News and updates, February 2009

Home > Math > Factorizations >

News and updates, February 2009

Feb 28, 2009 (7th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 28, 2009
(38·10¹⁶⁴+61)/9 = 4(2)₁₆₃9_<165> = 3 · 11 · 13 · 727 · 800001649 · 1032237454763_<13> · 4846862823541547_<16> · C123
C123 = P49 · P75
P49 = 1424218554316875399625038392232057599399988443713_<49>
P75 = 237487918334757094139099263647007383687709373624089339742165459109156850759_<75>

Number: 42229_164 N=338234699718451915584474464557708031138343751984940684675044970600595111547260673187174469507135439903150655763704612828167 ( 123 digits) SNFS difficulty: 166 digits. Divisors found: r1=1424218554316875399625038392232057599399988443713 r2=237487918334757094139099263647007383687709373624089339742165459109156850759 Version: Total time: 20.50 hours. Scaled time: 48.82 units (timescale=2.382). Factorization parameters were as follows: n: 338234699718451915584474464557708031138343751984940684675044970600595111547260673187174469507135439903150655763704612828167 m: 1000000000000000000000000000000000 deg: 5 c5: 19 c0: 305 skew: 1.74 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2300000, 3900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9507815 Max relations in full relation-set: Initial matrix: Pruned matrix : 752528 x 752776 Total sieving time: 18.30 hours. Total relation processing time: 0.77 hours. Matrix solve time: 1.26 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,51,51,2.4,2.4,100000 total time: 20.50 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 28, 2009 (6th): By Robert Backstrom / GGNFS, Msieve / Feb 28, 2009
(44·10¹²⁵-17)/9 = 4(8)₁₂₄7_<126> = 7 · 211 · 4453417 · C116
C116 = P43 · P74
P43 = 1602043501271566697868732461382414268534571_<43>
P74 = 46394019911217396269265065640038665422658070408067883179766258176382621433_<74>

Number: n N=74325238096629497479463277119643411178173653499498587019630169598148762753958763910702546007032640075828840366060243 ( 116 digits) SNFS difficulty: 126 digits. Divisors found: r1=1602043501271566697868732461382414268534571 (pp43) r2=46394019911217396269265065640038665422658070408067883179766258176382621433 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.59 hours. Scaled time: 2.91 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_8_124_7 n: 74325238096629497479463277119643411178173653499498587019630169598148762753958763910702546007032640075828840366060243 deg: 5 c5: 44 c0: -17 m: 10000000000000000000000000 skew: 0.83 type: snfs rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [350000, 530001) Primes: RFBsize:56543, AFBsize:56739, largePrimes:6408695 encountered Relations: rels:5600306, finalFF:171999 Max relations in full relation-set: 48 Initial matrix: 113350 x 171999 with sparse part having weight 23574962. Pruned matrix : 102616 x 103246 with weight 9631499. Total sieving time: 1.30 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.06 hours. Total square root time: 0.14 hours, sqrts: 7. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,700000,700000,28,28,56,56,2.5,2.5,50000 total time: 1.59 hours. --------- CPU info (if available) ----------
(44·10¹¹⁸-17)/9 = 4(8)₁₁₇7_<119> = C119
C119 = P52 · P67
P52 = 5119206635006373557156560747475490922102229350311527_<52>
P67 = 9550090936860184163762019684239003669175453223403396936392071157681_<67>

Number: n N=48888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 ( 119 digits) SNFS difficulty: 121 digits. Divisors found: Sat Feb 28 16:08:16 2009 prp52 factor: 5119206635006373557156560747475490922102229350311527 Sat Feb 28 16:08:16 2009 prp67 factor: 9550090936860184163762019684239003669175453223403396936392071157681 Sat Feb 28 16:08:16 2009 elapsed time 00:11:05 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.61 hours. Scaled time: 2.82 units (timescale=1.751). Factorization parameters were as follows: name: KA_4_8_117_7 n: 48888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 deg: 5 c5: 11 c0: -425 m: 1000000000000000000000000 skew: 2.08 type: snfs rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 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: 56/56 Sieved special-q in [250000, 413089) Primes: RFBsize:41538, AFBsize:41413, largePrimes:5166760 encountered Relations: rels:4518399, finalFF:83995 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 274027 hash collisions in 4762437 relations Msieve: matrix is 98251 x 98499 (25.3 MB) Total sieving time: 1.52 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000 total time: 1.61 hours. --------- CPU info (if available) ----------
(44·10¹²⁶-17)/9 = 4(8)₁₂₅7_<127> = 3 · 47653 · 71147 · C117
C117 = P45 · P72
P45 = 597361534589012167168440041910515739916420567_<45>
P72 = 804645930508513497385460242371516277261563191572489892715193841447820557_<72>

Number: n N=480664527849369266189969060980799482078884937664464172800653847852361236391117647744931659139661111090766438760195819 ( 117 digits) SNFS difficulty: 127 digits. Divisors found: r1=597361534589012167168440041910515739916420567 (pp45) r2=804645930508513497385460242371516277261563191572489892715193841447820557 (pp72) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.93 hours. Scaled time: 3.52 units (timescale=1.823). Factorization parameters were as follows: name: KA_4_8_125_7 n: 480664527849369266189969060980799482078884937664464172800653847852361236391117647744931659139661111090766438760195819 deg: 5 c5: 440 c0: -17 m: 10000000000000000000000000 skew: 0.52 type: snfs rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [350000, 610001) Primes: RFBsize:56543, AFBsize:56804, largePrimes:6699266 encountered Relations: rels:5887799, finalFF:149506 Max relations in full relation-set: 48 Initial matrix: 113414 x 149506 with sparse part having weight 22406191. Pruned matrix : 107903 x 108534 with weight 12662178. Total sieving time: 1.69 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.09 hours. Total square root time: 0.04 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,700000,700000,28,28,56,56,2.5,2.5,50000 total time: 1.93 hours. --------- CPU info (if available) ----------
(55·10¹⁸⁹-1)/9 = 6(1)₁₈₉_<190> = 3 · 7 · C189
C189 = P44 · P146
P44 = 10804513265786317319460462777997312080002291_<44>
P146 = 26933678903129430985310353961003134949691654361236458943029562303853859698336539161768227604516361368354018288214754655403161113549617827609433001_<146>

Number: n N=291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291 ( 189 digits) SNFS difficulty: 191 digits. Divisors found: Sat Feb 28 20:23:31 2009 prp44 factor: 10804513265786317319460462777997312080002291 Sat Feb 28 20:23:31 2009 prp146 factor: 26933678903129430985310353961003134949691654361236458943029562303853859698336539161768227604516361368354018288214754655403161113549617827609433001 Sat Feb 28 20:23:31 2009 elapsed time 05:43:31 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 25.68 hours. Scaled time: 51.74 units (timescale=2.015). Factorization parameters were as follows: name: KA_6_1_189 n: 291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291 deg: 5 c5: 11 c0: -2 m: 100000000000000000000000000000000000000 skew: 0.71 type: snfs rlim: 9000000 alim: 9000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [4500000, 12000091) Primes: RFBsize:602489, AFBsize:603256, largePrimes:35249275 encountered Relations: rels:31811549, finalFF:766356 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 3439632 hash collisions in 33747700 relations Msieve: matrix is 1996963 x 1997209 (545.6 MB) Total sieving time: 24.93 hours. Total relation processing time: 0.74 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,9000000,9000000,29,29,58,58,2.5,2.5,100000 total time: 25.68 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454) Total of 4 processors activated (22643.71 BogoMIPS).
Feb 28, 2009 (5th): By Wataru Sakai / Msieve / Feb 28, 2009
5·10¹⁹⁵-7 = 4(9)₁₉₄3_<196> = 103 · C194
C194 = P40 · P155
P40 = 1538107507489534601481055687712361944471_<40>
P155 = 31560660801675883119225896760035021175119702951582155400620760556441646547154939591760010210551656217315637522354907153165554249169443274017081188872379961_<155>

Number: 49993_195 N=48543689320388349514563106796116504854368932038834951456310679611650485436893203883495145631067961165048543689320388349514563106796116504854368932038834951456310679611650485436893203883495145631 ( 194 digits) SNFS difficulty: 195 digits. Divisors found: r1=1538107507489534601481055687712361944471 r2=31560660801675883119225896760035021175119702951582155400620760556441646547154939591760010210551656217315637522354907153165554249169443274017081188872379961 Version: Total time: 490.56 hours. Scaled time: 960.02 units (timescale=1.957). Factorization parameters were as follows: n: 48543689320388349514563106796116504854368932038834951456310679611650485436893203883495145631067961165048543689320388349514563106796116504854368932038834951456310679611650485436893203883495145631 m: 1000000000000000000000000000000000000000 deg: 5 c5: 5 c0: -7 skew: 1.07 type: snfs lss: 1 rlim: 12800000 alim: 12800000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 12800000/12800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6400000, 12100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2209599 x 2209846 Total sieving time: 490.56 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,195,5,0,0,0,0,0,0,0,0,12800000,12800000,28,28,55,55,2.5,2.5,100000 total time: 490.56 hours. --------- CPU info (if available) ----------
Feb 28, 2009 (4th): By Sinkiti Sibata / GGNFS, Msieve / Feb 28, 2009
(44·10¹⁶⁴-53)/9 = 4(8)₁₆₃3_<165> = 3 · 7 · 107 · 191 · 2011 · 74353 · 977464297 · 8323776453036833_<16> · 9095888398974523051_<19> · C108
C108 = P46 · P62
P46 = 7862625727717047507506747886063428866231417793_<46>
P62 = 13092697172411652719473407661621196298322843061510254562777291_<62>

Number: 48883_164 N=102942977633012101180739550347858143335187192258265597979941494870078161661437989140125181736468106633738763 ( 108 digits) Divisors found: r1=7862625727717047507506747886063428866231417793 (pp46) r2=13092697172411652719473407661621196298322843061510254562777291 (pp62) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 21.84 hours. Scaled time: 10.31 units (timescale=0.472). Factorization parameters were as follows: name: 48883_164 n: 102942977633012101180739550347858143335187192258265597979941494870078161661437989140125181736468106633738763 skew: 20692.37 # norm 1.34e+15 c5: 27600 c4: 3288080556 c3: -66558113477159 c2: -1080970303183105211 c1: 9820381395717295647051 c0: 99797268987273415522565403 # alpha -6.18 Y1: 172874243003 Y0: -326837632365735623162 # Murphy_E 1.34e-09 # M 29593209732172111755289090560667936426206250818983003423088700963706017810763694749058577282903162950489239 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2450001) Primes: RFBsize:183072, AFBsize:183778, largePrimes:4450675 encountered Relations: rels:4527310, finalFF:452352 Max relations in full relation-set: 28 Initial matrix: 366925 x 452352 with sparse part having weight 32939034. Pruned matrix : 301955 x 303853 with weight 19313258. Polynomial selection time: 1.24 hours. Total sieving time: 17.66 hours. Total relation processing time: 0.28 hours. Matrix solve time: 2.44 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: 21.84 hours. --------- CPU info (if available) ----------
(44·10¹⁵¹-53)/9 = 4(8)₁₅₀3_<152> = 89 · 3828689299_<10> · C141
C141 = P61 · P81
P61 = 1223424440156560969442482741818564284725731966756254692657813_<61>
P81 = 117271609007689616091476396520146862786413933843883272607744325347034802241242981_<81>

Number: 48883_151 N=143472952596491781054853177023595303753457066690313745153344570376869567149465397211683238998531186432590885097236794256571770660035621060553 ( 141 digits) SNFS difficulty: 153 digits. Divisors found: r1=1223424440156560969442482741818564284725731966756254692657813 r2=117271609007689616091476396520146862786413933843883272607744325347034802241242981 Version: Total time: 20.66 hours. Scaled time: 52.98 units (timescale=2.564). Factorization parameters were as follows: name: 48883_151 n: 143472952596491781054853177023595303753457066690313745153344570376869567149465397211683238998531186432590885097236794256571770660035621060553 m: 2000000000000000000000000000000 deg: 5 c5: 55 c0: -212 skew: 1.31 type: snfs lss: 1 rlim: 2500000 alim: 2500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1250000, 2250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 441545 x 441793 Total sieving time: 20.66 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,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000 total time: 20.66 hours. --------- CPU info (if available) ----------
Feb 28, 2009 (3rd): By Serge Batalov / GMP-ECM 6.2.1 / Feb 28, 2009
(44·10¹⁴⁶-17)/9 = 4(8)₁₄₅7_<147> = 29437746451_<11> · 39356253678142543_<17> · C120
C120 = P39 · P82
P39 = 145977862620685020006575147046184107331_<39>
P82 = 2890712197147550381221784038267660221257757249803464957889274361683240563824349089_<82>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=695496723 Step 1 took 13197ms Step 2 took 11773ms ********** Factor found in step 2: 145977862620685020006575147046184107331 Found probable prime factor of 39 digits: 145977862620685020006575147046184107331 Probable prime cofactor 2890712197147550381221784038267660221257757249803464957889274361683240563824349089 has 82 digits
(44·10¹⁹⁷-17)/9 = 4(8)₁₉₆7_<198> = 7 · 43 · 179 · C193
C193 = P30 · P164
P30 = 180192366370524429277382033171_<30>
P164 = 50356350969832803448648096347995128791247155483945461392799207399795166974995809400922218508687516833945192101225665458371976955557885982556232271977569349459988443_<164>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4228587319 Step 1 took 26145ms Step 2 took 18697ms ********** Factor found in step 2: 180192366370524429277382033171 Found probable prime factor of 30 digits: 180192366370524429277382033171 Probable prime cofactor has 164 digits
(44·10¹⁷⁰-17)/9 = 4(8)₁₆₉7_<171> = 523 · 26393 · 5248786129_<10> · C154
C154 = P29 · C126
P29 = 67204076825777480647940943101_<29>
C126 = [100407284951808774048499368281072908226415208673026207174570944509767601913362756510328274963943649362315407074660910461389377_<126>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=910978272 Step 1 took 15253ms Step 2 took 12953ms ********** Factor found in step 2: 67204076825777480647940943101 Found probable prime factor of 29 digits: 67204076825777480647940943101 Composite cofactor has 126 digits
(44·10¹⁶⁶-17)/9 = 4(8)₁₆₅7_<167> = 19 · 177636367 · 493973401 · C149
C149 = P35 · P115
P35 = 10130025607661052751984594948001591_<35>
P115 = 2894746758907489244526766490846737550788329151477578304420727802540456057343393197016694224714405763736055795654909_<115>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2251914498 Step 1 took 14833ms Step 2 took 13428ms ********** Factor found in step 2: 10130025607661052751984594948001591 Found probable prime factor of 35 digits: 10130025607661052751984594948001591 Probable prime cofactor has 115 digits
(44·10¹⁷⁶-17)/9 = 4(8)₁₇₅7_<177> = 43 · 659 · 98196426949_<11> · 24146313277163821_<17> · 192280009873992323_<18> · C128
C128 = P32 · C96
P32 = 40080386376207456114952753675681_<32>
C96 = [944155973540168858103069780436959607055778687934293351044551531753237918863965710505962721817613_<96>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4011473568 Step 1 took 13833ms Step 2 took 12244ms ********** Factor found in step 2: 40080386376207456114952753675681 Found probable prime factor of 32 digits: 40080386376207456114952753675681 Composite cofactor has 96 digits
Feb 28, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Feb 28, 2009
(44·10¹⁰⁴-17)/9 = 4(8)₁₀₃7_<105> = 1453 · 5568533287_<10> · C92
C92 = P43 · P50
P43 = 5335076764314319996463585618733855222723227_<43>
P50 = 11325648007691200306292519178705980717619362257871_<50>

Number: 48887_104 N=60423201526636093683096215646055084505807396854920856177881774149911269616988042460035269717 ( 92 digits) SNFS difficulty: 105 digits. Divisors found: r1=5335076764314319996463585618733855222723227 (pp43) r2=11325648007691200306292519178705980717619362257871 (pp50) Version: GGNFS-0.77.1-VC8(Sat Total time: 0.40 hours. Scaled time: 0.48 units (timescale=1.201). Factorization parameters were as follows: n: 60423201526636093683096215646055084505807396854920856177881774149911269616988042460035269717 m: 100000000000000000000000000 deg: 4 c4: 44 c0: -17 skew: 0.79 type: snfs lss: 1 rlim: 400000 alim: 400000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [200000, 280001) Primes: RFBsize:33860, AFBsize:33817, largePrimes:1146791 encountered Relations: rels:1124713, finalFF:144310 Max relations in full relation-set: 32 Initial matrix: 67743 x 144310 with sparse part having weight 5929428. Pruned matrix : 44033 x 44435 with weight 1341953. Total sieving time: 0.37 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000 total time: 0.40 hours. --------- CPU info (if available) ----------
(44·10¹⁰⁵-17)/9 = 4(8)₁₀₄7_<106> = 3 · 671323 · 2473609 · C93
C93 = P34 · P60
P34 = 2460362561262722710018034351313961_<34>
P60 = 398866188750874688871780951536826630692272742500588933046327_<60>

Number: 48887_105 N=981355437756202646545847788660158742199717984732887942496510975874151466019670362386934871247 ( 93 digits) SNFS difficulty: 106 digits. Divisors found: r1=2460362561262722710018034351313961 (pp34) r2=398866188750874688871780951536826630692272742500588933046327 (pp60) Version: GGNFS-0.77.1-VC8(Sat Total time: 0.43 hours. Scaled time: 0.48 units (timescale=1.123). Factorization parameters were as follows: n: 981355437756202646545847788660158742199717984732887942496510975874151466019670362386934871247 m: 200000000000000000000000000 deg: 4 c4: 55 c0: -34 skew: 0.89 type: snfs lss: 1 rlim: 420000 alim: 420000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 420000/420000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [210000, 290001) Primes: RFBsize:35390, AFBsize:35562, largePrimes:1153944 encountered Relations: rels:1133793, finalFF:148449 Max relations in full relation-set: 32 Initial matrix: 71018 x 148449 with sparse part having weight 5955462. Pruned matrix : 45383 x 45802 with weight 1386381. Total sieving time: 0.39 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,106,4,0,0,0,0,0,0,0,0,420000,420000,25,25,44,44,2.2,2.2,20000 total time: 0.43 hours. --------- CPU info (if available) ----------
(44·10¹⁰⁷-17)/9 = 4(8)₁₀₆7_<108> = 7 · 151 · 2591167 · 9364636130953_<13> · C86
C86 = P37 · P50
P37 = 1684619316590834232011834229283191761_<37>
P50 = 11314805483343756222966792594459489946735699966481_<50>

Fri Feb 27 16:38:55 2009 Fri Feb 27 16:38:55 2009 Fri Feb 27 16:38:55 2009 Msieve v. 1.39 Fri Feb 27 16:38:55 2009 random seeds: a52dbf50 a353c414 Fri Feb 27 16:38:55 2009 factoring 19061139880708782409319760633568622394892870084200765718273837254648507553224395363041 (86 digits) Fri Feb 27 16:38:55 2009 searching for 15-digit factors Fri Feb 27 16:38:56 2009 commencing quadratic sieve (86-digit input) Fri Feb 27 16:38:57 2009 using multiplier of 19 Fri Feb 27 16:38:57 2009 using 32kb Intel Core sieve core Fri Feb 27 16:38:57 2009 sieve interval: 14 blocks of size 32768 Fri Feb 27 16:38:57 2009 processing polynomials in batches of 15 Fri Feb 27 16:38:57 2009 using a sieve bound of 1446187 (55333 primes) Fri Feb 27 16:38:57 2009 using large prime bound of 115694960 (26 bits) Fri Feb 27 16:38:57 2009 using double large prime bound of 326562213825440 (41-49 bits) Fri Feb 27 16:38:57 2009 using trial factoring cutoff of 49 bits Fri Feb 27 16:38:57 2009 polynomial 'A' values have 11 factors Fri Feb 27 17:10:54 2009 55640 relations (15993 full + 39647 combined from 576459 partial), need 55429 Fri Feb 27 17:10:55 2009 begin with 592452 relations Fri Feb 27 17:10:55 2009 reduce to 131325 relations in 9 passes Fri Feb 27 17:10:55 2009 attempting to read 131325 relations Fri Feb 27 17:10:56 2009 recovered 131325 relations Fri Feb 27 17:10:56 2009 recovered 112086 polynomials Fri Feb 27 17:10:56 2009 attempting to build 55640 cycles Fri Feb 27 17:10:56 2009 found 55640 cycles in 5 passes Fri Feb 27 17:10:56 2009 distribution of cycle lengths: Fri Feb 27 17:10:56 2009 length 1 : 15993 Fri Feb 27 17:10:56 2009 length 2 : 11214 Fri Feb 27 17:10:56 2009 length 3 : 9830 Fri Feb 27 17:10:56 2009 length 4 : 7059 Fri Feb 27 17:10:56 2009 length 5 : 4878 Fri Feb 27 17:10:56 2009 length 6 : 3028 Fri Feb 27 17:10:56 2009 length 7 : 1708 Fri Feb 27 17:10:56 2009 length 9+: 1930 Fri Feb 27 17:10:56 2009 largest cycle: 17 relations Fri Feb 27 17:10:57 2009 matrix is 55333 x 55640 (12.7 MB) with weight 3100185 (55.72/col) Fri Feb 27 17:10:57 2009 sparse part has weight 3100185 (55.72/col) Fri Feb 27 17:10:57 2009 filtering completed in 3 passes Fri Feb 27 17:10:57 2009 matrix is 50382 x 50446 (11.6 MB) with weight 2837645 (56.25/col) Fri Feb 27 17:10:57 2009 sparse part has weight 2837645 (56.25/col) Fri Feb 27 17:10:57 2009 saving the first 48 matrix rows for later Fri Feb 27 17:10:57 2009 matrix is 50334 x 50446 (7.3 MB) with weight 2211621 (43.84/col) Fri Feb 27 17:10:57 2009 sparse part has weight 1613234 (31.98/col) Fri Feb 27 17:10:57 2009 matrix includes 64 packed rows Fri Feb 27 17:10:57 2009 using block size 20178 for processor cache size 4096 kB Fri Feb 27 17:10:57 2009 commencing Lanczos iteration Fri Feb 27 17:10:57 2009 memory use: 7.2 MB Fri Feb 27 17:11:08 2009 lanczos halted after 797 iterations (dim = 50328) Fri Feb 27 17:11:08 2009 recovered 16 nontrivial dependencies Fri Feb 27 17:11:08 2009 prp37 factor: 1684619316590834232011834229283191761 Fri Feb 27 17:11:08 2009 prp50 factor: 11314805483343756222966792594459489946735699966481 Fri Feb 27 17:11:08 2009 elapsed time 00:32:13
(44·10¹¹⁰-17)/9 = 4(8)₁₀₉7_<111> = 217003 · 1687573343_<10> · C97
C97 = P45 · P52
P45 = 981851775139662680653913806484673951169790561_<45>
P52 = 1359677287156986953147563312834625938221211913279323_<52>

Number: 48887_110 N=1335001558012168518348363004668761307750965113758421449552209044664630372326427757870752601870203 ( 97 digits) SNFS difficulty: 111 digits. Divisors found: r1=981851775139662680653913806484673951169790561 (pp45) r2=1359677287156986953147563312834625938221211913279323 (pp52) Version: GGNFS-0.77.1-VC8(Sat Total time: 0.54 hours. Scaled time: 0.64 units (timescale=1.191). Factorization parameters were as follows: n: 1335001558012168518348363004668761307750965113758421449552209044664630372326427757870752601870203 m: 10000000000000000000000 deg: 5 c5: 44 c0: -17 skew: 0.83 type: snfs lss: 1 rlim: 510000 alim: 510000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2Factor base limits: 510000/510000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [255000, 355001) Primes: RFBsize:42291, AFBsize:42417, largePrimes:1164161 encountered Relations: rels:1141095, finalFF:142153 Max relations in full relation-set: 32 Initial matrix: 84776 x 142153 with sparse part having weight 5736914. Pruned matrix : 60886 x 61373 with weight 1839283. Total sieving time: 0.49 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000 total time: 0.54 hours. --------- CPU info (if available) ----------
(44·10¹¹⁴-17)/9 = 4(8)₁₁₃7_<115> = 3 · 335809 · 2932883 · 23406287 · C95
C95 = P44 · P52
P44 = 26447950848946508125891246620051919927934567_<44>
P52 = 2672866621436084828667546678655921370908295550092983_<52>

Number: 48887_114 N=70691845029531284698770512690565030169046872661552376667469972646495013880968365567935989843361 ( 95 digits) SNFS difficulty: 116 digits. Divisors found: r1=26447950848946508125891246620051919927934567 (pp44) r2=2672866621436084828667546678655921370908295550092983 (pp52) Version: GGNFS-0.77.1-VC8(Sat Total time: 0.77 hours. Scaled time: 0.91 units (timescale=1.180). Factorization parameters were as follows: n: 70691845029531284698770512690565030169046872661552376667469972646495013880968365567935989843361 m: 100000000000000000000000 deg: 5 c5: 22 c0: -85 skew: 1.31 type: snfs lss: 1 rlim: 610000 alim: 610000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 610000/610000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [305000, 455001) Primes: RFBsize:49861, AFBsize:49685, largePrimes:1196972 encountered Relations: rels:1159168, finalFF:133478 Max relations in full relation-set: 32 Initial matrix: 99612 x 133478 with sparse part having weight 5722621. Pruned matrix : 82459 x 83021 with weight 2662959. Total sieving time: 0.70 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000 total time: 0.77 hours. --------- CPU info (if available) ----------
(44·10¹⁹¹-17)/9 = 4(8)₁₉₀7_<192> = 7 · 751 · 1229217511_<10> · 555335785751_<12> · 17600056050845750873641_<23> · 809722687213904864836267331_<27> · 3959130287390886271927035127231_<31> · C88
C88 = P36 · P53
P36 = 144550996278661975016517134044638733_<36>
P53 = 16703848779271170927251535893830201636903983700639807_<53>

Fri Feb 27 17:57:37 2009 Fri Feb 27 17:57:37 2009 Fri Feb 27 17:57:37 2009 Msieve v. 1.39 Fri Feb 27 17:57:37 2009 random seeds: 358661f0 a7325abd Fri Feb 27 17:57:37 2009 factoring 2414557982731759402829396316481997213725995106766293870774234544362028453002350273844531 (88 digits) Fri Feb 27 17:57:37 2009 searching for 15-digit factors Fri Feb 27 17:57:39 2009 commencing quadratic sieve (88-digit input) Fri Feb 27 17:57:39 2009 using multiplier of 1 Fri Feb 27 17:57:39 2009 using 32kb Intel Core sieve core Fri Feb 27 17:57:39 2009 sieve interval: 25 blocks of size 32768 Fri Feb 27 17:57:39 2009 processing polynomials in batches of 9 Fri Feb 27 17:57:39 2009 using a sieve bound of 1517671 (57486 primes) Fri Feb 27 17:57:39 2009 using large prime bound of 121413680 (26 bits) Fri Feb 27 17:57:39 2009 using double large prime bound of 356189977465520 (42-49 bits) Fri Feb 27 17:57:39 2009 using trial factoring cutoff of 49 bits Fri Feb 27 17:57:39 2009 polynomial 'A' values have 11 factors Fri Feb 27 18:32:02 2009 57591 relations (16453 full + 41138 combined from 603248 partial), need 57582 Fri Feb 27 18:32:02 2009 begin with 619701 relations Fri Feb 27 18:32:03 2009 reduce to 136773 relations in 9 passes Fri Feb 27 18:32:03 2009 attempting to read 136773 relations Fri Feb 27 18:32:04 2009 recovered 136773 relations Fri Feb 27 18:32:04 2009 recovered 109875 polynomials Fri Feb 27 18:32:04 2009 attempting to build 57591 cycles Fri Feb 27 18:32:04 2009 found 57591 cycles in 5 passes Fri Feb 27 18:32:04 2009 distribution of cycle lengths: Fri Feb 27 18:32:04 2009 length 1 : 16453 Fri Feb 27 18:32:04 2009 length 2 : 11427 Fri Feb 27 18:32:04 2009 length 3 : 10253 Fri Feb 27 18:32:04 2009 length 4 : 7428 Fri Feb 27 18:32:04 2009 length 5 : 5066 Fri Feb 27 18:32:04 2009 length 6 : 3145 Fri Feb 27 18:32:04 2009 length 7 : 1772 Fri Feb 27 18:32:04 2009 length 9+: 2047 Fri Feb 27 18:32:04 2009 largest cycle: 16 relations Fri Feb 27 18:32:04 2009 matrix is 57486 x 57591 (13.1 MB) with weight 3193032 (55.44/col) Fri Feb 27 18:32:04 2009 sparse part has weight 3193032 (55.44/col) Fri Feb 27 18:32:05 2009 filtering completed in 3 passes Fri Feb 27 18:32:05 2009 matrix is 52712 x 52775 (12.1 MB) with weight 2967477 (56.23/col) Fri Feb 27 18:32:05 2009 sparse part has weight 2967477 (56.23/col) Fri Feb 27 18:32:05 2009 saving the first 48 matrix rows for later Fri Feb 27 18:32:05 2009 matrix is 52664 x 52775 (7.4 MB) with weight 2253771 (42.71/col) Fri Feb 27 18:32:05 2009 sparse part has weight 1629875 (30.88/col) Fri Feb 27 18:32:05 2009 matrix includes 64 packed rows Fri Feb 27 18:32:05 2009 using block size 21110 for processor cache size 4096 kB Fri Feb 27 18:32:05 2009 commencing Lanczos iteration Fri Feb 27 18:32:05 2009 memory use: 7.5 MB Fri Feb 27 18:32:16 2009 lanczos halted after 834 iterations (dim = 52660) Fri Feb 27 18:32:16 2009 recovered 14 nontrivial dependencies Fri Feb 27 18:32:17 2009 prp36 factor: 144550996278661975016517134044638733 Fri Feb 27 18:32:17 2009 prp53 factor: 16703848779271170927251535893830201636903983700639807 Fri Feb 27 18:32:17 2009 elapsed time 00:34:40
(44·10¹²³-17)/9 = 4(8)₁₂₂7_<124> = 3 · 4026625162490093161507_<22> · C102
C102 = P45 · P58
P45 = 145178383648848147018910389708774434246239763_<45>
P58 = 2787698185156916726878264114124424897244941552415044169669_<58>

