 53657 (13.0 MB) with weight 3201131 (59.66/col) Wed Oct 15 06:57:32 2008 sparse part has weight 3201131 (59.66/col) Wed Oct 15 06:57:32 2008 saving the first 48 matrix rows for later Wed Oct 15 06:57:32 2008 matrix is 53545 x 53657 (9.3 MB) with weight 2631124 (49.04/col) Wed Oct 15 06:57:32 2008 sparse part has weight 2128145 (39.66/col) Wed Oct 15 06:57:32 2008 matrix includes 64 packed rows Wed Oct 15 06:57:32 2008 using block size 21462 for processor cache size 512 kB Wed Oct 15 06:57:33 2008 commencing Lanczos iteration Wed Oct 15 06:57:33 2008 memory use: 8.5 MB Wed Oct 15 06:58:05 2008 lanczos halted after 848 iterations (dim = 53545) Wed Oct 15 06:58:05 2008 recovered 18 nontrivial dependencies Wed Oct 15 06:58:07 2008 prp40 factor: 6001131512745860146554482788707579097961 Wed Oct 15 06:58:07 2008 prp49 factor: 1716466010916447043435880068391731173711732687851 Wed Oct 15 06:58:07 2008 elapsed time 01:30:55
(26·10¹²⁷-17)/9 = 2(8)₁₂₆7_<128> = 3² · 41 · 2410931 · C119
C119 = P45 · P75
P45 = 176708995742868033725601335173947516522546743_<45>
P75 = 183764252538525370473390572332885210401984688084514695855899989508440764331_<75>

Number: 28887_127 N=32472796519521605950704707962779367391733293104734093089187017362312920723741833758460503464549450724888744205594623933 ( 119 digits) SNFS difficulty: 128 digits. Divisors found: r1=176708995742868033725601335173947516522546743 (pp45) r2=183764252538525370473390572332885210401984688084514695855899989508440764331 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.81 hours. Scaled time: 2.98 units (timescale=0.783). Factorization parameters were as follows: name: 28887_127 n: 32472796519521605950704707962779367391733293104734093089187017362312920723741833758460503464549450724888744205594623933 m: 10000000000000000000000000 c5: 2600 c0: -17 skew: 0.37 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:63953, largePrimes:1446680 encountered Relations: rels:1429455, finalFF:159869 Max relations in full relation-set: 28 Initial matrix: 127971 x 159869 with sparse part having weight 9961803. Pruned matrix : 117646 x 118349 with weight 5787394. Total sieving time: 3.68 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.06 hours. Time per square root: 0.02 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: 3.81 hours. --------- CPU info (if available) ----------
(26·10¹³⁴-17)/9 = 2(8)₁₃₃7_<135> = 7 · 29 · 68113 · 3973247 · C121
C121 = P41 · P81
P41 = 15177348453623950838024813965176032894221_<41>
P81 = 346468154200169948635742296967949960762542906674809782261859479169727252266013559_<81>

Number: 28887_134 N=5258467904379893917425879319299797702544751262661304331982090981680291206386080564645724578974138223446115582384798742539 ( 121 digits) SNFS difficulty: 136 digits. Divisors found: r1=15177348453623950838024813965176032894221 (pp41) r2=346468154200169948635742296967949960762542906674809782261859479169727252266013559 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.36 hours. Scaled time: 8.38 units (timescale=1.002). Factorization parameters were as follows: name: 28887_134 n: 5258467904379893917425879319299797702544751262661304331982090981680291206386080564645724578974138223446115582384798742539 m: 1000000000000000000000000000 c5: 13 c0: -85 skew: 1.46 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:64473, largePrimes:1753499 encountered Relations: rels:1865992, finalFF:264471 Max relations in full relation-set: 28 Initial matrix: 143036 x 264471 with sparse part having weight 26412188. Pruned matrix : 117853 x 118632 with weight 11238155. Total sieving time: 8.22 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.02 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: 8.36 hours. --------- CPU info (if available) ----------
(26·10¹³⁷-17)/9 = 2(8)₁₃₆7_<138> = 41 · 109 · C134
C134 = P36 · P37 · P62
P36 = 526294333620542813446146956660416129_<36>
P37 = 2734255542207168448248267232752481223_<37>
P62 = 44921338536578715635599211917927596126790380075342452322497069_<62>

Number: 28887_137 N=64642848263345018771288630317495835508813803734367618905546853633673951418413266701474354193083215235822082991472116556027945600556923 ( 134 digits) SNFS difficulty: 138 digits. Divisors found: r1=526294333620542813446146956660416129 (pp36) r2=2734255542207168448248267232752481223 (pp37) r3=44921338536578715635599211917927596126790380075342452322497069 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.31 hours. Scaled time: 8.41 units (timescale=1.011). Factorization parameters were as follows: name: 28887_137 n: 64642848263345018771288630317495835508813803734367618905546853633673951418413266701474354193083215235822082991472116556027945600556923 m: 1000000000000000000000000000 c5: 2600 c0: -17 skew: 0.37 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:63953, largePrimes:1617804 encountered Relations: rels:1626585, finalFF:164691 Max relations in full relation-set: 28 Initial matrix: 142518 x 164691 with sparse part having weight 17091487. Pruned matrix : 136891 x 137667 with weight 12918139. Total sieving time: 8.15 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 8.31 hours. --------- CPU info (if available) ----------
Oct 15, 2008 (4th): By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(26·10¹¹¹-17)/9 = 2(8)₁₁₀7_<112> = C112
C112 = P35 · P77
P35 = 73754123201921790624647439007473229_<35>
P77 = 39169184900751608644593613969599919588169278840249296543982129934412148934803_<77>

SNFS difficulty: 113 digits. Divisors found: r1=73754123201921790624647439007473229 r2=39169184900751608644593613969599919588169278840249296543982129934412148934803 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.300). Factorization parameters were as follows: n: 2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 m: 10000000000000000000000000000 c4: 13 c0: -85 skew: 1.6 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, 345001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 48154 x 48371 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,113,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 0.60 hours.
(26·10¹⁰³-17)/9 = 2(8)₁₀₂7_<104> = 3 · 31 · 463 · 115597 · C94
C94 = P31 · P64
P31 = 1972108063362367189451376248797_<31>
P64 = 2942995695171047624969249628590188180420693681219570640764638677_<64>

N=5803905540887558263985489078759725396885725234535263165222238080255654302916465210789360921569 ( 94 digits) SNFS difficulty: 105 digits. Divisors found: r1=1972108063362367189451376248797 r2=2942995695171047624969249628590188180420693681219570640764638677 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.316). Factorization parameters were as follows: n: 5803905540887558263985489078759725396885725234535263165222238080255654302916465210789360921569 m: 100000000000000000000000000 c4: 13 c0: -85 skew: 1.6 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 : 37181 x 37410 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,105,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 0.40 hours.
(26·10¹²⁰-17)/9 = 2(8)₁₁₉7_<121> = 5653 · 11949605451227_<14> · 4379004068674901_<16> · C88
C88 = P31 · P58
P31 = 3759727749368860911148358537753_<31>
P58 = 2597565697150329074823057784392058457450845003898821264709_<58>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1986497679 Step 1 took 3732ms Step 2 took 2901ms ********** Factor found in step 2: 3759727749368860911148358537753 Found probable prime factor of 31 digits: 3759727749368860911148358537753 Probable prime cofactor 2597565697150329074823057784392058457450845003898821264709 has 58 digits
(26·10¹⁶⁵-17)/9 = 2(8)₁₆₄7_<166> = 263957 · 4058137 · C154
C154 = P31 · C123
P31 = 7818152593406970277472416624103_<31>
C123 = [344958465819430965530710574646567760779022977241793408151628340601011887317136749920912630213301975588157023174300056198581_<123>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2782357100 Step 1 took 14693ms Step 2 took 13021ms ********** Factor found in step 2: 7818152593406970277472416624103 Found probable prime factor of 31 digits: 7818152593406970277472416624103 Composite cofactor 344958465819430965530710574646567760779022977241793408151628340601011887317136749920912630213301975588157023174300056198581 has 123 digits
Oct 15, 2008 (3rd): By Serge Batalov / PFGW
(38·10³⁹⁸⁵⁵+61)/9 = 4(2)₃₉₈₅₄9_<39856> is PRP.
(19·10²⁷²²²+53)/9 = 2(1)₂₇₂₂₁7_<27223> is PRP.
Oct 15, 2008 (2nd): Factorizations of 288...887 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Oct 15, 2008: By matsui / GMP-ECM
4·10¹⁹²+9 = 4(0)₁₉₁9_<193> = 13 · 3084049 · 20054833 · 362793721871669762743297557966121_<33> · C146
C146 = P35 · P111
P35 = 34347828192180472650311406770836321_<35>
P111 = 399224581811496883777327450848889939055934413354952004388681194427258371965399996716709123759572132028042808069_<111>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 13712497346156392212676019147625431370510365650834689585981115102219563918727772856984851299023907414810459127022107546442249298162322016417074149 = 34347828192180472650311406770836321* 399224581811496883777327450848889939055934413354952004388681194427258371965399996716709123759572132028042808069
4·10¹⁹³+9 = 4(0)₁₉₂9_<194> = 7 · 11437 · 13853895929_<11> · 284374155722383_<15> · 40774884715492908428204364418823_<32> · C133
C133 = P31 · C103
P31 = 1455040861595700679822195920931_<31>
C103 = [2137567576041104372111455292736110616642012466158171115994587987948441933469530773750128809166787452761_<103>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 126820010468908806071880109357043266345981215766729369753337225868175064400665316164905372765852198104155866881930631191806135695255612601001613076169469586595362093 = 1455040861595700679822195920931* 87159071484651651948214084667005400934366096726356153793048130126152962818451986017052417673584656337918155219572308362365470331720303
Oct 14, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(25·10¹⁸⁶-43)/9 = 2(7)₁₈₅3_<187> = 131 · C185
C185 = P80 · P105
P80 = 31424022345942293721314643526777454557385387249420546118526109881135411541015663_<80>
P105 = 674783459735086705269541484554441010464640876312706928931469006792480841626496533516974299488863906180641_<105>

Number: n N=21204410517387616624257845631891433418150975402883799830364715860899067005937234944868532654792196776929601357082273112807463952502120441051738761662425784563189143341815097540288379983 ( 185 digits) SNFS difficulty: 187 digits. Divisors found: Tue Oct 14 05:57:25 2008 prp80 factor: 31424022345942293721314643526777454557385387249420546118526109881135411541015663 Tue Oct 14 05:57:25 2008 prp105 factor: 674783459735086705269541484554441010464640876312706928931469006792480841626496533516974299488863906180641 Tue Oct 14 05:57:26 2008 elapsed time 06:56:43 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 73.50 hours. Scaled time: 150.32 units (timescale=2.045). Factorization parameters were as follows: name: KA_2_7_185_3 n: 21204410517387616624257845631891433418150975402883799830364715860899067005937234944868532654792196776929601357082273112807463952502120441051738761662425784563189143341815097540288379983 type: snfs skew: 0.70 deg: 5 c5: 250 c0: -43 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 6500001) Primes: RFBsize:602489, AFBsize:602475, largePrimes:14280891 encountered Relations: rels:14024050, finalFF:1214304 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 73.14 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 73.50 hours. --------- CPU info (if available) ----------
Oct 14, 2008: By Serge Batalov / PFGW
(19·10¹⁷⁵²⁰+53)/9 = 2(1)₁₇₅₁₉7_<17521> is PRP.
(64·10¹⁷⁶⁶⁶+17)/9 = 7(1)₁₇₆₆₅3_<17667> is PRP.
(64·10²⁰⁸⁶⁴+17)/9 = 7(1)₂₀₈₆₃3_<20865> is PRP.
Oct 13, 2008 (3rd): By Serge Batalov / PFGW
(35·10¹⁰¹⁷⁶-17)/9 = 3(8)₁₀₁₇₅7_<10177> is PRP.
(46·10¹²⁸⁰⁹+53)/9 = 5(1)₁₂₈₀₈7_<12810> is PRP.
(46·10¹⁵⁰⁷¹+53)/9 = 5(1)₁₅₀₇₀7_<15072> is PRP.
(58·10¹¹³⁹¹+41)/9 = 6(4)₁₁₃₉₀9_<11392> is PRP.
(58·10¹¹⁶⁷³+41)/9 = 6(4)₁₁₆₇₂9_<11674> is PRP.
Oct 13, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁶⁷-53)/9 = 2(8)₁₆₆3_<168> = 7 · 2399 · 6323 · 127691 · 2938021 · 180397057763401_<15> · C134
C134 = P39 · P95
P39 = 641381666556496229620462884848095705753_<39>
P95 = 62678442074912406253135639578417547373032295596932760185025327623693360325589453770923938796959_<95>

Number: 28883_167 N=40200803635172132619878290809551400226863431975204543229129709070472743443263344426800924623027279256511540239797176634645520875205127 ( 134 digits) SNFS difficulty: 168 digits. Divisors found: r1=641381666556496229620462884848095705753 (pp39) r2=62678442074912406253135639578417547373032295596932760185025327623693360325589453770923938796959 (pp95) Version: GGNFS-0.77.1-20050930-nocona Total time: 143.96 hours. Scaled time: 145.25 units (timescale=1.009). Factorization parameters were as follows: name: 28883_167 n: 40200803635172132619878290809551400226863431975204543229129709070472743443263344426800924623027279256511540239797176634645520875205127 m: 1000000000000000000000000000000000 c5: 2600 c0: -53 skew: 0.46 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, 8050001) Primes: RFBsize:380800, AFBsize:380897, largePrimes:6325510 encountered Relations: rels:6667158, finalFF:966762 Max relations in full relation-set: 28 Initial matrix: 761764 x 966762 with sparse part having weight 80074010. Pruned matrix : 602881 x 606753 with weight 61848504. Total sieving time: 139.97 hours. Total relation processing time: 0.13 hours. Matrix solve time: 3.75 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 143.96 hours. --------- CPU info (if available) ----------
Oct 13, 2008: By Serge Batalov / Msieve-1.38
(68·10¹⁷³+13)/9 = 7(5)₁₇₂7_<174> = 11² · 107 · 6606011 · C163
C163 = P43 · P57 · P64
P43 = 6610570985981893588217485599928065911900503_<43>
P57 = 580045643086614207620043405574822802210547317327758301137_<57>
P64 = 2303863904620842108302141414515874627622737561828500894022443411_<64>

SNFS difficulty: 174 digits. Divisors found: r1=6610570985981893588217485599928065911900503 r2=580045643086614207620043405574822802210547317327758301137 r3=2303863904620842108302141414515874627622737561828500894022443411 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.596). Factorization parameters were as follows: n: 8834011550082961570244632107524709874248369610339476895245395710746521446283572650471917371886973695062656009852723821223435749028679163809470732622166742120828421 m: 20000000000000000000000000000000000 c5: 2125 c0: 13 skew: 0.36 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [3700000, 7200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1243431 x 1243679 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 6.00 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,174,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,54,54,2.6,2.6,100000 total time: 61.00 hours.
Oct 12, 2008 (2nd): By Jo Yeong Uk / GGNFS
(8·10¹⁶⁹+1)/9 = (8)₁₆₈9_<169> = 3 · 134838716741_<12> · 104450884973579663627_<21> · C138
C138 = P62 · P76
P62 = 67798627312166014383929640769882002342372388847421981172672289_<62>
P76 = 3102977219325565368707599249750650170581500768570091107590293404218912306981_<76>

Number: 88889_169 N=210377596051195229278114432178007432868301425550480627660077223627399086374121611283425294082727290932956598726259701763200994497679949509 ( 138 digits) SNFS difficulty: 170 digits. Divisors found: r1=67798627312166014383929640769882002342372388847421981172672289 (pp62) r2=3102977219325565368707599249750650170581500768570091107590293404218912306981 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 57.72 hours. Scaled time: 137.30 units (timescale=2.379). Factorization parameters were as follows: n: 210377596051195229278114432178007432868301425550480627660077223627399086374121611283425294082727290932956598726259701763200994497679949509 m: 10000000000000000000000000000000000 c5: 4 c0: 5 skew: 1.05 type: snfs Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [3500000, 6700001) Primes: RFBsize:476648, AFBsize:476559, largePrimes:6565015 encountered Relations: rels:7040243, finalFF:1111712 Max relations in full relation-set: 28 Initial matrix: 953271 x 1111712 with sparse part having weight 56167175. Pruned matrix : 811416 x 816246 with weight 37322717. Total sieving time: 53.99 hours. Total relation processing time: 0.10 hours. Matrix solve time: 3.57 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,7000000,7000000,27,27,49,49,2.5,2.5,100000 total time: 57.72 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
(52·10¹⁷⁵-7)/9 = 5(7)₁₇₅_<176> = 3 · 44119 · 505411 · 108654820435393_<15> · 107924410927665683001385431856290806743357967_<45> · C107
C107 = P53 · P55
P53 = 31288719349461934155851843896696720363661033230725719_<53>
P55 = 2354034136349944678676611987548074368673930574524031959_<55>

Number: 57777_175 N=73654713431306427074409733299667444457566434315864090073277343599353361668298394489931133898094003519253521 ( 107 digits) Divisors found: r1=31288719349461934155851843896696720363661033230725719 (pp53) r2=2354034136349944678676611987548074368673930574524031959 (pp55) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.93 hours. Scaled time: 21.32 units (timescale=2.388). Factorization parameters were as follows: name: 57777_175 n: 73654713431306427074409733299667444457566434315864090073277343599353361668298394489931133898094003519253521 skew: 17886.39 # norm 2.10e+15 c5: 110160 c4: 5442417444 c3: -149713271052144 c2: -1264206659453831591 c1: 16575436908728770826116 c0: 83199602893546180382049300 # alpha -7.26 Y1: 24471492101 Y0: -231758072512480916699 # Murphy_E 1.55e-09 # M 38194101069741355399707275664143179168743790556414615227357162011118711033618235651356369089463785195133086 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [900000, 1400001) Primes: RFBsize:135072, AFBsize:134855, largePrimes:4986712 encountered Relations: rels:5028126, finalFF:374807 Max relations in full relation-set: 28 Initial matrix: 270008 x 374807 with sparse part having weight 36527943. Pruned matrix : 213572 x 214986 with weight 18438358. Polynomial selection time: 0.55 hours. Total sieving time: 8.04 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.19 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,1800000,1800000,26,26,50,50,2.6,2.6,50000 total time: 8.93 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Oct 12, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(8·10¹⁶⁸-71)/9 = (8)₁₆₇1_<168> = 7 · 83 · 173 · 180380873 · 1899953897191177928067350987423_<31> · C125
C125 = P41 · P84
P41 = 30196695799267574612214510483582331213049_<41>
P84 = 854539752983938975409709010100505812475698391065616612344483235106134591693546624847_<84>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 25804276969237260916253285418344233476581942122469731457748077108761430322204665370889961476489935277885313096413193234028503 (125 digits) Using B1=6486000, B2=14271342550, polynomial Dickson(12), sigma=3532503115 Step 1 took 57942ms Step 2 took 23495ms ********** Factor found in step 2: 30196695799267574612214510483582331213049 Found probable prime factor of 41 digits: 30196695799267574612214510483582331213049 Probable prime cofactor 854539752983938975409709010100505812475698391065616612344483235106134591693546624847 has 84 digits
(26·10¹⁸⁵-53)/9 = 2(8)₁₈₄3_<186> = 7 · C185
C185 = P68 · P118
P68 = 11967880220222771535977473028528815286409995203134321966881379578399_<68>
P118 = 3448383549168999632700369166622141002514388314197364283079763510370070630825743226204284898075719770357515051628529131_<118>

Number: n N=41269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269 ( 185 digits) SNFS difficulty: 186 digits. Divisors found: Sun Oct 12 22:19:14 2008 prp68 factor: 11967880220222771535977473028528815286409995203134321966881379578399 Sun Oct 12 22:19:14 2008 prp118 factor: 3448383549168999632700369166622141002514388314197364283079763510370070630825743226204284898075719770357515051628529131 Sun Oct 12 22:19:14 2008 elapsed time 16:31:56 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 64.71 hours. Scaled time: 84.58 units (timescale=1.307). Factorization parameters were as follows: name: KA_2_8_184_3 n: 41269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269 type: snfs skew: 1.15 deg: 5 c5: 26 c0: -53 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 6100001) Primes: RFBsize:602489, AFBsize:601295, largePrimes:14538080 encountered Relations: rels:14376374, finalFF:1255184 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 64.04 hours. Total relation processing time: 0.67 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 64.71 hours. --------- CPU info (if available) ----------
Oct 11, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁶⁶-53)/9 = 2(8)₁₆₅3_<167> = 521 · 1597 · 197787847 · C153
C153 = P54 · P99
P54 = 265118142137434755285925832970724934903901408844488191_<54>
P99 = 662138969195960498557622691000644669495559191169984336202123246282041767740138009213412163051256367_<99>