Number: 48887_123 N=404713516621908573560883803475538757792929116276848385070404870112011575428570816498677996319826348447 ( 102 digits) SNFS difficulty: 126 digits. Divisors found: r1=145178383648848147018910389708774434246239763 (pp45) r2=2787698185156916726878264114124424897244941552415044169669 (pp58) Version: Msieve-1.39 Total time: 1.60 hours. Scaled time: 1.91 units (timescale=1.196). Factorization parameters were as follows: n: 404713516621908573560883803475538757792929116276848385070404870112011575428570816498677996319826348447 m: 10000000000000000000000000 deg: 5 c5: 11 c0: -425 skew: 2.08 type: snfs lss: 1 rlim: 880000 alim: 880000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 880000/880000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [440000, 740001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 109885 x 110130 Total sieving time: 1.60 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,126,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000 total time: 1.60 hours. --------- CPU info (if available) ----------
(44·10¹⁶³-53)/9 = 4(8)₁₆₂3_<164> = 30585951059_<11> · C154
C154 = P46 · P108
P46 = 3409381221648677307546535609243234419019084991_<46>
P108 = 468826997834597142439467798015574281037728660247030807287630943512703579760743270536065940594634112718677407_<108>

Number: 48883_163 N=1598409962619200596193855594467257493982145487120616427743983492682436548094421930883169039497314160954071802200907617979095677885648999229600476844498337 ( 154 digits) SNFS difficulty: 166 digits. Divisors found: r1=3409381221648677307546535609243234419019084991 (pp46) r2=468826997834597142439467798015574281037728660247030807287630943512703579760743270536065940594634112718677407 (pp108) Version: Msieve-1.39 Total time: 43.07 hours. Scaled time: 110.73 units (timescale=2.571). Factorization parameters were as follows: n: 1598409962619200596193855594467257493982145487120616427743983492682436548094421930883169039497314160954071802200907617979095677885648999229600476844498337 m: 1000000000000000000000000000000000 deg: 5 c5: 11 c0: -1325 skew: 2.61 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 4250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 809954 x 810202 Total sieving time: 43.07 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,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 43.07 hours. --------- CPU info (if available) ----------
(32·10¹⁶⁵+31)/9 = 3(5)₁₆₄9_<166> = 345912299 · 1961284511_<10> · C148
C148 = P50 · P99
P50 = 46393037881197844769329919028092780602515119298841_<50>
P99 = 112966079015722151503179720005482232418100365053255767820984303808963205364486267061134585021699491_<99>

Number: 35559_165 N=5240839583066786717102808797593959640532192845212103667267982451818208133709752857084047933147048892935211822889041927310853330956386924574126589931 ( 148 digits) SNFS difficulty: 166 digits. Divisors found: r1=46393037881197844769329919028092780602515119298841 (pp50) r2=112966079015722151503179720005482232418100365053255767820984303808963205364486267061134585021699491 (pp99) Version: Msieve-1.39 Total time: 32.66 hours. Scaled time: 84.30 units (timescale=2.581). Factorization parameters were as follows: n: 5240839583066786717102808797593959640532192845212103667267982451818208133709752857084047933147048892935211822889041927310853330956386924574126589931 m: 2000000000000000000000000000000000 deg: 5 c5: 1 c0: 31 skew: 1.99 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2100000, 3700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 760137 x 760385 Total sieving time: 32.66 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,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 32.66 hours. --------- CPU info (if available) ----------
(44·10¹³⁹-17)/9 = 4(8)₁₃₈7_<140> = 31 · 47 · C137
C137 = P42 · P96
P42 = 247241610213621214642616779079680643653573_<42>
P96 = 135715375271042152313074475367181093008863209189025885597583020412222531793776330579073842334267_<96>

Number: 48887_139 N=33554487912758331426828338290246320445359566842065126210630671852360253183863341721955311522916190040417905894913444673225043849614885991 ( 137 digits) SNFS difficulty: 141 digits. Divisors found: r1=247241610213621214642616779079680643653573 (pp42) r2=135715375271042152313074475367181093008863209189025885597583020412222531793776330579073842334267 (pp96) Version: Msieve-1.39 Total time: 3.89 hours. Scaled time: 4.63 units (timescale=1.189). Factorization parameters were as follows: n: 33554487912758331426828338290246320445359566842065126210630671852360253183863341721955311522916190040417905894913444673225043849614885991 m: 10000000000000000000000000000 deg: 5 c5: 22 c0: -85 skew: 1.31 type: snfs lss: 1 rlim: 1590000 alim: 1590000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1590000/1590000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [795000, 1495001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 221252 x 221500 Total sieving time: 3.89 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000 total time: 3.89 hours. --------- CPU info (if available) ----------
Feb 28, 2009: By Serge Batalov / PFGW / Feb 28, 2009
(35·10⁵⁶⁸⁹⁸-17)/9 = 3(8)₅₆₈₉₇7_<56899> is PRP.
Feb 27, 2009 (6th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 27, 2009
(43·10¹⁸⁵+11)/9 = 4(7)₁₈₄9_<186> = C186
C186 = P76 · P110
P76 = 6092161031711376573217867290800843504998437328608501888921342869012660587079_<76>
P110 = 78425008021096752968798242838308148647291250676054244791585916514921983250238038209750337111800904899951773301_<110>

Number: 47779_185 N=477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 186 digits) SNFS difficulty: 186 digits. Divisors found: r1=6092161031711376573217867290800843504998437328608501888921342869012660587079 r2=78425008021096752968798242838308148647291250676054244791585916514921983250238038209750337111800904899951773301 Version: Total time: 142.37 hours. Scaled time: 339.83 units (timescale=2.387). Factorization parameters were as follows: n: 477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 m: 10000000000000000000000000000000000000 deg: 5 c5: 43 c0: 11 skew: 0.76 type: snfs lss: 1 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 8100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 20439229 Max relations in full relation-set: Initial matrix: Pruned matrix : 1810029 x 1810277 Total sieving time: 129.27 hours. Total relation processing time: 3.92 hours. Matrix solve time: 8.89 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000 total time: 142.37 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 27, 2009 (5th): By Sinkiti Sibata / GGNFS, Msieve / Feb 27, 2009
(44·10¹⁴³-53)/9 = 4(8)₁₄₂3_<144> = 3² · 471671 · 5072605471_<10> · C128
C128 = P52 · P76
P52 = 3166361761003036680303142908682110958372709395350709_<52>
P76 = 7170292373088502235906232820143055411742367312635436307677957012591149333623_<76>

Number: 48883_143 N=22703739585359152834153630462313097456102458702056872748467242203681433200574940099692377148680851774990929417252110879730588707 ( 128 digits) SNFS difficulty: 146 digits. Divisors found: r1=3166361761003036680303142908682110958372709395350709 (pp52) r2=7170292373088502235906232820143055411742367312635436307677957012591149333623 (pp76) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 19.94 hours. Scaled time: 9.41 units (timescale=0.472). Factorization parameters were as follows: name: 48883_143 n: 22703739585359152834153630462313097456102458702056872748467242203681433200574940099692377148680851774990929417252110879730588707 m: 100000000000000000000000000000 deg: 5 c5: 11 c0: -1325 skew: 2.61 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [950000, 2450001) Primes: RFBsize:142029, AFBsize:142523, largePrimes:4104424 encountered Relations: rels:4229370, finalFF:348448 Max relations in full relation-set: 28 Initial matrix: 284618 x 348448 with sparse part having weight 35413561. Pruned matrix : 262138 x 263625 with weight 24173663. Total sieving time: 17.49 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.14 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 19.94 hours. --------- CPU info (if available) ----------
(44·10¹⁵³-53)/9 = 4(8)₁₅₂3_<154> = 17 · 1283 · 4019 · C146
C146 = P63 · P84
P63 = 200326200647338176783717118787364154206526143935667093756398611_<63>
P84 = 278406152648363885257167153873463163169044380062157145420913892618617561178604359417_<84>

Number: 48883_153 N=55772046796889604611565433373184869108095366970314153076733218930415322606287422908723895375387076542638241231242160565438609419535425162563569787 ( 146 digits) SNFS difficulty: 156 digits. Divisors found: r1=200326200647338176783717118787364154206526143935667093756398611 r2=278406152648363885257167153873463163169044380062157145420913892618617561178604359417 Version: Total time: 21.35 hours. Scaled time: 54.53 units (timescale=2.554). Factorization parameters were as follows: name: 48883_153 n: 55772046796889604611565433373184869108095366970314153076733218930415322606287422908723895375387076542638241231242160565438609419535425162563569787 m: 10000000000000000000000000000000 deg: 5 c5: 11 c0: -1325 skew: 2.61 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 556380 x 556627 Total sieving time: 21.35 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,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 21.35 hours. --------- CPU info (if available) ----------
Feb 27, 2009 (4th): By Ignacio Santos / GGNFS, Msieve / Feb 27, 2009
(44·10¹⁶¹-53)/9 = 4(8)₁₆₀3_<162> = 3³ · 127 · 557 · 809 · C153
C153 = P69 · P85
P69 = 270753400153194627352563532766388049026002628614359930789354579172611_<69>
P85 = 1168597750273654958778265117257632928376975109003170721228878788746067186593553414889_<85>

Number: 48883_161 N=316401814297965907394291797154972600399998639673545127845303781978003377261891752987666719911842619277112628571479923032120541297983200838818775228405179 ( 153 digits) SNFS difficulty: 163 digits. Divisors found: r1=270753400153194627352563532766388049026002628614359930789354579172611 (pp69) r2=1168597750273654958778265117257632928376975109003170721228878788746067186593553414889 (pp85) Version: Msieve-1.39 Total time: 38.09 hours. Scaled time: 97.94 units (timescale=2.571). Factorization parameters were as follows: n: 316401814297965907394291797154972600399998639673545127845303781978003377261891752987666719911842619277112628571479923032120541297983200838818775228405179 m: 200000000000000000000000000000000 deg: 5 c5: 55 c0: -212 skew: 1.31 type: snfs lss: 1 rlim: 3700000 alim: 3700000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3700000/3700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1850000, 3850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 695008 x 695256 Total sieving time: 38.09 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,163,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000 total time: 38.09 hours. --------- CPU info (if available) ----------
(44·10¹⁷¹-53)/9 = 4(8)₁₇₀3_<172> = C172
C172 = P59 · P113
P59 = 75059015380479339613706194125465158146139625871231697571901_<59>
P113 = 65133933133905008261265014533189153316103348018734416649842781849800236873376647775219658789236125956277334331183_<113>

Number: 48883_171 N=4888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 ( 172 digits) SNFS difficulty: 173 digits. Divisors found: r1=75059015380479339613706194125465158146139625871231697571901 (pp59) r2=65133933133905008261265014533189153316103348018734416649842781849800236873376647775219658789236125956277334331183 (pp113) Version: Msieve-1.39 Total time: 84.05 hours. Scaled time: 146.16 units (timescale=1.739). Factorization parameters were as follows: n: 4888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 m: 20000000000000000000000000000000000 deg: 5 c5: 55 c0: -212 skew: 1.31 type: snfs lss: 1 rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2700000, 7100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1078148 x 1078396 Total sieving time: 84.05 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,173,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000 total time: 84.05 hours. --------- CPU info (if available) ----------
Feb 27, 2009 (3rd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Feb 27, 2009
(44·10¹⁴¹-53)/9 = 4(8)₁₄₀3_<142> = 39161 · 123787 · 171881 · 6897173 · 269695261837_<12> · 6199736064021385889457145645067_<31> · C78
C78 = P31 · P47
P31 = 8369302132878724900360524015317_<31>
P47 = 60792023715215966066345455742641376351243291791_<47>

GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM] Input number is 508786813741771010621372438944508866566847913331596410044410894001651984362747 (78 digits) Using B1=452000, B2=347971482, polynomial Dickson(3), sigma=880082943 Step 1 took 3437ms Step 2 took 1875ms ********** Factor found in step 2: 8369302132878724900360524015317 Found probable prime factor of 31 digits: 8369302132878724900360524015317 Probable prime cofactor 60792023715215966066345455742641376351243291791 has 47 digits
(43·10¹⁷⁹-61)/9 = 4(7)₁₇₈1_<180> = 3² · 7 · C178
C178 = P38 · P45 · P96
P38 = 90888011291841593728293037617292729219_<38>
P45 = 509748305905847001126736992629137395340449583_<45>
P96 = 163690322664170779588161072669009425584870041615565614512563841959454808119330543582803439622121_<96>

Number: n N=7583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917 ( 178 digits) SNFS difficulty: 181 digits. Divisors found: Fri Feb 27 08:19:29 2009 prp38 factor: 90888011291841593728293037617292729219 Fri Feb 27 08:19:29 2009 prp45 factor: 509748305905847001126736992629137395340449583 Fri Feb 27 08:19:29 2009 prp96 factor: 163690322664170779588161072669009425584870041615565614512563841959454808119330543582803439622121 Fri Feb 27 08:19:29 2009 elapsed time 03:37:09 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 8.15 hours. Scaled time: 16.43 units (timescale=2.016). Factorization parameters were as follows: name: KA_4_7_178_1 n: 7583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917 deg: 5 c5: 43 c0: -610 m: 1000000000000000000000000000000000000 skew: 1.70 type: snfs rlim: 8000000 alim: 8000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [4000000, 5599990) Primes: RFBsize:539777, AFBsize:539266, largePrimes:30064188 encountered Relations: rels:23614284, finalFF:235540 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 3257735 hash collisions in 34545968 relations Msieve: matrix is 1564511 x 1564759 (427.1 MB) Total sieving time: 7.71 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,181,5,0,0,0,0,0,0,0,0,8000000,8000000,29,29,58,58,2.5,2.5,100000 total time: 8.15 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454) Total of 4 processors activated (22643.71 BogoMIPS).
Feb 27, 2009 (2nd): Factorizations of 488...887 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Feb 27, 2009: By Serge Batalov / PFGW / Feb 27, 2009
(61·10⁵²⁷⁶³-7)/9 = 6(7)₅₂₇₆₃_<52764> is PRP.
(76·10⁴⁰⁷⁴³-31)/9 = 8(4)₄₀₇₄₂1_<40744> is PRP.
Feb 26, 2009 (7th): By matsui / GGNFS / Feb 26, 2009
(86·10¹⁸¹+31)/9 = 9(5)₁₈₀9_<182> = 3³ · 11 · 38219 · C175
C175 = P53 · P123
P53 = 32928690580332125411741090087710651306629243139878707_<53>
P123 = 255649949770519847347395270618009705435442504020620821952131412204032479590771377721477095985577060681219537413453936952959_<123>

N=8418218092870897903880335538818376034304121264940636341132313176468061618263234097127070662630346440900237586586145040200760014348950625555339324814077046096605885076424744013 ( 175 digits) SNFS difficulty: 183 digits. Divisors found: r1=32928690580332125411741090087710651306629243139878707 (pp53) r2=255649949770519847347395270618009705435442504020620821952131412204032479590771377721477095985577060681219537413453936952959 (pp123) Version: GGNFS-0.77.1-20060722-nocona
Feb 26, 2009 (6th): By Robert Backstrom / Msieve, GGNFS / Feb 26, 2009
(44·10¹¹⁰-53)/9 = 4(8)₁₀₉3_<111> = 3 · 7² · 73 · 233 · 761 · 60433935059_<11> · C91
C91 = P40 · P51
P40 = 5206728456358460814368918326710497623619_<40>
P51 = 816551520937130805126208331277646872665420305239041_<51>

Thu Feb 26 12:33:30 2009 Thu Feb 26 12:33:30 2009 Thu Feb 26 12:33:30 2009 Msieve v. 1.39 Thu Feb 26 12:33:30 2009 random seeds: 1c0eaa08 647b5fed Thu Feb 26 12:33:30 2009 factoring 4251562040146140473214122361854652982848323985713055697350360731657598250913534246242509379 (91 digits) Thu Feb 26 12:33:30 2009 searching for 15-digit factors Thu Feb 26 12:33:31 2009 commencing quadratic sieve (91-digit input) Thu Feb 26 12:33:32 2009 using multiplier of 3 Thu Feb 26 12:33:32 2009 using 64kb Opteron sieve core Thu Feb 26 12:33:32 2009 sieve interval: 18 blocks of size 65536 Thu Feb 26 12:33:32 2009 processing polynomials in batches of 6 Thu Feb 26 12:33:32 2009 using a sieve bound of 1719869 (64602 primes) Thu Feb 26 12:33:32 2009 using large prime bound of 165107424 (27 bits) Thu Feb 26 12:33:32 2009 using double large prime bound of 619412223763104 (42-50 bits) Thu Feb 26 12:33:32 2009 using trial factoring cutoff of 50 bits Thu Feb 26 12:33:32 2009 polynomial 'A' values have 12 factors Thu Feb 26 14:20:01 2009 64779 relations (16935 full + 47844 combined from 763205 partial), need 64698 Thu Feb 26 14:20:02 2009 begin with 780140 relations Thu Feb 26 14:20:03 2009 reduce to 161345 relations in 11 passes Thu Feb 26 14:20:03 2009 attempting to read 161345 relations Thu Feb 26 14:20:04 2009 recovered 161345 relations Thu Feb 26 14:20:04 2009 recovered 140533 polynomials Thu Feb 26 14:20:05 2009 attempting to build 64779 cycles Thu Feb 26 14:20:05 2009 found 64779 cycles in 6 passes Thu Feb 26 14:20:05 2009 distribution of cycle lengths: Thu Feb 26 14:20:05 2009 length 1 : 16935 Thu Feb 26 14:20:05 2009 length 2 : 12091 Thu Feb 26 14:20:05 2009 length 3 : 11203 Thu Feb 26 14:20:05 2009 length 4 : 8860 Thu Feb 26 14:20:05 2009 length 5 : 6186 Thu Feb 26 14:20:05 2009 length 6 : 4047 Thu Feb 26 14:20:05 2009 length 7 : 2466 Thu Feb 26 14:20:05 2009 length 9+: 2991 Thu Feb 26 14:20:05 2009 largest cycle: 21 relations Thu Feb 26 14:20:06 2009 matrix is 64602 x 64779 (16.1 MB) with weight 3955790 (61.07/col) Thu Feb 26 14:20:06 2009 sparse part has weight 3955790 (61.07/col) Thu Feb 26 14:20:07 2009 filtering completed in 3 passes Thu Feb 26 14:20:07 2009 matrix is 60649 x 60713 (15.2 MB) with weight 3741452 (61.63/col) Thu Feb 26 14:20:07 2009 sparse part has weight 3741452 (61.63/col) Thu Feb 26 14:20:08 2009 saving the first 48 matrix rows for later Thu Feb 26 14:20:08 2009 matrix is 60601 x 60713 (9.7 MB) with weight 2963658 (48.81/col) Thu Feb 26 14:20:08 2009 sparse part has weight 2177748 (35.87/col) Thu Feb 26 14:20:08 2009 matrix includes 64 packed rows Thu Feb 26 14:20:08 2009 using block size 21845 for processor cache size 512 kB Thu Feb 26 14:20:08 2009 commencing Lanczos iteration Thu Feb 26 14:20:08 2009 memory use: 9.4 MB Thu Feb 26 14:20:43 2009 lanczos halted after 960 iterations (dim = 60599) Thu Feb 26 14:20:43 2009 recovered 16 nontrivial dependencies Thu Feb 26 14:20:44 2009 prp40 factor: 5206728456358460814368918326710497623619 Thu Feb 26 14:20:44 2009 prp51 factor: 816551520937130805126208331277646872665420305239041 Thu Feb 26 14:20:44 2009 elapsed time 01:47:14
(44·10¹²⁵-53)/9 = 4(8)₁₂₄3_<126> = 3² · 71 · 571 · 30429810494761178782216697_<26> · C95
C95 = P41 · P55
P41 = 21359195843830967403453380962112507429977_<41>
P55 = 2061527132411459461397036590954458932353735933027377703_<55>

Thu Feb 26 12:35:45 2009 Thu Feb 26 12:35:45 2009 Thu Feb 26 12:35:45 2009 Msieve v. 1.39 Thu Feb 26 12:35:45 2009 random seeds: 4e3e03e0 16ce5ef6 Thu Feb 26 12:35:45 2009 factoring 44032561758547617341803247676823990868053192972587863182516175908299645509602916744544203602831 (95 digits) Thu Feb 26 12:35:45 2009 searching for 15-digit factors Thu Feb 26 12:35:46 2009 commencing quadratic sieve (95-digit input) Thu Feb 26 12:35:46 2009 using multiplier of 1 Thu Feb 26 12:35:46 2009 using 64kb Opteron sieve core Thu Feb 26 12:35:46 2009 sieve interval: 18 blocks of size 65536 Thu Feb 26 12:35:46 2009 processing polynomials in batches of 6 Thu Feb 26 12:35:46 2009 using a sieve bound of 2162071 (79710 primes) Thu Feb 26 12:35:46 2009 using large prime bound of 324310650 (28 bits) Thu Feb 26 12:35:46 2009 using double large prime bound of 2087998231332900 (43-51 bits) Thu Feb 26 12:35:46 2009 using trial factoring cutoff of 51 bits Thu Feb 26 12:35:46 2009 polynomial 'A' values have 12 factors Thu Feb 26 14:29:17 2009 79910 relations (20477 full + 59433 combined from 1182055 partial), need 79806 Thu Feb 26 14:29:19 2009 begin with 1202532 relations Thu Feb 26 14:29:20 2009 reduce to 204460 relations in 10 passes Thu Feb 26 14:29:20 2009 attempting to read 204460 relations Thu Feb 26 14:29:23 2009 recovered 204460 relations Thu Feb 26 14:29:23 2009 recovered 182671 polynomials Thu Feb 26 14:29:23 2009 attempting to build 79910 cycles Thu Feb 26 14:29:23 2009 found 79910 cycles in 5 passes Thu Feb 26 14:29:24 2009 distribution of cycle lengths: Thu Feb 26 14:29:24 2009 length 1 : 20477 Thu Feb 26 14:29:24 2009 length 2 : 14443 Thu Feb 26 14:29:24 2009 length 3 : 13675 Thu Feb 26 14:29:24 2009 length 4 : 10718 Thu Feb 26 14:29:24 2009 length 5 : 7849 Thu Feb 26 14:29:24 2009 length 6 : 5123 Thu Feb 26 14:29:24 2009 length 7 : 3277 Thu Feb 26 14:29:24 2009 length 9+: 4348 Thu Feb 26 14:29:24 2009 largest cycle: 21 relations Thu Feb 26 14:29:24 2009 matrix is 79710 x 79910 (21.1 MB) with weight 5207940 (65.17/col) Thu Feb 26 14:29:24 2009 sparse part has weight 5207940 (65.17/col) Thu Feb 26 14:29:25 2009 filtering completed in 3 passes Thu Feb 26 14:29:25 2009 matrix is 75065 x 75129 (20.0 MB) with weight 4934428 (65.68/col) Thu Feb 26 14:29:25 2009 sparse part has weight 4934428 (65.68/col) Thu Feb 26 14:29:25 2009 saving the first 48 matrix rows for later Thu Feb 26 14:29:25 2009 matrix is 75017 x 75129 (13.0 MB) with weight 3925757 (52.25/col) Thu Feb 26 14:29:25 2009 sparse part has weight 2952697 (39.30/col) Thu Feb 26 14:29:25 2009 matrix includes 64 packed rows Thu Feb 26 14:29:25 2009 using block size 30051 for processor cache size 1024 kB Thu Feb 26 14:29:26 2009 commencing Lanczos iteration Thu Feb 26 14:29:26 2009 memory use: 12.2 MB Thu Feb 26 14:30:04 2009 lanczos halted after 1188 iterations (dim = 75016) Thu Feb 26 14:30:04 2009 recovered 17 nontrivial dependencies Thu Feb 26 14:30:05 2009 prp41 factor: 21359195843830967403453380962112507429977 Thu Feb 26 14:30:05 2009 prp55 factor: 2061527132411459461397036590954458932353735933027377703 Thu Feb 26 14:30:05 2009 elapsed time 01:54:20
(37·10²⁰⁵+17)/9 = 4(1)₂₀₄3_<206> = C206
C206 = P53 · P75 · P79
P53 = 38708903282648616349050646735593058494904684196090851_<53>
P75 = 523279404482581894105023739895022302701579043553621531881177081933138648717_<75>
P79 = 2029619869509639122374709122919684913926210413942382626800386423565291654417839_<79>

Number: n N=41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 ( 206 digits) SNFS difficulty: 206 digits. Divisors found: Thu Feb 26 18:48:16 2009 prp53 factor: 38708903282648616349050646735593058494904684196090851 Thu Feb 26 18:48:16 2009 prp75 factor: 523279404482581894105023739895022302701579043553621531881177081933138648717 Thu Feb 26 18:48:16 2009 prp79 factor: 2029619869509639122374709122919684913926210413942382626800386423565291654417839 Thu Feb 26 18:48:16 2009 elapsed time 16:58:34 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 111.52 hours. Scaled time: 224.70 units (timescale=2.015). Factorization parameters were as follows: name: KA_4_1_204_3 n: 41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 deg: 5 c5: 37 c0: 17 m: 100000000000000000000000000000000000000000 skew: 0.86 type: snfs rlim: 11000000 alim: 11000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 11000000/11000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [5500000, 32599990) Primes: RFBsize:726517, AFBsize:727428, largePrimes:36880338 encountered Relations: rels:31940379, finalFF:85284 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 8266595 hash collisions in 45511633 relations Msieve: matrix is 3184069 x 3184317 (863.6 MB) Total sieving time: 110.22 hours. Total relation processing time: 1.30 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,206,5,0,0,0,0,0,0,0,0,11000000,11000000,29,29,58,58,2.5,2.5,100000 total time: 111.52 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454) Total of 4 processors activated (22643.71 BogoMIPS).
Feb 26, 2009 (5th): By Serge Batalov / GMP-ECM 6.2.1 / Feb 26, 2009
(44·10²⁰⁰-53)/9 = 4(8)₁₉₉3_<201> = 3 · 7 · 23 · 490151 · 603522709 · 12983684697563_<14> · 485460576989519_<15> · C156
C156 = P34 · C122
P34 = 7046882295480502467634870497200027_<34>
C122 = [77035442509364829592824984655079160994427570285601319384761126720874299891224577489225266938170642713438522459468169082381_<122>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2540175551 Step 1 took 32875ms ********** Factor found in step 1: 7046882295480502467634870497200027 Found probable prime factor of 34 digits: 7046882295480502467634870497200027 Composite cofactor has 122 digits
(44·10²⁰⁴-53)/9 = 4(8)₂₀₃3_<205> = 31 · 131 · C202
C202 = P35 · C167
P35 = 75956254527312360496911296790966809_<35>
C167 = [15849429573449204111210382410071127103818486388678547282497647139185547003406911430474426852551951533584065408618982135342664560514133979604513938702039208944975046567_<167>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=100595225 Step 1 took 63234ms Step 2 took 31359ms ********** Factor found in step 2: 75956254527312360496911296790966809 Found probable prime factor of 35 digits: 75956254527312360496911296790966809 Composite cofactor has 167 digits
(44·10¹⁹²-53)/9 = 4(8)₁₉₁3_<193> = 696457 · 8169034619_<10> · 363391761793_<12> · 8428473113059_<13> · C153
C153 = P30 · P124
P30 = 133396886663428373837032220609_<30>
P124 = 2103175169457846601552806103544676440988572210079484013420789074998367704348399128910180822984955341604439165177509040355947_<124>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2020511789 Step 1 took 29469ms ********** Factor found in step 1: 133396886663428373837032220609 Found probable prime factor of 30 digits: 133396886663428373837032220609 Probable prime cofactor has 124 digits
Feb 26, 2009 (4th): By Ignacio Santos / GGNFS, Msieve / Feb 26, 2009
(4·10¹⁹⁰+41)/9 = (4)₁₈₉9_<190> = 3² · C189
C189 = P40 · P150
P40 = 2948837566996825795307130730192425607301_<40>
P150 = 167465026226166064292399776036696947548186926080316744399282734221869926819933052095255866949131779342147271334939590492205749388252413890515966641861_<150>

Number: 44449_190 N=493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827161 ( 189 digits) SNFS difficulty: 190 digits. Divisors found: r1=2948837566996825795307130730192425607301 (pp40) r2=167465026226166064292399776036696947548186926080316744399282734221869926819933052095255866949131779342147271334939590492205749388252413890515966641861 (pp150) Version: Msieve-1.39 Total time: 258.26 hours. Scaled time: 449.12 units (timescale=1.739). Factorization parameters were as follows: n: 493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827161 m: 100000000000000000000000000000000000000 deg: 5 c5: 4 c0: 41 skew: 1.59 type: snfs lss: 1 rlim: 10500000 alim: 10500000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10500000/10500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5250000, 9550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1923959 x 1924207 Total sieving time: 258.26 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,190,5,0,0,0,0,0,0,0,0,10500000,10500000,28,28,54,54,2.5,2.5,100000 total time: 258.26 hours. --------- CPU info (if available) ----------
(43·10¹⁶³+11)/9 = 4(7)₁₆₂9_<164> = 7 · 52419239 · 1739922117943453_<16> · C140
C140 = P68 · P73
P68 = 30725208977326294282026917154259056299124533303220352723575950353573_<68>
P73 = 2435636872107711589373030968932924793282530963776468209854648002649046067_<73>

Number: 47779_163 N=74835451888390795421193860921480029591140239303958107726711659068218174860236715990676357673712284630905548931915876695279066763919815047391 ( 140 digits) SNFS difficulty: 166 digits. Divisors found: r1=30725208977326294282026917154259056299124533303220352723575950353573 (pp68) r2=2435636872107711589373030968932924793282530963776468209854648002649046067 (pp73) Version: Msieve-1.39 Total time: 46.46 hours. Scaled time: 119.46 units (timescale=2.571). Factorization parameters were as follows: n: 74835451888390795421193860921480029591140239303958107726711659068218174860236715990676357673712284630905548931915876695279066763919815047391 m: 500000000000000000000000000000000 deg: 5 c5: 344 c0: 275 skew: 0.96 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 4450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 764035 x 764282 Total sieving time: 46.46 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,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 46.46 hours. --------- CPU info (if available) ----------
(44·10¹⁵⁶-53)/9 = 4(8)₁₅₅3_<157> = 23 · 54439171 · C148
C148 = P68 · P81
P68 = 22678645829390954202749404051050551174900006487478899476556840123289_<68>
P81 = 172168505322445876370816162423063654892260575030429034434333933237155428621798959_<81>

Number: 48883_156 N=3904548555183361474972152974898301500498034441516456316616201170811593739854587975847222604768148422814799459053584850965755880391863655682531856151 ( 148 digits) SNFS difficulty: 158 digits. Divisors found: r1=22678645829390954202749404051050551174900006487478899476556840123289 (pp68) r2=172168505322445876370816162423063654892260575030429034434333933237155428621798959 (pp81) Version: Msieve-1.39 Total time: 25.70 hours. Scaled time: 66.08 units (timescale=2.571). Factorization parameters were as follows: n: 3904548555183361474972152974898301500498034441516456316616201170811593739854587975847222604768148422814799459053584850965755880391863655682531856151 m: 20000000000000000000000000000000 deg: 5 c5: 55 c0: -212 skew: 1.31 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1500000, 2900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 569817 x 570065 Total sieving time: 25.70 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 25.70 hours. --------- CPU info (if available) ----------
(44·10¹³⁵-53)/9 = 4(8)₁₃₄3_<136> = 1097 · 7356997 · 4215858307_<10> · C117
C117 = P42 · P75
P42 = 332560041044241248900484291976845162767167_<42>
P75 = 432062813561467316727657432335915267712627225383416457686955661487805189323_<75>

Number: 48883_135 N=143686827011691925346526157094251099188322446463017116723156638837921518214692501721207858184843360138281649003357941 ( 117 digits) SNFS difficulty: 136 digits. Divisors found: r1=332560041044241248900484291976845162767167 (pp42) r2=432062813561467316727657432335915267712627225383416457686955661487805189323 (pp75) Version: Msieve-1.39 Total time: 3.60 hours. Scaled time: 9.25 units (timescale=2.571). Factorization parameters were as follows: n: 143686827011691925346526157094251099188322446463017116723156638837921518214692501721207858184843360138281649003357941 m: 1000000000000000000000000000 deg: 5 c5: 44 c0: -53 skew: 1.04 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1265001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 190904 x 191152 Total sieving time: 3.60 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,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 3.60 hours. --------- CPU info (if available) ----------
Feb 26, 2009 (3rd): By Sinkiti Sibata / GGNFS, Msieve / Feb 26, 2009
(44·10¹³⁹-71)/9 = 4(8)₁₃₈1_<140> = 1559 · 3121 · 30390539151758346199_<20> · C114
C114 = P31 · P83
P31 = 6461651849899623748232000554729_<31>
P83 = 51166807863622394221848695179553706577606524639170306964578149461210274319629978249_<83>

Number: 48881_139 N=330622098685434258936754116359866216587190321981358794573361525938189338670519776376487359516392275259786204089521 ( 114 digits) SNFS difficulty: 141 digits. Divisors found: r1=6461651849899623748232000554729 (pp31) r2=51166807863622394221848695179553706577606524639170306964578149461210274319629978249 (pp83) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 11.95 hours. Scaled time: 5.65 units (timescale=0.473). Factorization parameters were as follows: name: 48881_139 n: 330622098685434258936754116359866216587190321981358794573361525938189338670519776376487359516392275259786204089521 m: 10000000000000000000000000000 deg: 5 c5: 22 c0: -355 skew: 1.74 type: snfs lss: 1 rlim: 1590000 alim: 1590000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1590000/1590000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [795000, 1695001) Primes: RFBsize:120451, AFBsize:120405, largePrimes:3586520 encountered Relations: rels:3542114, finalFF:272496 Max relations in full relation-set: 28 Initial matrix: 240922 x 272496 with sparse part having weight 24250856. Pruned matrix : 230443 x 231711 with weight 18069601. Total sieving time: 10.45 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.28 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000 total time: 11.95 hours. --------- CPU info (if available) ----------
(31·10¹⁹¹+23)/9 = 3(4)₁₉₀7_<192> = 479 · C189
C189 = P75 · P114
P75 = 721654199380406659494358792402938501466495953581632403259971904944621801459_<75>
P114 = 996447743020499121699374464603815726961346486644180235752675167236186326151725810337002716980797888594745956623227_<114>

Number: 34447_191 N=719090698213871491533286940385061470656460218046856877754581303641846439341220134539549988401762932034330781721178380886105311992577128276501971700301554163767107399675249362096961261888193 ( 189 digits) SNFS difficulty: 192 digits. Divisors found: r1=721654199380406659494358792402938501466495953581632403259971904944621801459 r2=996447743020499121699374464603815726961346486644180235752675167236186326151725810337002716980797888594745956623227 Version: Total time: 366.43 hours. Scaled time: 935.87 units (timescale=2.554). Factorization parameters were as follows: name: 34447_191 n: 719090698213871491533286940385061470656460218046856877754581303641846439341220134539549988401762932034330781721178380886105311992577128276501971700301554163767107399675249362096961261888193 m: 100000000000000000000000000000000000000 deg: 5 c5: 310 c0: 23 skew: 0.59 type: snfs lss: 1 rlim: 11300000 alim: 11300000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 11300000/11300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [5650000, 10350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2016938 x 2017186 Total sieving time: 366.43 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,192,5,0,0,0,0,0,0,0,0,11300000,11300000,28,28,55,55,2.5,2.5,100000 total time: 366.43 hours. --------- CPU info (if available) ----------
Feb 26, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Feb 26, 2009
(44·10¹²⁸-53)/9 = 4(8)₁₂₇3_<129> = 3 · 7 · 109 · 613 · 11383 · C119
C119 = P41 · P79
P41 = 11596514298237038639067575234023927441349_<41>
P79 = 2639488026190419162144058720175270446979675692915179501209940086668045827264157_<79>

Number: 48883_128 N=30608860635742654933980094618371424703761115776636432481511316570990030268286904377930692261821975632452045301747427793 ( 119 digits) SNFS difficulty: 131 digits. Divisors found: r1=11596514298237038639067575234023927441349 r2=2639488026190419162144058720175270446979675692915179501209940086668045827264157 Version: Total time: 2.71 hours. Scaled time: 2.57 units (timescale=0.950). Factorization parameters were as follows: n: 30608860635742654933980094618371424703761115776636432481511316570990030268286904377930692261821975632452045301747427793 m: 100000000000000000000000000 deg: 5 c5: 11 c0: -1325 skew: 2.61 type: snfs lss: 1 rlim: 1070000 alim: 1070000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1070000/1070000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [535000, 935001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 164487 x 164734 Total sieving time: 2.71 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,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000 total time: 2.71 hours. --------- CPU info (if available) ----------
(44·10¹²⁴-53)/9 = 4(8)₁₂₃3_<125> = 27857387 · 27098180189257291_<17> · C101
C101 = P33 · P69
P33 = 105879858460003669738444647465173_<33>
P69 = 611668775478348043887642134207958264068062222551430503567302962499263_<69>

Number: 48883_124 N=64763403372051254345862180645606745671444139005957866904918665429237488531590248316682524769830667499 ( 101 digits) SNFS difficulty: 126 digits. Divisors found: r1=105879858460003669738444647465173 r2=611668775478348043887642134207958264068062222551430503567302962499263 Version: Total time: 2.66 hours. Scaled time: 2.09 units (timescale=0.787). Factorization parameters were as follows: n: 64763403372051254345862180645606745671444139005957866904918665429237488531590248316682524769830667499 m: 10000000000000000000000000 deg: 5 c5: 22 c0: -265 skew: 1.64 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 695001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 114200 x 114440 Total sieving time: 2.66 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,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 2.66 hours. --------- CPU info (if available) ----------
(44·10¹²⁹-53)/9 = 4(8)₁₂₈3_<130> = 19 · 31 · 1904637519067_<13> · C115
C115 = P45 · P71
P45 = 105441685305072759250343963660885215379364893_<45>
P71 = 41330456138185682306653571302025199180323207767883057670613596493709137_<71>

Number: 48883_129 N=4357952949637687480439860834487236713464822412626922260738831005387602493757440039797623836283296431890596931127341 ( 115 digits) SNFS difficulty: 131 digits. Divisors found: r1=105441685305072759250343963660885215379364893 r2=41330456138185682306653571302025199180323207767883057670613596493709137 Version: Total time: 2.55 hours. Scaled time: 2.54 units (timescale=0.997). Factorization parameters were as follows: n: 4357952949637687480439860834487236713464822412626922260738831005387602493757440039797623836283296431890596931127341 m: 100000000000000000000000000 deg: 5 c5: 22 c0: -265 skew: 1.64 type: snfs lss: 1 rlim: 1080000 alim: 1080000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1080000/1080000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [540000, 890001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 138240 x 138488 Total sieving time: 2.55 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,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000 total time: 2.55 hours. --------- CPU info (if available) ----------
Feb 26, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 26, 2009
(44·10¹⁶²-71)/9 = 4(8)₁₆₁1_<163> = 3 · 61 · 21602829725909_<14> · 13890992668947677_<17> · C131
C131 = P55 · P77
P55 = 2919528487754485360741130920221825593218288436977792273_<55>
P77 = 30493160198018619499137574747553107457658730557098544861937924757079677957063_<77>

Number: 48881_162 N=89025649879776563556284994705112048537492877537816182828421619511054800970064111601633295089238610188889885975117868575212627174199 ( 131 digits) SNFS difficulty: 163 digits. Divisors found: r1=2919528487754485360741130920221825593218288436977792273 r2=30493160198018619499137574747553107457658730557098544861937924757079677957063 Version: Total time: 23.99 hours. Scaled time: 57.03 units (timescale=2.377). Factorization parameters were as follows: n: 89025649879776563556284994705112048537492877537816182828421619511054800970064111601633295089238610188889885975117868575212627174199 m: 200000000000000000000000000000000 deg: 5 c5: 275 c0: -142 skew: 0.88 type: snfs lss: 1 rlim: 4400000 alim: 4400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2200000, 4100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9810253 Max relations in full relation-set: Initial matrix: Pruned matrix : 738638 x 738886 Total sieving time: 21.56 hours. Total relation processing time: 0.93 hours. Matrix solve time: 1.17 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 23.99 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(44·10¹⁴¹-53)/9 = 4(8)₁₄₀3_<142> = 39161 · 123787 · 171881 · 6897173 · 269695261837_<12> · C109
C109 = P31 · C78
P31 = 6199736064021385889457145645067_<31>
C78 = [508786813741771010621372438944508866566847913331596410044410894001651984362747_<78>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 3154343958053389376334984624566041695442685230963101653023859921211386889423050385418406800432231574239119049 (109 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1434853449 Step 1 took 3287ms Step 2 took 1989ms ********** Factor found in step 2: 6199736064021385889457145645067 Found probable prime factor of 31 digits: 6199736064021385889457145645067 Composite cofactor 508786813741771010621372438944508866566847913331596410044410894001651984362747 has 78 digits
(44·10¹¹¹-53)/9 = 4(8)₁₁₀3_<112> = 19 · 107 · C109
C109 = P47 · P63
P47 = 15072748997352795060939680449363695294889116749_<47>
P63 = 159543943113817436805969360550316504075555966470480954857298799_<63>

Number: 48883_111 N=2404765808602503142591681696452970432311307864677269497731868612340820899601027490845493796797289173088484451 ( 109 digits) SNFS difficulty: 113 digits. Divisors found: r1=15072748997352795060939680449363695294889116749 r2=159543943113817436805969360550316504075555966470480954857298799 Version: Total time: 0.55 hours. Scaled time: 1.31 units (timescale=2.380). Factorization parameters were as follows: n: 2404765808602503142591681696452970432311307864677269497731868612340820899601027490845493796797289173088484451 m: 20000000000000000000000 deg: 5 c5: 55 c0: -212 skew: 1.31 type: snfs lss: 1 rlim: 400000 alim: 400000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [200000, 400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 1137031 Max relations in full relation-set: Initial matrix: Pruned matrix : 51705 x 51933 Total sieving time: 0.50 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,400000,400000,25,25,45,45,2.2,2.2,25000 total time: 0.55 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 25, 2009 (7th): By Robert Backstrom / GGNFS, Msieve / Feb 25, 2009
(44·10¹⁴⁸-71)/9 = 4(8)₁₄₇1_<149> = 7 · C148
C148 = P45 · P104
P45 = 473996607386740060872943445846528011842562499_<45>
P104 = 14734550575440180609780035105536363694945692984151226981094395946180645394713692742435856565307183185517_<104>

Number: n N=6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126983 ( 148 digits) SNFS difficulty: 151 digits. Divisors found: Wed Feb 25 16:18:01 2009 prp45 factor: 473996607386740060872943445846528011842562499 Wed Feb 25 16:18:01 2009 prp104 factor: 14734550575440180609780035105536363694945692984151226981094395946180645394713692742435856565307183185517 Wed Feb 25 16:18:01 2009 elapsed time 01:34:40 (Msieve 1.39 - dependency 6) Version: GGNFS-0.77.1-20051202-athlon Total time: 22.68 hours. Scaled time: 39.73 units (timescale=1.752). Factorization parameters were as follows: name: KA_4_8_147_1 n: 6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126983 deg: 5 c5: 11 c0: -1775 m: 1000000000000000000000000000000 skew: 2.76 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1000000, 1788991) Primes: RFBsize:148933, AFBsize:149372, largePrimes:13961450 encountered Relations: rels:13132793, finalFF:269448 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1051593 hash collisions in 14069728 relations Msieve: matrix is 367270 x 367518 (97.5 MB) Total sieving time: 22.02 hours. Total relation processing time: 0.65 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,56,56,2.5,2.5,100000 total time: 22.68 hours. --------- CPU info (if available) ----------
Feb 25, 2009 (6th): By Sinkiti Sibata / GGNFS / Feb 25, 2009
(44·10¹³⁶-71)/9 = 4(8)₁₃₅1_<137> = 7 · 41 · 45481 · 3280681 · C124
C124 = P34 · P90
P34 = 2744064447066890196809404077767207_<34>
P90 = 416044662604396313993951723092527975044912145201118051288551518737312394333927471726272169_<90>

Number: 48881_136 N=1141653367044663660491761682722608073379051329153751902242675265147625385123173999076345161864440171891051539400931104961983 ( 124 digits) SNFS difficulty: 138 digits. Divisors found: r1=2744064447066890196809404077767207 (pp34) r2=416044662604396313993951723092527975044912145201118051288551518737312394333927471726272169 (pp90) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 9.29 hours. Scaled time: 4.39 units (timescale=0.472). Factorization parameters were as follows: name: 48881_136 n: 1141653367044663660491761682722608073379051329153751902242675265147625385123173999076345161864440171891051539400931104961983 m: 2000000000000000000000000000 deg: 5 c5: 55 c0: -284 skew: 1.39 type: snfs lss: 1 rlim: 1410000 alim: 1410000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1410000/1410000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [705000, 1455001) Primes: RFBsize:107805, AFBsize:108301, largePrimes:3367603 encountered Relations: rels:3384708, finalFF:322308 Max relations in full relation-set: 28 Initial matrix: 216173 x 322308 with sparse part having weight 27607988. Pruned matrix : 185337 x 186481 with weight 12402631. Total sieving time: 8.46 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.61 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000 total time: 9.29 hours. --------- CPU info (if available) ----------
(44·10¹³⁷-71)/9 = 4(8)₁₃₆1_<138> = 37 · C137
C137 = P33 · P104
P33 = 340868543207612725222075573719347_<33>
P104 = 38763369270966856217289969579602950513973542633663421837299638535905817359925420336650549634976872218479_<104>

Number: 48881_137 N=13213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213 ( 137 digits) SNFS difficulty: 138 digits. Divisors found: r1=340868543207612725222075573719347 (pp33) r2=38763369270966856217289969579602950513973542633663421837299638535905817359925420336650549634976872218479 (pp104) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 11.13 hours. Scaled time: 4.76 units (timescale=0.428). Factorization parameters were as follows: name: 48881_137 n: 13213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213 m: 2000000000000000000000000000 deg: 5 c5: 275 c0: -142 skew: 0.88 type: snfs lss: 1 rlim: 1450000 alim: 1450000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1450000/1450000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [725000, 1625001) Primes: RFBsize:110630, AFBsize:110661, largePrimes:3552440 encountered Relations: rels:3600847, finalFF:325726 Max relations in full relation-set: 28 Initial matrix: 221357 x 325726 with sparse part having weight 30493824. Pruned matrix : 191788 x 192958 with weight 14833527. Total sieving time: 10.14 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.75 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000 total time: 11.13 hours. --------- CPU info (if available) ----------
Feb 25, 2009 (5th): By Ignacio Santos / GGNFS, Msieve / Feb 25, 2009
(44·10¹⁵⁷-71)/9 = 4(8)₁₅₆1_<158> = 73 · C156
C156 = P57 · P100
P57 = 266760531775608133956050583465012094689794027545223607047_<57>
P100 = 2510531832574284225993222640708878791275251483907369761442063478864181134791112368628433935088415951_<100>

Number: 48881_157 N=669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697 ( 156 digits) SNFS difficulty: 158 digits. Divisors found: r1=266760531775608133956050583465012094689794027545223607047 (pp57) r2=2510531832574284225993222640708878791275251483907369761442063478864181134791112368628433935088415951 (pp100) Version: Msieve-1.39 Total time: 26.26 hours. Scaled time: 67.52 units (timescale=2.571). Factorization parameters were as follows: n: 669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697 m: 20000000000000000000000000000000 deg: 5 c5: 275 c0: -142 skew: 0.88 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor base limits: 3100000/3100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1550000, 2950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 538218 x 538466 Total sieving time: 26.26 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,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 26.26 hours. --------- CPU info (if available) ----------
(44·10¹⁶³-71)/9 = 4(8)₁₆₂1_<164> = 40293606533484649013_<20> · C145
C145 = P70 · P75
P70 = 2090142133341823514836371166394869125392607600423305654469844115347859_<70>
P75 = 580494629132693000760167098993643357602606695180416440687702991593086018143_<75>

Number: 48881_163 N=1213316282528877603116799145583708290172539600829303853559907218216047380074537193956932129439123596354105227950875751697368095787851087630205837 ( 145 digits) SNFS difficulty: 164 digits. Divisors found: r1=2090142133341823514836371166394869125392607600423305654469844115347859 (pp70) r2=580494629132693000760167098993643357602606695180416440687702991593086018143 (pp75) Version: Msieve-1.39 Total time: 42.36 hours. Scaled time: 108.90 units (timescale=2.571). Factorization parameters were as follows: n: 1213316282528877603116799145583708290172539600829303853559907218216047380074537193956932129439123596354105227950875751697368095787851087630205837 m: 200000000000000000000000000000000 deg: 5 c5: 1375 c0: -71 skew: 0.55 type: snfs lss: 1 rlim: 3900000 alim: 3900000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 3900000/3900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1950000, 4150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 732974 x 733222 Total sieving time: 42.36 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,164,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000 total time: 42.36 hours. --------- CPU info (if available) ----------
Feb 25, 2009 (4th): By Erik Branger / GGNFS, Msieve, GMP-ECM / Feb 25, 2009
(44·10¹⁵⁰-71)/9 = 4(8)₁₄₉1_<151> = 3² · 51197 · 4521741435891364483_<19> · C127
C127 = P57 · P71
P57 = 230042934078513792659027921169867040472521633549158310061_<57>
P71 = 10200196105649887861156671475312764849458021711987665441965423462292219_<71>

Number: 48881_150 N=2346483040319930262471884695240655852973736090122040956860740182038035783923398759608186873543390899886975864020261543389715359 ( 127 digits) SNFS difficulty: 151 digits. Divisors found: r1=230042934078513792659027921169867040472521633549158310061 r2=10200196105649887861156671475312764849458021711987665441965423462292219 Version: Total time: 19.56 hours. Scaled time: 20.23 units (timescale=1.034). Factorization parameters were as follows: n: 2346483040319930262471884695240655852973736090122040956860740182038035783923398759608186873543390899886975864020261543389715359 m: 1000000000000000000000000000000 deg: 5 c5: 44 c0: -71 skew: 1.10 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 433086 x 433334 Total sieving time: 19.56 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,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 19.56 hours. --------- CPU info (if available) ----------
(44·10¹⁴³-71)/9 = 4(8)₁₄₂1_<144> = 23 · 37 · 199 · 30302636207_<11> · 4307160298747_<13> · C116
C116 = P38 · P79
P38 = 16407153915374855716140672893295921439_<38>
P79 = 1348102242729470640250881292514087976844275396957524728539042720088578215437399_<79>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 22118520990124458332699006534768476475381642269965611325044514221416868763053419753069680858556126450701594126497161 (116 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=853145556 Step 1 took 31309ms Step 2 took 11544ms ********** Factor found in step 2: 16407153915374855716140672893295921439 Found probable prime factor of 38 digits: 16407153915374855716140672893295921439 Probable prime cofactor 1348102242729470640250881292514087976844275396957524728539042720088578215437399 has 79 digits
(43·10¹⁵⁸+11)/9 = 4(7)₁₅₇9_<159> = 223 · 15507127 · 14607641584687_<14> · C136
C136 = P50 · P87
P50 = 30394270223730515609456784038820180026129302682419_<50>
P87 = 311184469852027455725596184106294444408741498018266638730912165177164854047468063456183_<87>

Number: 47779_158 N=9458224866110844426386379033165601182210899487313783158712396653134358965763386452505542412533445380253027686320324072560877769970946677 ( 136 digits) SNFS difficulty: 161 digits. Divisors found: r1=30394270223730515609456784038820180026129302682419 r2=311184469852027455725596184106294444408741498018266638730912165177164854047468063456183 Version: Total time: 55.26 hours. Scaled time: 43.27 units (timescale=0.783). Factorization parameters were as follows: n: 9458224866110844426386379033165601182210899487313783158712396653134358965763386452505542412533445380253027686320324072560877769970946677 m: 50000000000000000000000000000000 deg: 5 c5: 344 c0: 275 skew: 0.96 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 683237 x 683485 Total sieving time: 55.26 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,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 55.26 hours. --------- CPU info (if available) ----------
Feb 25, 2009 (3rd): By Tyler Cadigan / GGNFS, Msieve / Feb 25, 2009
(10¹⁹⁶+53)/9 = (1)₁₉₅7_<196> = 19 · 739 · 1297 · 175039 · 259878475236857_<15> · 1510283330627080248420932638301_<31> · C138
C138 = P60 · P79
P60 = 276770545742713499359339707621751061182650942179447980819891_<60>
P79 = 3208751188163324485416450871925542565808986088227453373291593937334726893986197_<79>

Number: 11117_196 N=888087817500543690374777485610139659656184329191590913987962706355569305479165393738154255599358025085365797320711586900377767369297044527 ( 138 digits) Divisors found: r1=276770545742713499359339707621751061182650942179447980819891 (pp60) r2=3208751188163324485416450871925542565808986088227453373291593937334726893986197 (pp79) Version: Msieve-1.39 Total time: 949.97 hours. Scaled time: 2407.23 units (timescale=2.534). Factorization parameters were as follows: name: 11117_196 n: 888087817500543690374777485610139659656184329191590913987962706355569305479165393738154255599358025085365797320711586900377767369297044527 skew: 550372.48 # norm 1.41e+19 c5: 111720 c4: 790382198768 c3: -169446067282460132 c2: -364765162766298110614081 c1: 34335070314051591273192601162 c0: 18956319517172044216016560873788003 # alpha 7.114396 Y1: 2556859849182053 Y0: -380242682535105905692270984 type: gnfs lss: 1 rlim: 12900000 alim: 12900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 12900000/12900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6450000, 20450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1955255 x 1955503 Total sieving time: 949.97 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,137,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12900000,12900000,28,28,55,55,2.5,2.5,60000 total time: 949.97 hours. --------- CPU info (if available) ----------
Feb 25, 2009 (2nd): By Serge Batalov / PFGW / Feb 25, 2009
(76·10³⁵⁴²⁷-31)/9 = 8(4)₃₅₄₂₆1_<35428> is PRP.
Feb 25, 2009: Factorizations of 488...883 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Feb 24, 2009 (6th): By Wataru Sakai / GMP-ECM / Feb 24, 2009
(43·10¹⁹⁰+11)/9 = 4(7)₁₈₉9_<191> = C191
C191 = P43 · P47 · P50 · P53
P43 = 2296681587052719423860117114229198911432333_<43>
P47 = 15570079985107990077984373269745574874310941497_<47>
P50 = 60119068484720194413645850533910859383261467146867_<50>
P53 = 22223991954571482014953594682406371807911258907638637_<53>

------- Input number is 47777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 (191 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=208888904 Step 1 took 73125ms Step 2 took 24257ms ********** Factor found in step 2: 2296681587052719423860117114229198911432333 Found probable prime factor of 43 digits: 2296681587052719423860117114229198911432333 Composite cofactor 20802961127532676845791180520483094188690819112594979637430646939415754594890399668350082445540467751199882868417289174626988408216248330568874577663 has 149 digits ---------- Input number is 20802961127532676845791180520483094188690819112594979637430646939415754594890399668350082445540467751199882868417289174626988408216248330568874577663 (149 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1301257518 Step 1 took 185301ms Step 2 took 57413ms ********** Factor found in step 2: 60119068484720194413645850533910859383261467146867 Found probable prime factor of 50 digits: 60119068484720194413645850533910859383261467146867 Composite cofactor 346029332321074431997114693740257714417458796246588353710386771084181929049928930706702480523819589 has 99 digits ---------- Input number is 346029332321074431997114693740257714417458796246588353710386771084181929049928930706702480523819589 (99 digits) Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1827407922 Step 1 took 411700ms Step 2 took 119590ms ********** Factor found in step 2: 15570079985107990077984373269745574874310941497 Found probable prime factor of 47 digits: 15570079985107990077984373269745574874310941497 Probable prime cofactor 22223991954571482014953594682406371807911258907638637 has 53 digits ----------
Feb 24, 2009 (5th): By Ignacio Santos / GGNFS, Msieve / Feb 24, 2009
(7·10¹⁶⁹-43)/9 = (7)₁₆₈3_<169> = 3² · 113 · 49991 · 5632442647674936588605121832519_<31> · C131
C131 = P57 · P75
P57 = 165855014904250974498183632926088661986783788509769529269_<57>
P75 = 163763596475382264171981673046491009331053941417905993150662041160894520369_<75>

Number: 77773_169 N=27161013734198267779787441623856865261526769714349621384721227945530504045181223735394220143911476359430775105460879711466662180261 ( 131 digits) SNFS difficulty: 170 digits. Divisors found: r1=165855014904250974498183632926088661986783788509769529269 (pp57) r2=163763596475382264171981673046491009331053941417905993150662041160894520369 (pp75) Version: Msieve-1.39 Total time: 49.96 hours. Scaled time: 128.45 units (timescale=2.571). Factorization parameters were as follows: n: 27161013734198267779787441623856865261526769714349621384721227945530504045181223735394220143911476359430775105460879711466662180261 m: 5000000000000000000000000000000000 deg: 5 c5: 112 c0: -215 skew: 1.14 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2450000, 4850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 908762 x 909010 Total sieving time: 49.96 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,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 49.96 hours. --------- CPU info (if available) ----------
Feb 24, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 24, 2009
(44·10¹⁴⁰-71)/9 = 4(8)₁₃₉1_<141> = 13 · 37 · 18953839044024127688623_<23> · C116
C116 = P48 · P69
P48 = 509123278828127286216988563096938862260588684297_<48>
P69 = 105328269145172653612757075034695759465207254455961930240426228195271_<69>

Number: 48881_140 N=53625073740481772972409824072405535386545820550053849846053767223604814908309704448037052570648052207497954687359487 ( 116 digits) SNFS difficulty: 141 digits. Divisors found: r1=509123278828127286216988563096938862260588684297 r2=105328269145172653612757075034695759465207254455961930240426228195271 Version: Total time: 4.50 hours. Scaled time: 10.74 units (timescale=2.389). Factorization parameters were as follows: n: 53625073740481772972409824072405535386545820550053849846053767223604814908309704448037052570648052207497954687359487 m: 10000000000000000000000000000 deg: 5 c5: 44 c0: -71 skew: 1.10 type: snfs lss: 1 rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [600000, 1100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3360002 Max relations in full relation-set: Initial matrix: Pruned matrix : 198140 x 198388 Total sieving time: 4.21 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.09 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,48,48,2.3,2.3,50000 total time: 4.50 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(44·10¹⁵³-71)/9 = 4(8)₁₅₂1_<154> = 3 · 29 · 5686565066897115489601_<22> · 480561239432935951772923342469_<30> · C101
C101 = P30 · P71
P30 = 207788945034135538746511370141_<30>
P71 = 98962287285357687567718782537306001105195681542297973648064568489776647_<71>

Number: 48881_153 N=20563269273189518839408618741350859979878540178289245336713437567214603823608381501320185903034897227 ( 101 digits) Divisors found: r1=207788945034135538746511370141 r2=98962287285357687567718782537306001105195681542297973648064568489776647 Version: Total time: 2.54 hours. Scaled time: 6.07 units (timescale=2.385). Factorization parameters were as follows: name: 48881_153 n: 20563269273189518839408618741350859979878540178289245336713437567214603823608381501320185903034897227 skew: 5676.13 # norm 1.86e+14 c5: 344520 c4: -1637807466 c3: -26734948702069 c2: 70694864340124641 c1: 482804719370645285549 c0: 199362126528802262426345 # alpha -6.87 Y1: 36487728641 Y0: -9019391019254834158 # Murphy_E 3.44e-09 # M 15579905984155218821420874809478929204387125506285712518361026215595714425854941028538745894119301401 type: gnfs rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [600000, 1050001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4083039 Max relations in full relation-set: Initial matrix: Pruned matrix : 209301 x 209549 Polynomial selection time: 0.19 hours. Total sieving time: 1.93 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.10 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,26,26,49,49,2.5,2.5,50000 total time: 2.54 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(44·10¹⁵⁵-71)/9 = 4(8)₁₅₄1_<156> = 37 · 97 · 498889679 · 18697682263419627917303_<23> · 440832314293904601752619068922493_<33> · C89
C89 = P39 · P51
P39 = 261205238291645927272402074009059256239_<39>
P51 = 126820397395510759541604069650822061270444804667271_<51>