Number: 28883_166 N=175545053350029188479712622193807947858289238010646688835359710365749635407791235397932755833241463063172111251654787140131951630486754812817265645062097 ( 153 digits) SNFS difficulty: 167 digits. Divisors found: r1=265118142137434755285925832970724934903901408844488191 (pp54) r2=662138969195960498557622691000644669495559191169984336202123246282041767740138009213412163051256367 (pp99) Version: GGNFS-0.77.1-20050930-nocona Total time: 133.61 hours. Scaled time: 134.68 units (timescale=1.008). Factorization parameters were as follows: 28883_166 n: 175545053350029188479712622193807947858289238010646688835359710365749635407791235397932755833241463063172111251654787140131951630486754812817265645062097 m: 1000000000000000000000000000000000 c5: 260 c0: -53 skew: 0.73 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, 7650001) Primes: RFBsize:380800, AFBsize:381462, largePrimes:6278885 encountered Relations: rels:6593734, finalFF:945834 Max relations in full relation-set: 28 Initial matrix: 762329 x 945834 with sparse part having weight 74842668. Pruned matrix : 619288 x 623163 with weight 56284364. Total sieving time: 129.71 hours. Total relation processing time: 0.12 hours. Matrix solve time: 3.66 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: 133.61 hours. --------- CPU info (if available) ----------
Oct 11, 2008: By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
2·10¹⁷⁶-7 = 1(9)₁₇₅3_<177> = 31 · 167 · 84349 · 762539 · 5303471 · C156
C156 = P63 · P93
P63 = 337158791033264179423030381537184109066737553257391166972636621_<63>
P93 = 335903976890265082828384698860438605538743727883895495015727111914842671618296153307348566709_<93>

SNFS difficulty: 176 digits. Divisors found: r1=337158791033264179423030381537184109066737553257391166972636621 r2=335903976890265082828384698860438605538743727883895495015727111914842671618296153307348566709 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.735). Factorization parameters were as follows: n: 113252978751587285152120274127084084614582650358880557515891373662125548580378985430928277226131608413432226944828272335376297243741299360815777087034850289 Y1: 1 Y0: -100000000000000000000000000000000000 c5: 20 c0: -7 skew: 0.81 type: snfs Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [5000000, 7900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1260259 x 1260507 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,176,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000 total time: 60.00 hours.
9·10¹⁷³+1 = 9(0)₁₇₂1_<174> = 263 · 659 · 719503 · C163
C163 = P48 · P53 · P64
P48 = 119042288029767638893284897945328190576465889847_<48>
P53 = 17758729179548142956399209216703776600136321973088783_<53>
P64 = 3413937667616485389431567664007791715409001756176675366899769851_<64>

SNFS difficulty: 173 digits. Divisors found: r1=119042288029767638893284897945328190576465889847 r2=17758729179548142956399209216703776600136321973088783 r3=3413937667616485389431567664007791715409001756176675366899769851 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.924). Factorization parameters were as follows: n: 7217199947136759338491991713436421871033060911813262302390708730896124696133610146983344119522988647120966471514735115383937781143270879649291821299541605910126051 m: 10000000000000000000000000000000000 c5: 9000 c0: 1 skew: 0.16 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 8000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1277412 x 1277660 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,173,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 50.00 hours.
(23·10¹⁷⁷+1)/3 = 7(6)₁₇₆7_<178> = 11 · 31 · 113 · 659 · 17107 · 26189 · 7423487 · C155
C155 = P37 · P119
P37 = 1222827647443896135605384277317373191_<37>
P119 = 74237334747024884434878158461319294495747514134705484811961053103278950707050742632109379197705733552024608749051925771_<119>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=486638099 Step 1 took 18977ms Step 2 took 14697ms ********** Factor found in step 2: 1222827647443896135605384277317373191 Found probable prime factor of 37 digits: 1222827647443896135605384277317373191 Probable prime cofactor 74237334747024884434878158461319294495747514134705484811961053103278950707050742632109379197705733552024608749051925771 has 119 digits
(52·10¹⁷⁵-7)/9 = 5(7)₁₇₅_<176> = 3 · 44119 · 505411 · 108654820435393_<15> · C151
C151 = P45 · C107
P45 = 107924410927665683001385431856290806743357967_<45>
C107 = [73654713431306427074409733299667444457566434315864090073277343599353361668298394489931133898094003519253521_<107>]

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=4191283557 Step 1 took 61895ms Step 2 took 34491ms ********** Factor found in step 2: 107924410927665683001385431856290806743357967 Found probable prime factor of 45 digits: 107924410927665683001385431856290806743357967 Composite cofactor 73654713431306427074409733299667444457566434315864090073277343599353361668298394489931133898094003519253521 has 107 digits
Oct 10, 2008 (4th): By Wataru Sakai / GGNFS
(26·10¹⁸³-71)/9 = 2(8)₁₈₂1_<184> = C184
C184 = P54 · P130
P54 = 593003743193204034604146674734025028736359951238501379_<54>
P130 = 4871619988995031102117074254428860421831102448543408974537652092788862101145035929409514449229400537835795554628125214530032586939_<130>

Number: 28881_183 N=2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881 ( 184 digits) SNFS difficulty: 184 digits. Divisors found: r1=593003743193204034604146674734025028736359951238501379 (pp54) r2=4871619988995031102117074254428860421831102448543408974537652092788862101145035929409514449229400537835795554628125214530032586939 (pp130) Version: GGNFS-0.77.1-20060722-nocona Total time: 785.58 hours. Scaled time: 1582.94 units (timescale=2.015). Factorization parameters were as follows: n: 2888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881 m: 2000000000000000000000000000000000000 c5: 1625 c0: -142 skew: 0.61 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, 14200001) Primes: RFBsize:501962, AFBsize:500922, largePrimes:6904629 encountered Relations: rels:7420737, finalFF:1166355 Max relations in full relation-set: 32 Initial matrix: 1002950 x 1166355 with sparse part having weight 109741467. Pruned matrix : 875913 x 880991 with weight 88948169. Total sieving time: 776.71 hours. Total relation processing time: 0.13 hours. Matrix solve time: 8.48 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 785.58 hours. --------- CPU info (if available) ----------
Oct 10, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(25·10¹⁸⁵+11)/9 = 2(7)₁₈₄9_<186> = 3 · C185
C185 = P67 · P119
P67 = 1823763826037021477970377431624932839442513244497272766446966241367_<67>
P119 = 50770056555948494869560884191142325298211888542444804452840248720103134991812471526266558180708741955889392180067993879_<119>

Number: n N=92592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593 ( 185 digits) SNFS difficulty: 186 digits. Divisors found: Fri Oct 10 06:51:11 2008 prp67 factor: 1823763826037021477970377431624932839442513244497272766446966241367 Fri Oct 10 06:51:11 2008 prp119 factor: 50770056555948494869560884191142325298211888542444804452840248720103134991812471526266558180708741955889392180067993879 Fri Oct 10 06:51:12 2008 elapsed time 04:57:15 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 48.26 hours. Scaled time: 93.05 units (timescale=1.928). Factorization parameters were as follows: name: KA_2_7_184_9 n: 92592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593 type: snfs skew: 0.85 deg: 5 c5: 25 c0: 11 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 5300001) Primes: RFBsize:602489, AFBsize:601876, largePrimes:13793332 encountered Relations: rels:13528674, finalFF:1248100 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 47.92 hours. Total relation processing time: 0.34 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 48.26 hours. --------- CPU info (if available) ----------
(2·10¹⁶⁷-11)/9 = (2)₁₆₆1_<167> = 3³ · 211 · 345979 · 8190545575864479761627_<22> · C136
C136 = P44 · P92
P44 = 22483399937205086685698973749619580104633619_<44>
P92 = 61223296584507659608164240577076192938735095756775297725553210186474662678695824030849575959_<92>

Number: n N=1376507862583607912194299306720179473657830314931095313323900204083253155343440552393400001707363124784549392207334549098635997205565621 ( 136 digits) SNFS difficulty: 167 digits. Divisors found: Fri Oct 10 19:46:59 2008 prp44 factor: 22483399937205086685698973749619580104633619 Fri Oct 10 19:47:00 2008 prp92 factor: 61223296584507659608164240577076192938735095756775297725553210186474662678695824030849575959 Fri Oct 10 19:47:00 2008 elapsed time 01:21:20 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 10.30 hours. Scaled time: 21.06 units (timescale=2.045). Factorization parameters were as follows: name: KA_2_166_1 n: 1376507862583607912194299306720179473657830314931095313323900204083253155343440552393400001707363124784549392207334549098635997205565621 type: snfs skew: 0.56 deg: 5 c5: 200 c0: -11 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, 1800001) Primes: RFBsize:374362, AFBsize:375528, largePrimes:14838620 encountered Relations: rels:15562665, finalFF:1959922 Max relations in full relation-set: 28 Initial matrix: 749955 x 1959922 with sparse part having weight 219154798. Pruned matrix : Total sieving time: 9.93 hours. Total relation processing time: 0.36 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: 10.30 hours. --------- CPU info (if available) ----------
(13·10¹⁷⁰-31)/9 = 1(4)₁₆₉1_<171> = 3 · 19 · 236119276660919_<15> · C155
C155 = P60 · P95
P60 = 109065844527518766065659152112671088120780239748152362904203_<60>
P95 = 98402419407674987943082172616752732098497131153709107438685468235316808878942400958071245812309_<95>

Number: n N=10732342976249175501514261110742800869349996874710556532865562180039360327636609694024258570779685560647369177417833819967466747928851454103481701085234727 ( 155 digits) SNFS difficulty: 171 digits. Divisors found: Fri Oct 10 22:50:54 2008 prp60 factor: 109065844527518766065659152112671088120780239748152362904203 Fri Oct 10 22:50:54 2008 prp95 factor: 98402419407674987943082172616752732098497131153709107438685468235316808878942400958071245812309 Fri Oct 10 22:50:54 2008 elapsed time 03:40:28 (Msieve 1.38) Version: GGNFS-0.77.1-20050930-k8 Total time: 29.13 hours. Scaled time: 24.41 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_4_169_1 n: 10732342976249175501514261110742800869349996874710556532865562180039360327636609694024258570779685560647369177417833819967466747928851454103481701085234727 type: snfs skew: 1.19 deg: 5 c5: 13 c0: -31 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, 6100001) Primes: RFBsize:425648, AFBsize:426143, largePrimes:14169683 encountered Relations: rels:13493805, finalFF:875185 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 28.85 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000 total time: 29.13 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 Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Oct 10, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁷²-71)/9 = 2(8)₁₇₁1_<173> = 3 · 1867 · 9980458761793547_<16> · 32389267017818243837131_<23> · C131
C131 = P61 · P70
P61 = 2449546433911624471161459374915594356652322414642886072105793_<61>
P70 = 6513703188268288072413620827782285132171359163786368510031938034560281_<70>

Number: 28881_172 N=15955618416381363719105020564561792442731148624050997442594452601010541512632742936245978681162464959750190451806002119796467807833 ( 131 digits) SNFS difficulty: 173 digits. Divisors found: r1=2449546433911624471161459374915594356652322414642886072105793 (pp61) r2=6513703188268288072413620827782285132171359163786368510031938034560281 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 242.20 hours. Scaled time: 244.38 units (timescale=1.009). Factorization parameters were as follows: name: 28881_172 n: 15955618416381363719105020564561792442731148624050997442594452601010541512632742936245978681162464959750190451806002119796467807833 m: 10000000000000000000000000000000000 c5: 2600 c0: -71 skew: 0.49 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, 12200001) Primes: RFBsize:501962, AFBsize:500812, largePrimes:6616660 encountered Relations: rels:7076277, finalFF:1134545 Max relations in full relation-set: 28 Initial matrix: 1002841 x 1134545 with sparse part having weight 77981353. Pruned matrix : 891612 x 896690 with weight 60315465. Total sieving time: 235.01 hours. Total relation processing time: 0.15 hours. Matrix solve time: 6.90 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 242.20 hours. --------- CPU info (if available) ----------
Oct 10, 2008: By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(16·10¹⁶⁹-43)/9 = 1(7)₁₆₈3_<170> = 13 · 1337081204948276467921_<22> · C148
C148 = P47 · P101
P47 = 14960913929144985858253456596284691608551594667_<47>
P101 = 68362543450116714569706242160205915953260475026395859705760545962255010206177617289863648239322570803_<101>

SNFS difficulty: 170 digits. Divisors found: r1=14960913929144985858253456596284691608551594667 r2=68362543450116714569706242160205915953260475026395859705760545962255010206177617289863648239322570803 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 1022766128534630473716139749411132618557924540474766154578045443849993035831818663230810420705936920336800737164136824385552259626574190971664707601 m: 10000000000000000000000000000000000 c5: 8 c0: -215 skew: 1.93 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, 5600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1095583 x 1095831 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: 30.00 hours.
(10¹⁷⁶+11)/3 = (3)₁₇₅7_<176> = 37 · 619 · 5807147 · 25654907 · C157
C157 = P70 · P88
P70 = 4086161435966825565731672088764901305281427456131784256360630460786921_<70>
P88 = 2390768841211409882313112507942100812266380438329776481094137736714719683197884863631231_<88>

SNFS difficulty: 176 digits. Divisors found: r1=4086161435966825565731672088764901305281427456131784256360630460786921 r2=2390768841211409882313112507942100812266380438329776481094137736714719683197884863631231 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.618). Factorization parameters were as follows: n: 9769067441269158180523604400486296984649389790765301062586030897703330125403155429472917988622131386228273403986649763681756430041630652919266860669811929751 Y1: 1 Y0: -100000000000000000000000000000000000 c5: 10 c0: 11 skew: 1.02 type: snfs Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [5000000, 8100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1284153 x 1284401 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,176,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000 total time: 50.00 hours.
(22·10¹⁷⁷+41)/9 = 2(4)₁₇₆9_<178> = 173 · 1540115542109_<13> · C163
C163 = P31 · C133
P31 = 3988176640532111179738994803247_<31>
C133 = [2300415998333757249778490685464197237196599067392634238293373017266221785902267818855923626007378850090684685815884380328807466034631_<133>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1068787070 Step 1 took 18926ms ********** Factor found in step 1: 3988176640532111179738994803247 Found probable prime factor of 31 digits: 3988176640532111179738994803247 Composite cofactor 2300415998333757249778490685464197237196599067392634238293373017266221785902267818855923626007378850090684685815884380328807466034631 has 133 digits
(19·10¹⁷⁷+53)/9 = 2(1)₁₇₆7_<178> = 151 · 811 · 14901849676042845247_<20> · C154
C154 = P32 · P122
P32 = 34696836474803684531094725876141_<32>
P122 = 33341353998949281134084684490034526580396360733890803452497947844769267578107604119537306016289266699197332365783050679211_<122>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1881158939 Step 1 took 14161ms Step 2 took 5968ms ********** Factor found in step 2: 34696836474803684531094725876141 Found probable prime factor of 32 digits: 34696836474803684531094725876141 Probable prime cofactor 33341353998949281134084684490034526580396360733890803452497947844769267578107604119537306016289266699197332365783050679211 has 122 digits
(4·10¹⁷³-31)/9 = (4)₁₇₂1_<173> = 16231087 · 354269821 · C157
C157 = P61 · P97
P61 = 4498230111620791750209610078468593245067235231274070330521039_<61>
P97 = 1718280454213440932277591880486530693988757269147198266364252508172991305884293618799254053566797_<97>

SNFS difficulty: 173 digits. Divisors found: r1=4498230111620791750209610078468593245067235231274070330521039 r2=1718280454213440932277591880486530693988757269147198266364252508172991305884293618799254053566797 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.726). Factorization parameters were as follows: n: 7729220879352351153013101378082592843337556829023539351665660507177539117223814006573982196897174293351721382439223285549015530353367195285541263649400342083 Y1: 1 Y0: -20000000000000000000000000000000000 c5: 125 c0: -31 skew: 0.76 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 8000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1312353 x 1312601 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,173,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
Oct 9, 2008 (5th): By Jo Yeong Uk / GGNFS
(67·10¹⁷⁵+23)/9 = 7(4)₁₇₄7_<176> = 7 · 11 · 42487 · C170
C170 = P83 · P87
P83 = 32537127495497706794954789158042722494748647843639292901724992978991735797029256711_<83>
P87 = 699368861975805845572995184055315621277581863012055140909431384666070068950015730613723_<87>

Number: 74447_175 N=22755453828487933037559982272482566690206674201778586649252970716006468118878973964058813542184926373030969731136841076351985571276177814648405652712852562218250546445053 ( 170 digits) SNFS difficulty: 176 digits. Divisors found: r1=32537127495497706794954789158042722494748647843639292901724992978991735797029256711 (pp83) r2=699368861975805845572995184055315621277581863012055140909431384666070068950015730613723 (pp87) Version: GGNFS-0.77.1-20050930-nocona Total time: 114.12 hours. Scaled time: 270.93 units (timescale=2.374). Factorization parameters were as follows: n: 22755453828487933037559982272482566690206674201778586649252970716006468118878973964058813542184926373030969731136841076351985571276177814648405652712852562218250546445053 m: 100000000000000000000000000000000000 c5: 67 c0: 23 skew: 0.81 type: snfs Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [4000000, 6100001) Primes: RFBsize:539777, AFBsize:539305, largePrimes:10682829 encountered Relations: rels:10758829, finalFF:1265217 Max relations in full relation-set: 28 Initial matrix: 1079147 x 1265217 with sparse part having weight 84046143. Pruned matrix : 910123 x 915582 with weight 53529564. Total sieving time: 108.12 hours. Total relation processing time: 0.14 hours. Matrix solve time: 5.77 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,50,50,2.6,2.6,100000 total time: 114.12 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Oct 9, 2008 (4th): By Sinkiti Sibata / GGNFS
(26·10¹⁶⁰-53)/9 = 2(8)₁₅₉3_<161> = 139 · 11833111840768866262117_<23> · C137
C137 = P41 · P43 · P54
P41 = 24699164607397616188571642243521836798253_<41>
P43 = 4778115508280883342643806899807566682589691_<43>
P54 = 148825777520226664598083038604252245390400654880786267_<54>

Number: 28883_160 N=17563742810030346118482219962830768316393397876574007624819397524539131637145339947227845276968833406707060393815181493162114024771700741 ( 137 digits) SNFS difficulty: 161 digits. Divisors found: r1=24699164607397616188571642243521836798253 (pp41) r2=4778115508280883342643806899807566682589691 (pp43) r3=148825777520226664598083038604252245390400654880786267 (pp54) Version: GGNFS-0.77.1-20050930-nocona Total time: 75.15 hours. Scaled time: 57.57 units (timescale=0.766). Factorization parameters were as follows: name: 28883_160 n: 17563742810030346118482219962830768316393397876574007624819397524539131637145339947227845276968833406707060393815181493162114024771700741 m: 100000000000000000000000000000000 c5: 26 c0: -53 skew: 1.15 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, 4500001) Primes: RFBsize:283146, AFBsize:282797, largePrimes:5867428 encountered Relations: rels:5950995, finalFF:678604 Max relations in full relation-set: 28 Initial matrix: 566009 x 678604 with sparse part having weight 55712005. Pruned matrix : 491609 x 494503 with weight 40623709. Total sieving time: 71.62 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.19 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 75.15 hours. --------- CPU info (if available) ----------
(26·10¹⁶⁴-53)/9 = 2(8)₁₆₃3_<165> = 17 · 61 · 173 · 1570859 · 3678654851_<10> · 5556478709_<10> · 88233409332539930388136681_<26> · C108
C108 = P41 · P68
P41 = 22070470776022600268261014908547019424559_<41>
P68 = 25753450207192235293374738897634290020737717214515574604202694188217_<68>

Number: 28883_164 N=568390770179589408939872195752617880907878497620541326109998551022184578078602427260979786896871916978221303 ( 108 digits) Divisors found: r1=22070470776022600268261014908547019424559 (pp41) r2=25753450207192235293374738897634290020737717214515574604202694188217 (pp68) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 23.43 hours. Scaled time: 11.06 units (timescale=0.472). Factorization parameters were as follows: name: 28883_164 n: 568390770179589408939872195752617880907878497620541326109998551022184578078602427260979786896871916978221303 skew: 7666.01 # norm 2.95e+14 c5: 187200 c4: 843376632 c3: -3418951398874 c2: -175469085741270535 c1: -370049593689987005412 c0: 1943332529637999987863604 # alpha -5.56 Y1: 118808547149 Y0: -313666462701129548531 # Murphy_E 1.31e-09 # M 262874865414326697381161367861846653573701310987028493467367656403077279337065340473173389149331409696073463 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:182839, largePrimes:4583538 encountered Relations: rels:4786702, finalFF:525654 Max relations in full relation-set: 28 Initial matrix: 365992 x 525654 with sparse part having weight 44709387. Pruned matrix : 260833 x 262726 with weight 24752832. Polynomial selection time: 1.20 hours. Total sieving time: 19.51 hours. Total relation processing time: 0.34 hours. Matrix solve time: 2.17 hours. Time per square root: 0.21 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: 23.43 hours. --------- CPU info (if available) ----------
(26·10¹³⁰-53)/9 = 2(8)₁₂₉3_<131> = 2557961551_<10> · C122
C122 = P48 · P74
P48 = 236438277260853769814529260092665387318271835347_<48>
P74 = 47766018217713433955106464691584719775555236704971354158444251526906538639_<74>