Tue Feb 24 00:48:15 2009 Tue Feb 24 00:48:15 2009 Tue Feb 24 00:48:15 2009 Msieve v. 1.39 Tue Feb 24 00:48:15 2009 random seeds: 5915a884 8e521e17 Tue Feb 24 00:48:15 2009 factoring 33126152121935620473093722297086995034869661998940995868094417359149617683041111125853769 (89 digits) Tue Feb 24 00:48:16 2009 searching for 15-digit factors Tue Feb 24 00:48:17 2009 commencing quadratic sieve (89-digit input) Tue Feb 24 00:48:17 2009 using multiplier of 1 Tue Feb 24 00:48:17 2009 using VC8 32kb sieve core Tue Feb 24 00:48:17 2009 sieve interval: 32 blocks of size 32768 Tue Feb 24 00:48:17 2009 processing polynomials in batches of 7 Tue Feb 24 00:48:17 2009 using a sieve bound of 1550243 (59000 primes) Tue Feb 24 00:48:17 2009 using large prime bound of 124019440 (26 bits) Tue Feb 24 00:48:17 2009 using double large prime bound of 370067932007440 (42-49 bits) Tue Feb 24 00:48:17 2009 using trial factoring cutoff of 49 bits Tue Feb 24 00:48:17 2009 polynomial 'A' values have 11 factors Tue Feb 24 01:44:43 2009 59380 relations (15995 full + 43385 combined from 624990 partial), need 59096 Tue Feb 24 01:44:48 2009 begin with 640985 relations Tue Feb 24 01:44:48 2009 reduce to 143986 relations in 10 passes Tue Feb 24 01:44:48 2009 attempting to read 143986 relations Tue Feb 24 01:44:50 2009 recovered 143986 relations Tue Feb 24 01:44:50 2009 recovered 118738 polynomials Tue Feb 24 01:44:50 2009 attempting to build 59380 cycles Tue Feb 24 01:44:50 2009 found 59380 cycles in 5 passes Tue Feb 24 01:44:50 2009 distribution of cycle lengths: Tue Feb 24 01:44:50 2009 length 1 : 15995 Tue Feb 24 01:44:50 2009 length 2 : 11514 Tue Feb 24 01:44:50 2009 length 3 : 10428 Tue Feb 24 01:44:50 2009 length 4 : 7909 Tue Feb 24 01:44:50 2009 length 5 : 5509 Tue Feb 24 01:44:50 2009 length 6 : 3484 Tue Feb 24 01:44:50 2009 length 7 : 2091 Tue Feb 24 01:44:50 2009 length 9+: 2450 Tue Feb 24 01:44:50 2009 largest cycle: 17 relations Tue Feb 24 01:44:50 2009 matrix is 59000 x 59380 (15.1 MB) with weight 3493763 (58.84/col) Tue Feb 24 01:44:50 2009 sparse part has weight 3493763 (58.84/col) Tue Feb 24 01:44:51 2009 filtering completed in 3 passes Tue Feb 24 01:44:51 2009 matrix is 54792 x 54855 (14.1 MB) with weight 3246248 (59.18/col) Tue Feb 24 01:44:51 2009 sparse part has weight 3246248 (59.18/col) Tue Feb 24 01:44:51 2009 saving the first 48 matrix rows for later Tue Feb 24 01:44:51 2009 matrix is 54744 x 54855 (10.2 MB) with weight 2652281 (48.35/col) Tue Feb 24 01:44:51 2009 sparse part has weight 2118421 (38.62/col) Tue Feb 24 01:44:51 2009 matrix includes 64 packed rows Tue Feb 24 01:44:51 2009 using block size 21942 for processor cache size 4096 kB Tue Feb 24 01:44:52 2009 commencing Lanczos iteration Tue Feb 24 01:44:52 2009 memory use: 8.7 MB Tue Feb 24 01:45:13 2009 lanczos halted after 867 iterations (dim = 54742) Tue Feb 24 01:45:13 2009 recovered 15 nontrivial dependencies Tue Feb 24 01:45:13 2009 prp39 factor: 261205238291645927272402074009059256239 Tue Feb 24 01:45:13 2009 prp51 factor: 126820397395510759541604069650822061270444804667271 Tue Feb 24 01:45:13 2009 elapsed time 00:56:58
(44·10¹⁴³-71)/9 = 4(8)₁₄₂1_<144> = 23 · 37 · 199 · 30302636207_<11> · 4307160298747_<13> · C116
C116 = P38 · P79
P38 = 16407153915374855716140672893295921439_<38>
P79 = 1348102242729470640250881292514087976844275396957524728539042720088578215437399_<79>

Number: 48881_143 N=22118520990124458332699006534768476475381642269965611325044514221416868763053419753069680858556126450701594126497161 ( 116 digits) SNFS difficulty: 146 digits. Divisors found: r1=16407153915374855716140672893295921439 r2=1348102242729470640250881292514087976844275396957524728539042720088578215437399 Version: Total time: 5.53 hours. Scaled time: 13.18 units (timescale=2.384). Factorization parameters were as follows: n: 22118520990124458332699006534768476475381642269965611325044514221416868763053419753069680858556126450701594126497161 m: 100000000000000000000000000000 deg: 5 c5: 11 c0: -1775 skew: 2.76 type: snfs lss: 1 rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [750000, 1350001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3676723 Max relations in full relation-set: Initial matrix: Pruned matrix : 264624 x 264872 Total sieving time: 5.21 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.15 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,49,49,2.3,2.3,75000 total time: 5.53 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 24, 2009 (3rd): By Sinkiti Sibata / Msieve, GGNFS / Feb 24, 2009
(44·10¹⁴⁹-71)/9 = 4(8)₁₄₈1_<150> = 37 · 73 · 61961 · 24126935406859_<14> · 27995820258820794195604377373_<29> · C100
C100 = P43 · P58
P43 = 1823386628589600235665888424988868096924179_<43>
P58 = 2371881789921313843032874446987776090309859711930752765857_<58>

Mon Feb 23 13:53:09 2009 Msieve v. 1.39 Mon Feb 23 13:53:09 2009 random seeds: 79c73e94 b196d9d5 Mon Feb 23 13:53:09 2009 factoring 4324857540337690895886670133751822679873755496465154258190521001152601075515706549500196558668956403 (100 digits) Mon Feb 23 13:53:10 2009 searching for 15-digit factors Mon Feb 23 13:53:12 2009 commencing quadratic sieve (100-digit input) Mon Feb 23 13:53:12 2009 using multiplier of 11 Mon Feb 23 13:53:12 2009 using 32kb Intel Core sieve core Mon Feb 23 13:53:12 2009 sieve interval: 36 blocks of size 32768 Mon Feb 23 13:53:12 2009 processing polynomials in batches of 6 Mon Feb 23 13:53:12 2009 using a sieve bound of 2711333 (98824 primes) Mon Feb 23 13:53:12 2009 using large prime bound of 406699950 (28 bits) Mon Feb 23 13:53:12 2009 using double large prime bound of 3138292436875950 (43-52 bits) Mon Feb 23 13:53:12 2009 using trial factoring cutoff of 52 bits Mon Feb 23 13:53:12 2009 polynomial 'A' values have 13 factors Tue Feb 24 02:43:55 2009 99124 relations (22994 full + 76130 combined from 1499481 partial), need 98920 Tue Feb 24 02:43:58 2009 begin with 1522475 relations Tue Feb 24 02:43:59 2009 reduce to 263904 relations in 14 passes Tue Feb 24 02:43:59 2009 attempting to read 263904 relations Tue Feb 24 02:44:04 2009 recovered 263904 relations Tue Feb 24 02:44:04 2009 recovered 255780 polynomials Tue Feb 24 02:44:05 2009 attempting to build 99124 cycles Tue Feb 24 02:44:05 2009 found 99124 cycles in 6 passes Tue Feb 24 02:44:05 2009 distribution of cycle lengths: Tue Feb 24 02:44:05 2009 length 1 : 22994 Tue Feb 24 02:44:05 2009 length 2 : 16653 Tue Feb 24 02:44:05 2009 length 3 : 16437 Tue Feb 24 02:44:05 2009 length 4 : 13818 Tue Feb 24 02:44:05 2009 length 5 : 10262 Tue Feb 24 02:44:05 2009 length 6 : 7282 Tue Feb 24 02:44:05 2009 length 7 : 4731 Tue Feb 24 02:44:05 2009 length 9+: 6947 Tue Feb 24 02:44:05 2009 largest cycle: 22 relations Tue Feb 24 02:44:05 2009 matrix is 98824 x 99124 (27.6 MB) with weight 6829409 (68.90/col) Tue Feb 24 02:44:05 2009 sparse part has weight 6829409 (68.90/col) Tue Feb 24 02:44:07 2009 filtering completed in 3 passes Tue Feb 24 02:44:07 2009 matrix is 95251 x 95314 (26.6 MB) with weight 6588098 (69.12/col) Tue Feb 24 02:44:07 2009 sparse part has weight 6588098 (69.12/col) Tue Feb 24 02:44:07 2009 saving the first 48 matrix rows for later Tue Feb 24 02:44:08 2009 matrix is 95203 x 95314 (16.3 MB) with weight 5168196 (54.22/col) Tue Feb 24 02:44:08 2009 sparse part has weight 3703985 (38.86/col) Tue Feb 24 02:44:08 2009 matrix includes 64 packed rows Tue Feb 24 02:44:08 2009 using block size 38125 for processor cache size 1024 kB Tue Feb 24 02:44:08 2009 commencing Lanczos iteration Tue Feb 24 02:44:08 2009 memory use: 15.9 MB Tue Feb 24 02:45:13 2009 lanczos halted after 1507 iterations (dim = 95201) Tue Feb 24 02:45:13 2009 recovered 17 nontrivial dependencies Tue Feb 24 02:45:15 2009 prp43 factor: 1823386628589600235665888424988868096924179 Tue Feb 24 02:45:15 2009 prp58 factor: 2371881789921313843032874446987776090309859711930752765857 Tue Feb 24 02:45:15 2009 elapsed time 12:52:06
(44·10¹⁵¹-71)/9 = 4(8)₁₅₀1_<152> = 19 · 41 · 40795973 · 53086617357311_<14> · 787828356283625781569_<21> · C107
C107 = P36 · P71
P36 = 425947598878060367961552767720056277_<36>
P71 = 86354023540670324234290958731200652262153362934003180239457072040500101_<71>

Number: 48881_151 N=36782288980608025602558997767137002692332449728901869109100194795392576159672152415241702975132762944183977 ( 107 digits) Divisors found: r1=425947598878060367961552767720056277 (pp36) r2=86354023540670324234290958731200652262153362934003180239457072040500101 (pp71) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 18.41 hours. Scaled time: 8.71 units (timescale=0.473). Factorization parameters were as follows: name: 48881_151 n: 36782288980608025602558997767137002692332449728901869109100194795392576159672152415241702975132762944183977 skew: 12055.98 # norm 7.62e+14 c5: 155700 c4: 1637779484 c3: -13851048219839 c2: -236112434457720744 c1: -3660715319507968407076 c0: 16672546580673607696079200 # alpha -6.72 Y1: 92626107473 Y0: -188221650890861899581 # Murphy_E 1.53e-09 # M 18157611387834815042861964823819336260349267121385750848762299243356676082757506236419679403295869746734284 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:183993, largePrimes:4418375 encountered Relations: rels:4476604, finalFF:446496 Max relations in full relation-set: 28 Initial matrix: 367151 x 446496 with sparse part having weight 33191043. Pruned matrix : 303955 x 305854 with weight 19226197. Total sieving time: 15.49 hours. Total relation processing time: 0.33 hours. Matrix solve time: 2.39 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 18.41 hours. --------- CPU info (if available) ----------
(44·10¹³⁵-71)/9 = 4(8)₁₃₄1_<136> = 3 · 82549 · C131
C131 = P65 · P66
P65 = 38357340097329560078233395558992864916910707708764623785880080749_<65>
P66 = 514669713737333210325188168649284923465893594557365709330203361227_<66>

Number: 48881_135 N=19741361247618137465379709380242396996082685794251046404312949031843264359709137962054411678271446409158555883531352646665975719023 ( 131 digits) SNFS difficulty: 136 digits. Divisors found: r1=38357340097329560078233395558992864916910707708764623785880080749 (pp65) r2=514669713737333210325188168649284923465893594557365709330203361227 (pp66) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 9.13 hours. Scaled time: 4.31 units (timescale=0.472). Factorization parameters were as follows: name: 48881_135 n: 19741361247618137465379709380242396996082685794251046404312949031843264359709137962054411678271446409158555883531352646665975719023 m: 1000000000000000000000000000 deg: 5 c5: 44 c0: -71 skew: 1.10 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1415001) Primes: RFBsize:102146, AFBsize:102624, largePrimes:3331762 encountered Relations: rels:3328059, finalFF:289048 Max relations in full relation-set: 28 Initial matrix: 204836 x 289048 with sparse part having weight 25651418. Pruned matrix : 181849 x 182937 with weight 12934923. Total sieving time: 8.30 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.62 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 9.13 hours. --------- CPU info (if available) ----------
Feb 24, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Feb 24, 2009
(32·10¹⁶⁵+13)/9 = 3(5)₁₆₄7_<166> = 458981 · 630263 · C155
C155 = P44 · P111
P44 = 18681192180063273540908440345016705640959411_<44>
P111 = 657940106077601764355434130314334771812300887403075420900850959415178524121749594369791636050706233899226953629_<111>

Number: 35557_165 N=12291105564606894753648143531039730271512437525537283493091738158472357920721801541135677888602504092366897956430047188487377389072348162342113998368152519 ( 155 digits) SNFS difficulty: 166 digits. Divisors found: r1=18681192180063273540908440345016705640959411 r2=657940106077601764355434130314334771812300887403075420900850959415178524121749594369791636050706233899226953629 Version: Total time: 38.75 hours. Scaled time: 37.47 units (timescale=0.967). Factorization parameters were as follows: n: 12291105564606894753648143531039730271512437525537283493091738158472357920721801541135677888602504092366897956430047188487377389072348162342113998368152519 m: 2000000000000000000000000000000000 deg: 5 c5: 1 c0: 13 skew: 1.67 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2100000, 3600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 685665 x 685913 Total sieving time: 38.75 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,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 38.75 hours. --------- CPU info (if available) ----------
(44·10¹⁴⁴-71)/9 = 4(8)₁₄₃1_<145> = 3 · 3861802112461_<13> · C132
C132 = P50 · P83
P50 = 27176738312456067705423924254415620270867506101379_<50>
P83 = 15527500933247063626950184057751950006067441741686919878574402788064647788046405133_<83>

Number: 48881_144 N=421986829509272820353632573560155796304665185167618184592094823146824649144255133281704521784352850104568736051129758745664803978407 ( 132 digits) SNFS difficulty: 146 digits. Divisors found: r1=27176738312456067705423924254415620270867506101379 r2=15527500933247063626950184057751950006067441741686919878574402788064647788046405133 Version: Total time: 9.10 hours. Scaled time: 9.65 units (timescale=1.060). Factorization parameters were as follows: n: 421986829509272820353632573560155796304665185167618184592094823146824649144255133281704521784352850104568736051129758745664803978407 m: 100000000000000000000000000000 deg: 5 c5: 22 c0: -355 skew: 1.74 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 2200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 341023 x 341271 Total sieving time: 9.10 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000 total time: 9.10 hours. --------- CPU info (if available) ----------
Feb 24, 2009: By Serge Batalov / PFGW / Feb 23, 2009
(31·10³⁵⁹⁹⁰+23)/9 = 3(4)₃₅₉₈₉7_<35991> is PRP.
(13·10²²⁰⁴⁸-7)/3 = 4(3)₂₂₀₄₇1_<22049> is PRP.
Feb 23, 2009 (6th): By Sinkiti Sibata / Msieve / Feb 23, 2009
(44·10¹⁴¹-71)/9 = 4(8)₁₄₀1_<142> = 3² · 41 · 73 · 131 · 153953 · 789490181 · 4200148643_<10> · 583003741888800227_<18> · C94
C94 = P46 · P49
P46 = 1689109804305687021321287700092427147181180249_<46>
P49 = 2755883601781023358092221328064703478054177727799_<49>

Mon Feb 23 07:23:14 2009 Msieve v. 1.39 Mon Feb 23 07:23:14 2009 random seeds: df699430 3111daa0 Mon Feb 23 07:23:14 2009 factoring 4654990011293596264643196610177277729826715307937834774996988833394165195376426115665877041951 (94 digits) Mon Feb 23 07:23:15 2009 searching for 15-digit factors Mon Feb 23 07:23:17 2009 commencing quadratic sieve (94-digit input) Mon Feb 23 07:23:17 2009 using multiplier of 39 Mon Feb 23 07:23:17 2009 using 32kb Intel Core sieve core Mon Feb 23 07:23:17 2009 sieve interval: 36 blocks of size 32768 Mon Feb 23 07:23:17 2009 processing polynomials in batches of 6 Mon Feb 23 07:23:17 2009 using a sieve bound of 2059481 (76413 primes) Mon Feb 23 07:23:17 2009 using large prime bound of 284208378 (28 bits) Mon Feb 23 07:23:17 2009 using double large prime bound of 1646441586215862 (42-51 bits) Mon Feb 23 07:23:17 2009 using trial factoring cutoff of 51 bits Mon Feb 23 07:23:17 2009 polynomial 'A' values have 12 factors Mon Feb 23 10:36:21 2009 76733 relations (19105 full + 57628 combined from 1093329 partial), need 76509 Mon Feb 23 10:36:22 2009 begin with 1112434 relations Mon Feb 23 10:36:23 2009 reduce to 197760 relations in 11 passes Mon Feb 23 10:36:23 2009 attempting to read 197760 relations Mon Feb 23 10:36:26 2009 recovered 197760 relations Mon Feb 23 10:36:26 2009 recovered 180870 polynomials Mon Feb 23 10:36:27 2009 attempting to build 76733 cycles Mon Feb 23 10:36:27 2009 found 76733 cycles in 6 passes Mon Feb 23 10:36:27 2009 distribution of cycle lengths: Mon Feb 23 10:36:27 2009 length 1 : 19105 Mon Feb 23 10:36:27 2009 length 2 : 13731 Mon Feb 23 10:36:27 2009 length 3 : 13102 Mon Feb 23 10:36:27 2009 length 4 : 10332 Mon Feb 23 10:36:27 2009 length 5 : 7683 Mon Feb 23 10:36:27 2009 length 6 : 5124 Mon Feb 23 10:36:27 2009 length 7 : 3231 Mon Feb 23 10:36:27 2009 length 9+: 4425 Mon Feb 23 10:36:27 2009 largest cycle: 17 relations Mon Feb 23 10:36:27 2009 matrix is 76413 x 76733 (20.9 MB) with weight 5160119 (67.25/col) Mon Feb 23 10:36:27 2009 sparse part has weight 5160119 (67.25/col) Mon Feb 23 10:36:28 2009 filtering completed in 3 passes Mon Feb 23 10:36:28 2009 matrix is 72426 x 72490 (19.8 MB) with weight 4900322 (67.60/col) Mon Feb 23 10:36:28 2009 sparse part has weight 4900322 (67.60/col) Mon Feb 23 10:36:28 2009 saving the first 48 matrix rows for later Mon Feb 23 10:36:29 2009 matrix is 72378 x 72490 (13.7 MB) with weight 4007388 (55.28/col) Mon Feb 23 10:36:29 2009 sparse part has weight 3153350 (43.50/col) Mon Feb 23 10:36:29 2009 matrix includes 64 packed rows Mon Feb 23 10:36:29 2009 using block size 28996 for processor cache size 1024 kB Mon Feb 23 10:36:29 2009 commencing Lanczos iteration Mon Feb 23 10:36:29 2009 memory use: 12.4 MB Mon Feb 23 10:37:06 2009 lanczos halted after 1146 iterations (dim = 72376) Mon Feb 23 10:37:06 2009 recovered 18 nontrivial dependencies Mon Feb 23 10:37:07 2009 prp46 factor: 1689109804305687021321287700092427147181180249 Mon Feb 23 10:37:07 2009 prp49 factor: 2755883601781023358092221328064703478054177727799 Mon Feb 23 10:37:07 2009 elapsed time 03:13:53
Feb 23, 2009 (5th): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39, yafu-1.06 / Feb 23, 2009
(13·10¹⁷²-7)/3 = 4(3)₁₇₁1_<173> = 289733 · 341083 · 4227751937_<10> · 88169691859_<11> · C142
C142 = P37 · P105
P37 = 3446714640637299830656897972064937911_<37>
P105 = 341294988336445193728905705649852576939546047528827589956637878582237898276169125438517320288890233544833_<105>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1660133444 Step 1 took 26687ms Step 2 took 17954ms ********** Factor found in step 2: 3446714640637299830656897972064937911 Found probable prime factor of 37 digits: 3446714640637299830656897972064937911 Probable prime cofactor has 105 digits
(44·10¹²⁴-71)/9 = 4(8)₁₂₃1_<125> = 7² · 197 · 4679 · 31154132951377_<14> · C104
C104 = P32 · P73
P32 = 25396419038491858287986340454153_<32>
P73 = 1368064780176544709535508833324802532043828326786680880921691567406497923_<73>

SNFS difficulty: 126 digits. Divisors found: r1=25396419038491858287986340454153 r2=1368064780176544709535508833324802532043828326786680880921691567406497923 Version: Total time: 1.24 hours. Scaled time: 3.32 units (timescale=2.677). Factorization parameters were as follows: n: 34743946429165779062937821146668289023142555909174816609220785749295779247311346548900553474735071224219 m: 10000000000000000000000000 c5: 22 c0: -355 skew: 1.74 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 25 lpba: 25 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 48/48 Sieved rational special-q in [445000, 745001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 113205 x 113450 Total sieving time: 1.24 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,126,5,0,0,0,0,0,0,0,0,890000,890000,25,25,48,48,2.3,2.3,50000 total time: 1.24 hours.
(44·10¹⁷⁰-71)/9 = 4(8)₁₆₉1_<171> = 13 · 17 · 37 · 222919 · 5364775547_<10> · 4563975737099127801032473103_<28> · 58627240909157056665846947136373_<32> · C93
C93 = P42 · P51
P42 = 629413938427228336143257358605484317506289_<42>
P51 = 296850911885490573747756395058094668056965871611231_<51>

starting SIQS on c93: 186842101575560748251901609180483102105679639113695638170972246212189545448427085736405531759 ==== sieve params ==== n = 93 digits, 308 bits factor base: 74997 primes (max prime = 2013299) single large prime cutoff: 241595880 (120 * pmax) double large prime range from 43 to 51 bits double large prime cutoff: 1229026205170180 using 11 large prime slices of factor base buckets hold 1024 elements sieve interval: 22 blocks of size 32768 polynomial A has ~ 12 factors using multiplier of 2 using small prime variation correction of 20 bits trial factoring cutoff at 98 bits ==== sieving in progress: 75061 relations needed ==== ==== Press ctrl-c to abort and save state ==== 75075 rels found: 19639 full + 55436 from 963672 partial, (1.28 rels/poly, 202.06 rels/sec) sieve time = 1605.0670, relation time = 962.0480, poly_time = 2294.4940 trial division touched 46335727 sieve locations out of 1106774327296 trial division early aborted 32681170 times size of relation set in memory = 0 bytes QS elapsed time = 4866.5470 seconds. ==== post processing stage (msieve-1.38) ==== begin with 983311 relations reduce to 186463 relations in 11 passes attempting to read 186463 relations recovered 186463 relations recovered 165561 polynomials attempting to build 75075 cycles found 75075 cycles in 5 passes distribution of cycle lengths: length 1 : 19639 length 2 : 14403 length 3 : 13190 length 4 : 9949 length 5 : 7107 length 6 : 4609 length 7 : 2701 length 9+: 3477 largest cycle: 19 relations matrix is 74997 x 75075 (19.0 MB) with weight 4684698 (62.40/col) sparse part has weight 4684698 (62.40/col) filtering completed in 3 passes matrix is 70882 x 70946 (18.1 MB) with weight 4473451 (63.05/col) sparse part has weight 4473451 (63.05/col) saving the first 48 matrix rows for later matrix is 70834 x 70946 (12.3 MB) with weight 3649716 (51.44/col) sparse part has weight 2811715 (39.63/col) matrix includes 64 packed rows using block size 28378 for processor cache size 4096 kB commencing Lanczos iteration memory use: 11.5 MB lanczos halted after 1122 iterations (dim = 70833) recovered 17 nontrivial dependencies Lanczos elapsed time = 26.5630 seconds. Sqrt elapsed time = 1.5150 seconds. Total elapsed time = 4894.6250 seconds. ***factors found*** PRP42 = 629413938427228336143257358605484317506289 PRP51 = 296850911885490573747756395058094668056965871611231
Feb 23, 2009 (4th): By Ignacio Santos / GGNFS, Msieve / Feb 23, 2009
(37·10¹⁷⁵+17)/9 = 4(1)₁₇₄3_<176> = 23 · 2539 · C171
C171 = P74 · P98
P74 = 23586711719453871087522664522636742344493353264814241528919205959807570277_<74>
P98 = 29847040760283621496854245399203499887235219181116358275700688536486472950381821332414081846863577_<98>

Number: 41113_175 N=703993546091599073772815574620461857819941283132885441223198299760451925802885612464871673392659059730998357982620872837836038000430006868693787542358530594227633459100829 ( 171 digits) SNFS difficulty: 176 digits. Divisors found: r1=23586711719453871087522664522636742344493353264814241528919205959807570277 (pp74) r2=29847040760283621496854245399203499887235219181116358275700688536486472950381821332414081846863577 (pp98) Version: Msieve-1.39 Total time: 77.02 hours. Scaled time: 133.94 units (timescale=1.739). Factorization parameters were as follows: n: 703993546091599073772815574620461857819941283132885441223198299760451925802885612464871673392659059730998357982620872837836038000430006868693787542358530594227633459100829 m: 100000000000000000000000000000000000 deg: 5 c5: 37 c0: 17 skew: 0.86 type: snfs lss: 1 rlim: 6100000 alim: 6100000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6100000/6100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3050000, 6950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1306867 x 1307115 Total sieving time: 77.02 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,176,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000 total time: 77.02 hours. --------- CPU info (if available) ----------
Feb 23, 2009 (3rd): By Erik Branger / GGNFS, Msieve
(44·10¹¹⁸-71)/9 = 4(8)₁₁₇1_<119> = 7 · C118
C118 = P54 · P65
P54 = 416440717606357993741576196275666721789252219034067903_<54>
P65 = 16770999301583074158031570541847272998272867034768728791605138361_<65>

Number: 48881_118 N=6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126983 ( 118 digits) SNFS difficulty: 119 digits. Divisors found: r1=416440717606357993741576196275666721789252219034067903 r2=16770999301583074158031570541847272998272867034768728791605138361 Version: Total time: 1.68 hours. Scaled time: 1.66 units (timescale=0.989). Factorization parameters were as follows: n: 6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126983 m: 200000000000000000000000 deg: 5 c5: 1375 c0: -71 skew: 0.55 type: snfs lss: 1 rlim: 700000 alim: 700000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [350000, 600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 87398 x 87646 Total sieving time: 1.68 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,119,5,0,0,0,0,0,0,0,0,700000,700000,25,25,45,45,2.2,2.2,50000 total time: 1.68 hours. --------- CPU info (if available) ----------
(44·10¹²⁵-71)/9 = 4(8)₁₂₄1_<126> = 29 · 37 · 73 · 1481 · C118
C118 = P41 · P78
P41 = 12477073105331465445789572500714681458613_<41>
P78 = 337769014512650326216567018186916042346285216264847869760875598543396841692813_<78>

Number: 48881_125 N=4214368686790102824475544972011472419570332450119467343144868288579673570537216715847822445421317865443217046919048369 ( 118 digits) SNFS difficulty: 126 digits. Divisors found: r1=12477073105331465445789572500714681458613 r2=337769014512650326216567018186916042346285216264847869760875598543396841692813 Version: Total time: 2.17 hours. Scaled time: 2.09 units (timescale=0.965). Factorization parameters were as follows: n: 4214368686790102824475544972011472419570332450119467343144868288579673570537216715847822445421317865443217046919048369 m: 10000000000000000000000000 deg: 5 c5: 44 c0: -71 skew: 1.10 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 135095 x 135343 Total sieving time: 2.17 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,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.17 hours. --------- CPU info (if available) ----------
Feb 23, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 22, 2009
(44·10¹⁰⁹-71)/9 = 4(8)₁₀₈1_<110> = 73 · C108
C108 = P41 · P68
P41 = 35566845797976201162695764745383432956709_<41>
P68 = 18829637311701547205216682636999200838650523549983041259903340871733_<68>

Number: 48881_109 N=669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697 ( 108 digits) SNFS difficulty: 111 digits. Divisors found: r1=35566845797976201162695764745383432956709 r2=18829637311701547205216682636999200838650523549983041259903340871733 Version: Total time: 0.38 hours. Scaled time: 0.91 units (timescale=2.379). Factorization parameters were as follows: n: 669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697 m: 10000000000000000000000 deg: 5 c5: 22 c0: -355 skew: 1.74 type: snfs lss: 1 rlim: 320000 alim: 320000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 320000/320000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [160000, 300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 961229 Max relations in full relation-set: Initial matrix: Pruned matrix : 43983 x 44216 Total sieving time: 0.34 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.00 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,320000,320000,25,25,44,44,2.2,2.2,20000 total time: 0.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(44·10¹¹¹-71)/9 = 4(8)₁₁₀1_<112> = 3 · 41 · 619 · 1993 · 891763 · C98
C98 = P43 · P56
P43 = 1351980281510634921679265723748664648148189_<43>
P56 = 26723128574901564786591298311795686272646239432459060663_<56>

Number: 48881_111 N=36129142893540309774385216913572919724754103318722012008593516148461445958436410349932217364589307 ( 98 digits) SNFS difficulty: 113 digits. Divisors found: r1=1351980281510634921679265723748664648148189 r2=26723128574901564786591298311795686272646239432459060663 Version: Total time: 0.41 hours. Scaled time: 0.98 units (timescale=2.372). Factorization parameters were as follows: n: 36129142893540309774385216913572919724754103318722012008593516148461445958436410349932217364589307 m: 20000000000000000000000 deg: 5 c5: 55 c0: -284 skew: 1.39 type: snfs lss: 1 rlim: 360000 alim: 360000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [180000, 330001) Primes: rational ideals reading, algebraic ideals reading, Relations: 982594 Max relations in full relation-set: Initial matrix: Pruned matrix : 49757 x 49991 Total sieving time: 0.37 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,360000,360000,25,25,45,45,2.2,2.2,25000 total time: 0.41 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(44·10¹⁴²-71)/9 = 4(8)₁₄₁1_<143> = 7 · 601 · 1586766675259_<13> · 603149822923393391_<18> · 10114884012409807074443_<23> · C88
C88 = P32 · P56
P32 = 38857779451858321390658667718439_<32>
P56 = 30893029087204983813564181049616963052872694625767854991_<56>

Sun Feb 22 22:54:09 2009 Sun Feb 22 22:54:09 2009 Sun Feb 22 22:54:09 2009 Msieve v. 1.39 Sun Feb 22 22:54:09 2009 random seeds: 012cf744 94063b51 Sun Feb 22 22:54:09 2009 factoring 1200434510870455254743290303365774516525651954915925350818770002948070047475388968879049 (88 digits) Sun Feb 22 22:54:10 2009 searching for 15-digit factors Sun Feb 22 22:54:11 2009 commencing quadratic sieve (88-digit input) Sun Feb 22 22:54:11 2009 using multiplier of 5 Sun Feb 22 22:54:11 2009 using VC8 32kb sieve core Sun Feb 22 22:54:11 2009 sieve interval: 24 blocks of size 32768 Sun Feb 22 22:54:11 2009 processing polynomials in batches of 9 Sun Feb 22 22:54:11 2009 using a sieve bound of 1500533 (57333 primes) Sun Feb 22 22:54:11 2009 using large prime bound of 120042640 (26 bits) Sun Feb 22 22:54:11 2009 using double large prime bound of 348982681131840 (42-49 bits) Sun Feb 22 22:54:11 2009 using trial factoring cutoff of 49 bits Sun Feb 22 22:54:11 2009 polynomial 'A' values have 11 factors Sun Feb 22 23:43:15 2009 57727 relations (15785 full + 41942 combined from 604889 partial), need 57429 Sun Feb 22 23:43:15 2009 begin with 620674 relations Sun Feb 22 23:43:15 2009 reduce to 139072 relations in 9 passes Sun Feb 22 23:43:15 2009 attempting to read 139072 relations Sun Feb 22 23:43:17 2009 recovered 139072 relations Sun Feb 22 23:43:17 2009 recovered 116567 polynomials Sun Feb 22 23:43:17 2009 attempting to build 57727 cycles Sun Feb 22 23:43:17 2009 found 57727 cycles in 5 passes Sun Feb 22 23:43:17 2009 distribution of cycle lengths: Sun Feb 22 23:43:17 2009 length 1 : 15785 Sun Feb 22 23:43:17 2009 length 2 : 11179 Sun Feb 22 23:43:17 2009 length 3 : 10318 Sun Feb 22 23:43:17 2009 length 4 : 7571 Sun Feb 22 23:43:17 2009 length 5 : 5283 Sun Feb 22 23:43:17 2009 length 6 : 3301 Sun Feb 22 23:43:17 2009 length 7 : 1998 Sun Feb 22 23:43:17 2009 length 9+: 2292 Sun Feb 22 23:43:17 2009 largest cycle: 19 relations Sun Feb 22 23:43:17 2009 matrix is 57333 x 57727 (14.5 MB) with weight 3340533 (57.87/col) Sun Feb 22 23:43:17 2009 sparse part has weight 3340533 (57.87/col) Sun Feb 22 23:43:18 2009 filtering completed in 3 passes Sun Feb 22 23:43:18 2009 matrix is 52958 x 53021 (13.4 MB) with weight 3087569 (58.23/col) Sun Feb 22 23:43:18 2009 sparse part has weight 3087569 (58.23/col) Sun Feb 22 23:43:18 2009 saving the first 48 matrix rows for later Sun Feb 22 23:43:18 2009 matrix is 52910 x 53021 (9.2 MB) with weight 2470788 (46.60/col) Sun Feb 22 23:43:18 2009 sparse part has weight 1876061 (35.38/col) Sun Feb 22 23:43:18 2009 matrix includes 64 packed rows Sun Feb 22 23:43:18 2009 using block size 21208 for processor cache size 4096 kB Sun Feb 22 23:43:18 2009 commencing Lanczos iteration Sun Feb 22 23:43:18 2009 memory use: 8.0 MB Sun Feb 22 23:43:37 2009 lanczos halted after 838 iterations (dim = 52908) Sun Feb 22 23:43:37 2009 recovered 17 nontrivial dependencies Sun Feb 22 23:43:37 2009 prp32 factor: 38857779451858321390658667718439 Sun Feb 22 23:43:37 2009 prp56 factor: 30893029087204983813564181049616963052872694625767854991 Sun Feb 22 23:43:37 2009 elapsed time 00:49:28
By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 23, 2009
(44·10¹³²-71)/9 = 4(8)₁₃₁1_<133> = 3⁵ · 4339 · 15978271 · 93502943 · 105465168068487408287_<21> · C92
C92 = P45 · P48
P45 = 260189102411844591320932191190753612446510353_<45>
P48 = 113099589360575310311511645016805083348433825191_<48>

Sun Feb 22 23:46:51 2009 Sun Feb 22 23:46:51 2009 Sun Feb 22 23:46:51 2009 Msieve v. 1.39 Sun Feb 22 23:46:51 2009 random seeds: d93107a4 3bab7459 Sun Feb 22 23:46:51 2009 factoring 29427280638876298352094944415671764174672400927972612484598350746797758877263449175173702423 (92 digits) Sun Feb 22 23:46:52 2009 searching for 15-digit factors Sun Feb 22 23:46:52 2009 commencing quadratic sieve (92-digit input) Sun Feb 22 23:46:53 2009 using multiplier of 2 Sun Feb 22 23:46:53 2009 using VC8 32kb sieve core Sun Feb 22 23:46:53 2009 sieve interval: 36 blocks of size 32768 Sun Feb 22 23:46:53 2009 processing polynomials in batches of 6 Sun Feb 22 23:46:53 2009 using a sieve bound of 1776617 (67059 primes) Sun Feb 22 23:46:53 2009 using large prime bound of 186544785 (27 bits) Sun Feb 22 23:46:53 2009 using double large prime bound of 771630750831045 (42-50 bits) Sun Feb 22 23:46:53 2009 using trial factoring cutoff of 50 bits Sun Feb 22 23:46:53 2009 polynomial 'A' values have 12 factors Mon Feb 23 01:30:43 2009 67582 relations (17465 full + 50117 combined from 829202 partial), need 67155 Mon Feb 23 01:30:44 2009 begin with 846667 relations Mon Feb 23 01:30:44 2009 reduce to 169150 relations in 10 passes Mon Feb 23 01:30:44 2009 attempting to read 169150 relations Mon Feb 23 01:30:46 2009 recovered 169150 relations Mon Feb 23 01:30:46 2009 recovered 148216 polynomials Mon Feb 23 01:30:47 2009 attempting to build 67582 cycles Mon Feb 23 01:30:47 2009 found 67582 cycles in 5 passes Mon Feb 23 01:30:47 2009 distribution of cycle lengths: Mon Feb 23 01:30:47 2009 length 1 : 17465 Mon Feb 23 01:30:47 2009 length 2 : 12674 Mon Feb 23 01:30:47 2009 length 3 : 11758 Mon Feb 23 01:30:47 2009 length 4 : 9043 Mon Feb 23 01:30:47 2009 length 5 : 6478 Mon Feb 23 01:30:47 2009 length 6 : 4270 Mon Feb 23 01:30:47 2009 length 7 : 2643 Mon Feb 23 01:30:47 2009 length 9+: 3251 Mon Feb 23 01:30:47 2009 largest cycle: 19 relations Mon Feb 23 01:30:47 2009 matrix is 67059 x 67582 (17.7 MB) with weight 4108292 (60.79/col) Mon Feb 23 01:30:47 2009 sparse part has weight 4108292 (60.79/col) Mon Feb 23 01:30:48 2009 filtering completed in 3 passes Mon Feb 23 01:30:48 2009 matrix is 63161 x 63225 (16.6 MB) with weight 3844548 (60.81/col) Mon Feb 23 01:30:48 2009 sparse part has weight 3844548 (60.81/col) Mon Feb 23 01:30:48 2009 saving the first 48 matrix rows for later Mon Feb 23 01:30:48 2009 matrix is 63113 x 63225 (10.4 MB) with weight 2947191 (46.61/col) Mon Feb 23 01:30:48 2009 sparse part has weight 2083604 (32.96/col) Mon Feb 23 01:30:48 2009 matrix includes 64 packed rows Mon Feb 23 01:30:48 2009 using block size 25290 for processor cache size 4096 kB Mon Feb 23 01:30:48 2009 commencing Lanczos iteration Mon Feb 23 01:30:48 2009 memory use: 9.4 MB Mon Feb 23 01:31:14 2009 lanczos halted after 999 iterations (dim = 63111) Mon Feb 23 01:31:14 2009 recovered 17 nontrivial dependencies Mon Feb 23 01:31:14 2009 prp45 factor: 260189102411844591320932191190753612446510353 Mon Feb 23 01:31:14 2009 prp48 factor: 113099589360575310311511645016805083348433825191 Mon Feb 23 01:31:14 2009 elapsed time 01:44:23
(44·10¹⁵⁵-71)/9 = 4(8)₁₅₄1_<156> = 37 · 97 · 498889679 · 18697682263419627917303_<23> · C122
C122 = P33 · C89
P33 = 440832314293904601752619068922493_<33>
C89 = [33126152121935620473093722297086995034869661998940995868094417359149617683041111125853769_<89>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 14603078303564818279173845988926349653740533214373454335871022413890641803324821089370234331992907488797307054889512926117 (122 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3845036566 Step 1 took 3945ms Step 2 took 2293ms ********** Factor found in step 2: 440832314293904601752619068922493 Found probable prime factor of 33 digits: 440832314293904601752619068922493 Composite cofactor 33126152121935620473093722297086995034869661998940995868094417359149617683041111125853769 has 89 digits
(44·10¹⁵³-71)/9 = 4(8)₁₅₂1_<154> = 3 · 29 · 5686565066897115489601_<22> · C130
C130 = P30 · C101
P30 = 480561239432935951772923342469_<30>
C101 = [20563269273189518839408618741350859979878540178289245336713437567214603823608381501320185903034897227_<101>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 9881910168717163209631261810317703627882659164497899775880673087419777791936683716199703007690664433555697694512695772842739433463 (130 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1617530254 Step 1 took 3914ms Step 2 took 2376ms ********** Factor found in step 2: 480561239432935951772923342469 Found probable prime factor of 30 digits: 480561239432935951772923342469 Composite cofactor 20563269273189518839408618741350859979878540178289245336713437567214603823608381501320185903034897227 has 101 digits
(44·10¹⁶⁵-71)/9 = 4(8)₁₆₄1_<166> = 3 · 23² · 73 · 110567 · 93218987047_<11> · C145
C145 = P28 · P117
P28 = 4682812091093777041353233063_<28>
P117 = 874326705316405572786123234035850728935404455548662025784508076079796335019128265791706308917733245997267724658335013_<117>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 4094307667221849768503331020912509608304619865549751287988453380418056262380073505171906009921330949575502129726494033608850944517940838122134819 (145 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2266374876 Step 1 took 4701ms Step 2 took 2623ms ********** Factor found in step 2: 4682812091093777041353233063 Found probable prime factor of 28 digits: 4682812091093777041353233063 Probable prime cofactor 874326705316405572786123234035850728935404455548662025784508076079796335019128265791706308917733245997267724658335013 has 117 digits
(14·10¹⁶³+1)/3 = 4(6)₁₆₂7_<164> = 541 · 56552399 · 1300505580877_<13> · 6763759569124322149817_<22> · C120
C120 = P41 · P79
P41 = 87626829942236546445549104979905166220049_<41>
P79 = 1978887024576844368225830411346447797924000567626738265413690868084042418013093_<79>

Number: 46667_163 N=173403596777493614657332166591274041874084815925516146203645866528900650934565328260520164469099995823858736379801101557 ( 120 digits) SNFS difficulty: 165 digits. Divisors found: r1=87626829942236546445549104979905166220049 r2=1978887024576844368225830411346447797924000567626738265413690868084042418013093 Version: Total time: 22.87 hours. Scaled time: 54.51 units (timescale=2.383). Factorization parameters were as follows: n: 173403596777493614657332166591274041874084815925516146203645866528900650934565328260520164469099995823858736379801101557 m: 1000000000000000000000000000000000 deg: 5 c5: 7 c0: 50 skew: 1.48 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2000000, 3900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9787512 Max relations in full relation-set: Initial matrix: Pruned matrix : 725648 x 725896 Total sieving time: 20.43 hours. Total relation processing time: 0.91 hours. Matrix solve time: 1.15 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000 total time: 22.87 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 23, 2009: By Robert Backstrom / GGNFS, Msieve / Feb 22, 2009
(14·10¹⁵⁹-11)/3 = 4(6)₁₅₈3_<160> = 5766037489_<10> · C150
C150 = P54 · P97
P54 = 260455141077573786525035422943583702088538753349314693_<54>
P97 = 3107394444335760734125359606663890296019575646343939677484645823076134984300128089687641614775019_<97>

Number: n N=809336858383139566622867419699960030326931970224425064723450442114644854447748573538049479488333355625649950862930760710263336733339554370467026054167 ( 150 digits) SNFS difficulty: 160 digits. Divisors found: Mon Feb 23 00:56:38 2009 prp54 factor: 260455141077573786525035422943583702088538753349314693 Mon Feb 23 00:56:38 2009 prp97 factor: 3107394444335760734125359606663890296019575646343939677484645823076134984300128089687641614775019 Mon Feb 23 00:56:38 2009 elapsed time 02:44:21 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.59 hours. Scaled time: 39.48 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_6_158_3 n: 809336858383139566622867419699960030326931970224425064723450442114644854447748573538049479488333355625649950862930760710263336733339554370467026054167 deg: 5 c5: 7 c0: -55 m: 100000000000000000000000000000000 skew: 1.51 type: snfs rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2000000, 3200117) Primes: RFBsize:283146, AFBsize:282788, largePrimes:16763038 encountered Relations: rels:15061344, finalFF:470776 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1073168 hash collisions in 16406181 relations Msieve: matrix is 798613 x 798861 (216.7 MB) Total sieving time: 21.25 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,160,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.5,2.5,100000 total time: 21.59 hours. --------- CPU info (if available) ----------
Feb 22, 2009 (6th): By Wataru Sakai / Msieve / Feb 22, 2009
(14·10²⁰⁵-11)/3 = 4(6)₂₀₄3_<206> = C206
C206 = P103 · P104
P103 = 2121306592776648777932591399219834774802781918867930539380539448487074254168075843706510005973451437893_<103>
P104 = 21999020238551709776934090605708851713877528642400823630041963062954447513472170746146025058346596528891_<104>

Number: 46663_205 N=46666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 206 digits) SNFS difficulty: 206 digits. Divisors found: r1=2121306592776648777932591399219834774802781918867930539380539448487074254168075843706510005973451437893 r2=21999020238551709776934090605708851713877528642400823630041963062954447513472170746146025058346596528891 Version: Total time: 1093.48 hours. Scaled time: 1932.19 units (timescale=1.767). Factorization parameters were as follows: n: 46666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 m: 100000000000000000000000000000000000000000 deg: 5 c5: 14 c0: -11 skew: 0.95 type: snfs lss: 1 rlim: 19100000 alim: 19100000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 19100000/19100000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [9550000, 20850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3269052 x 3269300 Total sieving time: 1093.48 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,206,5,0,0,0,0,0,0,0,0,19100000,19100000,29,29,56,56,2.6,2.6,100000 total time: 1093.48 hours. --------- CPU info (if available) ----------
P103 is the largest prime factor which was found in our tables so far. Congratulations!
5·10¹⁹³-9 = 4(9)₁₉₂1_<194> = 2111 · C191
C191 = P53 · P138
P53 = 46280192363403452945907094423911587820648171502970737_<53>
P138 = 511783895437135635957154567370339647742796615436941073014585973056439262887348563848497984154002794113583812498276542761057932913246823513_<138>

Number: 49991_193 N=23685457129322595926101373756513500710563713879677877783041212695405021316911416390336333491236380862150639507342491710090004737091425864519185220274751302700142112742775935575556608242539081 ( 191 digits) SNFS difficulty: 194 digits. Divisors found: r1=46280192363403452945907094423911587820648171502970737 r2=511783895437135635957154567370339647742796615436941073014585973056439262887348563848497984154002794113583812498276542761057932913246823513 Version: Total time: 514.11 hours. Scaled time: 1035.93 units (timescale=2.015). Factorization parameters were as follows: n: 23685457129322595926101373756513500710563713879677877783041212695405021316911416390336333491236380862150639507342491710090004737091425864519185220274751302700142112742775935575556608242539081 m: 500000000000000000000000000000000000000 deg: 5 c5: 8 c0: -45 skew: 1.41 type: snfs lss: 1 rlim: 12200000 alim: 12200000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 12200000/12200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6100000, 11100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1742550 x 1742798 Total sieving time: 514.11 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,194,5,0,0,0,0,0,0,0,0,12200000,12200000,28,28,55,55,2.5,2.5,100000 total time: 514.11 hours. --------- CPU info (if available) ----------
Feb 22, 2009 (5th): By Serge Batalov / GMP-ECM 6.2.1, yafu-1.06 / Feb 22, 2009
(43·10¹⁹⁷+11)/9 = 4(7)₁₉₆9_<198> = 47 · 1321 · 1361 · 132338431180593418567771_<24> · C167
C167 = P42 · P126
P42 = 331708104640154262349394010682175102067601_<42>
P126 = 128802733727568111758695581281046348446516164327418168890927756109284401384948163029643002128681541870249908675847736129947407_<126>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=651099684 Step 1 took 36625ms Step 2 took 18719ms ********** Factor found in step 2: 331708104640154262349394010682175102067601 Found probable prime factor of 42 digits: 331708104640154262349394010682175102067601 Probable prime cofactor has 126 digits
(2·10¹⁷¹+61)/9 = (2)₁₇₀9_<171> = 461 · 151570609 · 216132972529_<12> · 2335216729459_<13> · C136
C136 = P42 · P45 · P51
P42 = 107307406764746593081378156040526559657763_<42>
P45 = 346004849803017639555116780811604078215096527_<45>
P51 = 169711573352147205928889097569640982156924008532511_<51>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1058474660 Step 1 took 26829ms Step 2 took 17359ms ********** Factor found in step 2: 346004849803017639555116780811604078215096527 Found probable prime factor of 45 digits: 346004849803017639555116780811604078215096527 Composite cofactor has 92 digits starting SIQS on c92: ==== sieve params ==== n = 92 digits, 304 bits factor base: 71746 primes (max prime = 1927319) single large prime cutoff: 231278280 (120 * pmax) double large prime range from 43 to 51 bits double large prime cutoff: 1136168456955099 using 10 large prime slices of factor base buckets hold 1024 elements sieve interval: 22 blocks of size 32768 polynomial A has ~ 12 factors using multiplier of 1 using small prime variation correction of 19 bits trial factoring cutoff at 98 bits ==== sieving in progress: 71810 relations needed ==== ==== Press ctrl-c to abort and save state ==== 71837 rels found: 19040 full + 52797 from 918502 partial, (1.45 rels/poly, 23 sieve time = 1329.8350, relation time = 831.9500, poly_time = 1843.4930 trial division touched 36530963 sieve locations out of 930211037184 trial division early aborted 24830250 times size of relation set in memory = 0 bytes QS elapsed time = 4009.3910 seconds. ==== post processing stage (msieve-1.38) ==== begin with 937542 relations reduce to 177059 relations in 10 passes attempting to read 177059 relations recovered 177059 relations recovered 154919 polynomials attempting to build 71837 cycles found 71837 cycles in 5 passes distribution of cycle lengths: length 1 : 19040 length 2 : 13960 length 3 : 12639 length 4 : 9626 length 5 : 6569 length 6 : 4326 length 7 : 2534 length 9+: 3143 largest cycle: 19 relations matrix is 71746 x 71837 (17.5 MB) with weight 4299912 (59.86/col) sparse part has weight 4299912 (59.86/col) filtering completed in 4 passes matrix is 67493 x 67557 (16.6 MB) with weight 4084336 (60.46/col) sparse part has weight 4084336 (60.46/col) saving the first 48 matrix rows for later matrix is 67445 x 67557 (10.9 MB) with weight 3243734 (48.01/col) sparse part has weight 2463447 (36.46/col) matrix includes 64 packed rows using block size 27022 for processor cache size 4096 kB commencing Lanczos iteration memory use: 10.6 MB lanczos halted after 1069 iterations (dim = 67443) recovered 15 nontrivial dependencies Lanczos elapsed time = 21.5630 seconds. Sqrt elapsed time = 2.8590 seconds. Total elapsed time = 4033.8130 seconds. ***factors found*** PRP51 = 169711573352147205928889097569640982156924008532511 PRP42 = 107307406764746593081378156040526559657763
Feb 22, 2009 (4th): By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Feb 22, 2009
(43·10¹⁶⁰+11)/9 = 4(7)₁₅₉9_<161> = 24460091 · 11342534099773_<14> · C141
C141 = P33 · P108
P33 = 554530125227161494702649780672981_<33>
P108 = 310550790918183757138040292450770137837000349722124572567731528164572899124874670393566999702736101247089513_<108>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 172209768977254485464791824792255114721860563702277174648505747761995164855752309554901813150171274613701938489623941891084638103124687548253 (141 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2608419802 Step 1 took 4656ms Step 2 took 2602ms ********** Factor found in step 2: 554530125227161494702649780672981 Found probable prime factor of 33 digits: 554530125227161494702649780672981 Probable prime cofactor 310550790918183757138040292450770137837000349722124572567731528164572899124874670393566999702736101247089513 has 108 digits
(43·10¹⁵⁷+11)/9 = 4(7)₁₅₆9_<158> = 7 · 19 · 71 · 634793981 · C145
C145 = P60 · P86
P60 = 569398400463786844822991231371199194147265537056016392601101_<60>
P86 = 13998029790680444609644935809592066783975004954562700212966249573206820485535946233113_<86>

Number: 47779_157 N=7970455772457882142378370810311293034070800362661745376018533241192809998167135231459500149657003373220030542303745103840118021642124004966457413 ( 145 digits) SNFS difficulty: 158 digits. Divisors found: r1=569398400463786844822991231371199194147265537056016392601101 r2=13998029790680444609644935809592066783975004954562700212966249573206820485535946233113 Version: Total time: 15.16 hours. Scaled time: 35.95 units (timescale=2.371). Factorization parameters were as follows: n: 7970455772457882142378370810311293034070800362661745376018533241192809998167135231459500149657003373220030542303745103840118021642124004966457413 m: 10000000000000000000000000000000 deg: 5 c5: 4300 c0: 11 skew: 0.3 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1700000, 3000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8611651 Max relations in full relation-set: Initial matrix: Pruned matrix : 542033 x 542281 Total sieving time: 13.77 hours. Total relation processing time: 0.57 hours. Matrix solve time: 0.67 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,50,50,2.4,2.4,100000 total time: 15.16 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 22, 2009 (3rd): By Erik Branger / GGNFS, Msieve / Feb 22, 2009
(43·10¹⁶⁰-61)/9 = 4(7)₁₅₉1_<161> = 945435727446149_<15> · 153348803163867721_<18> · C129
C129 = P57 · P72
P57 = 507677995989841246989194634726525592636366766426170255699_<57>
P72 = 649120320669006679097042822232948846496567890641704033432611051708405901_<72>

Number: 47771_160 N=329544103553524437142630573737847138140672187662421531344207977931454906200837907178392131176682093632910926826470819616850479799 ( 129 digits) SNFS difficulty: 161 digits. Divisors found: r1=507677995989841246989194634726525592636366766426170255699 r2=649120320669006679097042822232948846496567890641704033432611051708405901 Version: Total time: 56.69 hours. Scaled time: 44.05 units (timescale=0.777). Factorization parameters were as follows: n: 329544103553524437142630573737847138140672187662421531344207977931454906200837907178392131176682093632910926826470819616850479799 m: 100000000000000000000000000000000 deg: 5 c5: 43 c0: -61 skew: 1.07 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1750000, 3350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 633074 x 633322 Total sieving time: 56.69 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,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 56.69 hours. --------- CPU info (if available) ----------
(43·10¹⁵³+11)/9 = 4(7)₁₅₂9_<154> = 3 · 13956860129130757_<17> · C138
C138 = P55 · P83
P55 = 2390398834710402655240393538570122004850597163918549889_<55>
P83 = 47736062871370708505479132371741318962492341955898192429827608909943783990709854941_<83>

Number: 47779_153 N=114108229061387059407795316515320184476644107180547072391599074615035448306680841601658779924230943441450886744859116513862646670261651549 ( 138 digits) SNFS difficulty: 156 digits. Divisors found: r1=2390398834710402655240393538570122004850597163918549889 r2=47736062871370708505479132371741318962492341955898192429827608909943783990709854941 Version: Total time: 26.00 hours. Scaled time: 27.27 units (timescale=1.049). Factorization parameters were as follows: n: 114108229061387059407795316515320184476644107180547072391599074615035448306680841601658779924230943441450886744859116513862646670261651549 m: 5000000000000000000000000000000 deg: 5 c5: 344 c0: 275 skew: 0.96 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 485116 x 485364 Total sieving time: 26.00 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,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 26.00 hours. --------- CPU info (if available) ----------
Feb 22, 2009 (2nd): Factorizations of 488...881 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Feb 22, 2009: By Serge Batalov / PFGW / Feb 22, 2009
(65·10¹²¹⁷⁵-11)/9 = 7(2)₁₂₁₇₄1_<12176> is PRP.
Feb 21, 2009 (8th): By Ignacio Santos / GGNFS, Msieve / Feb 21, 2009
(11·10¹⁸⁸+43)/9 = 1(2)₁₈₇7_<189> = 1321 · C185
C185 = P44 · P69 · P73
P44 = 32500590808365891660494126460420756674718181_<44>
P69 = 543030414799904978254708147320654776932247308215000344723661626079893_<69>
P73 = 5242421637376962007933603554526722658769614576691122109338592923947287939_<73>

Number: 12227_188 N=92522499789721591386996383211371856337791235595929010009252249978972159138699638321137185633779123559592901000925224997897215913869963832113718563377912355959290100092522499789721591387 ( 185 digits) SNFS difficulty: 190 digits. Divisors found: r1=32500590808365891660494126460420756674718181 (pp44) r2=543030414799904978254708147320654776932247308215000344723661626079893 (pp69) r3=5242421637376962007933603554526722658769614576691122109338592923947287939 (pp73) Version: Msieve-1.39 Total time: 320.82 hours. Scaled time: 557.90 units (timescale=1.739). Factorization parameters were as follows: n: 92522499789721591386996383211371856337791235595929010009252249978972159138699638321137185633779123559592901000925224997897215913869963832113718563377912355959290100092522499789721591387 m: 50000000000000000000000000000000000000 deg: 5 c5: 88 c0: 1075 skew: 1.65 type: snfs lss: 1 rlim: 10400000 alim: 10400000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10400000/10400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5200000, 10500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1944125 x 1944373 Total sieving time: 320.82 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,190,5,0,0,0,0,0,0,0,0,10400000,10400000,28,28,54,54,2.5,2.5,100000 total time: 320.82 hours. --------- CPU info (if available) ----------
Feb 21, 2009 (7th): By Sinkiti Sibata / GGNFS / Feb 21, 2009
(43·10¹³¹+11)/9 = 4(7)₁₃₀9_<132> = 55001 · 3884083551878620423_<19> · C109
C109 = P41 · P69
P41 = 11966861624006845044170697133053452418829_<41>
P69 = 186890199515821385603655482586900451315521584217335048559569919540337_<69>

Number: 47779_131 N=2236489156488865591889647066020115676177330652039542505529233844200322483485327020696231388249200924483805373 ( 109 digits) SNFS difficulty: 133 digits. Divisors found: r1=11966861624006845044170697133053452418829 (pp41) r2=186890199515821385603655482586900451315521584217335048559569919540337 (pp69) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 6.36 hours. Scaled time: 3.00 units (timescale=0.472). Factorization parameters were as follows: name: 47779_131 n: 2236489156488865591889647066020115676177330652039542505529233844200322483485327020696231388249200924483805373 m: 200000000000000000000000000 deg: 5 c5: 215 c0: 176 skew: 0.96 type: snfs lss: 1 rlim: 1190000 alim: 1190000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1190000/1190000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [595000, 1120001) Primes: RFBsize:92225, AFBsize:92618, largePrimes:3053285 encountered Relations: rels:3041735, finalFF:295264 Max relations in full relation-set: 28 Initial matrix: 184910 x 295264 with sparse part having weight 24278213. Pruned matrix : 153701 x 154689 with weight 9384043. Total sieving time: 5.84 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.34 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1190000,1190000,26,26,47,47,2.3,2.3,75000 total time: 6.36 hours. --------- CPU info (if available) ----------
Feb 21, 2009 (6th): By Serge Batalov / Msieve / Feb 21, 2009
(43·10¹⁰⁹+11)/9 = 4(7)₁₀₈9_<110> = 7 · 9326851 · 147552919 · C94
C94 = P34 · P60
P34 = 5186641571572763891836425583825171_<34>
P60 = 956222206640134678845241597923401166745068949951938745849003_<60>