Number: 28883_130 N=11293715059006721125218699148808624484633189425484405527285773064729262964941605914266882930520205027463639498969501472733 ( 122 digits) SNFS difficulty: 131 digits. Divisors found: r1=236438277260853769814529260092665387318271835347 (pp48) r2=47766018217713433955106464691584719775555236704971354158444251526906538639 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.80 hours. Scaled time: 4.54 units (timescale=0.783). Factorization parameters were as follows: name: 28883_130 n: 11293715059006721125218699148808624484633189425484405527285773064729262964941605914266882930520205027463639498969501472733 m: 100000000000000000000000000 c5: 26 c0: -53 skew: 1.15 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, 1150001) Primes: RFBsize:63951, AFBsize:63973, largePrimes:1545334 encountered Relations: rels:1548381, finalFF:166677 Max relations in full relation-set: 28 Initial matrix: 127990 x 166677 with sparse part having weight 14699325. Pruned matrix : 118264 x 118967 with weight 8717232. Total sieving time: 5.63 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,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.80 hours. --------- CPU info (if available) ----------
Oct 9, 2008 (3rd): By Justin Card / msieve 1.38, ggnfs
(10¹⁷⁶+17)/9 = (1)₁₇₅3_<176> = 13 · 1879391 · 6718199 · 43731936268508244866927446133249317_<35> · C127
C127 = P48 · P79
P48 = 710124167792898446935804545868140581401807318057_<48>
P79 = 2179772311514524087931982060767986518870830842019718570624060123823472397032281_<79>

Msieve v. 1.38 Wed Oct 8 17:36:45 2008 random seeds: 52413acf cf6c524a factoring 1547908998692254006817668407385442013503701471074265130054570365447559543406277463390309132007591482864040879451770914663198017 (127 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (127-digit input) R0: -100000000000000000000000000000 R1: 1 A0: 17 A1: 0 A2: 0 A3: 0 A4: 0 A5: 0 A6: 100 size score = 8.015950e-09, Murphy alpha = -1.265032, combined = 1.150603e-08 commencing relation filtering commencing duplicate removal, pass 1 error -15 reading relation 30050 error -11 reading relation 57741 error -15 reading relation 3597789 error -15 reading relation 5167541 error -11 reading relation 9339118 found 958927 hash collisions in 10721948 relations commencing duplicate removal, pass 2 found 835100 duplicates and 9886848 unique relations memory use: 50.6 MB reading rational ideals above 4915200 reading algebraic ideals above 4915200 commencing singleton removal, pass 1 relations with 0 large ideals: 137456 relations with 1 large ideals: 871545 relations with 2 large ideals: 2638586 relations with 3 large ideals: 3621314 relations with 4 large ideals: 1942464 relations with 5 large ideals: 82128 relations with 6 large ideals: 1244 relations with 7+ large ideals: 592111 9886848 relations and about 10243474 large ideals commencing singleton removal, pass 2 found 3672509 singletons current dataset: 6214339 relations and about 5185675 large ideals commencing singleton removal, pass 3 found 1055209 singletons current dataset: 5159130 relations and about 4059385 large ideals commencing singleton removal, pass 4 found 268425 singletons current dataset: 4890705 relations and about 3784822 large ideals commencing singleton removal, final pass memory use: 85.6 MB commencing in-memory singleton removal begin with 4890705 relations and 3998829 unique ideals reduce to 4317250 relations and 3413986 ideals in 15 passes max relations containing the same ideal: 55 reading rational ideals above 720000 reading algebraic ideals above 720000 commencing singleton removal, final pass keeping 3681423 ideals with weight <= 20, new excess is 429104 memory use: 127.8 MB commencing in-memory singleton removal begin with 4318889 relations and 3681423 unique ideals reduce to 4317135 relations and 3669929 ideals in 5 passes max relations containing the same ideal: 20 removing 561927 relations and 487204 ideals in 74723 cliques commencing in-memory singleton removal begin with 3755208 relations and 3669929 unique ideals reduce to 3697378 relations and 3123500 ideals in 8 passes max relations containing the same ideal: 20 removing 423906 relations and 349183 ideals in 74723 cliques commencing in-memory singleton removal begin with 3273472 relations and 3123500 unique ideals reduce to 3236125 relations and 2736235 ideals in 7 passes max relations containing the same ideal: 20 relations with 0 large ideals: 38894 relations with 1 large ideals: 235104 relations with 2 large ideals: 678797 relations with 3 large ideals: 1034849 relations with 4 large ideals: 822119 relations with 5 large ideals: 323075 relations with 6 large ideals: 64340 relations with 7+ large ideals: 38947 commencing 2-way merge reduce to 2013829 relation sets and 1513939 unique ideals commencing full merge memory use: 138.3 MB found 969439 cycles, need 902139 weight of 902139 cycles is about 63203125 (70.06/cycle) distribution of cycle lengths: 1 relations: 102303 2 relations: 96867 3 relations: 98547 4 relations: 92829 5 relations: 85292 6 relations: 77434 7 relations: 67639 8 relations: 58867 9 relations: 51014 10+ relations: 171347 heaviest cycle: 18 relations commencing cycle optimization start with 5307933 relations pruned 150799 relations memory use: 173.8 MB distribution of cycle lengths: 1 relations: 102303 2 relations: 99276 3 relations: 102677 4 relations: 96095 5 relations: 88079 6 relations: 79370 7 relations: 68613 8 relations: 59191 9 relations: 51176 10+ relations: 155359 heaviest cycle: 18 relations elapsed time 00:14:12 justin@riall:~/factoring_projects/11113_176$ ~/ggnfs/msieve -nc2 -nf 11113_176.fb -s 11113_176.dat -v -i 11113_176.ini Msieve v. 1.38 Wed Oct 8 18:53:11 2008 random seeds: 6da1b961 3bdc077b factoring 1547908998692254006817668407385442013503701471074265130054570365447559543406277463390309132007591482864040879451770914663198017 (127 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (127-digit input) R0: -100000000000000000000000000000 R1: 1 A0: 17 A1: 0 A2: 0 A3: 0 A4: 0 A5: 0 A6: 100 size score = 8.015950e-09, Murphy alpha = -1.265032, combined = 1.150603e-08 commencing linear algebra read 902139 cycles cycles contain 2879140 unique relations read 2879140 relations using 32 quadratic characters above 134217324 building initial matrix memory use: 356.1 MB read 902139 cycles matrix is 901831 x 902139 (268.9 MB) with weight 86502896 (95.89/col) sparse part has weight 60564938 (67.13/col) filtering completed in 3 passes matrix is 895277 x 895477 (267.8 MB) with weight 86093846 (96.14/col) sparse part has weight 60354117 (67.40/col) read 895477 cycles matrix is 895277 x 895477 (267.8 MB) with weight 86093846 (96.14/col) sparse part has weight 60354117 (67.40/col) saving the first 48 matrix rows for later matrix is 895229 x 895477 (258.7 MB) with weight 67221065 (75.07/col) sparse part has weight 58856479 (65.73/col) matrix includes 64 packed rows using block size 10922 for processor cache size 256 kB commencing Lanczos iteration memory use: 247.2 MB linear algebra completed 894740 of 895477 dimensions (99.9%, ETA 0h 0m) lanczos halted after 14159 iterations (dim = 895225) recovered 50 nontrivial dependencies elapsed time 03:47:21 justin@riall:~/factoring_projects/11113_176$ ~/ggnfs/msieve -nc3 -nf 11113_176.fb -s 11113_176.dat -v -i 11113_176.ini Msieve v. 1.38 Wed Oct 8 23:20:44 2008 random seeds: ddd9cea2 c865422e factoring 1547908998692254006817668407385442013503701471074265130054570365447559543406277463390309132007591482864040879451770914663198017 (127 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (127-digit input) R0: -100000000000000000000000000000 R1: 1 A0: 17 A1: 0 A2: 0 A3: 0 A4: 0 A5: 0 A6: 100 size score = 8.015950e-09, Murphy alpha = -1.265032, combined = 1.150603e-08 commencing square root phase reading relations for dependency 1 read 447370 cycles cycles contain 1763729 unique relations read 1763729 relations multiplying 1435668 relations multiply complete, coefficients have about 41.54 million bits initial square root is modulo 919693 reading relations for dependency 2 read 447432 cycles cycles contain 1761594 unique relations read 1761594 relations multiplying 1433372 relations multiply complete, coefficients have about 41.47 million bits initial square root is modulo 899161 prp48 factor: 710124167792898446935804545868140581401807318057 prp79 factor: 2179772311514524087931982060767986518870830842019718570624060123823472397032281 elapsed time 00:26:34 Sieve time: 51.75 hours Filtering: 0.25 hours Block Lanczos: 3.78 hours Square root: 0.5 hours Had to manually restart the filtering/linalg/sqrt, so all I had were the newest run times and the time spent sieving
Oct 9, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(8·10¹⁸⁶-17)/9 = (8)₁₈₅7_<186> = 122041 · 600760122234227247339021404369_<30> · C152
C152 = P46 · P49 · P58
P46 = 3064396278824864704453221938558760266788976239_<46>
P49 = 2068999825167536250079312154581792851089121116323_<49>
P58 = 1912208492840357290420849493550726386987869589952298531099_<58>

Number: n N=12123851911813520689442426339677939520762900296076844725658595042305449072115945719786865839939239072337205062999312826980398145833769450425203032477503 ( 152 digits) SNFS difficulty: 187 digits. Divisors found: Thu Oct 09 10:20:58 2008 prp46 factor: 3064396278824864704453221938558760266788976239 Thu Oct 09 10:20:58 2008 prp49 factor: 2068999825167536250079312154581792851089121116323 Thu Oct 09 10:20:58 2008 prp58 factor: 1912208492840357290420849493550726386987869589952298531099 Thu Oct 09 10:20:58 2008 elapsed time 12:57:42 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 60.70 hours. Scaled time: 79.28 units (timescale=1.306). Factorization parameters were as follows: name: KA_8_185_7 n: 12123851911813520689442426339677939520762900296076844725658595042305449072115945719786865839939239072337205062999312826980398145833769450425203032477503 type: snfs skew: 1.47 deg: 5 c5: 5 c0: -34 m: 20000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 5600001) Primes: RFBsize:602489, AFBsize:602555, largePrimes:14506280 encountered Relations: rels:14387661, finalFF:1299453 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 60.15 hours. Total relation processing time: 0.55 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 60.70 hours. --------- CPU info (if available) ----------
Oct 9, 2008: By Serge Batalov / Msieve-1.38
(89·10¹⁷³+1)/9 = 9(8)₁₇₂9_<174> = 11² · 401 · 1972031 · C164
C164 = P44 · P59 · P62
P44 = 36508796972420217359188613859528017520402107_<44>
P59 = 26223045467053073103521145401907892655457523884058353664729_<59>
P62 = 10795017884319115590619497478062896384036042183481493808139013_<62>

SNFS difficulty: 174 digits. Divisors found: r1=36508796972420217359188613859528017520402107 r2=26223045467053073103521145401907892655457523884058353664729 r3=10795017884319115590619497478062896384036042183481493808139013 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.927). Factorization parameters were as follows: n: 10334846166644773118947276370372213703596548275653083075970650843413193899166892826813873902967045814628347177312759151240329845214046927329358818292276154861809039 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 89000 c0: 1 skew: 0.103 type: snfs rlim: 9000000 alim: 9000000 lpbr: 27 lpba: 27 mfbr: 54 mfba: 54 rlambda: 2.6 alambda: 2.6 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 7100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1248890 x 1249138 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,174,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 40.00 hours.
10¹⁷⁵+9 = 1(0)₁₇₄9_<176> = 3851 · 219533 · 85277080211_<11> · C156
C156 = P47 · P109
P47 = 16208367959129657766791547475962271323480435637_<47>
P109 = 8557660626492680468621533137816698825726336699568343271840514655920348964720598883835279448245250317366446089_<109>

SNFS difficulty: 175 digits. Divisors found: r1=16208367959129657766791547475962271323480435637 r2=8557660626492680468621533137816698825726336699568343271840514655920348964720598883835279448245250317366446089 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.735). Factorization parameters were as follows: n: 138705712303549395821421358642400204296070680855511012025776877011088224302623733204392953440147869792198011279515236944228094761620670597318606436194873693 Y1: 1 Y0: -100000000000000000000000000000000000 c5: 1 c0: 9 skew: 1.55 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [3700000, 6400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1175765 x 1176013 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,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,54,54,2.6,2.6,100000 total time: 50.00 hours.
Oct 8, 2008 (4th): By Tyler Cadigan / GGNFS + Msieve 1.38
(25·10¹⁹⁵-61)/9 = 2(7)₁₉₄1_<196> = 17 · C195
C195 = P96 · P100
P96 = 119509737931441137246596335232308772579390887315656085068081433412471176766596851200060667993821_<96>
P100 = 1367241662802357158967844931268345670438128299143736962843556968202636908577271893194737300367939703_<100>

Number: 15557_195 N=163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163 ( 195 digits) SNFS difficulty: 196 digits. Divisors found: r1=119509737931441137246596335232308772579390887315656085068081433412471176766596851200060667993821 r2=1367241662802357158967844931268345670438128299143736962843556968202636908577271893194737300367939703 Version: Total time: 1129.81 hours. Scaled time: 2875.38 units (timescale=2.545). Factorization parameters were as follows: n: 163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163398692810457516339869281045751633986928104575163 m: 1000000000000000000000000000000000000000 c5: 25 c0: -61 skew: 1.2 type: snfs Y0: 1000000000000000000000000000000000000000 Y1: -1 rlambda: 2.6 alambda: 2.6 rlim: 20000000 alim: 20000000 qintsize: 1000000Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [10000000, 26000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1695139 x 1695356 Total sieving time: 1129.81 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,196,5,0,0,0,0,0,0,0,0,20000000,20000000,27,27,48,48,2.6,2.6,100000 total time: 1129.81 hours. --------- CPU info (if available) ----------
Oct 8, 2008 (3rd): By Sinkiti Sibata / GGNFS, Msieve
(26·10¹⁴⁹-53)/9 = 2(8)₁₄₈3_<150> = 7 · 269 · 1531 · 4229 · 70639 · 12856007 · 4742624878308117767_<19> · C109
C109 = P35 · P74
P35 = 97788970591581258252270720835373003_<35>
P74 = 56261117004221928191795911695451058499504506266353625153621755380206925363_<74>

Number: 28883_149 N=5501716716175370397325516787455730544812029811212504821841017486779689125976143858501663582405137361886175089 ( 109 digits) SNFS difficulty: 151 digits. Divisors found: r1=97788970591581258252270720835373003 (pp35) r2=56261117004221928191795911695451058499504506266353625153621755380206925363 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.19 hours. Scaled time: 24.45 units (timescale=1.011). Factorization parameters were as follows: name: 28883_149 n: 5501716716175370397325516787455730544812029811212504821841017486779689125976143858501663582405137361886175089 m: 1000000000000000000000000000000 c5: 13 c0: -265 skew: 1.83 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:176698, largePrimes:6417293 encountered Relations: rels:7070190, finalFF:1144358 Max relations in full relation-set: 28 Initial matrix: 353065 x 1144358 with sparse part having weight 107679175. Pruned matrix : 220217 x 222046 with weight 44610337. Total sieving time: 23.50 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.54 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 24.19 hours. --------- CPU info (if available) ----------
(26·10¹³⁷-53)/9 = 2(8)₁₃₆3_<138> = 7 · 21563 · C133
C133 = P29 · P104
P29 = 41029142321912814750708583949_<29>
P104 = 46647801149261483258230864451435677225991269707280561420744207532823419482080864353602554573078146542987_<104>

Number: 28883_137 N=1913919272357337561622679648928315625899450042658316089656812190782417559767650200335819220019006690620102483015806764821280426715663 ( 133 digits) SNFS difficulty: 138 digits. Divisors found: r1=41029142321912814750708583949 (pp29) r2=46647801149261483258230864451435677225991269707280561420744207532823419482080864353602554573078146542987 (pp104) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.37 hours. Scaled time: 11.46 units (timescale=1.008). Factorization parameters were as follows: name: 28883_137 n: 1913919272357337561622679648928315625899450042658316089656812190782417559767650200335819220019006690620102483015806764821280426715663 m: 1000000000000000000000000000 c5: 2600 c0: -53 skew: 0.46 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, 2275001) Primes: RFBsize:78498, AFBsize:64048, largePrimes:1748682 encountered Relations: rels:1827123, finalFF:206065 Max relations in full relation-set: 28 Initial matrix: 142613 x 206065 with sparse part having weight 24284636. Pruned matrix : 129253 x 130030 with weight 14132842. Total sieving time: 11.20 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 11.37 hours. --------- CPU info (if available) ----------
(26·10¹⁴⁵-53)/9 = 2(8)₁₄₄3_<146> = 11239 · 216179 · 5232607 · 2857515761752823077296380205207103_<34> · C96
C96 = P43 · P54
P43 = 6321322749840508001653491196321933073104039_<43>
P54 = 125798350480661208614497151909486922156386678885355697_<54>

Tue Oct 7 22:38:21 2008 Msieve v. 1.38 Tue Oct 7 22:38:21 2008 random seeds: dcc069ef 6a45db20 Tue Oct 7 22:38:21 2008 factoring 795211974785813302750461673722896568366746906042605051709158919773319198321998699917820402360183 (96 digits) Tue Oct 7 22:38:23 2008 searching for 15-digit factors Tue Oct 7 22:38:25 2008 commencing quadratic sieve (96-digit input) Tue Oct 7 22:38:25 2008 using multiplier of 7 Tue Oct 7 22:38:25 2008 using 64kb Pentium 4 sieve core Tue Oct 7 22:38:25 2008 sieve interval: 18 blocks of size 65536 Tue Oct 7 22:38:25 2008 processing polynomials in batches of 6 Tue Oct 7 22:38:25 2008 using a sieve bound of 2298871 (84706 primes) Tue Oct 7 22:38:25 2008 using large prime bound of 344830650 (28 bits) Tue Oct 7 22:38:25 2008 using double large prime bound of 2331795890236200 (43-52 bits) Tue Oct 7 22:38:25 2008 using trial factoring cutoff of 52 bits Tue Oct 7 22:38:25 2008 polynomial 'A' values have 13 factors Wed Oct 8 08:11:12 2008 85140 relations (20193 full + 64947 combined from 1290119 partial), need 84802 Wed Oct 8 08:11:17 2008 begin with 1310312 relations Wed Oct 8 08:11:19 2008 reduce to 225183 relations in 10 passes Wed Oct 8 08:11:19 2008 attempting to read 225183 relations Wed Oct 8 08:11:26 2008 recovered 225183 relations Wed Oct 8 08:11:26 2008 recovered 213287 polynomials Wed Oct 8 08:11:27 2008 attempting to build 85140 cycles Wed Oct 8 08:11:27 2008 found 85140 cycles in 5 passes Wed Oct 8 08:11:27 2008 distribution of cycle lengths: Wed Oct 8 08:11:27 2008 length 1 : 20193 Wed Oct 8 08:11:27 2008 length 2 : 14574 Wed Oct 8 08:11:27 2008 length 3 : 14166 Wed Oct 8 08:11:27 2008 length 4 : 11703 Wed Oct 8 08:11:27 2008 length 5 : 8966 Wed Oct 8 08:11:27 2008 length 6 : 6093 Wed Oct 8 08:11:27 2008 length 7 : 4011 Wed Oct 8 08:11:27 2008 length 9+: 5434 Wed Oct 8 08:11:27 2008 largest cycle: 20 relations Wed Oct 8 08:11:27 2008 matrix is 84706 x 85140 (23.0 MB) with weight 5695354 (66.89/col) Wed Oct 8 08:11:27 2008 sparse part has weight 5695354 (66.89/col) Wed Oct 8 08:11:29 2008 filtering completed in 3 passes Wed Oct 8 08:11:29 2008 matrix is 81132 x 81196 (22.0 MB) with weight 5438057 (66.97/col) Wed Oct 8 08:11:29 2008 sparse part has weight 5438057 (66.97/col) Wed Oct 8 08:11:30 2008 saving the first 48 matrix rows for later Wed Oct 8 08:11:30 2008 matrix is 81084 x 81196 (13.8 MB) with weight 4318391 (53.18/col) Wed Oct 8 08:11:30 2008 sparse part has weight 3130861 (38.56/col) Wed Oct 8 08:11:30 2008 matrix includes 64 packed rows Wed Oct 8 08:11:30 2008 using block size 21845 for processor cache size 512 kB Wed Oct 8 08:11:31 2008 commencing Lanczos iteration Wed Oct 8 08:11:31 2008 memory use: 13.3 MB Wed Oct 8 08:12:42 2008 lanczos halted after 1284 iterations (dim = 81079) Wed Oct 8 08:12:42 2008 recovered 14 nontrivial dependencies Wed Oct 8 08:12:45 2008 prp43 factor: 6321322749840508001653491196321933073104039 Wed Oct 8 08:12:45 2008 prp54 factor: 125798350480661208614497151909486922156386678885355697 Wed Oct 8 08:12:45 2008 elapsed time 09:34:24
Oct 8, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38, Msieve-1.38+polyselect
(26·10¹⁵⁵-53)/9 = 2(8)₁₅₄3_<156> = 7 · 23 · 601751861 · C145
C145 = P36 · P109
P36 = 434606430250744155498232965602831581_<36>
P109 = 6861062456898643456131174629095768996957912069600254884539207471769541324001009925483131949479653797412862483_<109>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1810396645 Step 1 took 18717ms Step 2 took 16371ms ********** Factor found in step 2: 434606430250744155498232965602831581 Found probable prime factor of 36 digits: 434606430250744155498232965602831581 Probable prime cofactor 6861062456898643456131174629095768996957912069600254884539207471769541324001009925483131949479653797412862483 has 109 digits
(26·10¹⁶¹-53)/9 = 2(8)₁₆₀3_<162> = 7² · 499 · 1787 · 69191 · C149
C149 = P73 · P77
P73 = 2820898047146817411392847106167872926575917073080403520030662745443696079_<73>
P77 = 33874481999243789182317500712459693487731094537714674684152288464812979533931_<77>