Fri Feb 20 19:28:21 2009 Msieve v. 1.39 Fri Feb 20 19:28:21 2009 random seeds: 70e09421 4868b65f Fri Feb 20 19:28:21 2009 factoring 4959581848620764314873082640202983684038637690697228712941474720772791534728505411094716654513 (94 digits) Fri Feb 20 19:28:22 2009 searching for 15-digit factors Fri Feb 20 19:28:23 2009 commencing number field sieve (94-digit input) Fri Feb 20 19:28:23 2009 R0: -10000000000000000000000 Fri Feb 20 19:28:23 2009 R1: 1 Fri Feb 20 19:28:23 2009 A0: 110 Fri Feb 20 19:28:23 2009 A1: 0 Fri Feb 20 19:28:23 2009 A2: 0 Fri Feb 20 19:28:23 2009 A3: 0 Fri Feb 20 19:28:23 2009 A4: 0 Fri Feb 20 19:28:23 2009 A5: 43 Fri Feb 20 19:28:23 2009 size score = 6.059901e-08, Murphy alpha = 0.621738, combined = 4.925606e-08 Fri Feb 20 19:28:23 2009 Fri Feb 20 19:28:23 2009 commencing square root phase Fri Feb 20 19:28:23 2009 reading relations for dependency 1 Fri Feb 20 19:28:23 2009 read 25324 cycles Fri Feb 20 19:28:23 2009 cycles contain 90261 unique relations Fri Feb 20 19:28:24 2009 read 90261 relations Fri Feb 20 19:28:24 2009 multiplying 69680 relations Fri Feb 20 19:28:27 2009 multiply complete, coefficients have about 1.69 million bits Fri Feb 20 19:28:27 2009 initial square root is modulo 62099671 Fri Feb 20 19:28:32 2009 Newton iteration failed to converge Fri Feb 20 19:28:32 2009 algebraic square root failed Fri Feb 20 19:28:32 2009 reading relations for dependency 2 Fri Feb 20 19:28:32 2009 read 25291 cycles Fri Feb 20 19:28:32 2009 cycles contain 90029 unique relations Fri Feb 20 19:28:33 2009 read 90029 relations Fri Feb 20 19:28:33 2009 multiplying 69474 relations Fri Feb 20 19:28:36 2009 multiply complete, coefficients have about 1.68 million bits Fri Feb 20 19:28:36 2009 initial square root is modulo 58919291 Fri Feb 20 19:28:41 2009 prp34 factor: 5186641571572763891836425583825171 Fri Feb 20 19:28:41 2009 prp60 factor: 956222206640134678845241597923401166745068949951938745849003 Fri Feb 20 19:28:41 2009 elapsed time 00:00:20
Feb 21, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 21, 2009
(43·10¹⁴⁸+11)/9 = 4(7)₁₄₇9_<149> = 55434706652456510426180009_<26> · C123
C123 = P36 · P87
P36 = 880473705643800323008781414226040537_<36>
P87 = 978876272798095084184897796318874119497804652497593236125475126377821797059918500810163_<87>

Number: 47779_148 N=861874819277330356327609514781646580120356516383198868090420835498813576559283961722781870003966532142251375809846179577531 ( 123 digits) SNFS difficulty: 151 digits. Divisors found: r1=880473705643800323008781414226040537 r2=978876272798095084184897796318874119497804652497593236125475126377821797059918500810163 Version: Total time: 9.29 hours. Scaled time: 22.19 units (timescale=2.388). Factorization parameters were as follows: n: 861874819277330356327609514781646580120356516383198868090420835498813576559283961722781870003966532142251375809846179577531 m: 1000000000000000000000000000000 deg: 5 c5: 43 c0: 1100 skew: 1.91 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7230844 Max relations in full relation-set: Initial matrix: Pruned matrix : 368529 x 368777 Total sieving time: 8.56 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.29 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 9.29 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 21, 2009 (4th): By Sinkiti Sibata / GGNFS / Feb 21, 2009
(43·10¹²⁷+11)/9 = 4(7)₁₂₆9_<128> = 7² · 17 · 3823 · 36191 · 222552349 · C109
C109 = P32 · P77
P32 = 44081140412735548636973386146047_<32>
P77 = 42256260316589121143556886855498657765076762677937532780858710902359236274497_<77>

Number: 47779_127 N=1862704144332670156720268853192338984265184891905277609373267801082571490102306484312947988653238917023463359 ( 109 digits) SNFS difficulty: 129 digits. Divisors found: r1=44081140412735548636973386146047 (pp32) r2=42256260316589121143556886855498657765076762677937532780858710902359236274497 (pp77) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 4.71 hours. Scaled time: 2.22 units (timescale=0.472). Factorization parameters were as follows: name: 47779_127 n: 1862704144332670156720268853192338984265184891905277609373267801082571490102306484312947988653238917023463359 m: 20000000000000000000000000 deg: 5 c5: 1075 c0: 88 skew: 0.61 type: snfs lss: 1 rlim: 1010000 alim: 1010000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1010000/1010000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [505000, 905001) Primes: RFBsize:79251, AFBsize:79252, largePrimes:2661170 encountered Relations: rels:2570098, finalFF:217499 Max relations in full relation-set: 28 Initial matrix: 158570 x 217499 with sparse part having weight 16509802. Pruned matrix : 139367 x 140223 with weight 7866099. Total sieving time: 4.30 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.26 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,1010000,1010000,26,26,47,47,2.3,2.3,50000 total time: 4.71 hours. --------- CPU info (if available) ----------
Feb 21, 2009 (3rd): By Ignacio Santos / GGNFS, Msieve / Feb 21, 2009
(43·10¹⁵⁹+11)/9 = 4(7)₁₅₈9_<160> = 3 · 17 · 23 · C157
C157 = P50 · P52 · P57
P50 = 11231391656393485544496622672465008980700034909609_<50>
P52 = 3014196135867233202687935157625883361795625141037437_<52>
P57 = 120315852673499043834233788846040848684277725755808369531_<57>

Number: 47779_159 N=4073126835275172871080799469546272615326323766221464431183101259827602538599981055224021975940134507909443970825044993842947807142180543715070569290518139623 ( 157 digits) SNFS difficulty: 161 digits. Divisors found: r1=11231391656393485544496622672465008980700034909609 (pp50) r2=3014196135867233202687935157625883361795625141037437 (pp52) r3=120315852673499043834233788846040848684277725755808369531 (pp57) Version: Msieve-1.39 Total time: 30.34 hours. Scaled time: 77.98 units (timescale=2.570). Factorization parameters were as follows: n: 4073126835275172871080799469546272615326323766221464431183101259827602538599981055224021975940134507909443970825044993842947807142180543715070569290518139623 m: 100000000000000000000000000000000 deg: 5 c5: 43 c0: 110 skew: 1.21 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1750000, 3150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 620461 x 620709 Total sieving time: 30.34 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,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 30.34 hours. --------- CPU info (if available) ----------
Feb 21, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.1 / Feb 21, 2009
(43·10¹⁸⁴+11)/9 = 4(7)₁₈₃9_<185> = 502173835561_<12> · 1764054615755273_<16> · C158
C158 = P35 · P124
P35 = 19779660838974429503159350745426911_<35>
P124 = 2726722849829117633288105012852610477794751506660331369964335151196302306688943733512946151533573442920320969197061013111613_<124>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3925499624 Step 1 took 33172ms Step 2 took 31609ms ********** Factor found in step 2: 19779660838974429503159350745426911 Found probable prime factor of 35 digits: 19779660838974429503159350745426911 Probable prime cofactor has 124 digits
(43·10¹⁵⁴+11)/9 = 4(7)₁₅₃9_<155> = 61 · 2521 · 6621191 · 847749629250263763887_<21> · C122
C122 = P35 · C88
P35 = 16675085747257594544754493982884013_<35>
C88 = [3319337902489520751226070898363623293975319262802295525732486647927953485243921707385579_<88>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1862379626 Step 1 took 21938ms Step 2 took 23406ms ********** Factor found in step 2: 16675085747257594544754493982884013 Found probable prime factor of 35 digits: 16675085747257594544754493982884013 Composite cofactor has 88 digits
(43·10¹⁷²+11)/9 = 4(7)₁₇₁9_<173> = 509 · 49201 · 11533729 · C159
C159 = P32 · P127
P32 = 57344023234304788989693444726809_<32>
P127 = 2884538444478075465915083887707291101979033666860029443770170453897934362899979487077169234337132170666443297398816898669830871_<127>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4028011784 Step 1 took 33562ms Step 2 took 31500ms ********** Factor found in step 2: 57344023234304788989693444726809 Found probable prime factor of 32 digits: 57344023234304788989693444726809 Probable prime cofactor has 127 digits
Feb 21, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 21, 2009
(43·10¹⁴⁶+11)/9 = 4(7)₁₄₅9_<147> = 29 · 5939380283_<10> · 211859631176295106006771_<24> · C113
C113 = P50 · P63
P50 = 15087489785086270771497404761812202993118278003931_<50>
P63 = 867803933596246020684967505127274412556662504314507971740173597_<63>

Number: 47779_146 N=13092982983591046266291176692464995493840491391051995577697638177682986033121860520529575409164790910616588409807 ( 113 digits) SNFS difficulty: 147 digits. Divisors found: r1=15087489785086270771497404761812202993118278003931 r2=867803933596246020684967505127274412556662504314507971740173597 Version: Total time: 6.49 hours. Scaled time: 15.49 units (timescale=2.388). Factorization parameters were as follows: n: 13092982983591046266291176692464995493840491391051995577697638177682986033121860520529575409164790910616588409807 m: 100000000000000000000000000000 deg: 5 c5: 430 c0: 11 skew: 0.48 type: snfs lss: 1 rlim: 1650000 alim: 1650000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1650000/1650000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [825000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4161154 Max relations in full relation-set: Initial matrix: Pruned matrix : 254636 x 254884 Total sieving time: 6.09 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.13 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,49,49,2.3,2.3,75000 total time: 6.49 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(28·10¹⁹⁴+71)/9 = 3(1)₁₉₃9_<195> = 11² · 41 · 1674922471_<10> · 1474538095136372480044028131_<28> · 267407641043367558042632242380571217_<36> · C119
C119 = P32 · P88
P32 = 12106194029400988433886496553153_<32>
P88 = 7843576659298273046592920579513889096997867755355782782493662806320570224295195937674179_<88>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 94955860921945704007355546974800936804246583000431312236385646536971406882241375331831813631952300999296434499069136387 (119 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=235263376 Step 1 took 11871ms Step 2 took 5314ms ********** Factor found in step 2: 12106194029400988433886496553153 Found probable prime factor of 32 digits: 12106194029400988433886496553153 Probable prime cofactor 7843576659298273046592920579513889096997867755355782782493662806320570224295195937674179 has 88 digits
(43·10¹⁵⁴+11)/9 = 4(7)₁₅₃9_<155> = 61 · 2521 · 6621191 · 847749629250263763887_<21> · 16675085747257594544754493982884013_<35> · C88
C88 = P40 · P48
P40 = 5636508307787864317600687433160633242081_<40>
P48 = 588899673562664672531521296334719610351148598859_<48>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 55350244148134926631508712649392541668678343419702755748874150275125536746147316396440138150515401329333495269396625848527 (122 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3859335070 Step 1 took 12059ms ********** Factor found in step 1: 5636508307787864317600687433160633242081 Found probable prime factor of 40 digits: 5636508307787864317600687433160633242081 Composite cofactor 9819952553189439735588237898709102832197648043856985505276394036828197492861141167 has 82 digits
Feb 20, 2009 (5th): By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Feb 20, 2009
(43·10¹²⁵+11)/9 = 4(7)₁₂₄9_<126> = 2351653 · C120
C120 = P34 · P87
P34 = 1266553334462239478412150091931083_<34>
P87 = 160409181960779313344897035534485477224261426249638458525237845325877356661108151236421_<87>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 203166784290785153157280337608387707615782506083073386157642210724872154938580554944874000448951345193265238441971573943 (120 digits) Using B1=1474000, B2=2140044280, polynomial Dickson(6), sigma=3687375578 Step 1 took 12812ms Step 2 took 6485ms ********** Factor found in step 2: 1266553334462239478412150091931083 Found probable prime factor of 34 digits: 1266553334462239478412150091931083 Probable prime cofactor 160409181960779313344897035534485477224261426249638458525237845325877356661108151236421 has 87 digits
(41·10²⁰³+31)/9 = 4(5)₂₀₂9_<204> = 3 · 13 · C203
C203 = P93 · P110
P93 = 457387337981603800293347279194388993095518723402417924356630498257271643329743269622387958219_<93>
P110 = 25538336352856119614320678777293019262107045729253609068129147639376452298149730952253210525759589139805192099_<110>

Number: n N=11680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911681 ( 203 digits) SNFS difficulty: 206 digits. Divisors found: Fri Feb 20 21:41:51 2009 prp93 factor: 457387337981603800293347279194388993095518723402417924356630498257271643329743269622387958219 Fri Feb 20 21:41:51 2009 prp110 factor: 25538336352856119614320678777293019262107045729253609068129147639376452298149730952253210525759589139805192099 Fri Feb 20 21:41:51 2009 elapsed time 24:43:38 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20050930-k8 Total time: 171.01 hours. Scaled time: 344.07 units (timescale=2.012). Factorization parameters were as follows: name: KA_4_5_202_9 n: 11680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911681 deg: 5 c5: 41 c0: 3100 m: 100000000000000000000000000000000000000000 skew: 2.38 type: snfs rlim: 11000000 alim: 11000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 11000000/11000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 47599990) Primes: RFBsize:726517, AFBsize:725685, largePrimes:32641643 encountered Relations: rels:24382690, finalFF:56661 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 9194383 hash collisions in 46991467 relations Msieve: matrix is 3662245 x 3662493 (995.4 MB) Total sieving time: 169.65 hours. Total relation processing time: 1.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,206,5,0,0,0,0,0,0,0,0,11000000,11000000,29,29,58,58,2.5,2.5,100000 total time: 171.01 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.92 BogoMIPS (lpj=2830461) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22643.63 BogoMIPS).
Feb 20, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 20, 2009
(14·10¹⁶¹-11)/3 = 4(6)₁₆₀3_<162> = 2875802551489229275389845286190879_<34> · C129
C129 = P40 · P41 · P49
P40 = 7961407472498715044312651769180597757613_<40>
P41 = 17841291452200529199647842314509698688099_<41>
P49 = 1142435201272643601345229374671734463684938243231_<49>

Number: 46663_161 N=162273542189120096933435105385323543745120089475806304724912872877238918245061625164527994822545703074883859629274728091025656697 ( 129 digits) SNFS difficulty: 162 digits. Divisors found: r1=7961407472498715044312651769180597757613 r2=17841291452200529199647842314509698688099 r3=1142435201272643601345229374671734463684938243231 Version: Total time: 16.13 hours. Scaled time: 38.51 units (timescale=2.387). Factorization parameters were as follows: n: 162273542189120096933435105385323543745120089475806304724912872877238918245061625164527994822545703074883859629274728091025656697 m: 100000000000000000000000000000000 deg: 5 c5: 140 c0: -11 skew: 0.60 type: snfs lss: 1 rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1800000, 3100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9428208 Max relations in full relation-set: Initial matrix: Pruned matrix : 603820 x 604068 Total sieving time: 14.16 hours. Total relation processing time: 0.61 hours. Matrix solve time: 0.82 hours. Time per square root: 0.54 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000 total time: 16.13 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 20, 2009 (3rd): By Sinkiti Sibata / Msieve, GGNFS / Feb 20, 2009
(43·10¹²⁹+11)/9 = 4(7)₁₂₈9_<130> = 3² · 390307 · 26599219579_<11> · 1064068310384686629507983_<25> · C89
C89 = P38 · P52
P38 = 27140931207690852879667282035137002753_<38>
P52 = 1770573452161694692999975192547293750680635048843173_<52>

Fri Feb 20 06:52:14 2009 Msieve v. 1.39 Fri Feb 20 06:52:14 2009 random seeds: 21016154 f81c930e Fri Feb 20 06:52:14 2009 factoring 48055012263284266871337658562328737011072592194561029695649063803572406500776859166255269 (89 digits) Fri Feb 20 06:52:15 2009 searching for 15-digit factors Fri Feb 20 06:52:16 2009 commencing quadratic sieve (89-digit input) Fri Feb 20 06:52:16 2009 using multiplier of 1 Fri Feb 20 06:52:16 2009 using 32kb Intel Core sieve core Fri Feb 20 06:52:16 2009 sieve interval: 32 blocks of size 32768 Fri Feb 20 06:52:16 2009 processing polynomials in batches of 7 Fri Feb 20 06:52:16 2009 using a sieve bound of 1556173 (58969 primes) Fri Feb 20 06:52:16 2009 using large prime bound of 124493840 (26 bits) Fri Feb 20 06:52:16 2009 using double large prime bound of 372619898133360 (42-49 bits) Fri Feb 20 06:52:16 2009 using trial factoring cutoff of 49 bits Fri Feb 20 06:52:16 2009 polynomial 'A' values have 11 factors Fri Feb 20 07:59:21 2009 59187 relations (15670 full + 43517 combined from 631081 partial), need 59065 Fri Feb 20 07:59:22 2009 begin with 646751 relations Fri Feb 20 07:59:23 2009 reduce to 145134 relations in 9 passes Fri Feb 20 07:59:23 2009 attempting to read 145134 relations Fri Feb 20 07:59:24 2009 recovered 145134 relations Fri Feb 20 07:59:24 2009 recovered 123372 polynomials Fri Feb 20 07:59:25 2009 attempting to build 59187 cycles Fri Feb 20 07:59:25 2009 found 59187 cycles in 5 passes Fri Feb 20 07:59:25 2009 distribution of cycle lengths: Fri Feb 20 07:59:25 2009 length 1 : 15670 Fri Feb 20 07:59:25 2009 length 2 : 11090 Fri Feb 20 07:59:25 2009 length 3 : 10545 Fri Feb 20 07:59:25 2009 length 4 : 7913 Fri Feb 20 07:59:25 2009 length 5 : 5579 Fri Feb 20 07:59:25 2009 length 6 : 3664 Fri Feb 20 07:59:25 2009 length 7 : 2137 Fri Feb 20 07:59:25 2009 length 9+: 2589 Fri Feb 20 07:59:25 2009 largest cycle: 17 relations Fri Feb 20 07:59:25 2009 matrix is 58969 x 59187 (14.4 MB) with weight 3532633 (59.69/col) Fri Feb 20 07:59:25 2009 sparse part has weight 3532633 (59.69/col) Fri Feb 20 07:59:26 2009 filtering completed in 3 passes Fri Feb 20 07:59:26 2009 matrix is 55025 x 55089 (13.5 MB) with weight 3314938 (60.17/col) Fri Feb 20 07:59:26 2009 sparse part has weight 3314938 (60.17/col) Fri Feb 20 07:59:26 2009 saving the first 48 matrix rows for later Fri Feb 20 07:59:26 2009 matrix is 54977 x 55089 (9.6 MB) with weight 2720133 (49.38/col) Fri Feb 20 07:59:26 2009 sparse part has weight 2174140 (39.47/col) Fri Feb 20 07:59:26 2009 matrix includes 64 packed rows Fri Feb 20 07:59:26 2009 using block size 22035 for processor cache size 1024 kB Fri Feb 20 07:59:27 2009 commencing Lanczos iteration Fri Feb 20 07:59:27 2009 memory use: 8.8 MB Fri Feb 20 07:59:46 2009 lanczos halted after 871 iterations (dim = 54977) Fri Feb 20 07:59:46 2009 recovered 17 nontrivial dependencies Fri Feb 20 07:59:47 2009 prp38 factor: 27140931207690852879667282035137002753 Fri Feb 20 07:59:47 2009 prp52 factor: 1770573452161694692999975192547293750680635048843173 Fri Feb 20 07:59:47 2009 elapsed time 01:07:33
(43·10¹⁴²+11)/9 = 4(7)₁₄₁9_<143> = 401 · 1321 · 1867727 · 14366243 · 608193757 · 1383871068526152654861029_<25> · C91
C91 = P35 · P57
P35 = 24378346084486836937126300457149213_<35>
P57 = 163825055878536304330382129043609238283062757523353906131_<57>

Fri Feb 20 08:21:18 2009 Msieve v. 1.39 Fri Feb 20 08:21:18 2009 random seeds: 8f5564e0 c40a7580 Fri Feb 20 08:21:18 2009 factoring 3993783909517352782752855055687311510858077698847215776271767549538611990502412608262524903 (91 digits) Fri Feb 20 08:21:19 2009 searching for 15-digit factors Fri Feb 20 08:21:20 2009 commencing quadratic sieve (91-digit input) Fri Feb 20 08:21:20 2009 using multiplier of 7 Fri Feb 20 08:21:20 2009 using 32kb Intel Core sieve core Fri Feb 20 08:21:20 2009 sieve interval: 36 blocks of size 32768 Fri Feb 20 08:21:20 2009 processing polynomials in batches of 6 Fri Feb 20 08:21:20 2009 using a sieve bound of 1685933 (63261 primes) Fri Feb 20 08:21:20 2009 using large prime bound of 155105836 (27 bits) Fri Feb 20 08:21:20 2009 using double large prime bound of 553516580371368 (42-49 bits) Fri Feb 20 08:21:20 2009 using trial factoring cutoff of 49 bits Fri Feb 20 08:21:20 2009 polynomial 'A' values have 12 factors Fri Feb 20 10:02:11 2009 63847 relations (16461 full + 47386 combined from 729762 partial), need 63357 Fri Feb 20 10:02:12 2009 begin with 746223 relations Fri Feb 20 10:02:13 2009 reduce to 158830 relations in 11 passes Fri Feb 20 10:02:13 2009 attempting to read 158830 relations Fri Feb 20 10:02:15 2009 recovered 158830 relations Fri Feb 20 10:02:15 2009 recovered 139831 polynomials Fri Feb 20 10:02:15 2009 attempting to build 63847 cycles Fri Feb 20 10:02:15 2009 found 63847 cycles in 6 passes Fri Feb 20 10:02:15 2009 distribution of cycle lengths: Fri Feb 20 10:02:15 2009 length 1 : 16461 Fri Feb 20 10:02:15 2009 length 2 : 11921 Fri Feb 20 10:02:15 2009 length 3 : 11240 Fri Feb 20 10:02:15 2009 length 4 : 8716 Fri Feb 20 10:02:15 2009 length 5 : 6117 Fri Feb 20 10:02:15 2009 length 6 : 3998 Fri Feb 20 10:02:15 2009 length 7 : 2425 Fri Feb 20 10:02:15 2009 length 9+: 2969 Fri Feb 20 10:02:15 2009 largest cycle: 20 relations Fri Feb 20 10:02:16 2009 matrix is 63261 x 63847 (15.7 MB) with weight 3848842 (60.28/col) Fri Feb 20 10:02:16 2009 sparse part has weight 3848842 (60.28/col) Fri Feb 20 10:02:17 2009 filtering completed in 3 passes Fri Feb 20 10:02:17 2009 matrix is 59516 x 59580 (14.6 MB) with weight 3588684 (60.23/col) Fri Feb 20 10:02:17 2009 sparse part has weight 3588684 (60.23/col) Fri Feb 20 10:02:17 2009 saving the first 48 matrix rows for later Fri Feb 20 10:02:17 2009 matrix is 59468 x 59580 (8.8 MB) with weight 2770890 (46.51/col) Fri Feb 20 10:02:17 2009 sparse part has weight 1957825 (32.86/col) Fri Feb 20 10:02:17 2009 matrix includes 64 packed rows Fri Feb 20 10:02:17 2009 using block size 23832 for processor cache size 1024 kB Fri Feb 20 10:02:17 2009 commencing Lanczos iteration Fri Feb 20 10:02:17 2009 memory use: 8.8 MB Fri Feb 20 10:02:37 2009 lanczos halted after 942 iterations (dim = 59467) Fri Feb 20 10:02:37 2009 recovered 17 nontrivial dependencies Fri Feb 20 10:02:38 2009 prp35 factor: 24378346084486836937126300457149213 Fri Feb 20 10:02:38 2009 prp57 factor: 163825055878536304330382129043609238283062757523353906131 Fri Feb 20 10:02:38 2009 elapsed time 01:41:20
(43·10¹¹⁹+11)/9 = 4(7)₁₁₈9_<120> = 59² · 877169 · 43205687870409677_<17> · C94
C94 = P40 · P55
P40 = 1629543914890988045527593250715973643091_<40>
P55 = 2222448240333959828698516219357710508359559810761141373_<55>

Fri Feb 20 10:12:46 2009 Msieve v. 1.39 Fri Feb 20 10:12:46 2009 random seeds: bc4c5380 61111fb9 Fri Feb 20 10:12:46 2009 factoring 3621577006196388380317543352631061323163065442252020335260657653797868983538297184444095703943 (94 digits) Fri Feb 20 10:12:47 2009 searching for 15-digit factors Fri Feb 20 10:12:48 2009 commencing quadratic sieve (94-digit input) Fri Feb 20 10:12:48 2009 using multiplier of 3 Fri Feb 20 10:12:48 2009 using 32kb Intel Core sieve core Fri Feb 20 10:12:48 2009 sieve interval: 36 blocks of size 32768 Fri Feb 20 10:12:48 2009 processing polynomials in batches of 6 Fri Feb 20 10:12:48 2009 using a sieve bound of 2017133 (75294 primes) Fri Feb 20 10:12:48 2009 using large prime bound of 270295822 (28 bits) Fri Feb 20 10:12:48 2009 using double large prime bound of 1504217873095760 (42-51 bits) Fri Feb 20 10:12:48 2009 using trial factoring cutoff of 51 bits Fri Feb 20 10:12:48 2009 polynomial 'A' values have 12 factors Fri Feb 20 13:30:21 2009 75562 relations (18319 full + 57243 combined from 1073394 partial), need 75390 Fri Feb 20 13:30:23 2009 begin with 1091713 relations Fri Feb 20 13:30:24 2009 reduce to 197045 relations in 15 passes Fri Feb 20 13:30:24 2009 attempting to read 197045 relations Fri Feb 20 13:30:27 2009 recovered 197045 relations Fri Feb 20 13:30:27 2009 recovered 180850 polynomials Fri Feb 20 13:30:27 2009 attempting to build 75562 cycles Fri Feb 20 13:30:27 2009 found 75562 cycles in 6 passes Fri Feb 20 13:30:27 2009 distribution of cycle lengths: Fri Feb 20 13:30:27 2009 length 1 : 18319 Fri Feb 20 13:30:27 2009 length 2 : 13159 Fri Feb 20 13:30:27 2009 length 3 : 12641 Fri Feb 20 13:30:27 2009 length 4 : 10177 Fri Feb 20 13:30:27 2009 length 5 : 7828 Fri Feb 20 13:30:27 2009 length 6 : 5356 Fri Feb 20 13:30:27 2009 length 7 : 3413 Fri Feb 20 13:30:27 2009 length 9+: 4669 Fri Feb 20 13:30:27 2009 largest cycle: 20 relations Fri Feb 20 13:30:28 2009 matrix is 75294 x 75562 (19.7 MB) with weight 4853868 (64.24/col) Fri Feb 20 13:30:28 2009 sparse part has weight 4853868 (64.24/col) Fri Feb 20 13:30:29 2009 filtering completed in 3 passes Fri Feb 20 13:30:29 2009 matrix is 71919 x 71983 (18.8 MB) with weight 4643042 (64.50/col) Fri Feb 20 13:30:29 2009 sparse part has weight 4643042 (64.50/col) Fri Feb 20 13:30:29 2009 saving the first 48 matrix rows for later Fri Feb 20 13:30:29 2009 matrix is 71871 x 71983 (11.6 MB) with weight 3613430 (50.20/col) Fri Feb 20 13:30:29 2009 sparse part has weight 2611838 (36.28/col) Fri Feb 20 13:30:29 2009 matrix includes 64 packed rows Fri Feb 20 13:30:29 2009 using block size 28793 for processor cache size 1024 kB Fri Feb 20 13:30:29 2009 commencing Lanczos iteration Fri Feb 20 13:30:29 2009 memory use: 11.4 MB Fri Feb 20 13:31:02 2009 lanczos halted after 1139 iterations (dim = 71869) Fri Feb 20 13:31:03 2009 recovered 16 nontrivial dependencies Fri Feb 20 13:31:04 2009 prp40 factor: 1629543914890988045527593250715973643091 Fri Feb 20 13:31:04 2009 prp55 factor: 2222448240333959828698516219357710508359559810761141373 Fri Feb 20 13:31:04 2009 elapsed time 03:18:18
(43·10¹³²+11)/9 = 4(7)₁₃₁9_<133> = 3 · 139 · 1617060083_<10> · 5214396783389_<13> · C109
C109 = P50 · P59
P50 = 50541247719731333587997428474350383605813549419067_<50>
P59 = 26885226523835445887875722827790004920957495463615810581103_<59>

Number: 47779_132 N=1358812893742258597789747014238676024239796240176713828444379631747797948175870514261049944549847657338090901 ( 109 digits) SNFS difficulty: 134 digits. Divisors found: r1=50541247719731333587997428474350383605813549419067 (pp50) r2=26885226523835445887875722827790004920957495463615810581103 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 7.22 hours. Scaled time: 3.41 units (timescale=0.472). Factorization parameters were as follows: naqme: 47779_132 n: 1358812893742258597789747014238676024239796240176713828444379631747797948175870514261049944549847657338090901 m: 200000000000000000000000000 deg: 5 c5: 1075 c0: 88 skew: 0.61 type: snfs lss: 1 rlim: 1220000 alim: 1220000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1220000/1220000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [610000, 1210001) Primes: RFBsize:94358, AFBsize:94464, largePrimes:3034738 encountered Relations: rels:2961930, finalFF:243551 Max relations in full relation-set: 28 Initial matrix: 188889 x 243551 with sparse part having weight 19965553. Pruned matrix : 172717 x 173725 with weight 11107596. Total sieving time: 6.54 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.50 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1220000,1220000,26,26,47,47,2.3,2.3,75000 total time: 7.22 hours. --------- CPU info (if available) ----------
(43·10¹²⁰+11)/9 = 4(7)₁₁₉9_<121> = 3² · 93827 · C115
C115 = P31 · P84
P31 = 7038155769238927850882817067061_<31>
P84 = 803890195150983067956507741009808847217713781424351512089994883241101368694024928773_<84>

Number: 47779_120 N=5657904414836499062432606792616882107824658121125733504544152509734556124898634695033030977552987919584599289446153 ( 115 digits) SNFS difficulty: 121 digits. Divisors found: r1=7038155769238927850882817067061 (pp31) r2=803890195150983067956507741009808847217713781424351512089994883241101368694024928773 (pp84) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.25 hours. Scaled time: 1.53 units (timescale=0.472). Factorization parameters were as follows: name: 47779_120 n: 5657904414836499062432606792616882107824658121125733504544152509734556124898634695033030977552987919584599289446153 m: 1000000000000000000000000 deg: 5 c5: 43 c0: 11 skew: 0.76 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 675001) Primes: RFBsize:60238, AFBsize:60292, largePrimes:1430749 encountered Relations: rels:1457858, finalFF:198259 Max relations in full relation-set: 28 Initial matrix: 120595 x 198259 with sparse part having weight 9889634. Pruned matrix : 94071 x 94737 with weight 3577001. Total sieving time: 3.10 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.07 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 3.25 hours. --------- CPU info (if available) ----------
Feb 20, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Feb 20, 2009
4·10¹⁹⁹+9 = 4(0)₁₉₈9_<200> = 7 · 167 · 807609247 · 69410343209_<11> · 3583758997367_<13> · 4408808231743453_<16> · 902378687429809728877943_<24> · C125
C125 = P56 · P70
P56 = 34354547702604499771852060945580290335045785027459957891_<56>
P70 = 1246197671815972306658825990912399156490027586001311061642622929565689_<70>

Number: 40009_199 N=42812557363276487782916934524262511105753525850950546127721797492871267553551320202026578618974150388644911007529878858401899 ( 125 digits) Divisors found: r1=34354547702604499771852060945580290335045785027459957891 r2=1246197671815972306658825990912399156490027586001311061642622929565689 Version: Total time: 97.56 hours. Scaled time: 95.51 units (timescale=0.979). Factorization parameters were as follows: name: 40009_199 n: 42812557363276487782916934524262511105753525850950546127721797492871267553551320202026578618974150388644911007529878858401899 skew: 65485.13 # norm 6.24e+016 c5: 68820 c4: 15113653308 c3: 959756630908979 c2: -113306794408852250946 c1: -1423181321023806426462144 c0: 147911972968623758768192128 # alpha -5.27 Y1: 21201521590249 Y0: -909433307150304267179703 # Murphy_E 1.49e-010 # M 32842432499441896725282475792804844789405376223120805660169649129695932462276002551250689726016767061919229024782184398833998 type: gnfs rlim: 8000000 alim: 8000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [4000000, 7600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 942045 x 942293 Total sieving time: 97.56 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,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,27,27,51,51,2.5,2.5,100000 total time: 97.56 hours. --------- CPU info (if available) ----------
(43·10¹³⁸+11)/9 = 4(7)₁₃₇9_<139> = 3³ · 827 · C135
C135 = P34 · P102
P34 = 1607990073692464275813762654005857_<34>
P102 = 133067901779035413042325512388656807161085244651646675288949326546221468227376511792074081928684625643_<102>

Number: 47779_138 N=213971865187772751926990809161976701947143973208732042535616363373987987719010156199461587074108906703290688242992421415100442374391051 ( 135 digits) SNFS difficulty: 141 digits. Divisors found: r1=1607990073692464275813762654005857 r2=133067901779035413042325512388656807161085244651646675288949326546221468227376511792074081928684625643 Version: Total time: 7.39 hours. Scaled time: 7.12 units (timescale=0.963). Factorization parameters were as follows: n: 213971865187772751926990809161976701947143973208732042535616363373987987719010156199461587074108906703290688242992421415100442374391051 m: 5000000000000000000000000000 deg: 5 c5: 344 c0: 275 skew: 0.96 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [785000, 1785001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 254465 x 254713 Total sieving time: 7.39 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 7.39 hours. --------- CPU info (if available) ----------
(43·10¹³³+11)/9 = 4(7)₁₃₂9_<134> = 7 · 4297 · 655021 · C124
C124 = P62 · P63
P62 = 11346499132520100806728972455098551130381922768598092307243241_<62>
P63 = 213720137275370303790128482759435136117254500175820246299702841_<63>

Number: 47779_133 N=2424975352197066012744415971921744477993322570850246873141852961150303718684874715843679972242569935216148066118330205747681 ( 124 digits) SNFS difficulty: 136 digits. Divisors found: r1=11346499132520100806728972455098551130381922768598092307243241 r2=213720137275370303790128482759435136117254500175820246299702841 Version: Total time: 5.54 hours. Scaled time: 5.40 units (timescale=0.975). Factorization parameters were as follows: n: 2424975352197066012744415971921744477993322570850246873141852961150303718684874715843679972242569935216148066118330205747681 m: 500000000000000000000000000 deg: 5 c5: 344 c0: 275 skew: 0.96 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1325001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 201665 x 201913 Total sieving time: 5.54 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,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 5.54 hours. --------- CPU info (if available) ----------
Feb 20, 2009: By Serge Batalov / GMP-ECM 6.2.1 / Feb 20, 2009
(10²¹⁵+17)/9 = (1)₂₁₄3_<215> = 19 · 8461 · 4461943 · 43154329 · 233686394639_<12> · 3159117892938247_<16> · 10104647752741917108451_<23> · C146
C146 = P33 · P113
P33 = 501928547260793544603300585296669_<33>
P113 = 95867515236356305111343622696905285564256741353453902846428516503461544038617123729098432688474118148620085298703_<113>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=141999233 Step 1 took 30390ms Step 2 took 29422ms ********** Factor found in step 2: 501928547260793544603300585296669 Found probable prime factor of 33 digits: 501928547260793544603300585296669 Probable prime cofactor 95867515236356305111343622696905285564256741353453902846428516503461544038617123729098432688474118148620085298703 has 113 digits
(10²³⁵+17)/9 = (1)₂₃₄3_<235> = 3 · C234
C234 = P37 · C198
P37 = 1462632956704910743229377279655903083_<37>
C198 = [253221677162778007115933666937499898630720100146308997547782269439806975654231771169379649040305075932932943995847187788035663927744145241864622405151602202392552517630064393035746096398124433056137_<198>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3955205230 Step 1 took 84796ms Step 2 took 55438ms ********** Factor found in step 2: 1462632956704910743229377279655903083 Found probable prime factor of 37 digits: 1462632956704910743229377279655903083 Composite cofactor has 198 digits
Feb 19, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 19, 2009
(14·10¹⁶⁶-11)/3 = 4(6)₁₆₅3_<167> = 149 · 185903 · 368231 · 9731163539_<10> · 1043796167165768018697691187783_<31> · C114
C114 = P51 · P63
P51 = 494708760820451125848952720900188160753421001266359_<51>
P63 = 910507854449915240799919859053471284297372043363584815488929473_<63>

Number: 46663_166 N=450436212392205245158977097476905739315982037445676265753566615858125703057142741445006681401990315834878238498807 ( 114 digits) Divisors found: r1=494708760820451125848952720900188160753421001266359 r2=910507854449915240799919859053471284297372043363584815488929473 Version: Total time: 15.97 hours. Scaled time: 38.13 units (timescale=2.388). Factorization parameters were as follows: name: 46663_166 n: 450436212392205245158977097476905739315982037445676265753566615858125703057142741445006681401990315834878238498807 skew: 27512.07 # norm 2.14e+15 c5: 51660 c4: -2900960325 c3: -142057854067848 c2: 1898402704471809028 c1: 36240627074749100550306 c0: -188164729597955528825118040 # alpha -5.15 Y1: 438006036127 Y0: -6138978709709931512157 # Murphy_E 5.94e-10 # M 448558176564726215625748641011569023622740611486017860202758900290125331933431385049191181063798011377365875845011 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.6 alambda: 2.6 qintsize: 70000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [1400000, 2520001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9170106 Max relations in full relation-set: Initial matrix: Pruned matrix : 539874 x 540122 Polynomial selection time: 1.15 hours. Total sieving time: 13.07 hours. Total relation processing time: 0.70 hours. Matrix solve time: 0.66 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000 total time: 15.97 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 19, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Feb 19, 2009
(14·10¹⁵⁹+1)/3 = 4(6)₁₅₈7_<160> = 13 · 23283681427_<11> · 191171963208617_<15> · 1118699180060677_<16> · C119
C119 = P41 · P79
P41 = 11174819369441197114738866818706428965753_<41>
P79 = 6451099618540499233273736884263980249879617664845365580552739306543961653391721_<79>

Number: 46667_159 N=72089872971461088881510076819431699394836374891179644631331325694824456779438131337001864179041635058446583330602730913 ( 119 digits) SNFS difficulty: 160 digits. Divisors found: r1=11174819369441197114738866818706428965753 (pp41) r2=6451099618540499233273736884263980249879617664845365580552739306543961653391721 (pp79) Version: Msieve-1.39 Total time: 20.77 hours. Scaled time: 53.41 units (timescale=2.571). Factorization parameters were as follows: n: 72089872971461088881510076819431699394836374891179644631331325694824456779438131337001864179041635058446583330602730913 m: 100000000000000000000000000000000 deg: 5 c5: 7 c0: 5 skew: 0.93 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 2700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 576094 x 576342 Total sieving time: 20.77 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 20.77 hours. --------- CPU info (if available) ----------
(43·10¹⁵⁹-61)/9 = 4(7)₁₅₈1_<160> = 13 · 2689 · 4481225199742768913_<19> · 5783879069787889733681_<22> · C115
C115 = P41 · P75
P41 = 25751251215386511006956956407779078076869_<41>
P75 = 204775258284067508010307871544880791955964544084259425523964948382641441579_<75>

Number: 47771_159 N=5273219118768680122071708571506706716912016856156729728638835595725334023723100878336479878234453392900749134736151 ( 115 digits) SNFS difficulty: 161 digits. Divisors found: r1=25751251215386511006956956407779078076869 (pp41) r2=204775258284067508010307871544880791955964544084259425523964948382641441579 (pp75) Version: Msieve-1.39 Total time: 36.92 hours. Scaled time: 94.51 units (timescale=2.560). Factorization parameters were as follows: n: 5273219118768680122071708571506706716912016856156729728638835595725334023723100878336479878234453392900749134736151 m: 100000000000000000000000000000000 deg: 5 c5: 43 c0: -610 skew: 1.70 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1750000, 3250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 604530 x 604778 Total sieving time: 36.92 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,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 36.92 hours. --------- CPU info (if available) ----------
Feb 19, 2009: Factorizations of 477...779 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Feb 18, 2009 (5th): By matsui / GGNFS / Feb 18, 2009
4·10¹⁹⁸+9 = 4(0)₁₉₇9_<199> = 13 · C198
C198 = P87 · P112
P87 = 119161480369370553888738724548996511607859620678122425499095327719568445123612055947061_<87>
P112 = 2582145729799085189864734222137758538649682303628164199071706577153193715726836851292948073706300167943278781913_<112>

N=307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693 ( 198 digits) SNFS difficulty: 198 digits. Divisors found: r1=119161480369370553888738724548996511607859620678122425499095327719568445123612055947061 (pp87) r2=2582145729799085189864734222137758538649682303628164199071706577153193715726836851292948073706300167943278781913 (pp112) Version: GGNFS-0.77.1-20060722-nocona
Feb 18, 2009 (4th): By Ignacio Santos / GGNFS, Msieve / Feb 18, 2009
(14·10¹⁷⁹+1)/3 = 4(6)₁₇₈7_<180> = 29 · C179
C179 = P38 · P141
P38 = 92675896264996983590750934289457199517_<38>
P141 = 173636885873488126303743651617020492024657710926734399245020902788494883365428374403641911428951894559811517313745583408396839097490999409619_<141>

Number: 46667_179 N=16091954022988505747126436781609195402298850574712643678160919540229885057471264367816091954022988505747126436781609195402298850574712643678160919540229885057471264367816091954023 ( 179 digits) SNFS difficulty: 180 digits. Divisors found: r1=92675896264996983590750934289457199517 (pp38) r2=173636885873488126303743651617020492024657710926734399245020902788494883365428374403641911428951894559811517313745583408396839097490999409619 (pp141) Version: Msieve-1.39 Total time: 120.30 hours. Scaled time: 307.98 units (timescale=2.560). Factorization parameters were as follows: n: 16091954022988505747126436781609195402298850574712643678160919540229885057471264367816091954022988505747126436781609195402298850574712643678160919540229885057471264367816091954023 m: 1000000000000000000000000000000000000 deg: 5 c5: 7 c0: 5 skew: 0.93 type: snfs lss: 1 rlim: 7200000 alim: 7200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3600000, 5400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1311235 x 1311483 Total sieving time: 120.30 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,180,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000 total time: 120.30 hours. --------- CPU info (if available) ----------
(14·10¹⁵⁸-11)/3 = 4(6)₁₅₇3_<159> = 347 · 491 · 125053 · 727032431635420269844340393_<27> · C122
C122 = P36 · P36 · P51
P36 = 234803378827784030361597153387592303_<36>
P36 = 310713995993218869665380397868638747_<36>
P51 = 412936009293891525760838697224581450103900217364471_<51>

Number: 46663_158 N=30126446942224599374723108632407551078384197415597531296302534156777173628577007643433952264201441997937407902630281128611 ( 122 digits) SNFS difficulty: 160 digits. Divisors found: r1=234803378827784030361597153387592303 (pp36) r2=310713995993218869665380397868638747 (pp36) r3=412936009293891525760838697224581450103900217364471 (pp51) Version: Msieve-1.39 Total time: 26.56 hours. Scaled time: 68.55 units (timescale=2.581). Factorization parameters were as follows: n: 30126446942224599374723108632407551078384197415597531296302534156777173628577007643433952264201441997937407902630281128611 m: 50000000000000000000000000000000 deg: 5 c5: 112 c0: -275 skew: 1.20 type: snfs lss: 1 rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1650000, 3050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 624870 x 625118 Total sieving time: 26.56 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000 total time: 26.56 hours. --------- CPU info (if available) ----------
Feb 18, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 18, 2009
(43·10¹⁴⁸-61)/9 = 4(7)₁₄₇1_<149> = 46769 · 2629210397582974763360451419_<28> · C117
C117 = P44 · P73
P44 = 69658373543494025241174894925771756251923011_<44>
P73 = 5577880312046131909818066047850483955999577280283171864433498801873353451_<73>

Number: 47771_148 N=388546070357410472888762122414019432805997798219949048919437242587685416530014291285085014722220535373757598043160961 ( 117 digits) SNFS difficulty: 151 digits. Divisors found: r1=69658373543494025241174894925771756251923011 r2=5577880312046131909818066047850483955999577280283171864433498801873353451 Version: Total time: 10.24 hours. Scaled time: 24.17 units (timescale=2.359). Factorization parameters were as follows: n: 388546070357410472888762122414019432805997798219949048919437242587685416530014291285085014722220535373757598043160961 m: 1000000000000000000000000000000 deg: 5 c5: 43 c0: -6100 skew: 2.69 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7428740 Max relations in full relation-set: Initial matrix: Pruned matrix : 368502 x 368750 Total sieving time: 9.50 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.30 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 10.24 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(43·10¹⁵⁴-61)/9 = 4(7)₁₅₃1_<155> = 31 · 269 · 1723 · 11717 · 88339 · 102451 · C134
C134 = P36 · P99
P36 = 144998455525129973735485583611764881_<36>
P99 = 216261000622321818515855235227174561862847527613062975417782961788362713610454628027413792585977831_<99>

Number: 47771_154 N=31357511080555835774399090121316456047579255614504315798291457403930937839118791844386060841950607986280672665057609217229883050353111 ( 134 digits) SNFS difficulty: 156 digits. Divisors found: r1=144998455525129973735485583611764881 r2=216261000622321818515855235227174561862847527613062975417782961788362713610454628027413792585977831 Version: Total time: 11.55 hours. Scaled time: 27.55 units (timescale=2.385). Factorization parameters were as follows: n: 31357511080555835774399090121316456047579255614504315798291457403930937839118791844386060841950607986280672665057609217229883050353111 m: 10000000000000000000000000000000 deg: 5 c5: 43 c0: -610 skew: 1.70 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7959798 Max relations in full relation-set: Initial matrix: Pruned matrix : 536710 x 536958 Total sieving time: 10.25 hours. Total relation processing time: 0.40 hours. Matrix solve time: 0.65 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 11.55 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 18, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Feb 17, 2009
(43·10¹⁴⁵-61)/9 = 4(7)₁₄₄1_<146> = 843901 · 293991666959251_<15> · C126
C126 = P60 · P66
P60 = 918101328123974051862278530274961583258199669722430734090181_<60>
P66 = 209753302917850389604880863916559051862645756212210465413357673241_<66>

Number: 47771_145 N=192574785987268684455780319215148361749984341794729274246592538316541197471849039135275279536004523144463306494469797224546621 ( 126 digits) SNFS difficulty: 146 digits. Divisors found: r1=918101328123974051862278530274961583258199669722430734090181 r2=209753302917850389604880863916559051862645756212210465413357673241 Version: Total time: 15.17 hours. Scaled time: 11.88 units (timescale=0.783). Factorization parameters were as follows: n: 192574785987268684455780319215148361749984341794729274246592538316541197471849039135275279536004523144463306494469797224546621 m: 100000000000000000000000000000 deg: 5 c5: 43 c0: -61 skew: 1.07 type: snfs lss: 1 rlim: 1950000 alim: 1950000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1950000/1950000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [975000, 2375001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 322228 x 322476 Total sieving time: 15.17 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000 total time: 15.17 hours. --------- CPU info (if available) ----------
Feb 18, 2009: Factorizations of 11...113 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Feb 17, 2009 (6th): By Wataru Sakai / GMP-ECM 6.2.1 / Feb 17, 2009
4·10²⁵⁰+1 = 4(0)₂₄₉1_<251> = 13 · 609367039316849421092272000364917_<33> · C217
C217 = P28 · C190
P28 = 3646063837616479765543282237_<28>
C190 = [1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213_<190>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1542610798 Step 1 took 31294ms Step 2 took 11523ms ********** Factor found in step 2: 3646063837616479765543282237 Found probable prime factor of 28 digits: 3646063837616479765543282237 Composite cofactor 1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213 has 190 digits
Feb 17, 2009 (5th): By Sinkiti Sibata / Msieve / Feb 17, 2009
(43·10¹⁴⁰-61)/9 = 4(7)₁₃₉1_<141> = 3 · 19 · 613 · 12014939130369479_<17> · 2807781173984016080101272676799_<31> · C90
C90 = P43 · P47
P43 = 7723640672041417684521576904447403699170337_<43>
P47 = 52478779051999590207042356963788789748797491103_<47>

Mon Feb 16 21:12:07 2009 Msieve v. 1.39 Mon Feb 16 21:12:07 2009 random seeds: 24d6521f 26e401d8 Mon Feb 16 21:12:07 2009 factoring 405327232305099187365298506794707503782075648245778252701956086130956454512842708239011711 (90 digits) Mon Feb 16 21:12:08 2009 searching for 15-digit factors Mon Feb 16 21:12:10 2009 commencing quadratic sieve (90-digit input) Mon Feb 16 21:12:10 2009 using multiplier of 11 Mon Feb 16 21:12:10 2009 using 64kb Pentium 4 sieve core Mon Feb 16 21:12:10 2009 sieve interval: 18 blocks of size 65536 Mon Feb 16 21:12:10 2009 processing polynomials in batches of 6 Mon Feb 16 21:12:10 2009 using a sieve bound of 1584403 (60000 primes) Mon Feb 16 21:12:10 2009 using large prime bound of 126752240 (26 bits) Mon Feb 16 21:12:10 2009 using double large prime bound of 384875318121120 (42-49 bits) Mon Feb 16 21:12:10 2009 using trial factoring cutoff of 49 bits Mon Feb 16 21:12:10 2009 polynomial 'A' values have 12 factors Mon Feb 16 23:51:54 2009 60283 relations (15605 full + 44678 combined from 641499 partial), need 60096 Mon Feb 16 23:51:56 2009 begin with 657104 relations Mon Feb 16 23:51:57 2009 reduce to 148545 relations in 11 passes Mon Feb 16 23:51:57 2009 attempting to read 148545 relations Mon Feb 16 23:52:01 2009 recovered 148545 relations Mon Feb 16 23:52:01 2009 recovered 130823 polynomials Mon Feb 16 23:52:01 2009 attempting to build 60283 cycles Mon Feb 16 23:52:01 2009 found 60283 cycles in 5 passes Mon Feb 16 23:52:01 2009 distribution of cycle lengths: Mon Feb 16 23:52:01 2009 length 1 : 15605 Mon Feb 16 23:52:01 2009 length 2 : 11482 Mon Feb 16 23:52:01 2009 length 3 : 10488 Mon Feb 16 23:52:01 2009 length 4 : 8082 Mon Feb 16 23:52:01 2009 length 5 : 5828 Mon Feb 16 23:52:01 2009 length 6 : 3718 Mon Feb 16 23:52:01 2009 length 7 : 2305 Mon Feb 16 23:52:01 2009 length 9+: 2775 Mon Feb 16 23:52:01 2009 largest cycle: 18 relations Mon Feb 16 23:52:02 2009 matrix is 60000 x 60283 (14.8 MB) with weight 3645163 (60.47/col) Mon Feb 16 23:52:02 2009 sparse part has weight 3645163 (60.47/col) Mon Feb 16 23:52:03 2009 filtering completed in 3 passes Mon Feb 16 23:52:03 2009 matrix is 56611 x 56675 (14.0 MB) with weight 3440546 (60.71/col) Mon Feb 16 23:52:03 2009 sparse part has weight 3440546 (60.71/col) Mon Feb 16 23:52:03 2009 saving the first 48 matrix rows for later Mon Feb 16 23:52:03 2009 matrix is 56563 x 56675 (8.8 MB) with weight 2717635 (47.95/col) Mon Feb 16 23:52:03 2009 sparse part has weight 1974818 (34.84/col) Mon Feb 16 23:52:03 2009 matrix includes 64 packed rows Mon Feb 16 23:52:03 2009 using block size 21845 for processor cache size 512 kB Mon Feb 16 23:52:04 2009 commencing Lanczos iteration Mon Feb 16 23:52:04 2009 memory use: 8.6 MB Mon Feb 16 23:52:34 2009 lanczos halted after 896 iterations (dim = 56562) Mon Feb 16 23:52:34 2009 recovered 17 nontrivial dependencies Mon Feb 16 23:52:35 2009 prp43 factor: 7723640672041417684521576904447403699170337 Mon Feb 16 23:52:35 2009 prp47 factor: 52478779051999590207042356963788789748797491103 Mon Feb 16 23:52:35 2009 elapsed time 02:40:28
(43·10¹⁴³-61)/9 = 4(7)₁₄₂1_<144> = 3³ · 7 · 5743 · 432337 · 7595130892169_<13> · 177081686227891007_<18> · C102
C102 = P39 · P64
P39 = 102624840455862064407000833817896986463_<39>
P64 = 7376349985613162477584632245935778321122766520937732169503100401_<64>

Mon Feb 16 07:33:36 2009 Msieve v. 1.39 Mon Feb 16 07:33:36 2009 random seeds: 1efa2ba8 3f80fda9 Mon Feb 16 07:33:36 2009 factoring 756996740420151233386293617974273659264620199260250699674158397990327213454264657595630963113226871663 (102 digits) Mon Feb 16 07:33:37 2009 searching for 15-digit factors Mon Feb 16 07:33:39 2009 commencing quadratic sieve (102-digit input) Mon Feb 16 07:33:40 2009 using multiplier of 2 Mon Feb 16 07:33:40 2009 using 32kb Intel Core sieve core Mon Feb 16 07:33:40 2009 sieve interval: 36 blocks of size 32768 Mon Feb 16 07:33:40 2009 processing polynomials in batches of 6 Mon Feb 16 07:33:40 2009 using a sieve bound of 3272387 (117500 primes) Mon Feb 16 07:33:40 2009 using large prime bound of 490858050 (28 bits) Mon Feb 16 07:33:40 2009 using double large prime bound of 4402715446837350 (44-52 bits) Mon Feb 16 07:33:40 2009 using trial factoring cutoff of 52 bits Mon Feb 16 07:33:40 2009 polynomial 'A' values have 13 factors Tue Feb 17 03:20:09 2009 117796 relations (27579 full + 90217 combined from 1762840 partial), need 117596 Tue Feb 17 03:20:11 2009 begin with 1790419 relations Tue Feb 17 03:20:13 2009 reduce to 313239 relations in 12 passes Tue Feb 17 03:20:13 2009 attempting to read 313239 relations Tue Feb 17 03:20:19 2009 recovered 313239 relations Tue Feb 17 03:20:19 2009 recovered 305305 polynomials Tue Feb 17 03:20:20 2009 attempting to build 117796 cycles Tue Feb 17 03:20:20 2009 found 117795 cycles in 5 passes Tue Feb 17 03:20:20 2009 distribution of cycle lengths: Tue Feb 17 03:20:20 2009 length 1 : 27579 Tue Feb 17 03:20:20 2009 length 2 : 19739 Tue Feb 17 03:20:20 2009 length 3 : 19664 Tue Feb 17 03:20:20 2009 length 4 : 15984 Tue Feb 17 03:20:20 2009 length 5 : 12454 Tue Feb 17 03:20:20 2009 length 6 : 8760 Tue Feb 17 03:20:20 2009 length 7 : 5606 Tue Feb 17 03:20:20 2009 length 9+: 8009 Tue Feb 17 03:20:20 2009 largest cycle: 19 relations Tue Feb 17 03:20:21 2009 matrix is 117500 x 117795 (34.8 MB) with weight 8657234 (73.49/col) Tue Feb 17 03:20:21 2009 sparse part has weight 8657234 (73.49/col) Tue Feb 17 03:20:23 2009 filtering completed in 3 passes Tue Feb 17 03:20:23 2009 matrix is 113209 x 113273 (33.6 MB) with weight 8359768 (73.80/col) Tue Feb 17 03:20:23 2009 sparse part has weight 8359768 (73.80/col) Tue Feb 17 03:20:23 2009 saving the first 48 matrix rows for later Tue Feb 17 03:20:23 2009 matrix is 113161 x 113273 (23.6 MB) with weight 6934256 (61.22/col) Tue Feb 17 03:20:23 2009 sparse part has weight 5513657 (48.68/col) Tue Feb 17 03:20:23 2009 matrix includes 64 packed rows Tue Feb 17 03:20:23 2009 using block size 43690 for processor cache size 1024 kB Tue Feb 17 03:20:25 2009 commencing Lanczos iteration Tue Feb 17 03:20:25 2009 memory use: 21.1 MB Tue Feb 17 03:22:09 2009 lanczos halted after 1791 iterations (dim = 113159) Tue Feb 17 03:22:10 2009 recovered 16 nontrivial dependencies Tue Feb 17 03:22:11 2009 prp39 factor: 102624840455862064407000833817896986463 Tue Feb 17 03:22:11 2009 prp64 factor: 7376349985613162477584632245935778321122766520937732169503100401 Tue Feb 17 03:22:11 2009 elapsed time 19:48:35
(43·10¹²⁵-61)/9 = 4(7)₁₂₄1_<126> = 3² · 7 · 167 · 16667869 · 493736484911653679987_<21> · C94
C94 = P44 · P50
P44 = 98302269014734626147638425900634857243929937_<44>
P50 = 56134529111699639152696867219348421245265838793141_<50>

Tue Feb 17 07:51:21 2009 Msieve v. 1.39 Tue Feb 17 07:51:21 2009 random seeds: 4e82ded0 626dabf8 Tue Feb 17 07:51:21 2009 factoring 5518151581753750275625959440828313150369530075974461894895744348308024266777754720900040162117 (94 digits) Tue Feb 17 07:51:22 2009 searching for 15-digit factors Tue Feb 17 07:51:23 2009 commencing quadratic sieve (94-digit input) Tue Feb 17 07:51:24 2009 using multiplier of 13 Tue Feb 17 07:51:24 2009 using 32kb Intel Core sieve core Tue Feb 17 07:51:24 2009 sieve interval: 36 blocks of size 32768 Tue Feb 17 07:51:24 2009 processing polynomials in batches of 6 Tue Feb 17 07:51:24 2009 using a sieve bound of 2050679 (76471 primes) Tue Feb 17 07:51:24 2009 using large prime bound of 282993702 (28 bits) Tue Feb 17 07:51:24 2009 using double large prime bound of 1633797068989626 (42-51 bits) Tue Feb 17 07:51:24 2009 using trial factoring cutoff of 51 bits Tue Feb 17 07:51:24 2009 polynomial 'A' values have 12 factors Tue Feb 17 10:46:01 2009 76683 relations (19245 full + 57438 combined from 1089796 partial), need 76567 Tue Feb 17 10:46:02 2009 begin with 1109041 relations Tue Feb 17 10:46:04 2009 reduce to 197134 relations in 14 passes Tue Feb 17 10:46:04 2009 attempting to read 197134 relations Tue Feb 17 10:46:07 2009 recovered 197134 relations Tue Feb 17 10:46:07 2009 recovered 178691 polynomials Tue Feb 17 10:46:07 2009 attempting to build 76683 cycles Tue Feb 17 10:46:07 2009 found 76682 cycles in 5 passes Tue Feb 17 10:46:07 2009 distribution of cycle lengths: Tue Feb 17 10:46:07 2009 length 1 : 19245 Tue Feb 17 10:46:07 2009 length 2 : 13786 Tue Feb 17 10:46:07 2009 length 3 : 12988 Tue Feb 17 10:46:07 2009 length 4 : 10368 Tue Feb 17 10:46:07 2009 length 5 : 7746 Tue Feb 17 10:46:07 2009 length 6 : 5041 Tue Feb 17 10:46:07 2009 length 7 : 3234 Tue Feb 17 10:46:07 2009 length 9+: 4274 Tue Feb 17 10:46:07 2009 largest cycle: 23 relations Tue Feb 17 10:46:07 2009 matrix is 76471 x 76682 (20.3 MB) with weight 5018304 (65.44/col) Tue Feb 17 10:46:07 2009 sparse part has weight 5018304 (65.44/col) Tue Feb 17 10:46:09 2009 filtering completed in 3 passes Tue Feb 17 10:46:09 2009 matrix is 72546 x 72610 (19.4 MB) with weight 4785339 (65.90/col) Tue Feb 17 10:46:09 2009 sparse part has weight 4785339 (65.90/col) Tue Feb 17 10:46:09 2009 saving the first 48 matrix rows for later Tue Feb 17 10:46:09 2009 matrix is 72498 x 72610 (12.8 MB) with weight 3853848 (53.08/col) Tue Feb 17 10:46:09 2009 sparse part has weight 2914060 (40.13/col) Tue Feb 17 10:46:09 2009 matrix includes 64 packed rows Tue Feb 17 10:46:09 2009 using block size 29044 for processor cache size 1024 kB Tue Feb 17 10:46:10 2009 commencing Lanczos iteration Tue Feb 17 10:46:10 2009 memory use: 11.9 MB Tue Feb 17 10:46:45 2009 lanczos halted after 1148 iterations (dim = 72498) Tue Feb 17 10:46:45 2009 recovered 18 nontrivial dependencies Tue Feb 17 10:46:46 2009 prp44 factor: 98302269014734626147638425900634857243929937 Tue Feb 17 10:46:46 2009 prp50 factor: 56134529111699639152696867219348421245265838793141 Tue Feb 17 10:46:46 2009 elapsed time 02:55:25
Feb 17, 2009 (4th): By Andreas Tete / Msieve-1.39 ECM / Feb 17, 2009
(4·10¹⁹⁹+23)/9 = (4)₁₉₈7_<199> = 7 · 1231 · C195
C195 = P38 · P158
P38 = 14225762137075170435338246532576567317_<38>
P158 = 36256497391523557391150836153499812526265014545716861850062848979279699883581750510325625228713377300801607790879317559258903710821964811855003806638790958123_<158>