N=95556460119776824140681734005614945558557064412858747129162824146979553114842635616632409878886974756421559331683241340660947531973593588107432156549 ( 149 digits) SNFS difficulty: 162 digits. Divisors found: r1=2820898047146817411392847106167872926575917073080403520030662745443696079 r2=33874481999243789182317500712459693487731094537714674684152288464812979533931 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 95556460119776824140681734005614945558557064412858747129162824146979553114842635616632409878886974756421559331683241340660947531973593588107432156549 Y1: 1 Y0: -100000000000000000000000000000000 c5: 260 c0: -53 skew: 0.73 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [2250000, 3950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 812374 x 812622 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,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,54,54,2.5,2.5,100000 total time: 20.00 hours.
(26·10¹⁴⁷-53)/9 = 2(8)₁₄₆3_<148> = 3 · 56729549 · C140
C140 = P32 · P51 · P58
P32 = 29588801926945123689788161696051_<32>
P51 = 139196806868612644199754015153798471168262938060269_<51>
P58 = 4121388922514085391358255144517180551116771872537841893331_<58>

SNFS difficulty: 148 digits. Divisors found: r1=29588801926945123689788161696051 r2=139196806868612644199754015153798471168262938060269 r3=4121388922514085391358255144517180551116771872537841893331 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.719). Factorization parameters were as follows: n: 16974627507843627717945773955702749601675186294235530815923866466186131022528717141096308785443772221121711419968506412116249381128747611989 Y1: 1 Y0: -100000000000000000000000000000 c5: 2600 c0: -53 skew: 0.46 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, 3750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 291409 x 291640 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,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 11.00 hours.
9·10¹⁷³-1 = 8(9)₁₇₃_<174> = 1289 · 1997 · 34668071675443361_<17> · C152
C152 = P64 · P88
P64 = 3806940299291622726460350337947914704889277467532053374128676991_<64>
P88 = 2649145276309295977725794028033536754856664922424512618104600287851523960480215455939453_<88>

SNFS difficulty: 173 digits. Divisors found: r1=3806940299291622726460350337947914704889277467532053374128676991 r2=2649145276309295977725794028033536754856664922424512618104600287851523960480215455939453 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.729). Factorization parameters were as follows: n: 10085137911059899814189806692481744412911545555803075485333634280013678423569068540994799208916444935039759847996393359202808120784082348266403890225923 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 9000 c0: -1 skew: 0.16 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 8000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1301900 x 1302148 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,173,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 20.00 hours.
(26·10¹⁵⁹-53)/9 = 2(8)₁₅₈3_<160> = 3³ · 29 · 287107 · 23759322402380015305157_<23> · 10313704067523250659900937829730796309_<38> · C92
C92 = P44 · P49
P44 = 11921264837382755488951323168235476632314123_<44>
P49 = 4399002839960155168477804483921875138150723586357_<49>

Number: 28883_159 N=52441677875563878773945469819992980394894802790218697762200342387440721101475627254741219911 ( 92 digits) Divisors found: r1=11921264837382755488951323168235476632314123 r2=4399002839960155168477804483921875138150723586357 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.943). Factorization parameters were as follows: name: 28883_159 n: 52441677875563878773945469819992980394894802790218697762200342387440721101475627254741219911 Y1: 1 Y0: -1064529985727826489681 deg: 4 c4: 40836168 c3: 202395460292 c2: 37363335780110865 c1: -807240905915521234 c0: -18833047913277457717700 skew: 1635.250 type: gnfs # adj. I(F,S) = 52.156 # E(F1,F2) = 1.052910e-04 # GGNFS version 0.77.1-20060722-k8 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1223408207. # maxskew=2000.0 # These parameters should be manually set: rlim: 700000 alim: 700000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.4 alambda: 2.4 qintsize: 40000 type: gnfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [350000, 790001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 122147 x 122395 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: gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000 total time: 1.00 hours.
(26·10¹⁷⁰-53)/9 = 2(8)₁₆₉3_<171> = 7229 · C167
C167 = P83 · P85
P83 = 24035351007699908057581878367616649511683898296781394921019100136189478983771471809_<83>
P85 = 1662655008492786764992070871336132080310708411773454004559517256637120059624426981103_<85>

SNFS difficulty: 171 digits. Divisors found: r1=24035351007699908057581878367616649511683898296781394921019100136189478983771471809 r2=1662655008492786764992070871336132080310708411773454004559517256637120059624426981103 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.738). Factorization parameters were as follows: n: 39962496733834401561611410829836614869122823196692334885722629532285086303622754030832603249258388281766342355635480549023224358678778377215228785293801201948940225327 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 26 c0: -53 skew: 1.15 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, 6200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1134038 x 1134286 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,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
Oct 8, 2008: By Robert Backstrom / GGNFS, Msieve
(26·10¹⁴²-53)/9 = 2(8)₁₄₁3_<143> = 53089 · 340047641 · 991880503657452655844894459_<27> · C103
C103 = P42 · P62
P42 = 132486450373648223508514208908735758773123_<42>
P62 = 12177431881605206398029290707267400696763668300063466828015931_<62>

Number: n N=1613344724660769886649916619810211394771546044497351298684758158261984306026169867062528357836858622513 ( 103 digits) SNFS difficulty: 143 digits. Divisors found: Wed Oct 08 09:00:44 2008 prp42 factor: 132486450373648223508514208908735758773123 Wed Oct 08 09:00:44 2008 prp62 factor: 12177431881605206398029290707267400696763668300063466828015931 Wed Oct 08 09:00:44 2008 elapsed time 00:26:15 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.07 hours. Scaled time: 11.10 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_8_141_3 n: 1613344724660769886649916619810211394771546044497351298684758158261984306026169867062528357836858622513 type: snfs skew: 0.46 deg: 5 c5: 2600 c0: -53 m: 10000000000000000000000000000 rlim: 1300000 alim: 1300000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 1180001) Primes: RFBsize:100021, AFBsize:100068, largePrimes:9478504 encountered Relations: rels:8279703, finalFF:207932 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 5.87 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,28,28,52,52,2.5,2.5,100000 total time: 6.07 hours. --------- CPU info (if available) ----------
Oct 7, 2008 (7th): By Robert Backstrom / GGNFS, Msieve
(22·10¹⁸²+41)/9 = 2(4)₁₈₁9_<183> = 3 · C182
C182 = P68 · P115
P68 = 11131817333645608134880826432818812343782233091922887565788360266449_<68>
P115 = 7319692646698933068447008380320554226838232071464676446580397185871101360352917608275605713660449939915296564240667_<115>

Number: n N=81481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481483 ( 182 digits) SNFS difficulty: 183 digits. Divisors found: Wed Oct 08 01:16:41 2008 prp68 factor: 11131817333645608134880826432818812343782233091922887565788360266449 Wed Oct 08 01:16:41 2008 prp115 factor: 7319692646698933068447008380320554226838232071464676446580397185871101360352917608275605713660449939915296564240667 Wed Oct 08 01:16:42 2008 elapsed time 06:28:41 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 54.73 hours. Scaled time: 111.92 units (timescale=2.045). Factorization parameters were as follows: name: KA_2_4_181_9 n: 81481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481483 type: snfs skew: 0.45 deg: 5 c5: 2200 c0: 41 m: 1000000000000000000000000000000000000 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, 4500001) Primes: RFBsize:571119, AFBsize:570514, largePrimes:14085472 encountered Relations: rels:13769297, finalFF:1174408 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 54.36 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,183,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,52,52,2.5,2.5,100000 total time: 54.73 hours. --------- CPU info (if available) ----------
Oct 7, 2008 (6th): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(26·10¹⁵⁸-53)/9 = 2(8)₁₅₇3_<159> = 130811 · 973426505769073_<15> · 34425015087386547163_<20> · 3241490273279072043571_<22> · C98
C98 = P41 · P58
P41 = 12344721383578441602570691129719532666583_<41>
P58 = 1646960755389981787462956664892649361997386854346581393679_<58>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 20331271654977211294393339555490793753127508716336082890964068276470475952992887907854903370728857 (98 digits) Using B1=2008000, B2=2853999340, polynomial Dickson(6), sigma=809588647 Step 1 took 14062ms ********** Factor found in step 1: 12344721383578441602570691129719532666583 Found probable prime factor of 41 digits: 12344721383578441602570691129719532666583 Probable prime cofactor 1646960755389981787462956664892649361997386854346581393679 has 58 digits
(26·10¹²¹-53)/9 = 2(8)₁₂₀3_<122> = 19 · 173 · 991 · 67489 · C111
C111 = P43 · P68
P43 = 2007712048273207184446462298497217117810023_<43>
P68 = 65452021084529422210274885461837884035260977024336997039822115743117_<68>

Number: n N=131408811315241709778882446115455544690473727820806141910612876582430405380071525155184407438686776994275861691 ( 111 digits) SNFS difficulty: 122 digits. Divisors found: r1=2007712048273207184446462298497217117810023 (pp43) r2=65452021084529422210274885461837884035260977024336997039822115743117 (pp68) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.61 hours. Scaled time: 2.94 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_8_120_3 n: 131408811315241709778882446115455544690473727820806141910612876582430405380071525155184407438686776994275861691 type: snfs skew: 0.73 deg: 5 c5: 260 c0: -53 m: 1000000000000000000000000 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved algebraic special-q in [100000, 320001) Primes: RFBsize:41538, AFBsize:41737, largePrimes:4668741 encountered Relations: rels:4058830, finalFF:149942 Max relations in full relation-set: 48 Initial matrix: 83342 x 149942 with sparse part having weight 20829512. Pruned matrix : 73830 x 74310 with weight 6580037. Total sieving time: 1.46 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.03 hours. Total square root time: 0.04 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,500000,500000,28,28,52,52,2.5,2.5,50000 total time: 1.61 hours. --------- CPU info (if available) ----------
(26·10¹²⁸-53)/9 = 2(8)₁₂₇3_<129> = 3259 · 6329 · 10861 · 29861809811904979_<17> · C101
C101 = P46 · P56
P46 = 2131370352579613462233814865258221222956640337_<46>
P56 = 20261263429298435688151884603702447939050574911133385351_<56>

Number: n N=43184256179012235031192687636333472190588881801215689091140993405776276872330744228362505736131503287 ( 101 digits) SNFS difficulty: 129 digits. Divisors found: Wed Oct 08 00:36:52 2008 prp46 factor: 2131370352579613462233814865258221222956640337 Wed Oct 08 00:36:52 2008 prp56 factor: 20261263429298435688151884603702447939050574911133385351 Wed Oct 08 00:36:52 2008 elapsed time 00:10:12 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.31 hours. Scaled time: 4.22 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_8_127_3 n: 43184256179012235031192687636333472190588881801215689091140993405776276872330744228362505736131503287 type: snfs skew: 0.58 deg: 5 c5: 1625 c0: -106 m: 20000000000000000000000000 rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 440001) Primes: RFBsize:63951, AFBsize:64263, largePrimes:5797517 encountered Relations: rels:4914384, finalFF:132843 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 2.22 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,28,28,52,52,2.5,2.5,50000 total time: 2.31 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Oct 7, 2008 (5th): By Sinkiti Sibata / Msieve, GGNFS
(26·10¹⁰¹-53)/9 = 2(8)₁₀₀3_<102> = 7 · 2054853599791_<13> · C89
C89 = P36 · P54
P36 = 121426997166013585257945094641811871_<36>
P54 = 165400438930491170714093139841463045980448069972087429_<54>

ue Oct 7 11:47:53 2008 Msieve v. 1.38 Tue Oct 7 11:47:53 2008 random seeds: 1d892829 4d448959 Tue Oct 7 11:47:53 2008 factoring 20084078629270154464915312484066295599082921065544328970184837510862039456747676582069659 (89 digits) Tue Oct 7 11:47:55 2008 searching for 15-digit factors Tue Oct 7 11:47:56 2008 commencing quadratic sieve (89-digit input) Tue Oct 7 11:47:57 2008 using multiplier of 19 Tue Oct 7 11:47:57 2008 using 64kb Pentium 4 sieve core Tue Oct 7 11:47:57 2008 sieve interval: 15 blocks of size 65536 Tue Oct 7 11:47:57 2008 processing polynomials in batches of 7 Tue Oct 7 11:47:57 2008 using a sieve bound of 1538939 (58667 primes) Tue Oct 7 11:47:57 2008 using large prime bound of 123115120 (26 bits) Tue Oct 7 11:47:57 2008 using double large prime bound of 365224943163840 (42-49 bits) Tue Oct 7 11:47:57 2008 using trial factoring cutoff of 49 bits Tue Oct 7 11:47:57 2008 polynomial 'A' values have 11 factors Tue Oct 7 13:17:05 2008 59144 relations (16771 full + 42373 combined from 612311 partial), need 58763 Tue Oct 7 13:17:07 2008 begin with 629082 relations Tue Oct 7 13:17:08 2008 reduce to 140845 relations in 10 passes Tue Oct 7 13:17:08 2008 attempting to read 140845 relations Tue Oct 7 13:17:12 2008 recovered 140845 relations Tue Oct 7 13:17:12 2008 recovered 115844 polynomials Tue Oct 7 13:17:12 2008 attempting to build 59144 cycles Tue Oct 7 13:17:12 2008 found 59144 cycles in 5 passes Tue Oct 7 13:17:12 2008 distribution of cycle lengths: Tue Oct 7 13:17:12 2008 length 1 : 16771 Tue Oct 7 13:17:12 2008 length 2 : 11626 Tue Oct 7 13:17:12 2008 length 3 : 10380 Tue Oct 7 13:17:12 2008 length 4 : 7739 Tue Oct 7 13:17:12 2008 length 5 : 5283 Tue Oct 7 13:17:12 2008 length 6 : 3224 Tue Oct 7 13:17:12 2008 length 7 : 1938 Tue Oct 7 13:17:12 2008 length 9+: 2183 Tue Oct 7 13:17:12 2008 largest cycle: 18 relations Tue Oct 7 13:17:12 2008 matrix is 58667 x 59144 (14.3 MB) with weight 3505818 (59.28/col) Tue Oct 7 13:17:12 2008 sparse part has weight 3505818 (59.28/col) Tue Oct 7 13:17:13 2008 filtering completed in 3 passes Tue Oct 7 13:17:13 2008 matrix is 54053 x 54117 (13.1 MB) with weight 3220858 (59.52/col) Tue Oct 7 13:17:13 2008 sparse part has weight 3220858 (59.52/col) Tue Oct 7 13:17:14 2008 saving the first 48 matrix rows for later Tue Oct 7 13:17:14 2008 matrix is 54005 x 54117 (9.9 MB) with weight 2692096 (49.75/col) Tue Oct 7 13:17:14 2008 sparse part has weight 2262300 (41.80/col) Tue Oct 7 13:17:14 2008 matrix includes 64 packed rows Tue Oct 7 13:17:14 2008 using block size 21646 for processor cache size 512 kB Tue Oct 7 13:17:15 2008 commencing Lanczos iteration Tue Oct 7 13:17:15 2008 memory use: 8.8 MB Tue Oct 7 13:17:48 2008 lanczos halted after 856 iterations (dim = 54005) Tue Oct 7 13:17:48 2008 recovered 18 nontrivial dependencies Tue Oct 7 13:17:49 2008 prp36 factor: 121426997166013585257945094641811871 Tue Oct 7 13:17:49 2008 prp54 factor: 165400438930491170714093139841463045980448069972087429 Tue Oct 7 13:17:49 2008 elapsed time 01:29:56
(26·10¹²⁷-53)/9 = 2(8)₁₂₆3_<128> = 71 · 223 · 1131379 · C118
C118 = P59 · P60
P59 = 15345026787558290531448963866298651876102210421274475955901_<59>
P60 = 105097373460091410047218511082896636270831228339123800626269_<60>

Number: 28883_127 N=1612722011047120431126093651159581582679062156542549515978111750383441311031911185410142095485998023922924326226163369 ( 118 digits) SNFS difficulty: 128 digits. Divisors found: r1=15345026787558290531448963866298651876102210421274475955901 (pp59) r2=105097373460091410047218511082896636270831228339123800626269 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.61 hours. Scaled time: 3.60 units (timescale=0.780). Factorization parameters were as follows: name: 28883_127 n: 1612722011047120431126093651159581582679062156542549515978111750383441311031911185410142095485998023922924326226163369 m: 10000000000000000000000000 c5: 2600 c0: -53 skew: 0.46 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:64048, largePrimes:1503692 encountered Relations: rels:1505752, finalFF:174921 Max relations in full relation-set: 28 Initial matrix: 128066 x 174921 with sparse part having weight 12955403. Pruned matrix : 114003 x 114707 with weight 6745759. Total sieving time: 4.47 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,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.61 hours. --------- CPU info (if available) ----------
(26·10¹⁰⁴-53)/9 = 2(8)₁₀₃3_<105> = 61 · 1123 · 1470236641_<10> · C91
C91 = P40 · P51
P40 = 6918276745362442304529579011355599487433_<40>
P51 = 414606469566875297250530265767866835398335555183037_<51>

Tue Oct 7 13:26:14 2008 Msieve v. 1.38 Tue Oct 7 13:26:14 2008 random seeds: a8c52f61 feb94d20 Tue Oct 7 13:26:14 2008 factoring 2868362296881334515585997025651531016682339074705062742924681119186664562240834443696274021 (91 digits) Tue Oct 7 13:26:16 2008 searching for 15-digit factors Tue Oct 7 13:26:17 2008 commencing quadratic sieve (91-digit input) Tue Oct 7 13:26:18 2008 using multiplier of 1 Tue Oct 7 13:26:18 2008 using 64kb Pentium 4 sieve core Tue Oct 7 13:26:18 2008 sieve interval: 18 blocks of size 65536 Tue Oct 7 13:26:18 2008 processing polynomials in batches of 6 Tue Oct 7 13:26:18 2008 using a sieve bound of 1685869 (63499 primes) Tue Oct 7 13:26:18 2008 using large prime bound of 155099948 (27 bits) Tue Oct 7 13:26:18 2008 using double large prime bound of 553478662336492 (42-49 bits) Tue Oct 7 13:26:18 2008 using trial factoring cutoff of 49 bits Tue Oct 7 13:26:18 2008 polynomial 'A' values have 12 factors Tue Oct 7 15:42:48 2008 63914 relations (16908 full + 47006 combined from 723821 partial), need 63595 Tue Oct 7 15:42:50 2008 begin with 740729 relations Tue Oct 7 15:42:51 2008 reduce to 156965 relations in 10 passes Tue Oct 7 15:42:51 2008 attempting to read 156965 relations Tue Oct 7 15:42:55 2008 recovered 156965 relations Tue Oct 7 15:42:55 2008 recovered 133565 polynomials Tue Oct 7 15:42:55 2008 attempting to build 63914 cycles Tue Oct 7 15:42:55 2008 found 63914 cycles in 6 passes Tue Oct 7 15:42:55 2008 distribution of cycle lengths: Tue Oct 7 15:42:55 2008 length 1 : 16908 Tue Oct 7 15:42:55 2008 length 2 : 12442 Tue Oct 7 15:42:55 2008 length 3 : 11234 Tue Oct 7 15:42:55 2008 length 4 : 8455 Tue Oct 7 15:42:55 2008 length 5 : 5982 Tue Oct 7 15:42:55 2008 length 6 : 3880 Tue Oct 7 15:42:55 2008 length 7 : 2258 Tue Oct 7 15:42:55 2008 length 9+: 2755 Tue Oct 7 15:42:55 2008 largest cycle: 19 relations Tue Oct 7 15:42:56 2008 matrix is 63499 x 63914 (15.5 MB) with weight 3794539 (59.37/col) Tue Oct 7 15:42:56 2008 sparse part has weight 3794539 (59.37/col) Tue Oct 7 15:42:57 2008 filtering completed in 3 passes Tue Oct 7 15:42:57 2008 matrix is 59321 x 59385 (14.4 MB) with weight 3538343 (59.58/col) Tue Oct 7 15:42:57 2008 sparse part has weight 3538343 (59.58/col) Tue Oct 7 15:42:57 2008 saving the first 48 matrix rows for later Tue Oct 7 15:42:57 2008 matrix is 59273 x 59385 (9.0 MB) with weight 2762056 (46.51/col) Tue Oct 7 15:42:57 2008 sparse part has weight 2003226 (33.73/col) Tue Oct 7 15:42:57 2008 matrix includes 64 packed rows Tue Oct 7 15:42:57 2008 using block size 21845 for processor cache size 512 kB Tue Oct 7 15:42:58 2008 commencing Lanczos iteration Tue Oct 7 15:42:58 2008 memory use: 8.9 MB Tue Oct 7 15:43:33 2008 lanczos halted after 939 iterations (dim = 59273) Tue Oct 7 15:43:34 2008 recovered 17 nontrivial dependencies Tue Oct 7 15:43:35 2008 prp40 factor: 6918276745362442304529579011355599487433 Tue Oct 7 15:43:35 2008 prp51 factor: 414606469566875297250530265767866835398335555183037 Tue Oct 7 15:43:35 2008 elapsed time 02:17:21
(26·10¹²²-53)/9 = 2(8)₁₂₁3_<123> = 1396273 · C117
C117 = P32 · P86
P32 = 19402957166974971366426216788597_<32>
P86 = 10663323221080904571958089552579308973412592003811372507188170021888642482959500866743_<86>

Number: 28883_122 N=206900003716242374441738033241986981692612325017305991656996080916044991838192738016769563608899469436771239498929571 ( 117 digits) SNFS difficulty: 123 digits. Divisors found: r1=19402957166974971366426216788597 (pp32) r2=10663323221080904571958089552579308973412592003811372507188170021888642482959500866743 (pp86) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.76 hours. Scaled time: 2.12 units (timescale=0.768). Factorization parameters were as follows: name: 28883_122 n: 206900003716242374441738033241986981692612325017305991656996080916044991838192738016769563608899469436771239498929571 m: 1000000000000000000000000 c5: 2600 c0: -53 skew: 0.46 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:64048, largePrimes:2190048 encountered Relations: rels:2274759, finalFF:199026 Max relations in full relation-set: 28 Initial matrix: 113213 x 199026 with sparse part having weight 19677855. Pruned matrix : 97348 x 97978 with weight 6954336. Total sieving time: 2.63 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.76 hours. --------- CPU info (if available) ----------
(26·10¹⁰⁶-53)/9 = 2(8)₁₀₅3_<107> = 5198788583502427_<16> · C91
C91 = P39 · P53
P39 = 335500273381690253463142691283043816681_<39>
P53 = 16562878025476215601525675460299270300212300146053409_<53>

Tue Oct 7 15:52:28 2008 Msieve v. 1.38 Tue Oct 7 15:52:28 2008 random seeds: 16d200f0 5ed508d6 Tue Oct 7 15:52:28 2008 factoring 5556850105534860400941856415980529361598976848281810529616069149916703991904509622631115529 (91 digits) Tue Oct 7 15:52:30 2008 searching for 15-digit factors Tue Oct 7 15:52:31 2008 commencing quadratic sieve (91-digit input) Tue Oct 7 15:52:31 2008 using multiplier of 1 Tue Oct 7 15:52:31 2008 using 64kb Pentium 4 sieve core Tue Oct 7 15:52:31 2008 sieve interval: 18 blocks of size 65536 Tue Oct 7 15:52:31 2008 processing polynomials in batches of 6 Tue Oct 7 15:52:31 2008 using a sieve bound of 1718107 (64706 primes) Tue Oct 7 15:52:31 2008 using large prime bound of 164938272 (27 bits) Tue Oct 7 15:52:31 2008 using double large prime bound of 618270452838912 (42-50 bits) Tue Oct 7 15:52:31 2008 using trial factoring cutoff of 50 bits Tue Oct 7 15:52:31 2008 polynomial 'A' values have 12 factors Tue Oct 7 18:39:51 2008 65214 relations (16974 full + 48240 combined from 766306 partial), need 64802 Tue Oct 7 18:39:54 2008 begin with 783280 relations Tue Oct 7 18:39:55 2008 reduce to 162786 relations in 10 passes Tue Oct 7 18:39:55 2008 attempting to read 162786 relations Tue Oct 7 18:39:59 2008 recovered 162786 relations Tue Oct 7 18:39:59 2008 recovered 142392 polynomials Tue Oct 7 18:39:59 2008 attempting to build 65214 cycles Tue Oct 7 18:39:59 2008 found 65213 cycles in 5 passes Tue Oct 7 18:39:59 2008 distribution of cycle lengths: Tue Oct 7 18:39:59 2008 length 1 : 16974 Tue Oct 7 18:39:59 2008 length 2 : 12127 Tue Oct 7 18:39:59 2008 length 3 : 11248 Tue Oct 7 18:39:59 2008 length 4 : 8709 Tue Oct 7 18:39:59 2008 length 5 : 6255 Tue Oct 7 18:39:59 2008 length 6 : 4176 Tue Oct 7 18:39:59 2008 length 7 : 2520 Tue Oct 7 18:39:59 2008 length 9+: 3204 Tue Oct 7 18:39:59 2008 largest cycle: 17 relations Tue Oct 7 18:40:00 2008 matrix is 64706 x 65213 (16.0 MB) with weight 3920348 (60.12/col) Tue Oct 7 18:40:00 2008 sparse part has weight 3920348 (60.12/col) Tue Oct 7 18:40:01 2008 filtering completed in 3 passes Tue Oct 7 18:40:01 2008 matrix is 60922 x 60986 (14.9 MB) with weight 3666150 (60.11/col) Tue Oct 7 18:40:01 2008 sparse part has weight 3666150 (60.11/col) Tue Oct 7 18:40:01 2008 saving the first 48 matrix rows for later Tue Oct 7 18:40:02 2008 matrix is 60874 x 60986 (9.2 MB) with weight 2856674 (46.84/col) Tue Oct 7 18:40:02 2008 sparse part has weight 2041678 (33.48/col) Tue Oct 7 18:40:02 2008 matrix includes 64 packed rows Tue Oct 7 18:40:02 2008 using block size 21845 for processor cache size 512 kB Tue Oct 7 18:40:02 2008 commencing Lanczos iteration Tue Oct 7 18:40:02 2008 memory use: 9.1 MB Tue Oct 7 18:40:39 2008 lanczos halted after 963 iterations (dim = 60870) Tue Oct 7 18:40:39 2008 recovered 15 nontrivial dependencies Tue Oct 7 18:40:40 2008 prp39 factor: 335500273381690253463142691283043816681 Tue Oct 7 18:40:40 2008 prp53 factor: 16562878025476215601525675460299270300212300146053409 Tue Oct 7 18:40:40 2008 elapsed time 02:48:12
(26·10¹²⁶-53)/9 = 2(8)₁₂₅3_<127> = 3 · 1447 · 28935371 · C116
C116 = P39 · P78
P39 = 165228653254615932145236476570314596911_<39>
P78 = 139195961274715951475738988525401637958819321233452897120611300841286875640923_<78>

Number: 28883_126 N=22999161219902989050763756242254328115413953432130767044127223526570030118688305537411634697583777575015585520988853 ( 116 digits) SNFS difficulty: 127 digits. Divisors found: r1=165228653254615932145236476570314596911 (pp39) r2=139195961274715951475738988525401637958819321233452897120611300841286875640923 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.67 hours. Scaled time: 3.57 units (timescale=0.765). Factorization parameters were as follows: name: 28883_126 n: 22999161219902989050763756242254328115413953432130767044127223526570030118688305537411634697583777575015585520988853 m: 10000000000000000000000000 c5: 260 c0: -53 skew: 0.73 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, 850001) Primes: RFBsize:49098, AFBsize:64238, largePrimes:2372758 encountered Relations: rels:2620192, finalFF:260114 Max relations in full relation-set: 28 Initial matrix: 113403 x 260114 with sparse part having weight 29757285. Pruned matrix : 95261 x 95892 with weight 9517273. Total sieving time: 4.50 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.67 hours. --------- CPU info (if available) ----------
(26·10¹⁴³-53)/9 = 2(8)₁₄₂3_<144> = 7 · 283 · 577 · 639430311176401939_<18> · C120
C120 = P47 · P73
P47 = 72608421793173348599781043468017773823555749411_<47>
P73 = 5443651740505919077345587202768020121504697287012529543072932930028188871_<73>

Number: 28883_143 N=395254961669796004987946127703194385910388393704209881767151146015249881172862281036767220131736918647909394011455004981 ( 120 digits) SNFS difficulty: 144 digits. Divisors found: r1=72608421793173348599781043468017773823555749411 (pp47) r2=5443651740505919077345587202768020121504697287012529543072932930028188871 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.55 hours. Scaled time: 17.69 units (timescale=1.008). Factorization parameters were as follows: name: 28883_143 n: 395254961669796004987946127703194385910388393704209881767151146015249881172862281036767220131736918647909394011455004981 m: 20000000000000000000000000000 c5: 1625 c0: -106 skew: 0.58 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:100028, largePrimes:3026076 encountered Relations: rels:3108906, finalFF:263940 Max relations in full relation-set: 28 Initial matrix: 200115 x 263940 with sparse part having weight 33430537. Pruned matrix : 184887 x 185951 with weight 22544896. Total sieving time: 17.21 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.24 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: 17.55 hours. --------- CPU info (if available) ----------
(26·10¹³³-53)/9 = 2(8)₁₃₂3_<134> = 23² · 97 · 135571 · 2876131 · 109545440891568721810547809_<27> · C92
C92 = P34 · P58
P34 = 5002428365042696296439157033787319_<34>
P58 = 2634831116987297229287109977599312699036948502466768118621_<58>

Tue Oct 7 18:56:25 2008 Msieve v. 1.38 Tue Oct 7 18:56:25 2008 random seeds: 83ca2303 33019c16 Tue Oct 7 18:56:25 2008 factoring 13180553916714386534909752569425608716853442786350982542867254483031175653902223819877567099 (92 digits) Tue Oct 7 18:56:26 2008 searching for 15-digit factors Tue Oct 7 18:56:28 2008 commencing quadratic sieve (92-digit input) Tue Oct 7 18:56:28 2008 using multiplier of 11 Tue Oct 7 18:56:28 2008 using 64kb Pentium 4 sieve core Tue Oct 7 18:56:28 2008 sieve interval: 18 blocks of size 65536 Tue Oct 7 18:56:28 2008 processing polynomials in batches of 6 Tue Oct 7 18:56:28 2008 using a sieve bound of 1753553 (65561 primes) Tue Oct 7 18:56:28 2008 using large prime bound of 177108853 (27 bits) Tue Oct 7 18:56:28 2008 using double large prime bound of 702801048059511 (42-50 bits) Tue Oct 7 18:56:28 2008 using trial factoring cutoff of 50 bits Tue Oct 7 18:56:28 2008 polynomial 'A' values have 12 factors Tue Oct 7 22:29:52 2008 65765 relations (16425 full + 49340 combined from 804803 partial), need 65657 Tue Oct 7 22:29:55 2008 begin with 821228 relations Tue Oct 7 22:29:56 2008 reduce to 167642 relations in 10 passes Tue Oct 7 22:29:56 2008 attempting to read 167642 relations Tue Oct 7 22:30:01 2008 recovered 167642 relations Tue Oct 7 22:30:01 2008 recovered 150130 polynomials Tue Oct 7 22:30:01 2008 attempting to build 65765 cycles Tue Oct 7 22:30:01 2008 found 65765 cycles in 6 passes Tue Oct 7 22:30:01 2008 distribution of cycle lengths: Tue Oct 7 22:30:01 2008 length 1 : 16425 Tue Oct 7 22:30:01 2008 length 2 : 11908 Tue Oct 7 22:30:01 2008 length 3 : 11132 Tue Oct 7 22:30:01 2008 length 4 : 9002 Tue Oct 7 22:30:01 2008 length 5 : 6712 Tue Oct 7 22:30:01 2008 length 6 : 4291 Tue Oct 7 22:30:01 2008 length 7 : 2786 Tue Oct 7 22:30:01 2008 length 9+: 3509 Tue Oct 7 22:30:01 2008 largest cycle: 20 relations Tue Oct 7 22:30:01 2008 matrix is 65561 x 65765 (16.2 MB) with weight 3995981 (60.76/col) Tue Oct 7 22:30:01 2008 sparse part has weight 3995981 (60.76/col) Tue Oct 7 22:30:02 2008 filtering completed in 3 passes Tue Oct 7 22:30:02 2008 matrix is 62136 x 62200 (15.5 MB) with weight 3802683 (61.14/col) Tue Oct 7 22:30:02 2008 sparse part has weight 3802683 (61.14/col) Tue Oct 7 22:30:03 2008 saving the first 48 matrix rows for later Tue Oct 7 22:30:03 2008 matrix is 62088 x 62200 (9.0 MB) with weight 2903630 (46.68/col) Tue Oct 7 22:30:03 2008 sparse part has weight 1995181 (32.08/col) Tue Oct 7 22:30:03 2008 matrix includes 64 packed rows Tue Oct 7 22:30:03 2008 using block size 21845 for processor cache size 512 kB Tue Oct 7 22:30:04 2008 commencing Lanczos iteration Tue Oct 7 22:30:04 2008 memory use: 9.2 MB Tue Oct 7 22:30:42 2008 lanczos halted after 983 iterations (dim = 62086) Tue Oct 7 22:30:42 2008 recovered 17 nontrivial dependencies Tue Oct 7 22:30:43 2008 prp34 factor: 5002428365042696296439157033787319 Tue Oct 7 22:30:43 2008 prp58 factor: 2634831116987297229287109977599312699036948502466768118621 Tue Oct 7 22:30:43 2008 elapsed time 03:34:18
(26·10¹²³-53)/9 = 2(8)₁₂₂3_<124> = 3² · 31 · 479 · 88657 · 10411764445779331_<17> · C98
C98 = P49 · P49
P49 = 4577386029919616907920358735921111593023502164133_<49>
P49 = 5116066918556820603101831088148502094912304324933_<49>

Number: 28883_123 N=23418213241135893111654536836037973463107834917996575496935072255016382759107548568754821130228089 ( 98 digits) SNFS difficulty: 124 digits. Divisors found: r1=4577386029919616907920358735921111593023502164133 (pp49) r2=5116066918556820603101831088148502094912304324933 (pp49) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.74 hours. Scaled time: 2.09 units (timescale=0.762). Factorization parameters were as follows: name: 28883_123 n: 23418213241135893111654536836037973463107834917996575496935072255016382759107548568754821130228089 m: 2000000000000000000000000 c5: 1625 c0: -106 skew: 0.58 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:64263, largePrimes:2115498 encountered Relations: rels:2111676, finalFF:135551 Max relations in full relation-set: 28 Initial matrix: 113427 x 135551 with sparse part having weight 12279235. Pruned matrix : 108186 x 108817 with weight 8199310. Total sieving time: 2.59 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,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.74 hours. --------- CPU info (if available) ----------
Oct 7, 2008 (4th): By Serge Batalov / GMP-ECM 6.2.1; Msieve-1.38, Msieve v. 1.36
(26·10¹⁰⁵-53)/9 = 2(8)₁₀₄3_<106> = 3⁴ · 109 · 199 · C100
C100 = P30 · P34 · P37
P30 = 849624280316155038972453763277_<30>
P34 = 1577350554019897265169205252353313_<34>
P37 = 1226905483766051707687131862935370973_<37>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2391236779 Step 1 took 3248ms Step 2 took 3033ms ********** Factor found in step 2: 849624280316155038972453763277 Found probable prime factor of 30 digits: 849624280316155038972453763277 Mon Oct 6 19:24:09 2008 Msieve v. 1.36 Mon Oct 6 19:24:09 2008 random seeds: 06327895 4682e542 Mon Oct 6 19:24:09 2008 factoring 1935260044548431731260988683498011215653904307146361370089234920583549 (70 digits) Mon Oct 6 19:24:10 2008 no P-1/P+1/ECM available, skipping Mon Oct 6 19:24:10 2008 commencing quadratic sieve (70-digit input) Mon Oct 6 19:24:10 2008 using multiplier of 5 Mon Oct 6 19:24:10 2008 using 64kb Opteron sieve core Mon Oct 6 19:24:10 2008 sieve interval: 6 blocks of size 65536 Mon Oct 6 19:24:10 2008 processing polynomials in batches of 17 Mon Oct 6 19:24:10 2008 using a sieve bound of 215143 (9551 primes) Mon Oct 6 19:24:10 2008 using large prime bound of 20438585 (24 bits) Mon Oct 6 19:24:10 2008 using trial factoring cutoff of 24 bits Mon Oct 6 19:24:10 2008 polynomial 'A' values have 9 factors Mon Oct 6 19:25:37 2008 10205 relations (4704 full + 5501 combined from 55773 partial), need 9647 Mon Oct 6 19:25:37 2008 begin with 60477 relations Mon Oct 6 19:25:37 2008 reduce to 14980 relations in 2 passes Mon Oct 6 19:25:37 2008 attempting to read 14980 relations Mon Oct 6 19:25:37 2008 recovered 14980 relations Mon Oct 6 19:25:38 2008 recovered 12682 polynomials Mon Oct 6 19:25:38 2008 attempting to build 10205 cycles Mon Oct 6 19:25:38 2008 found 10205 cycles in 1 passes Mon Oct 6 19:25:38 2008 distribution of cycle lengths: Mon Oct 6 19:25:38 2008 length 1 : 4704 Mon Oct 6 19:25:38 2008 length 2 : 5501 Mon Oct 6 19:25:38 2008 largest cycle: 2 relations Mon Oct 6 19:25:38 2008 matrix is 9551 x 10205 (1.4 MB) with weight 297849 (29.19/col) Mon Oct 6 19:25:38 2008 sparse part has weight 297849 (29.19/col) Mon Oct 6 19:25:38 2008 filtering completed in 4 passes Mon Oct 6 19:25:38 2008 matrix is 8767 x 8831 (1.2 MB) with weight 249813 (28.29/col) Mon Oct 6 19:25:38 2008 sparse part has weight 249813 (28.29/col) Mon Oct 6 19:25:38 2008 commencing Lanczos iteration Mon Oct 6 19:25:38 2008 memory use: 1.6 MB Mon Oct 6 19:25:39 2008 lanczos halted after 140 iterations (dim = 8762) Mon Oct 6 19:25:39 2008 recovered 63 nontrivial dependencies Mon Oct 6 19:25:40 2008 prp34 factor: 1577350554019897265169205252353313 Mon Oct 6 19:25:40 2008 prp37 factor: 1226905483766051707687131862935370973 Mon Oct 6 19:25:40 2008 elapsed time 00:01:31
(26·10¹²⁵-53)/9 = 2(8)₁₂₄3_<126> = 7 · 6310145134591339_<16> · C109
C109 = P37 · P72
P37 = 7155330995836183377322672101607069373_<37>
P72 = 914036885595968065221316256368672623704512840186938586508794752515903627_<72>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1904982041 Step 1 took 3273ms Step 2 took 3168ms ********** Factor found in step 2: 7155330995836183377322672101607069373 Found probable prime factor of 37 digits: 7155330995836183377322672101607069373 Probable prime cofactor 914036885595968065221316256368672623704512840186938586508794752515903627 has 72 digits
(26·10¹⁹⁷-53)/9 = 2(8)₁₉₆3_<198> = 7 · 71 · 5827 · 33931 · 11178789730567_<14> · 160474133236419241_<18> · 56306547250849852600833678809_<29> · C128
C128 = P29 · P99
P29 = 75596565104432146039405528529_<29>
P99 = 385009979678762504086786747134199125917805790129411664760128132679332492042940092757602857005240341_<99>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3961827852 Step 1 took 4420ms Step 2 took 3764ms ********** Factor found in step 2: 75596565104432146039405528529 Found probable prime factor of 29 digits: 75596565104432146039405528529 Probable prime cofactor 385009979678762504086786747134199125917805790129411664760128132679332492042940092757602857005240341 has 99 digits
(26·10¹⁰²-53)/9 = 2(8)₁₀₁3_<103> = 3 · 541 · 7056254953606319_<16> · C84
C84 = P42 · P43
P42 = 121810470780205711661897992036627074980747_<42>
P43 = 2070872842870751685650025646347946691354497_<43>

Mon Oct 6 19:27:00 2008 Msieve v. 1.36 Mon Oct 6 19:27:00 2008 random seeds: c8b1b998 262548ec Mon Oct 6 19:27:00 2008 factoring 252253995916029232215594555960055997739757430421020264159842100261129995557626869259 (84 digits) Mon Oct 6 19:27:01 2008 no P-1/P+1/ECM available, skipping Mon Oct 6 19:27:01 2008 commencing quadratic sieve (84-digit input) Mon Oct 6 19:27:01 2008 using multiplier of 35 Mon Oct 6 19:27:01 2008 using 64kb Opteron sieve core Mon Oct 6 19:27:01 2008 sieve interval: 6 blocks of size 65536 Mon Oct 6 19:27:01 2008 processing polynomials in batches of 17 Mon Oct 6 19:27:01 2008 using a sieve bound of 1400453 (53488 primes) Mon Oct 6 19:27:01 2008 using large prime bound of 120438958 (26 bits) Mon Oct 6 19:27:01 2008 using double large prime bound of 351059328825056 (41-49 bits) Mon Oct 6 19:27:01 2008 using trial factoring cutoff of 49 bits Mon Oct 6 19:27:01 2008 polynomial 'A' values have 11 factors Mon Oct 6 19:57:53 2008 53681 relations (16403 full + 37278 combined from 566333 partial), need 53584 Mon Oct 6 19:57:53 2008 begin with 582736 relations Mon Oct 6 19:57:53 2008 reduce to 123581 relations in 9 passes Mon Oct 6 19:57:53 2008 attempting to read 123581 relations Mon Oct 6 19:57:54 2008 recovered 123581 relations Mon Oct 6 19:57:54 2008 recovered 96905 polynomials Mon Oct 6 19:57:55 2008 attempting to build 53681 cycles Mon Oct 6 19:57:55 2008 found 53681 cycles in 5 passes Mon Oct 6 19:57:55 2008 distribution of cycle lengths: Mon Oct 6 19:57:55 2008 length 1 : 16403 Mon Oct 6 19:57:55 2008 length 2 : 11163 Mon Oct 6 19:57:55 2008 length 3 : 9472 Mon Oct 6 19:57:55 2008 length 4 : 6739 Mon Oct 6 19:57:55 2008 length 5 : 4402 Mon Oct 6 19:57:55 2008 length 6 : 2532 Mon Oct 6 19:57:55 2008 length 7 : 1382 Mon Oct 6 19:57:55 2008 length 9+: 1588 Mon Oct 6 19:57:55 2008 largest cycle: 17 relations Mon Oct 6 19:57:55 2008 matrix is 53488 x 53681 (12.1 MB) with weight 2745542 (51.15/col) Mon Oct 6 19:57:55 2008 sparse part has weight 2745542 (51.15/col) Mon Oct 6 19:57:56 2008 filtering completed in 4 passes Mon Oct 6 19:57:56 2008 matrix is 47610 x 47674 (10.9 MB) with weight 2470762 (51.83/col) Mon Oct 6 19:57:56 2008 sparse part has weight 2470762 (51.83/col) Mon Oct 6 19:57:56 2008 saving the first 48 matrix rows for later Mon Oct 6 19:57:56 2008 matrix is 47562 x 47674 (6.3 MB) with weight 1818216 (38.14/col) Mon Oct 6 19:57:56 2008 sparse part has weight 1182930 (24.81/col) Mon Oct 6 19:57:56 2008 matrix includes 64 packed rows Mon Oct 6 19:57:56 2008 using block size 19069 for processor cache size 1024 kB Mon Oct 6 19:57:56 2008 commencing Lanczos iteration Mon Oct 6 19:57:56 2008 memory use: 6.1 MB Mon Oct 6 19:58:11 2008 lanczos halted after 754 iterations (dim = 47556) Mon Oct 6 19:58:11 2008 recovered 14 nontrivial dependencies Mon Oct 6 19:58:12 2008 prp42 factor: 121810470780205711661897992036627074980747 Mon Oct 6 19:58:12 2008 prp43 factor: 2070872842870751685650025646347946691354497 Mon Oct 6 19:58:12 2008 elapsed time 00:31:12
(26·10¹⁵⁶-53)/9 = 2(8)₁₅₅3_<157> = 3 · 331 · 587 · 9377 · 32537 · 82779547 · C135
C135 = P32 · P103
P32 = 29861311761897452258856672790427_<32>
P103 = 6571585131207911210838823149579888907845030427984588149967313321690114167689229511352163744579597243273_<103>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3981921852 Step 1 took 5012ms Step 2 took 4817ms ********** Factor found in step 2: 29861311761897452258856672790427 Found probable prime factor of 32 digits: 29861311761897452258856672790427 Probable prime cofactor 6571585131207911210838823149579888907845030427984588149967313321690114167689229511352163744579597243273 has 103 digits
(26·10¹⁵⁷-53)/9 = 2(8)₁₅₆3_<158> = 19 · 313 · 34321501 · 1671089759_<10> · 21638934139807_<14> · 57074054446152619_<17> · 2220772121157679073_<19> · C89
C89 = P32 · P58
P32 = 18327578493929997273111231602653_<32>
P58 = 1684935087308557261733642836693608542354060512864471113923_<58>

Mon Oct 6 19:09:21 2008 Msieve v. 1.36 Mon Oct 6 19:09:21 2008 random seeds: 912b2852 0c5bdc26 Mon Oct 6 19:09:21 2008 factoring 30880780069824376361574877541433529546434253609647535122483720592782720577763879432037719 (89 digits) Mon Oct 6 19:09:22 2008 no P-1/P+1/ECM available, skipping Mon Oct 6 19:09:22 2008 commencing quadratic sieve (89-digit input) Mon Oct 6 19:09:23 2008 using multiplier of 59 Mon Oct 6 19:09:23 2008 using 64kb Opteron sieve core Mon Oct 6 19:09:23 2008 sieve interval: 15 blocks of size 65536 Mon Oct 6 19:09:23 2008 processing polynomials in batches of 7 Mon Oct 6 19:09:23 2008 using a sieve bound of 1545001 (58667 primes) Mon Oct 6 19:09:23 2008 using large prime bound of 123600080 (26 bits) Mon Oct 6 19:09:23 2008 using double large prime bound of 367818635270160 (42-49 bits) Mon Oct 6 19:09:23 2008 using trial factoring cutoff of 49 bits Mon Oct 6 19:09:23 2008 polynomial 'A' values have 12 factors Mon Oct 6 20:22:39 2008 58782 relations (16284 full + 42498 combined from 616885 partial), need 58763 Mon Oct 6 20:22:39 2008 begin with 633169 relations Mon Oct 6 20:22:40 2008 reduce to 141208 relations in 11 passes Mon Oct 6 20:22:40 2008 attempting to read 141208 relations Mon Oct 6 20:22:41 2008 recovered 141208 relations Mon Oct 6 20:22:41 2008 recovered 121099 polynomials Mon Oct 6 20:22:41 2008 attempting to build 58782 cycles Mon Oct 6 20:22:41 2008 found 58782 cycles in 5 passes Mon Oct 6 20:22:41 2008 distribution of cycle lengths: Mon Oct 6 20:22:41 2008 length 1 : 16284 Mon Oct 6 20:22:41 2008 length 2 : 11594 Mon Oct 6 20:22:41 2008 length 3 : 10265 Mon Oct 6 20:22:41 2008 length 4 : 7688 Mon Oct 6 20:22:41 2008 length 5 : 5399 Mon Oct 6 20:22:41 2008 length 6 : 3363 Mon Oct 6 20:22:41 2008 length 7 : 1903 Mon Oct 6 20:22:41 2008 length 9+: 2286 Mon Oct 6 20:22:41 2008 largest cycle: 17 relations Mon Oct 6 20:22:41 2008 matrix is 58667 x 58782 (14.9 MB) with weight 3437105 (58.47/col) Mon Oct 6 20:22:41 2008 sparse part has weight 3437105 (58.47/col) Mon Oct 6 20:22:42 2008 filtering completed in 3 passes Mon Oct 6 20:22:42 2008 matrix is 54537 x 54601 (14.0 MB) with weight 3223743 (59.04/col) Mon Oct 6 20:22:42 2008 sparse part has weight 3223743 (59.04/col) Mon Oct 6 20:22:42 2008 saving the first 48 matrix rows for later Mon Oct 6 20:22:42 2008 matrix is 54489 x 54601 (9.0 MB) with weight 2509159 (45.95/col) Mon Oct 6 20:22:42 2008 sparse part has weight 1807075 (33.10/col) Mon Oct 6 20:22:42 2008 matrix includes 64 packed rows Mon Oct 6 20:22:42 2008 using block size 21840 for processor cache size 1024 kB Mon Oct 6 20:22:43 2008 commencing Lanczos iteration Mon Oct 6 20:22:43 2008 memory use: 8.0 MB Mon Oct 6 20:23:04 2008 lanczos halted after 863 iterations (dim = 54485) Mon Oct 6 20:23:04 2008 recovered 14 nontrivial dependencies Mon Oct 6 20:23:05 2008 prp32 factor: 18327578493929997273111231602653 Mon Oct 6 20:23:05 2008 prp58 factor: 1684935087308557261733642836693608542354060512864471113923 Mon Oct 6 20:23:05 2008 elapsed time 01:13:44
(26·10¹²⁴-53)/9 = 2(8)₁₂₃3_<125> = C125
C125 = P58 · P67
P58 = 4702771018702305749095782377707818488983640114722149202591_<58>
P67 = 6142950352888021378812891699753388017001993925608663874220496607213_<67>

SNFS difficulty: 126 digits. Divisors found: r1=4702771018702305749095782377707818488983640114722149202591 r2=6142950352888021378812891699753388017001993925608663874220496607213 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.725). Factorization parameters were as follows: n: 28888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 Y1: 1 Y0: -10000000000000000000000000 c5: 13 c0: -265 skew: 1.83 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 : 121605 x 121827 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: 1.00 hours.
(26·10¹⁰³-53)/9 = 2(8)₁₀₂3_<104> = 19 · 29 · 227 · 5189 · C95
C95 = P41 · P54
P41 = 89692426478836592784300376550795841826967_<41>
P54 = 496265333259345156772057309654185119335498040025379133_<54>

SNFS difficulty: 105 digits. Divisors found: r1=89692426478836592784300376550795841826967 r2=496265333259345156772057309654185119335498040025379133 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 44511241917359155577106323878765321362023863046193398616907007659676149245603176570253558479611 Y1: 1 Y0: -100000000000000000000000000 c4: 13 c0: -265 skew: 2.5 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, 265001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 46343 x 46563 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,105,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 0.20 hours.
(26·10¹⁷⁴-53)/9 = 2(8)₁₇₃3_<175> = 3 · 151 · 18917 · C168
C168 = P31 · C138
P31 = 2243086562866881513988079273467_<31>
C138 = [150291472292069767424055033263206434728976210392907193097679201540140532262561658836638110174056704378245409474091400576686840194702606449_<138>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1153297637 Step 1 took 19225ms ********** Factor found in step 1: 2243086562866881513988079273467 Found probable prime factor of 31 digits: 2243086562866881513988079273467 Composite cofactor 150291472292069767424055033263206434728976210392907193097679201540140532262561658836638110174056704378245409474091400576686840194702606449 has 138 digits
(26·10¹⁶⁹-53)/9 = 2(8)₁₆₈3_<170> = 599 · 564251 · 18224693 · 177056177 · 4722398199915096083_<19> · 4741302251973319790706989_<25> · C103
C103 = P35 · P68
P35 = 56575334809536652290971314862111609_<35>
P68 = 20910913013535396971131194830319308120739735863239243650630700492909_<68>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=67958517 Step 1 took 13433ms Step 2 took 12543ms ********** Factor found in step 2: 56575334809536652290971314862111609 Found probable prime factor of 35 digits: 56575334809536652290971314862111609 Probable prime cofactor 20910913013535396971131194830319308120739735863239243650630700492909 has 68 digits
(26·10²⁰⁴-53)/9 = 2(8)₂₀₃3_<205> = 3² · 199 · 463 · 868884451118897_<15> · 156502951782418193_<18> · C167
C167 = P33 · P134
P33 = 694430743408346543317934266065283_<33>
P134 = 36892727464062353803746935998125110790437863065618259953712823593194923501179666721819922557179370336183877369556062715328482342983457_<134>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2172110407 Step 1 took 20453ms Step 2 took 15109ms ********** Factor found in step 2: 694430743408346543317934266065283 Found probable prime factor of 33 digits: 694430743408346543317934266065283 Probable prime cofactor 36892727464062353803746935998125110790437863065618259953712823593194923501179666721819922557179370336183877369556062715328482342983457 has 134 digits
2·10¹⁷⁵-9 = 1(9)₁₇₄1_<176> = 11 · 2104936691786471_<16> · C159
C159 = P70 · P90
P70 = 2999235301404108672880852229001943743610905187225557697685545402923389_<70>
P90 = 287996846831064477423205097882532373558238456659108938210015914290084744018871680277303599_<90>

SNFS difficulty: 175 digits. Divisors found: r1=2999235301404108672880852229001943743610905187225557697685545402923389 r2=287996846831064477423205097882532373558238456659108938210015914290084744018871680277303599 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.739). Factorization parameters were as follows: n: 863770309708800587661565784926991363552067036251619250125149999067901342834852215125908090950700120597465563999602721827174720277628477497212972232080890977011 Y1: 1 Y0: -100000000000000000000000000000000000 c5: 2 c0: -9 skew: 1.35 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [3700000, 6400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1083635 x 1083883 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,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,54,54,2.6,2.6,100000 total time: 35.00 hours.
(26·10¹⁶⁸-53)/9 = 2(8)₁₆₇3_<169> = 3² · 31 · 666737 · C161
C161 = P40 · P122
P40 = 1167093673337653327127830327069259661809_<40>
P122 = 13306577381392358475255309881615503665415368980360269644105388734553589493156498969747963330291726610161219478491166215269_<122>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=304196581 Step 1 took 18965ms Step 2 took 14725ms ********** Factor found in step 2: 1167093673337653327127830327069259661809 Found probable prime factor of 40 digits: 1167093673337653327127830327069259661809 Probable prime cofactor 13306577381392358475255309881615503665415368980360269644105388734553589493156498969747963330291726610161219478491166215269 has 122 digits
(26·10¹⁵⁹-53)/9 = 2(8)₁₅₈3_<160> = 3³ · 29 · 287107 · 23759322402380015305157_<23> · C129
C129 = P38 · C92
P38 = 10313704067523250659900937829730796309_<38>
C92 = [52441677875563878773945469819992980394894802790218697762200342387440721101475627254741219911_<92>]

Input number is 540867946412947238983837576736402476646300389187376607989044293296034269709414547519382982732739649482451258823652599480116108499 (129 digits) Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1193863371 Step 1 took 15386ms Step 2 took 15370ms ********** Factor found in step 2: 10313704067523250659900937829730796309 Found probable prime factor of 38 digits: 10313704067523250659900937829730796309 Composite cofactor 52441677875563878773945469819992980394894802790218697762200342387440721101475627254741219911 has 92 digits
(26·10¹⁷⁴-53)/9 = 2(8)₁₇₃3_<175> = 3 · 151 · 18917 · 2243086562866881513988079273467_<31> · C138
C138 = P40 · P98
P40 = 9505588734014909843517432505768084428737_<40>
P98 = 15810853645946726698592400974520411575672816481225283858869417945537837498204945702733827218560177_<98>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=481747367 Step 1 took 25522ms Step 2 took 19983ms ********** Factor found in step 2: 9505588734014909843517432505768084428737 Found probable prime factor of 40 digits: 9505588734014909843517432505768084428737
Oct 7, 2008 (3rd): By matsui / GMP-ECM
(5·10¹⁸²-23)/9 = (5)₁₈₁3_<182> = 11587 · C178
C178 = P32 · C147
P32 = 22164089254899828504746140018019_<32>
C147 = [216324942791152081793580282576603715592327742295380183409321402881799332508862151634956890785529810487524741549747806557894880895635721994907999801_<147>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 4794645340084193972171878446151338185514417498537633171274320838487577073923841853418102662946021882761332144261288992453228234707478687801463325757793696000306857301765388414219 =22164089254899828504746140018019* 216324942791152081793580282576603715592327742295380183409321402881799332508862151634956890785529810487524741549747806557894880895635721994907999801
Oct 7, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.38
(16·10²⁰⁰-7)/9 = 1(7)₂₀₀_<201> = 3 · 29 · 113 · 17239 · 183167 · C187
C187 = P35 · P152
P35 = 73650921956704125918421412553905053_<35>
P152 = 77757499705047821516199564486492518620219929342504211246580583218570399145822019564955875866277439662266095840431970859014732292772322991513398308879003_<152>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=437088288 Step 1 took 28010ms Step 2 took 10289ms ********** Factor found in step 2: 73650921956704125918421412553905053 Found probable prime factor of 35 digits: 73650921956704125918421412553905053 Probable prime cofactor 77757499705047821516199564486492518620219929342504211246580583218570399145822019564955875866277439662266095840431970859014732292772322991513398308879003 has 152 digits
(55·10¹⁷⁴-1)/9 = 6(1)₁₇₄_<175> = 3² · 4597775143424143997_<19> · C156
C156 = P43 · P114
P43 = 1229252059113818413091149720294853232697801_<43>
P114 = 120140379125834124954583462842564535156416411241662126164981729522718127588795637427044066299014456569821516369507_<114>

SNFS difficulty: 176 digits. Divisors found: r1=1229252059113818413091149720294853232697801 r2=120140379125834124954583462842564535156416411241662126164981729522718127588795637427044066299014456569821516369507 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.854). Factorization parameters were as follows: n: 147682808423146405493156532543584238917034823309657064787055774798020076967093264949590809254482259992363365073823088990550667441301074161608069140782354107 Y1: 1 Y0: -100000000000000000000000000000000000 c5: 11 c0: -2 skew: 0.71 type: snfs Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [5000000, 7800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1260653 x 1260901 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,176,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
(23·10¹⁶⁸+31)/9 = 2(5)₁₆₇9_<169> = 3² · 236812287285483410929_<21> · C148
C148 = P43 · P105
P43 = 4399881371891076411517211881007444147724161_<43>
P105 = 272519521223774045867200767539451361177012007095888916737879651496577799389203378273684289426752607226079_<105>

SNFS difficulty: 169 digits. Divisors found: r1=4399881371891076411517211881007444147724161 r2=272519521223774045867200767539451361177012007095888916737879651496577799389203378273684289426752607226079 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.291). Factorization parameters were as follows: n: 1199053564909158263764865435863424465914489971376071052470965230844971018946176597623262002158130529740670738185026088323656292700989789111057594719 Y1: 1 Y0: -1000000000000000000000000000000000 c5: 23000 c0: 31 skew: 0.27 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, 6100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1069246 x 1069494 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,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
Oct 7, 2008: Factorizations of 288...883 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.
Oct 6, 2008 (3rd): By Sinkiti Sibata / GGNFS
(26·10¹⁷¹-71)/9 = 2(8)₁₇₀1_<172> = 43 · 1380617898681809_<16> · C155
C155 = P73 · P83
P73 = 3669494174838085730319346360886510108147157739379354571402691886612341441_<73>
P83 = 13261195602581412992450307530343836667060648761360730528724076800274659175677939043_<83>

Number: 28881_171 N=48661880015060933137981457416002802132480114106356745333892966732948461875636848914080280263954783190211344349331132472591262877557224150237206443500780963 ( 155 digits) SNFS difficulty: 172 digits. Divisors found: r1=3669494174838085730319346360886510108147157739379354571402691886612341441 (pp73) r2=13261195602581412992450307530343836667060648761360730528724076800274659175677939043 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 221.80 hours. Scaled time: 223.57 units (timescale=1.008). Factorization parameters were as follows: name: 28881_171 n: 48661880015060933137981457416002802132480114106356745333892966732948461875636848914080280263954783190211344349331132472591262877557224150237206443500780963 m: 10000000000000000000000000000000000 c5: 260 c0: -71 skew: 0.77 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, 11500001) Primes: RFBsize:412849, AFBsize:412212, largePrimes:6501610 encountered Relations: rels:6831268, finalFF:949374 Max relations in full relation-set: 28 Initial matrix: 825128 x 949374 with sparse part having weight 91645762. Pruned matrix : 732702 x 736891 with weight 74084923. Total sieving time: 215.68 hours. Total relation processing time: 0.15 hours. Matrix solve time: 5.83 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 221.80 hours. --------- CPU info (if available) ----------
Oct 6, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(10¹⁸⁷+71)/9 = (1)₁₈₆9_<187> = 3 · 170759 · C181
C181 = P60 · P122
P60 = 118556060853532355684657119016905151082226412154225341230741_<60>
P122 = 18294850799511873801677071498271275076680523886468931501062534084271591363969148990966231170862572128613900878977069885767_<122>

Number: n N=2168965444693224780950757326819496309830640671182018929429022015649953269639494084472094415933393673952004698846739383402165451720672821756805617099950048725808715033294704058763347 ( 181 digits) SNFS difficulty: 187 digits. Divisors found: Mon Oct 06 07:01:53 2008 prp60 factor: 118556060853532355684657119016905151082226412154225341230741 Mon Oct 06 07:01:53 2008 prp122 factor: 18294850799511873801677071498271275076680523886468931501062534084271591363969148990966231170862572128613900878977069885767 Mon Oct 06 07:01:53 2008 elapsed time 13:58:33 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 70.75 hours. Scaled time: 91.41 units (timescale=1.292). Factorization parameters were as follows: name: KA_1_186_9 n: 2168965444693224780950757326819496309830640671182018929429022015649953269639494084472094415933393673952004698846739383402165451720672821756805617099950048725808715033294704058763347 type: snfs skew: 0.93 deg: 5 c5: 100 c0: 71 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 6100001) Primes: RFBsize:602489, AFBsize:603001, largePrimes:14684678 encountered Relations: rels:14609629, finalFF:1302685 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 70.18 hours. Total relation processing time: 0.57 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 70.75 hours. --------- CPU info (if available) ----------
Oct 6, 2008: By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(89·10¹⁷¹+1)/9 = 9(8)₁₇₀9_<172> = 11 · 29 · 31153 · C165
C165 = P65 · P101
P65 = 20859158360218646280250430937682237384800186664930597024627057321_<65>
P101 = 47704588922816156402622683680592959261170977885583403442268477509804178279463931489193875017204443487_<101>

SNFS difficulty: 172 digits. Divisors found: r1=20859158360218646280250430937682237384800186664930597024627057321 r2=47704588922816156402622683680592959261170977885583403442268477509804178279463931489193875017204443487 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.945). Factorization parameters were as follows: n: 995077574850154454487684142878694352676489781788767772295123953291595307585354484031425533710695819398473817099576283669917204961707234693618912994475429930254118327 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 890 c0: 1 skew: 0.26 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 7000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1147835 x 1148083 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,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
(86·10¹⁷⁰+31)/9 = 9(5)₁₆₉9_<171> = 7 · 137 · 2579 · 3582718889_<10> · C156
C156 = P50 · P106
P50 = 73044612100303015021615574110453666513439422703861_<50>
P106 = 1476335530587363807889463028248959534110527268122976885451689164688958624422893045288065598247542738990111_<106>

SNFS difficulty: 171 digits. Divisors found: r1=73044612100303015021615574110453666513439422703861 r2=1476335530587363807889463028248959534110527268122976885451689164688958624422893045288065598247542738990111 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.731). Factorization parameters were as follows: n: 107838356161649026351577516693291315248999841606208829510603234036113769212515591345037604034970771261765500380483485337838846613658594572419135364160518571 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 86 c0: 31 skew: 0.82 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 : 1061379 x 1061627 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,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
(23·10¹⁷³-41)/9 = 2(5)₁₇₂1_<174> = 673 · 853 · 5591061403121_<13> · C155
C155 = P46 · P47 · P63
P46 = 7006809008629239360483702710486422780612342481_<46>
P47 = 25181631057758153981933321553668940225037068307_<47>
P63 = 451255837422041310778962833166372971071264336217045028875777297_<63>

SNFS difficulty: 174 digits. Divisors found: r1=7006809008629239360483702710486422780612342481 r2=25181631057758153981933321553668940225037068307 r3=451255837422041310778962833166372971071264336217045028875777297 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 79620879277102236161350777737232714052888759619073923411143140991524898238688532735937210657700343773756579155877217308484407849335553097765189963046610099 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 23000 c0: -41 skew: 0.28 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 8800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1366742 x 1366990 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,174,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
(22·10¹⁷⁰+41)/9 = 2(4)₁₆₉9_<171> = 3 · 17 · 139 · 367 · 80993649263_<11> · C154
C154 = P49 · P105
P49 = 5658141762156826678442825564795456282008165567021_<49>
P105 = 205023828685265645027427152433093505046281741380993784990718808353878468660941885633315531455901334965301_<105>

SNFS difficulty: 171 digits. Divisors found: r1=5658141762156826678442825564795456282008165567021 r2=205023828685265645027427152433093505046281741380993784990718808353878468660941885633315531455901334965301 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.724). Factorization parameters were as follows: n: 1160053887321388306247894317985684521194560853620648242948063882893486761625576778027346877448599606173015566550740807961330613627642328527504536024938321 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 22 c0: 41 skew: 1.13 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, 5900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1117066 x 1117314 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,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
(13·10¹⁷⁴+23)/9 = 1(4)₁₇₃7_<175> = 19 · 233584627 · 327017448697_<12> · C153
C153 = P49 · P105
P49 = 1508884939339678464343119204491325903774757813009_<49>
P105 = 659592843928901000722573606753947216311128546998729114026951853355308952821337342212632003472349819672303_<105>

SNFS difficulty: 176 digits. Divisors found: r1=1508884939339678464343119204491325903774757813009 r2=659592843928901000722573606753947216311128546998729114026951853355308952821337342212632003472349819672303 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: n: 995249708300545791129799221580502120491420761030163428196894321573713576560876946695413362256842523332134667375458489194130944953153275856117997330389727 Y1: 1 Y0: -100000000000000000000000000000000000 c5: 13 c0: 230 skew: 1.78 type: snfs Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [5000000, 8900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1375609 x 1375857 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,176,5,0,0,0,0,0,0,0,0,10000000,10000000,27,27,54,54,2.6,2.6,100000 total time: 32.00 hours.
(5·10¹⁷⁰+13)/9 = (5)₁₆₉7_<170> = 3 · 503 · 207041 · 7023543563_<10> · C152
C152 = P64 · P88
P64 = 6757843255424349562422360600427818373615137317957647846931199517_<64>
P88 = 3746428975831510131769641735411669473409387191490552876044280413845098431855725258972543_<88>

SNFS difficulty: 170 digits. Divisors found: r1=6757843255424349562422360600427818373615137317957647846931199517 r2=3746428975831510131769641735411669473409387191490552876044280413845098431855725258972543 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.316). Factorization parameters were as follows: n: 25317779786249324256984188517325628223953057120399900583722505923834812071552989221685696863859315525075555386181217047735768127271487751932309957861731 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 5 c0: 13 skew: 1.21 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, 5300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 999105 x 999353 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: 30.00 hours.
(16·10¹⁸⁹-7)/9 = 1(7)₁₈₉_<190> = 97 · 565257584232221_<15> · 2894757784480057_<16> · C158
C158 = P33 · C125
P33 = 313874266742039388275321127723139_<33>
C125 = [35685468203316383629285285631630576483658593506329090236596327342634932358233727998968557498199790458256613246731307616845327_<125>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=349201591 Step 1 took 26185ms Step 2 took 9028ms ********** Factor found in step 2: 313874266742039388275321127723139 Found probable prime factor of 33 digits: 313874266742039388275321127723139 Composite cofactor 35685468203316383629285285631630576483658593506329090236596327342634932358233727998968557498199790458256613246731307616845327 has 125 digits
Oct 5, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
4·10¹⁸⁸+3 = 4(0)₁₈₇3_<189> = 13 · 151 · 50311 · C181
C181 = P44 · P55 · P83
P44 = 24875180711963832920631823391799924802362043_<44>
P55 = 1752874383582602263485228831981881536452332411343350533_<55>
P83 = 92888019522893020037527962353614086664215590109173413876816904217403183939544249209_<83>

Number: n N=4050202544047648688833499443952755480878371070909903214031140974559533638618025124682194528939826171179603163787365865012439741466256147587274599773413443774526317927554290357785071 ( 181 digits) SNFS difficulty: 188 digits. Divisors found: Sun Oct 05 10:57:16 2008 prp44 factor: 24875180711963832920631823391799924802362043 Sun Oct 05 10:57:16 2008 prp55 factor: 1752874383582602263485228831981881536452332411343350533 Sun Oct 05 10:57:16 2008 prp83 factor: 92888019522893020037527962353614086664215590109173413876816904217403183939544249209 Sun Oct 05 10:57:17 2008 elapsed time 06:48:28 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 69.83 hours. Scaled time: 137.98 units (timescale=1.976). Factorization parameters were as follows: name: KA_4_0_187_3 n: 4050202544047648688833499443952755480878371070909903214031140974559533638618025124682194528939826171179603163787365865012439741466256147587274599773413443774526317927554290357785071 type: snfs skew: 0.47 deg: 5 c5: 125 c0: 3 m: 20000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved special-q in [100000, 6900001) Primes: RFBsize:602489, AFBsize:601580, largePrimes:14186992 encountered Relations: rels:13935264, finalFF:1227975 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 69.46 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,52,52,2.5,2.5,100000 total time: 69.83 hours. --------- CPU info (if available) ----------
(52·10¹⁹³-7)/9 = 5(7)₁₉₃_<194> = 3 · 1517945766670785449_<19> · 7229865440639606423_<19> · 36201349029514598526708460117_<29> · C128
C128 = P43 · P86
P43 = 1361633458879307976532980614815947376699811_<43>
P86 = 35601487205328491845602471971596039725155115291438663960324094921313571336527310320491_<86>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 48476176164638862053734691122979671227372039614455965680139465155443601982618066197127877857347079214807473440402864044309127201 (128 digits) Using B1=6942000, B2=17125579390, polynomial Dickson(12), sigma=2494068609 Step 1 took 69080ms Step 2 took 28676ms ********** Factor found in step 2: 1361633458879307976532980614815947376699811 Found probable prime factor of 43 digits: 1361633458879307976532980614815947376699811 Probable prime cofactor 35601487205328491845602471971596039725155115291438663960324094921313571336527310320491 has 86 digits
Oct 5, 2008: By Serge Batalov / Msieve-1.38, GMP-ECM 6.2.1
(26·10¹⁷⁰-71)/9 = 2(8)₁₆₉1_<171> = 281 · 1036151797_<10> · C159
C159 = P43 · P117
P43 = 8352757623297097696332618845370352702448983_<43>
P117 = 118787640151714003352535632523216976307927450058745101074936089603900745826743578588056704612356256078974602954505651_<117>

SNFS difficulty: 171 digits. Divisors found: r1=8352757623297097696332618845370352702448983 r2=118787640151714003352535632523216976307927450058745101074936089603900745826743578588056704612356256078974602954505651 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.943). Factorization parameters were as follows: n: 992204366830701552260601889495933995632772966000609277532605334444861061300128325310454559138001358509582850301327815420242221382563071698277700080441812702933 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 26 c0: -71 skew: 1.22 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, 6100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1163491 x 1163739 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 4.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
(8·10¹⁷²-11)/3 = 2(6)₁₇₁3_<173> = 7 · 13 · 257 · 12729680113627_<14> · C155
C155 = P48 · P108
P48 = 379919932959707519722966083766347941284954305359_<48>
P108 = 235767884328121729344442224036858091022336279014513197183862800102339634118624490038634191101266307973040593_<108>

SNFS difficulty: 172 digits. Divisors found: r1=379919932959707519722966083766347941284954305359 r2=235767884328121729344442224036858091022336279014513197183862800102339634118624490038634191101266307973040593 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 89572918807992084599135765143735520891413934611338714495828143684100870450188258262831597166069426537504778163501521975640172727386960968697358477424437887 Y1: 1 Y0: -20000000000000000000000000000000000 c5: 25 c0: -11 skew: 0.85 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 6700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1208103 x 1208351 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,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
6·10¹⁷²-1 = 5(9)₁₇₂_<173> = 71 · 5333 · C168
C168 = P32 · C137
P32 = 10527309174692505715358220955631_<32>
C137 = [15052337248182079245295376732473140587727231583696298965536998382697969877116207805028160665561308034389058830834673663504559791338218603_<137>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3257129926 Step 1 took 26700ms ********** Factor found in step 1: 10527309174692505715358220955631 Found probable prime factor of 32 digits: 10527309174692505715358220955631 Composite cofactor 15052337248182079245295376732473140587727231583696298965536998382697969877116207805028160665561308034389058830834673663504559791338218603 has 137 digits
(11·10¹⁶⁹+7)/9 = 1(2)₁₆₈3_<170> = 13 · 199 · 23117 · 21154360223_<11> · C151
C151 = P71 · P81
P71 = 56614438302582048814610056890653305828644096999449225595894307044593297_<71>
P81 = 170645631849406535892466311038242263821975056450557183563575141057584461818693727_<81>

SNFS difficulty: 171 digits. Divisors found: r1=56614438302582048814610056890653305828644096999449225595894307044593297 r2=170645631849406535892466311038242263821975056450557183563575141057584461818693727 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.722). Factorization parameters were as follows: n: 9661006595943356569335913717277784341104880983330214595309914724528045964926430879738402044162773517773405484364046472591892578927791104378358520147919 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 11 c0: 70 skew: 1.45 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 : 1040091 x 1040339 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,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,54,54,2.6,2.6,100000 total time: 30.00 hours.
(16·10¹⁷⁴+11)/9 = 1(7)₁₇₃9_<175> = 3 · 367 · 69677 · 229637 · C162
C162 = P33 · C129
P33 = 168059235324598838433859428519907_<33>
C129 = [600477118485275904046986059283468225318011819543399844819021644617823346316693276523484494374747561974398107937389166265935378453_<129>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=151457020 Step 1 took 26818ms Step 2 took 16347ms ********** Factor found in step 2: 168059235324598838433859428519907 Found probable prime factor of 33 digits: 168059235324598838433859428519907 Composite cofactor 600477118485275904046986059283468225318011819543399844819021644617823346316693276523484494374747561974398107937389166265935378453 has 129 digits
Oct 4, 2008 (3rd): By Sinkiti Sibata / GGNFS
(26·10¹⁶⁶-71)/9 = 2(8)₁₆₅1_<167> = 3² · 251 · 331 · 5263090523549879_<16> · C145
C145 = P46 · P100
P46 = 1510502859597760806417065936942084544672808513_<46>
P100 = 4859865188787395072098314485948357294398599462740799180745466247719147971275211882335881557251224807_<100>

Number: 28881_166 N=7340840264922971933894794829417861112201031590340036998496018396191265355575127755600652658160478266119929479034056755293239804822403937826381991 ( 145 digits) SNFS difficulty: 167 digits. Divisors found: r1=1510502859597760806417065936942084544672808513 (pp46) r2=4859865188787395072098314485948357294398599462740799180745466247719147971275211882335881557251224807 (pp100) Version: GGNFS-0.77.1-20050930-nocona Total time: 134.13 hours. Scaled time: 135.34 units (timescale=1.009). Factorization parameters were as follows: name: 28881_166 n: 7340840264922971933894794829417861112201031590340036998496018396191265355575127755600652658160478266119929479034056755293239804822403937826381991 m: 1000000000000000000000000000000000 c5: 260 c0: -71 skew: 0.77 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, 7650001) Primes: RFBsize:380800, AFBsize:380063, largePrimes:6291023 encountered Relations: rels:6618048, finalFF:955138 Max relations in full relation-set: 28 Initial matrix: 760930 x 955138 with sparse part having weight 75716287. Pruned matrix : 609006 x 612874 with weight 57216633. Total sieving time: 130.33 hours. Total relation processing time: 0.12 hours. Matrix solve time: 3.57 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: 134.13 hours. --------- CPU info (if available) ----------
Oct 4, 2008 (2nd): By Serge Batalov / Msieve-1.38
(26·10¹⁶⁷-71)/9 = 2(8)₁₆₆1_<168> = 47 · 3623 · 160163 · C158
C158 = P71 · P87
P71 = 62177173667916090994125727316510673911399562654031399314878446246681393_<71>
P87 = 170361507648356832458459057572079293694991001668148898771440660882317084143196327486739_<87>

SNFS difficulty: 168 digits. Divisors found: r1=62177173667916090994125727316510673911399562654031399314878446246681393 r2=170361507648356832458459057572079293694991001668148898771440660882317084143196327486739 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 10592597047379898181857972294175227389945639616830971048303006763410773656749525762983982387259612103870860289508693080736858983683550573934343464506965547427 Y1: 1 Y0: -1000000000000000000000000000000000 c5: 2600 c0: -71 skew: 0.49 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, 4450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1039542 x 1039790 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 3.00 hours. Time per square root: 0.10 hours. 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: 30.00 hours.
Oct 4, 2008: By Jo Yeong Uk / GGNFS, GMP-ECM
(25·10¹⁹²+11)/9 = 2(7)₁₉₁9_<193> = 28850999 · 29654969 · 433264503167730948116363789_<27> · 21023680370390040093666753767791_<32> · C120
C120 = P54 · P66
P54 = 523283330570262509507095968646219549154589782060264537_<54>
P66 = 681146319566940643603387966607299632516460088185410724746611917543_<66>

Number: 27779_192 N=356432514708665067434889972034144550754335969029805940899612059115982464982373416977480490869176337160263355155411072591 ( 120 digits) Divisors found: r1=523283330570262509507095968646219549154589782060264537 (pp54) r2=681146319566940643603387966607299632516460088185410724746611917543 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 38.90 hours. Scaled time: 92.46 units (timescale=2.377). Factorization parameters were as follows: name: 27779_192 n: 356432514708665067434889972034144550754335969029805940899612059115982464982373416977480490869176337160263355155411072591 skew: 45877.59 # norm 2.10e+16 c5: 59220 c4: 4268148652 c3: -54178355275093 c2: -32310008489240418903 c1: -452211177823445963143823 c0: -93973871227905947990253765 # alpha -5.48 Y1: 4244062156877 Y0: -90344452061388090682912 # Murphy_E 2.82e-10 # M 255242693196056850117205220883103512579840869547747893244572149774913258474069373072912491588421647886917861100495805716 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [2500000, 4600001) Primes: RFBsize:348513, AFBsize:348452, largePrimes:8679735 encountered Relations: rels:8845813, finalFF:843049 Max relations in full relation-set: 28 Initial matrix: 697049 x 843049 with sparse part having weight 74015787. Pruned matrix : 573546 x 577095 with weight 47186435. Polynomial selection time: 2.62 hours. Total sieving time: 33.93 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.01 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,51,51,2.4,2.4,100000 total time: 38.90 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
(2·10¹⁷⁵+1)/3 = (6)₁₇₄7_<175> = 7 · 34429 · C170
C170 = P49 · P122
P49 = 1050191318423217125232464277698554503013130761249_<49>
P122 = 26340127233392236974087975009212418003633400562423119067589738496416129946457990774500568552310756834852983770264132755361_<122>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 27662172946671479884759387504166614800092391657641882742815096354263916493432308588136523888361002421823241481088063910684375989787125748088889626546834133461685815805889 (170 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1712934266 Step 1 took 16245ms Step 2 took 7139ms ********** Factor found in step 2: 1050191318423217125232464277698554503013130761249 Found probable prime factor of 49 digits: 1050191318423217125232464277698554503013130761249 Probable prime cofactor 26340127233392236974087975009212418003633400562423119067589738496416129946457990774500568552310756834852983770264132755361 has 122 digits
Oct 3, 2008 (3rd): By Wataru Sakai / GGNFS
(2·10¹⁹⁰+61)/9 = (2)₁₈₉9_<190> = 3² · C189
C189 = P68 · P122
P68 = 15037230780948987466386569695720830218543444409461952110026324979003_<68>
P122 = 16420149683393438216632983454542924702334404553643490266996276078158368227441725013767141314944794683769900016944611993527_<122>

Number: 22229_190 N=246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913581 ( 189 digits) SNFS difficulty: 190 digits. Divisors found: r1=15037230780948987466386569695720830218543444409461952110026324979003 (pp68) r2=16420149683393438216632983454542924702334404553643490266996276078158368227441725013767141314944794683769900016944611993527 (pp122) Version: GGNFS-0.77.1-20060722-nocona Total time: 1316.55 hours. Scaled time: 2589.65 units (timescale=1.967). Factorization parameters were as follows: n: 246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913581 m: 100000000000000000000000000000000000000 c5: 2 c0: 61 skew: 1.98 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, 22700001) Primes: RFBsize:501962, AFBsize:501692, largePrimes:7358473 encountered Relations: rels:8000424, finalFF:1177185 Max relations in full relation-set: 32 Initial matrix: 1003721 x 1177185 with sparse part having weight 156407719. Pruned matrix : 883064 x 888146 with weight 138266463. Total sieving time: 1304.28 hours. Total relation processing time: 0.17 hours. Matrix solve time: 11.79 hours. Time per square root: 0.31 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1316.55 hours. --------- CPU info (if available) ----------
Oct 3, 2008 (2nd): By Jo Yeong Uk / GGNFS
3·10¹⁹⁶-1 = 2(9)₁₉₆_<197> = C197
C197 = P54 · P54 · P90
P54 = 122344767534061284667205826233542620221024729103782351_<54>
P54 = 349916959335497159053279727421119255555113601555011417_<54>
P90 = 700762515289784210874039143325825539548489780330736974377987653994531387998577206825482297_<90>

Number: 29999_196 N=29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 ( 197 digits) SNFS difficulty: 196 digits. Divisors found: r1=122344767534061284667205826233542620221024729103782351 (pp54) r2=349916959335497159053279727421119255555113601555011417 (pp54) r3=700762515289784210874039143325825539548489780330736974377987653994531387998577206825482297 (pp90) Version: GGNFS-0.77.1-20050930-nocona Total time: 516.20 hours. Scaled time: 1233.71 units (timescale=2.390). Factorization parameters were as follows: n: 29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 m: 1000000000000000000000000000000000000000 c5: 30 c0: -1 skew: 0.51 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, 18300001) Primes: RFBsize:1270607, AFBsize:1269815, largePrimes:23687268 encountered Relations: rels:24203236, finalFF:2931375 Max relations in full relation-set: 28 Initial matrix: 2540489 x 2931375 with sparse part having weight 208140655. Pruned matrix : 2176346 x 2189112 with weight 145380897. Total sieving time: 472.02 hours. Total relation processing time: 1.03 hours. Matrix solve time: 42.87 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,53,53,2.6,2.6,100000 total time: 516.20 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Oct 3, 2008: By Robert Backstrom / GMP-ECM
6·10¹⁶⁷+1 = 6(0)₁₆₆1_<168> = 19 · 53 · 151888273037_<12> · 285222132532084029211_<21> · C134
C134 = P38 · P97
P38 = 11344553699289079283476154821341898793_<38>
P97 = 1212346876153485600056159157453359594304541020922218903516315067388636750613885280058055706162793_<97>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 13753534238688584322143339202854565292590236731829919256769931192382804504625818230345229409471072118823813652385708513638874588208849 (134 digits) Using B1=5466000, B2=11416630690, polynomial Dickson(12), sigma=2706353897 Step 1 took 54142ms Step 2 took 21534ms ********** Factor found in step 2: 11344553699289079283476154821341898793 Found probable prime factor of 38 digits: 11344553699289079283476154821341898793 Probable prime cofactor 1212346876153485600056159157453359594304541020922218903516315067388636750613885280058055706162793 has 97 digits
Oct 2, 2008 (4th): By Serge Batalov / GMP-ECM 6.2.1
2·10¹⁷⁰+9 = 2(0)₁₆₉9_<171> = 11 · 20856546081214729_<17> · C153
C153 = P35 · P119
P35 = 31898045403876622590018206760962939_<35>
P119 = 27329447332447825571832005501356411557247380282440211338517340420235479911185535153515772085011975930967362685161689849_<119>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=2478872043 Step 1 took 262323ms Step 2 took 79158ms ********** Factor found in step 2: 31898045403876622590018206760962939 Found probable prime factor of 35 digits: 31898045403876622590018206760962939 Probable prime cofactor 27329447332447825571832005501356411557247380282440211338517340420235479911185535153515772085011975930967362685161689849 has 119 digits
Oct 2, 2008 (3rd): By matsui / GMP-ECM
5·10¹⁸⁶-3 = 4(9)₁₈₅7_<187> = 67317521395141_<14> · 46615341719911308568542113_<26> · C148
C148 = P36 · P112
P36 = 440247862165415629914964024062743623_<36>
P112 = 3619226468217882437161494597428834606600520897650913186570957157465554197450093428407182748230547242163506739583_<112>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 1593356715325410319172868890988741940658975404678256641171322555945504876672202381871531579446721699351252766811856458978967108352978533218354929209 =440247862165415629914964024062743623* 3619226468217882437161494597428834606600520897650913186570957157465554197450093428407182748230547242163506739583
Oct 2, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁶¹-71)/9 = 2(8)₁₆₀1_<162> = 19 · C161
C161 = P72 · P89
P72 = 632162252911445335796435973980354556377945502963326151746830745204115223_<72>
P89 = 24051860566725428718633081455487317525885368126175025927404218378326986147965349318982413_<89>

Number: 28881_161 N=15204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099 ( 161 digits) SNFS difficulty: 162 digits. Divisors found: r1=632162252911445335796435973980354556377945502963326151746830745204115223 (pp72) r2=24051860566725428718633081455487317525885368126175025927404218378326986147965349318982413 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 77.65 hours. Scaled time: 78.28 units (timescale=1.008). Factorization parameters were as follows: name: 28881_161 n: 15204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099 m: 100000000000000000000000000000000 c5: 260 c0: -71 skew: 0.77 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:315212, largePrimes:5888530 encountered Relations: rels:5992989, finalFF:725848 Max relations in full relation-set: 28 Initial matrix: 631227 x 725848 with sparse part having weight 54679237. Pruned matrix : 563033 x 566253 with weight 40813096. Total sieving time: 74.92 hours. Total relation processing time: 0.10 hours. Matrix solve time: 2.54 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 77.65 hours. --------- CPU info (if available) ----------
Oct 2, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(17·10¹⁷⁰-53)/9 = 1(8)₁₆₉3_<171> = 3 · 31 · 2333 · 90168271 · C157
C157 = P33 · P34 · P92
P33 = 115142149344161629850376984688397_<33>
P34 = 1772963737984840369465746226474583_<34>
P92 = 47295606304386422476579305729270226175133053046692469208394133140258992145305451848568435167_<92>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 9655060123620669206025974738195444050561032290005483080386739714241489585777600926399707507460520910682304298115846620265195528870797762599462867740469931317 (157 digits) Using B1=1252000, B2=1426326730, polynomial Dickson(6), sigma=374355149 Step 1 took 15984ms Step 2 took 6844ms ********** Factor found in step 2: 115142149344161629850376984688397 Found probable prime factor of 33 digits: 115142149344161629850376984688397 Composite cofactor 83853394943684333473055241658152182035340424420224832510221965919173132871571422640806640872525599975611826059405083408860361 has 125 digits GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 83853394943684333473055241658152182035340424420224832510221965919173132871571422640806640872525599975611826059405083408860361 (125 digits) Using B1=1372000, B2=1426564240, polynomial Dickson(6), sigma=495894633 Step 1 took 12015ms Step 2 took 5141ms ********** Factor found in step 2: 1772963737984840369465746226474583 Found probable prime factor of 34 digits: 1772963737984840369465746226474583 Probable prime cofactor 47295606304386422476579305729270226175133053046692469208394133140258992145305451848568435167 has 92 digits
(5·10¹⁷⁰-23)/9 = (5)₁₆₉3_<170> = 31643 · 769507357 · C157
C157 = P56 · P101
P56 = 45001623418203325386019413691245428244292701406687273123_<56>
P101 = 50700108208826272869285692148550799344352074012722932660038293634721356836394536023755688749101133861_<101>

Number: n N=2281587176875759054520890703509527182715102806806507622366468975418052184720131042409246726276126043931951476891864183073846751143457027596919608277490517903 ( 157 digits) SNFS difficulty: 170 digits. Divisors found: Thu Oct 02 03:06:19 2008 prp56 factor: 45001623418203325386019413691245428244292701406687273123 Thu Oct 02 03:06:19 2008 prp101 factor: 50700108208826272869285692148550799344352074012722932660038293634721356836394536023755688749101133861 Thu Oct 02 03:06:19 2008 elapsed time 04:09:19 (Msieve 1.38 **dep=7**) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 0.78 hours. Scaled time: 1.02 units (timescale=1.299). Factorization parameters were as follows: name: KA_5_169_3 n: 2281587176875759054520890703509527182715102806806507622366468975418052184720131042409246726276126043931951476891864183073846751143457027596919608277490517903 type: snfs skew: 1.36 deg: 5 c5: 5 c0: -23 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, 200001) Primes: RFBsize:425648, AFBsize:426252, largePrimes:14739769 encountered Relations: rels:15116534, finalFF:1557464 Max relations in full relation-set: 28 Initial matrix: 851965 x 1557464 with sparse part having weight 149351625. Pruned matrix : Total sieving time: 0.35 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,170,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000 total time: 0.78 hours. --------- CPU info (if available) ----------
(4·10¹⁷⁰+41)/9 = (4)₁₆₉9_<170> = 7² · 383 · 190938968767_<12> · C155
C155 = P32 · P124
P32 = 11076321807868186689085681697297_<32>
P124 = 1119779442197062735519303413885522946726562495949180557564827738640396690905680513942218528205584546242743238956698113861153_<124>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 12403037455609799575206813257751283380841275957391153538977388063043774573103258275233257298220454720621344967752277641859121318792311574674879151233403441 (155 digits) Using B1=784000, B2=696767622, polynomial Dickson(3), sigma=1997601525 Step 1 took 9391ms Step 2 took 3984ms ********** Factor found in step 2: 11076321807868186689085681697297 Found probable prime factor of 32 digits: 11076321807868186689085681697297 Probable prime cofactor 1119779442197062735519303413885522946726562495949180557564827738640396690905680513942218528205584546242743238956698113861153 has 124 digits
5·10¹⁷⁰-1 = 4(9)₁₇₀_<171> = 31 · 4688909 · 5962171 · C156
C156 = P36 · P121
P36 = 414098898368494463344506663169333769_<36>
P121 = 1393246636581073462780644946707410311348854022175587735092066569086144683145170283932792460440716222911271989247205306919_<121>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 576941897363832680247990659532154636533269260043447804982278645257355362380723176817840997220371791999561855565743580805836706271803510382912248634396047711 (156 digits) Using B1=1114000, B2=1426247560, polynomial Dickson(6), sigma=3235219842 Step 1 took 14359ms Step 2 took 6828ms ********** Factor found in step 2: 414098898368494463344506663169333769 Found probable prime factor of 36 digits: 414098898368494463344506663169333769 Probable prime cofactor 1393246636581073462780644946707410311348854022175587735092066569086144683145170283932792460440716222911271989247205306919 has 121 digits
3·10¹⁷¹-7 = 2(9)₁₇₀3_<172> = 73 · 26103770121167_<14> · C157
C157 = P71 · P86
P71 = 69185802781796879642077085597448791268734799821577537651715919383668229_<71>
P86 = 22755069893669253071145751833555900531496535657694741960060249774778750742959661038387_<86>

Number: n N=1574327777949404635376174768673852196943179488710897574632998700132319413715457346172529249449492909562247276388632517481561461992754350763645351691241306623 ( 157 digits) SNFS difficulty: 171 digits. Divisors found: Thu Oct 02 04:55:00 2008 prp71 factor: 69185802781796879642077085597448791268734799821577537651715919383668229 Thu Oct 02 04:55:01 2008 prp86 factor: 22755069893669253071145751833555900531496535657694741960060249774778750742959661038387 Thu Oct 02 04:55:01 2008 elapsed time 02:13:30 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 16.58 hours. Scaled time: 34.00 units (timescale=2.051). Factorization parameters were as follows: name: KA_2_9_170_3 n: 1574327777949404635376174768673852196943179488710897574632998700132319413715457346172529249449492909562247276388632517481561461992754350763645351691241306623 type: snfs skew: 0.75 deg: 5 c5: 30 c0: -7 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, 3800001) Primes: RFBsize:425648, AFBsize:425482, largePrimes:13895280 encountered Relations: rels:13425134, finalFF:1026037 Max relations in full relation-set: 28 Initial matrix: 851197 x 1026037 with sparse part having weight 114941916. Pruned matrix : Total sieving time: 16.25 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,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000 total time: 16.58 hours. --------- CPU info (if available) ----------
Oct 1, 2008 (5th): By Robert Backstrom / GGNFS, Msieve
(79·10¹⁶⁹-7)/9 = 8(7)₁₆₉_<170> = 3 · 19 · 29 · 1725943553750443_<16> · C152
C152 = P76 · P76
P76 = 3116549881367973389270395010859470666928419469489925409699923580919060881933_<76>
P76 = 9872134366631629882925427065540193668246546885604057444260571641728324014211_<76>

Number: n N=30766999189174499224689468894868725545675655898997098145447140665073696881219316660229533882153414599964581869484884935996126880831097168266744485149863 ( 152 digits) SNFS difficulty: 171 digits. Divisors found: Wed Oct 01 10:57:02 2008 prp76 factor: 3116549881367973389270395010859470666928419469489925409699923580919060881933 Wed Oct 01 10:57:02 2008 prp76 factor: 9872134366631629882925427065540193668246546885604057444260571641728324014211 Wed Oct 01 10:57:02 2008 elapsed time 02:23:05 (Msieve 1.38) Version: GGNFS-0.77.1-20051202-athlon Total time: 14.24 hours. Scaled time: 27.78 units (timescale=1.951). Factorization parameters were as follows: name: KA_8_7_169 n: 30766999189174499224689468894868725545675655898997098145447140665073696881219316660229533882153414599964581869484884935996126880831097168266744485149863 type: snfs skew: 0.98 deg: 5 c5: 79 c0: -70 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, 3000001) Primes: RFBsize:425648, AFBsize:426147, largePrimes:13749595 encountered Relations: rels:13289628, finalFF:1055105 Max relations in full relation-set: 28 Initial matrix: 851860 x 1055105 with sparse part having weight 108793998. Pruned matrix : Total sieving time: 13.93 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,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,52,52,2.5,2.5,100000 total time: 14.24 hours. --------- CPU info (if available) ----------
The two P76s are the largest "nice split" in our tables so far. Congratulations!
(13·10¹⁹³+23)/9 = 1(4)₁₉₂7_<194> = 17 · C192
C192 = P64 · P64 · P66
P64 = 1196455461628544734772941131559603494899791069387129434425021729_<64>
P64 = 5746234301488081463418161619215684930851366835539570351147091267_<64>
P66 = 123586790714944675816525046385603864129642170689196698566797580037_<66>

Number: n N=849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143791 ( 192 digits) SNFS difficulty: 194 digits. Divisors found: Wed Oct 01 20:28:23 2008 prp64 factor: 1196455461628544734772941131559603494899791069387129434425021729 Wed Oct 01 20:28:23 2008 prp64 factor: 5746234301488081463418161619215684930851366835539570351147091267 Wed Oct 01 20:28:23 2008 prp66 factor: 123586790714944675816525046385603864129642170689196698566797580037 Wed Oct 01 20:28:23 2008 elapsed time 24:38:46 (Msieve 1.38) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 207.28 hours. Scaled time: 266.77 units (timescale=1.287). Factorization parameters were as follows: name: KA_1_4_192_7 n: 849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143790849673202614379084967320261437908496732026143791 type: snfs skew: 0.28 deg: 5 c5: 13000 c0: 23 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, 17600001) Primes: RFBsize:633578, AFBsize:634378, largePrimes:15782300 encountered Relations: rels:16300207, finalFF:1288581 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 206.17 hours. Total relation processing time: 1.11 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: 207.28 hours. --------- CPU info (if available) ----------
Oct 1, 2008 (4th): By Jo Yeong Uk / GGNFS
(25·10¹⁷²+11)/9 = 2(7)₁₇₁9_<173> = 23981 · 53995615589_<11> · 7460424273338579899_<19> · 13239143598630449657_<20> · C120
C120 = P57 · P64
P57 = 109489131787240102633809097207760966409512000943817713697_<57>
P64 = 1983705886913857198927917859022711403667837530552000416457450961_<64>

Number: 27779_172 N=217194235279435322578068101831818127012956773396156707671960089661930773720951196887833399196951403371695218091515512817 ( 120 digits) Divisors found: r1=109489131787240102633809097207760966409512000943817713697 (pp57) r2=1983705886913857198927917859022711403667837530552000416457450961 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 39.03 hours. Scaled time: 88.36 units (timescale=2.264). Factorization parameters were as follows: name: 27779_172 n: 217194235279435322578068101831818127012956773396156707671960089661930773720951196887833399196951403371695218091515512817 skew: 120743.00 # norm 2.20e+16 c5: 12540 c4: -2801895919 c3: -707820581642247 c2: 37147529845475201007 c1: 3152016688089544702881334 c0: -61311511986314671396522758936 # alpha -5.67 Y1: 5015245439623 Y0: -111612034227956946874235 # Murphy_E 2.91e-10 # M 31924727766020902462974355133718177632421051733378130399990588470417387964299356643973755470171567151060421048341657594 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [2500000, 4600001) Primes: RFBsize:348513, AFBsize:348407, largePrimes:8681924 encountered Relations: rels:8873385, finalFF:860548 Max relations in full relation-set: 28 Initial matrix: 697004 x 860548 with sparse part having weight 75775813. Pruned matrix : 560161 x 563710 with weight 47440428. Polynomial selection time: 2.63 hours. Total sieving time: 34.03 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.02 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,51,51,2.4,2.4,100000 total time: 39.03 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, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673800) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.40 BogoMIPS (lpj=2672204) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Oct 1, 2008 (3rd): By matsui / GMP-ECM
4·10¹⁹³+9 = 4(0)₁₉₂9_<194> = 7 · 11437 · 13853895929_<11> · 284374155722383_<15> · C165
C165 = P32 · C133
P32 = 40774884715492908428204364418823_<32>
C133 = [3110248167561881935201485645217781199329548107070074852028048966879022371455995745826435473920853302379411133812169289220566053640491_<133>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 126820010468908806071880109357043266345981215766729369753337225868175064400665316164905372765852198104155866881930631191806135695255612601001613076169469586595362093 =40774884715492908428204364418823* 3110248167561881935201485645217781199329548107070074852028048966879022371455995745826435473920853302379411133812169289220566053640491
Oct 1, 2008 (2nd): By Sinkiti Sibata / GGNFS
(26·10¹⁶⁰-71)/9 = 2(8)₁₅₉1_<161> = 3 · C160
C160 = P70 · P91
P70 = 1094998023968034643446213026625908789762145086429066485506433912988981_<70>
P91 = 8794198180133646807441422534325880565522933789319895295254625222992854439653169060283985967_<91>

Number: 28881_160 N=9629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629627 ( 160 digits) SNFS difficulty: 161 digits. Divisors found: r1=1094998023968034643446213026625908789762145086429066485506433912988981 (pp70) r2=8794198180133646807441422534325880565522933789319895295254625222992854439653169060283985967 (pp91) Version: GGNFS-0.77.1-20050930-nocona Total time: 66.55 hours. Scaled time: 67.29 units (timescale=1.011). Factorization parameters were as follows: name: 28881_160 n: 9629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629627 m: 100000000000000000000000000000000 c5: 26 c0: -71 skew: 1.22 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, 4500001) Primes: RFBsize:283146, AFBsize:284453, largePrimes:6116457 encountered Relations: rels:6399110, finalFF:847689 Max relations in full relation-set: 28 Initial matrix: 567665 x 847689 with sparse part having weight 74518698. Pruned matrix : 396349 x 399251 with weight 60554454. Total sieving time: 64.50 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.87 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 66.55 hours. --------- CPU info (if available) ----------
(26·10¹⁷⁶-71)/9 = 2(8)₁₇₅1_<177> = 107 · 613 · 5414231 · 10578209 · 230072970263_<12> · 4597194814998215328498307_<25> · C122
C122 = P41 · P82
P41 = 54750566371088487970140619870411787020199_<41>
P82 = 1327976953687722400410338375555843000971594563026585227832663573259827714155008331_<82>

Number: 28881_176 N=72707490342155548476515019381711751468610942138147232179566137303158185999391724808661810254764068692558145383814510277869 ( 122 digits) Divisors found: r1=54750566371088487970140619870411787020199 (pp41) r2=1327976953687722400410338375555843000971594563026585227832663573259827714155008331 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 104.16 hours. Scaled time: 79.47 units (timescale=0.763). Factorization parameters were as follows: name: 28881_176 n: 72707490342155548476515019381711751468610942138147232179566137303158185999391724808661810254764068692558145383814510277869 skew: 195914.61 # norm 6.01e+16 c5: 16920 c4: -2370698138 c3: -1945543577514837 c2: 94960906202510051988 c1: 32239981473917970843344652 c0: -350196706109857443759359141920 # alpha -6.48 Y1: 1223064843187 Y0: -336229491185560213282809 # Murphy_E 2.30e-10 # M 62554245738941506985845956102807922475403985619745266129749410940345544183912752389781863871923413333511066297556897473815 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, 5560001) Primes: RFBsize:348513, AFBsize:347798, largePrimes:7893977 encountered Relations: rels:8200076, finalFF:872826 Max relations in full relation-set: 28 Initial matrix: 696394 x 872826 with sparse part having weight 85171281. Pruned matrix : 554875 x 558420 with weight 58323465. Total sieving time: 98.04 hours. Total relation processing time: 0.62 hours. Matrix solve time: 5.04 hours. Time per square root: 0.45 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 104.16 hours. --------- CPU info (if available) ----------
Oct 1, 2008: By Serge Batalov / GMP-ECM 6.2.1
5·10¹⁹⁴-7 = 4(9)₁₉₃3_<195> = 17 · 1981997 · 128401228061807_<15> · C174
C174 = P33 · P141
P33 = 132786590634016095535035300329071_<33>
P141 = 870351520581469776388414556682719376942987278061824153278788586760800351254966171514056538147644847695340761111994287303596157877520893178381_<141>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2621838758 Step 1 took 99259ms Step 2 took 29938ms ********** Factor found in step 2: 132786590634016095535035300329071 Found probable prime factor of 33 digits: 132786590634016095535035300329071 Probable prime cofactor 870351520581469776388414556682719376942987278061824153278788586760800351254966171514056538147644847695340761111994287303596157877520893178381 has 141 digits

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