Fri Feb 13 18:48:52 2009 Msieve v. 1.39 Fri Feb 13 18:48:52 2009 random seeds: 471c3938 94b24410 Fri Feb 13 18:48:52 2009 factoring 515776307815300504171340889456242827485719443477363867290755999123180276713989142908720487924387193274276946088481425605714801490593529586218457055175170528541771433729191649581576470284837465991 (195 digits) Fri Feb 13 18:48:55 2009 searching for 15-digit factors Fri Feb 13 18:48:58 2009 searching for 20-digit factors Fri Feb 13 18:49:40 2009 searching for 25-digit factors Fri Feb 13 18:57:51 2009 searching for 30-digit factors Fri Feb 13 20:15:25 2009 searching for 35-digit factors Sat Feb 14 07:16:27 2009 searching for 40-digit factors Mon Feb 16 20:05:38 2009 ECM stage 2 factor found Mon Feb 16 20:05:39 2009 prp38 factor: 14225762137075170435338246532576567317 Mon Feb 16 20:05:39 2009 prp158 factor: 36256497391523557391150836153499812526265014545716861850062848979279699883581750510325625228713377300801607790879317559258903710821964811855003806638790958123 Mon Feb 16 20:05:39 2009 elapsed time 73:16:47
Feb 17, 2009 (3rd): By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Feb 17, 2009
(43·10¹⁶⁷-61)/9 = 4(7)₁₆₆1_<168> = 3 · 7 · 1201 · 12893 · C160
C160 = P42 · P58 · P60
P42 = 319763349029725752411560301820144379646161_<42>
P58 = 6014427291190661113921720374543389795594170837747841101189_<58>
P60 = 763988283777773635783075645741983142491685470331316503861583_<60>

SNFS difficulty: 168 digits. Divisors found: r1=319763349029725752411560301820144379646161 (pp42) r2=6014427291190661113921720374543389795594170837747841101189 (pp58) r3=763988283777773635783075645741983142491685470331316503861583 (pp60) Version: Msieve-1.39 Total time: 40.84 hours. Scaled time: units (timescale=2.949). Factorization parameters were as follows: n: 1469297235067544757374446987145317016369300741801669019628303151502780964333241182086023179625663090895049087028637150168413736423357403521235814614745394074107 m: 1000000000000000000000000000000000 deg: 5 c5: 4300 c0: -61 skew: 0.5 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2350000, 5350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 959321 x 959569 Total sieving time: 32.84 hours. Total relation processing time: 0.00 hours. Matrix solve time: 2.00 hours. x 4 cpu Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,200000 total time: 40.84 hours.
4·10²⁰⁹+1 = 4(0)₂₀₈1_<210> = 7 · 19 · C208
C208 = P100 · P108
P100 = 3868312352905881234614717303045694938316220300630823137841921435236696906862947702213074172986063797_<100>
P108 = 777475685161057172420107889087596154100076593781412039785204592057085537200948941303744478811373723078515001_<108>

# well, can't have a p102, but I have more than one p100 :-) # (rest in peace, St. George Carlin!) SNFS difficulty: 210 digits. Divisors found: r1=3868312352905881234614717303045694938316220300630823137841921435236696906862947702213074172986063797 (pp100) r2=777475685161057172420107889087596154100076593781412039785204592057085537200948941303744478811373723078515001 (pp108) Version: Msieve-1.39 Total time: 1000.01 hours. Scaled time: 2735.04 units (timescale=2.735). Factorization parameters were as follows: n: 3007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518797 m: 1000000000000000000000000000000000000000000 c5: 2 c0: 5 skew: 1.20 type: snfs lss: 1 rlim: 24000000 alim: 24000000 lpbr: 29 lpba: 29 mfbr: 57 mfba: 57 rlambda: 2.6 alambda: 2.6 Factor base limits: 24000000/24000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 57/57 Sieved rational special-q in [12000000, 28800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 50191195 relations (45865473 unique relations and about 35456933 large ideals) Max relations in full relation-set: Initial matrix: Pruned matrix : 3128545 x 3128793 Total sieving time: 900.01 hours. Total relation processing time: 0.00 hours. Matrix solve time: 29.10 hours. * 4 cpu Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,210,5,0,0,0,0,0,0,0,0,24000000,24000000,29,29,57,57,2.6,2.6,200000 total time: 1000.01 hours. # quintic was faster than sextic; tested both; sieved on one side to minimize redundant relations
4·10²¹¹+1 = 4(0)₂₁₀1_<212> = 41 · 59 · 148721 · C204
C204 = P43 · C161
P43 = 1332356352410729241381459477648619855405009_<43>
C161 = [83450977684793282694551706981476556088621921512009377560353348583288515960273808416054497177857020031325682869956011963367750061419815803842510520381026012953211_<161>]

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1854358772 Step 1 took 267563ms Step 2 took 91155ms ********** Factor found in step 2: 1332356352410729241381459477648619855405009 Found probable prime factor of 43 digits: 1332356352410729241381459477648619855405009 Composite cofactor has 161 digits
(64·10³³¹-1)/9 = 7(1)₃₃₁_<332> = 1627 · 5507 · 10546009 · 145180731511060009_<18> · 623478735428331443_<18> · C283
C283 = P38 · P246
P38 = 23456386816454549108790357240236910413_<38>
P246 = 354449980168239535745303077765553350378792474439978401690941252988338747486305028374580076545491280877079036161017542178942829000740483344638466667222237280561425839512652267467737233102180796563105230664353426524559063796193515087840859358054081_<246>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=3294908386 Step 1 took 111556ms Step 2 took 60526ms ********** Factor found in step 2: 23456386816454549108790357240236910413 Found probable prime factor of 38 digits: 23456386816454549108790357240236910413 Probable prime cofactor 354449980168239535745303077765553350378792474439978401690941252988338747486305028374580076545491280877079036161017542178942829000740483344638466667222237280561425839512652267467737233102180796563105230664353426524559063796193515087840859358054081 has 246 digits
(64·10³³⁹-1)/9 = 7(1)₃₃₉_<340> = 13 · 31 · 157 · 3837923 · 34741013129584239530947685332231348396862921255411672754594954962184841471111675073557581361932830161869671_<107> · C222
C222 = P43 · C180
P43 = 1601837752074052763584458486041045553597079_<43>
C180 = [526229880308897806430105246913759491169408945893819869505892057808030029041536086980688560962160211962119608854022769551651299899931637375167849847544953178072548577431851592405163_<180>]

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1474824190 Step 1 took 318827ms Step 2 took 101271ms ********** Factor found in step 2: 1601837752074052763584458486041045553597079 Found probable prime factor of 43 digits: 1601837752074052763584458486041045553597079 Composite cofactor has 180 digits
5·10¹⁹³-1 = 4(9)₁₉₃_<194> = 7 · 8839 · C189
C189 = P42 · C148
P42 = 107516249752971035684650211176390698878497_<42>
C148 = [7516137612365669741489365283749544184373803307710159983061153726053943367711447968803833931459424804091388388814143702729443123989730707737970742479_<148>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3184635571 Step 1 took 16335ms Step 2 took 17245ms ********** Factor found in step 2: 107516249752971035684650211176390698878497 Found probable prime factor of 42 digits: 107516249752971035684650211176390698878497 Composite cofactor has 148 digits
(35·10²⁰⁴-71)/9 = 3(8)₂₀₃1_<205> = 61 · 67 · C201
C201 = P37 · C165
P37 = 3902505814693479946914232122945187201_<37>
C165 = [243824497793396457157695281071537524590427598565699673829660810250881151190575939082501252646909037808114080747612376446679162713152731850998085293276833764395008663_<165>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3483678870 Step 1 took 18399ms Step 2 took 18677ms ********** Factor found in step 2: 3902505814693479946914232122945187201 Found probable prime factor of 37 digits: 3902505814693479946914232122945187201 Composite cofactor has 165 digits
Feb 17, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Feb 16, 2009
(38·10¹⁷¹+61)/9 = 4(2)₁₇₀9_<172> = 131 · C170
C170 = P56 · P115
P56 = 19656586353109644988628428880782557935174813548674463961_<56>
P115 = 1639689791881402852262937784707669473345717597586097018290930889928565528828480997000727743404647721038578540516319_<115>

Number: 42229_171 N=32230703986429177268871925360474978795589482612383375742154368108566581849024597116200169635284139100932994062765055131467345207803223070398642917726887192536047497879559 ( 170 digits) SNFS difficulty: 172 digits. Divisors found: r1=19656586353109644988628428880782557935174813548674463961 (pp56) r2=1639689791881402852262937784707669473345717597586097018290930889928565528828480997000727743404647721038578540516319 (pp115) Version: Msieve-1.39 Total time: 63.58 hours. Scaled time: 110.57 units (timescale=1.739). Factorization parameters were as follows: n: 32230703986429177268871925360474978795589482612383375742154368108566581849024597116200169635284139100932994062765055131467345207803223070398642917726887192536047497879559 m: 10000000000000000000000000000000000 deg: 5 c5: 380 c0: 61 skew: 0.69 type: snfs lss: 1 rlim: 5300000 alim: 5300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5300000/5300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2650000, 5950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 984707 x 984955 Total sieving time: 63.58 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,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000 total time: 63.58 hours. --------- CPU info (if available) ----------
(41·10¹⁷³+31)/9 = 4(5)₁₇₂9_<174> = 3² · 13³ · C170
C170 = P43 · P57 · P71
P43 = 3029238009120866184274345315387011894129521_<43>
P57 = 679776460891127365680164499381757723798582319378637295351_<57>
P71 = 11188432898523632839484220414481435452661059309668165398028722268040373_<71>

Number: 45559_173 N=23039273532370179312980101934737043218305545721719291739015604893316924875110279449529942626589569390358344993453474715802131975701995425861303573335131520535859786352883 ( 170 digits) SNFS difficulty: 176 digits. Divisors found: r1=3029238009120866184274345315387011894129521 (pp43) r2=679776460891127365680164499381757723798582319378637295351 (pp57) r3=11188432898523632839484220414481435452661059309668165398028722268040373 (pp71) Version: Msieve-1.39 Total time: 113.83 hours. Scaled time: 292.66 units (timescale=2.571). Factorization parameters were as follows: n: 23039273532370179312980101934737043218305545721719291739015604893316924875110279449529942626589569390358344993453474715802131975701995425861303573335131520535859786352883 m: 50000000000000000000000000000000000 deg: 5 c5: 328 c0: 775 skew: 1.19 type: snfs lss: 1 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3000000, 8400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1341651 x 1341899 Total sieving time: 113.83 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,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000 total time: 113.83 hours. --------- CPU info (if available) ----------
By Ignacio Santos / GGNFS, Msieve / Feb 17, 2009
(13·10¹⁷⁵+11)/3 = 4(3)₁₇₄7_<176> = 29 · 61 · C173
C173 = P40 · P40 · P47 · P48
P40 = 1288621095191851780372499073998595818057_<40>
P40 = 7132302930944498108158521532994477253953_<40>
P47 = 26155680541725035222970324444772014948886396049_<47>
P48 = 101899774506178196286892707388314296027824602137_<48>

Number: 43337_175 N=24495948746938006406632749199170906350103636706237045411720369323534953834558130770680233653664970793291878650838515168645185603919351799510081025061239871867345016016581873 ( 173 digits) SNFS difficulty: 176 digits. Divisors found: r1=1288621095191851780372499073998595818057 (pp40) r2=7132302930944498108158521532994477253953 (pp40) r3=26155680541725035222970324444772014948886396049 (pp47) r4=101899774506178196286892707388314296027824602137 (pp48) Version: Msieve-1.39 Total time: 66.16 hours. Scaled time: 115.05 units (timescale=1.739). Factorization parameters were as follows: n: 24495948746938006406632749199170906350103636706237045411720369323534953834558130770680233653664970793291878650838515168645185603919351799510081025061239871867345016016581873 m: 100000000000000000000000000000000000 deg: 5 c5: 13 c0: 11 skew: 0.97 type: snfs lss: 1 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3000000, 6300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1195582 x 1195828 Total sieving time: 66.16 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,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000 total time: 66.16 hours. --------- CPU info (if available) ----------
Feb 17, 2009: By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Feb 16, 2009
(35·10¹⁶⁵-17)/9 = 3(8)₁₆₄7_<166> = 13 · 29 · 200041 · 6591395639_<10> · 10664333440055130067457_<23> · C126
C126 = P39 · P88
P39 = 109280386502103256471935743911750090597_<39>
P88 = 6712925841213146837839103821365744689243652680605247737247853841651220452334798552144461_<88>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 733591130487729320041466339475378877828506230498071346123108945591659364833598799646116043576499629418508345462979745381733217 (126 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2491864470 Step 1 took 11843ms Step 2 took 5342ms ********** Factor found in step 2: 109280386502103256471935743911750090597 Found probable prime factor of 39 digits: 109280386502103256471935743911750090597 Probable prime cofactor 6712925841213146837839103821365744689243652680605247737247853841651220452334798552144461 has 88 digits
(43·10¹²⁴-61)/9 = 4(7)₁₂₃1_<125> = 31 · 163 · 6389 · 41959 · C113
C113 = P44 · P69
P44 = 57670739452665100371167339196616006651255717_<44>
P69 = 611593851386938504114770827406703530934017650552297959822029434697721_<69>

Number: 47771_124 N=35271069654188110604310693579449758929093792694822280641027184497713020658439788776775525020655692211494968120957 ( 113 digits) SNFS difficulty: 126 digits. Divisors found: r1=57670739452665100371167339196616006651255717 r2=611593851386938504114770827406703530934017650552297959822029434697721 Version: Total time: 1.00 hours. Scaled time: 2.33 units (timescale=2.335). Factorization parameters were as follows: n: 35271069654188110604310693579449758929093792694822280641027184497713020658439788776775525020655692211494968120957 m: 10000000000000000000000000 deg: 5 c5: 43 c0: -610 skew: 1.70 type: snfs lss: 1 rlim: 800000 alim: 800000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [400000, 680001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2328603 Max relations in full relation-set: Initial matrix: Pruned matrix : 127754 x 128002 Total sieving time: 0.87 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,26,26,46,46,2.3,2.3,40000 total time: 1.00 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Feb 17, 2009
(43·10¹⁴²-61)/9 = 4(7)₁₄₁1_<143> = 35768251 · 971975142044493496125235627_<27> · C109
C109 = P49 · P60
P49 = 6359029958009305926862739463303985620388379963359_<49>
P60 = 216113657076574346992381331592346705690321604633547083159597_<60>

Number: 47771_142 N=1374273219684886110425633843081179314367550784801415167464068283959390961846904203558375753774865608809206323 ( 109 digits) SNFS difficulty: 143 digits. Divisors found: r1=6359029958009305926862739463303985620388379963359 r2=216113657076574346992381331592346705690321604633547083159597 Version: Total time: 6.13 hours. Scaled time: 14.57 units (timescale=2.375). Factorization parameters were as follows: n: 1374273219684886110425633843081179314367550784801415167464068283959390961846904203558375753774865608809206323 m: 10000000000000000000000000000 deg: 5 c5: 4300 c0: -61 skew: 0.43 type: snfs lss: 1 rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [750000, 1400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3850387 Max relations in full relation-set: Initial matrix: Pruned matrix : 251977 x 252225 Total sieving time: 5.71 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.14 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,49,49,2.3,2.3,50000 total time: 6.13 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(43·10¹⁴⁴-61)/9 = 4(7)₁₄₃1_<145> = 502657741 · 2309269179827263_<16> · C121
C121 = P45 · P77
P45 = 110193612870242212645693272924122113622791783_<45>
P77 = 37352750701688809281498611377219784036007829353980004226140370590943237683439_<77>

Number: 47771_144 N=4116034550460564813748098138709870879452440801197676121176679269551367554028928848439137916612448202103176435268764381737 ( 121 digits) SNFS difficulty: 146 digits. Divisors found: r1=110193612870242212645693272924122113622791783 r2=37352750701688809281498611377219784036007829353980004226140370590943237683439 Version: Total time: 6.41 hours. Scaled time: 14.86 units (timescale=2.319). Factorization parameters were as follows: n: 4116034550460564813748098138709870879452440801197676121176679269551367554028928848439137916612448202103176435268764381737 m: 100000000000000000000000000000 deg: 5 c5: 43 c0: -610 skew: 1.70 type: snfs lss: 1 rlim: 1650000 alim: 1650000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1650000/1650000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [825000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4241738 Max relations in full relation-set: Initial matrix: Pruned matrix : 246727 x 246975 Total sieving time: 6.08 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,49,49,2.3,2.3,75000 total time: 6.41 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 16, 2009 (7th): By Robert Backstrom / GGNFS, Msieve / Feb 16, 2009
(43·10¹¹⁹-61)/9 = 4(7)₁₁₈1_<120> = 3 · 7 · 33786569 · 75207302532881_<14> · C97
C97 = P45 · P53
P45 = 686841041276857189302957733169540389755111199_<45>
P53 = 13036058767483538717215947584356676918200426562472841_<53>

Number: n N=8953700178004697272850078007323773932868947994732885669881369760907449234154980288975464372446359 ( 97 digits) SNFS difficulty: 121 digits. Divisors found: Mon Feb 16 16:33:14 2009 prp45 factor: 686841041276857189302957733169540389755111199 Mon Feb 16 16:33:14 2009 prp53 factor: 13036058767483538717215947584356676918200426562472841 Mon Feb 16 16:33:14 2009 elapsed time 00:16:20 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 1.96 hours. Scaled time: 2.57 units (timescale=1.316). Factorization parameters were as follows: name: KA_4_7_118_1 n: 8953700178004697272850078007323773932868947994732885669881369760907449234154980288975464372446359 deg: 5 c5: 43 c0: -610 m: 1000000000000000000000000 skew: 1.70 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 480203) Primes: RFBsize:49098, AFBsize:49047, largePrimes:5511719 encountered Relations: rels:4688886, finalFF:109219 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 243840 hash collisions in 4898442 relations Msieve: matrix is 124992 x 125240 (33.4 MB) Total sieving time: 1.85 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,28,28,56,56,2.5,2.5,50000 total time: 1.96 hours. --------- CPU info (if available) ----------
Feb 16, 2009 (6th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 16, 2009
4·10¹⁸¹+9 = 4(0)₁₈₀9_<182> = 7 · 4463 · 9013 · 44939 · 54440369 · 646495019927_<12> · 17375472304230114852745301318776299103_<38> · C112
C112 = P47 · P65
P47 = 96680330851377897032675335617773667304146317489_<47>
P65 = 53466443788604542141782787390935555045766340238599979694824022367_<65>

Number: 40009_181 N=5169153474928885848324348321675877484252277469106881063647738317793449445476644541605020599482510225817619276463 ( 112 digits) Divisors found: r1=96680330851377897032675335617773667304146317489 r2=53466443788604542141782787390935555045766340238599979694824022367 Version: Total time: 11.56 hours. Scaled time: 27.56 units (timescale=2.384). Factorization parameters were as follows: name: 40009_181 n: 5169153474928885848324348321675877484252277469106881063647738317793449445476644541605020599482510225817619276463 skew: 11307.69 # norm 4.27e+15 c5: 81900 c4: 15515914875 c3: -252443578509548 c2: -2026077604162000042 c1: 2623866671835000250456 c0: 6610025439422676503234535 # alpha -5.84 Y1: 426573340633 Y0: -2290994471364759764248 # Murphy_E 7.55e-10 # M 599980959666439027133329231836971032000226273846861958358850094938446921738455534823840668568287349303771514218 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1200000, 2040001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8194253 Max relations in full relation-set: Initial matrix: Pruned matrix : 442248 x 442496 Polynomial selection time: 0.87 hours. Total sieving time: 9.62 hours. Total relation processing time: 0.56 hours. Matrix solve time: 0.42 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000 total time: 11.56 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 16, 2009 (5th): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Feb 16, 2009
(43·10¹⁴⁰-61)/9 = 4(7)₁₃₉1_<141> = 3 · 19 · 613 · 12014939130369479_<17> · C121
C121 = P31 · C90
P31 = 2807781173984016080101272676799_<31>
C90 = [405327232305099187365298506794707503782075648245778252701956086130956454512842708239011711_<90>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2177330287 Step 1 took 9832ms Step 2 took 12144ms ********** Factor found in step 2: 2807781173984016080101272676799 Found probable prime factor of 31 digits: 2807781173984016080101272676799 Composite cofactor has 90 digits
(43·10¹⁴²-61)/9 = 4(7)₁₄₁1_<143> = 35768251 · C136
C136 = P27 · C109
P27 = 971975142044493496125235627_<27>
C109 = [1374273219684886110425633843081179314367550784801415167464068283959390961846904203558375753774865608809206323_<109>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3401780523 Step 1 took 12739ms Step 2 took 13538ms ********** Factor found in step 2: 971975142044493496125235627 Found probable prime factor of 27 digits: 971975142044493496125235627 Composite cofactor has 109 digits
(43·10¹⁹⁰-61)/9 = 4(7)₁₈₉1_<191> = 63793 · 1164937 · 8792622349836405869542771_<25> · C155
C155 = P38 · P117
P38 = 83298832294425500958607625722801434401_<38>
P117 = 877795089404486954963782457552404091105528419858714925670383392791228993400713983819414032809076686946161566570798161_<117>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2603822046 Step 1 took 14402ms Step 2 took 15584ms ********** Factor found in step 2: 83298832294425500958607625722801434401 Found probable prime factor of 38 digits: 83298832294425500958607625722801434401 Probable prime cofactor has 117 digits
(43·10¹⁷¹-61)/9 = 4(7)₁₇₀1_<172> = 13 · 17 · 41 · C168
C168 = P34 · P134
P34 = 7845455428462107106676257169548517_<34>
P134 = 67209653484714549323117321466492145147605549149413730004693507794615691079450687744110971209177162816167855429388847000741239221795683_<134>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4178244371 Step 1 took 13637ms Step 2 took 15854ms ********** Factor found in step 2: 7845455428462107106676257169548517 Found probable prime factor of 34 digits: 7845455428462107106676257169548517 Probable prime cofactor has 134 digits
(43·10¹²⁷-61)/9 = 4(7)₁₂₆1_<128> = 3911 · 7397642663_<10> · 524720936425589_<15> · C100
C100 = P33 · P67
P33 = 509054986545985914315609096394579_<33>
P67 = 6182323008851373913280520769101995173342062958201255762686072243637_<67>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3547595471 Step 1 took 8268ms Step 2 took 10640ms ********** Factor found in step 2: 509054986545985914315609096394579 Found probable prime factor of 33 digits: 509054986545985914315609096394579 Probable prime cofactor 6182323008851373913280520769101995173342062958201255762686072243637 has 67 digits
(43·10¹⁸¹-61)/9 = 4(7)₁₈₀1_<182> = 41 · 4993 · 4637239 · 23447794511_<11> · 2238586197354816928711_<22> · C138
C138 = P39 · P100
P39 = 787520244228026613351141308129216378279_<39>
P100 = 1217540722763297522505208509838978461879989223390529575643052343951874281431929038985853638287595867_<100>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4086981410 Step 1 took 11891ms Step 2 took 13652ms ********** Factor found in step 2: 787520244228026613351141308129216378279 Found probable prime factor of 39 digits: 787520244228026613351141308129216378279 Probable prime cofactor 1217540722763297522505208509838978461879989223390529575643052343951874281431929038985853638287595867 has 100 digits
(43·10¹⁹³-61)/9 = 4(7)₁₉₂1_<194> = 7194113 · 1121757930540769_<16> · C172
C172 = P35 · P137
P35 = 71199310765325297693532708112008109_<35>
P137 = 83152201696408126546070047639498561500691348762681096052862159690720257463473192817296392702546939875802035388838203099768227067086826327_<137>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1650842304 Step 1 took 13686ms Step 2 took 15855ms ********** Factor found in step 2: 71199310765325297693532708112008109 Found probable prime factor of 35 digits: 71199310765325297693532708112008109 Probable prime cofactor has 137 digits
(43·10¹⁸⁸-61)/9 = 4(7)₁₈₇1_<189> = 3² · 883 · 66071 · C180
C180 = P32 · C149
P32 = 19525460771553668149596808042841_<32>
C149 = [46602644501345193158597898914670594145834189426831461696667881665565602998778190931880816833841590944874547410124468413046847275701045361362861642463_<149>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=637296109 Step 1 took 16324ms ********** Factor found in step 1: 19525460771553668149596808042841 Found probable prime factor of 32 digits: 19525460771553668149596808042841 Composite cofactor has 149 digits
(43·10¹⁶⁶-61)/9 = 4(7)₁₆₅1_<167> = 41 · 3361 · 56851564871_<11> · 54458529178463_<14> · 1356201014051082287469709_<25> · C113
C113 = P33 · P38 · P43
P33 = 897280718820561928249807356357529_<33>
P38 = 73970249053547678867643207278372778361_<38>
P43 = 1244101359385847412349825255921033918644487_<43>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=59274701 Step 1 took 8344ms Step 2 took 10793ms ********** Factor found in step 2: 897280718820561928249807356357529 Found probable prime factor of 33 digits: 897280718820561928249807356357529 Composite cofactor has 80 digits Sun Feb 15 14:10:39 2009 Sun Feb 15 14:10:39 2009 Msieve v. 1.39 Sun Feb 15 14:10:39 2009 random seeds: d29fd19c 3cf57266 Sun Feb 15 14:10:39 2009 factoring 92026487401628360238713977917529420698694663305061074443251871502594085205545807 (80 digits) Sun Feb 15 14:10:40 2009 searching for 15-digit factors Sun Feb 15 14:10:40 2009 commencing quadratic sieve (80-digit input) Sun Feb 15 14:10:40 2009 using multiplier of 7 Sun Feb 15 14:10:40 2009 using 64kb Opteron sieve core Sun Feb 15 14:10:40 2009 sieve interval: 6 blocks of size 65536 Sun Feb 15 14:10:40 2009 processing polynomials in batches of 17 Sun Feb 15 14:10:40 2009 using a sieve bound of 1301077 (49996 primes) Sun Feb 15 14:10:40 2009 using large prime bound of 130107700 (26 bits) Sun Feb 15 14:10:40 2009 using trial factoring cutoff of 27 bits Sun Feb 15 14:10:40 2009 polynomial 'A' values have 10 factors Sun Feb 15 14:22:26 2009 50288 relations (26258 full + 24030 combined from 270126 partial), need 50092 Sun Feb 15 14:22:27 2009 begin with 296384 relations Sun Feb 15 14:22:27 2009 reduce to 71381 relations in 2 passes Sun Feb 15 14:22:27 2009 attempting to read 71381 relations Sun Feb 15 14:22:27 2009 recovered 71381 relations Sun Feb 15 14:22:27 2009 recovered 58949 polynomials Sun Feb 15 14:22:27 2009 attempting to build 50288 cycles Sun Feb 15 14:22:27 2009 found 50288 cycles in 1 passes Sun Feb 15 14:22:27 2009 distribution of cycle lengths: Sun Feb 15 14:22:27 2009 length 1 : 26258 Sun Feb 15 14:22:27 2009 length 2 : 24030 Sun Feb 15 14:22:27 2009 largest cycle: 2 relations Sun Feb 15 14:22:27 2009 matrix is 49996 x 50288 (7.4 MB) with weight 1533099 (30.49/col) Sun Feb 15 14:22:27 2009 sparse part has weight 1533099 (30.49/col) Sun Feb 15 14:22:28 2009 filtering completed in 3 passes Sun Feb 15 14:22:28 2009 matrix is 34735 x 34799 (5.6 MB) with weight 1196408 (34.38/col) Sun Feb 15 14:22:28 2009 sparse part has weight 1196408 (34.38/col) Sun Feb 15 14:22:28 2009 saving the first 48 matrix rows for later Sun Feb 15 14:22:28 2009 matrix is 34687 x 34799 (4.2 MB) with weight 930902 (26.75/col) Sun Feb 15 14:22:28 2009 sparse part has weight 740458 (21.28/col) Sun Feb 15 14:22:28 2009 matrix includes 64 packed rows Sun Feb 15 14:22:28 2009 using block size 13919 for processor cache size 1024 kB Sun Feb 15 14:22:28 2009 commencing Lanczos iteration Sun Feb 15 14:22:28 2009 memory use: 4.0 MB Sun Feb 15 14:22:34 2009 lanczos halted after 551 iterations (dim = 34686) Sun Feb 15 14:22:34 2009 recovered 17 nontrivial dependencies Sun Feb 15 14:22:34 2009 prp38 factor: 73970249053547678867643207278372778361 Sun Feb 15 14:22:34 2009 prp43 factor: 1244101359385847412349825255921033918644487 Sun Feb 15 14:22:34 2009 elapsed time 00:11:55
Feb 16, 2009 (4th): By Erik Branger / Msieve, GGNFS / Feb 16, 2009
(43·10¹⁰⁷-61)/9 = 4(7)₁₀₆1_<108> = 3² · 7² · 17 · 541 · 5623 · 14393833 · C91
C91 = P32 · P60
P32 = 14226811194310956229338618806873_<32>
P60 = 102303162456309080732822575209405595505437738286521037113289_<60>

Sun Feb 15 14:55:03 2009 Msieve v. 1.39 Sun Feb 15 14:55:03 2009 random seeds: f5ae9c98 fff75bb0 Sun Feb 15 14:55:03 2009 factoring 1455447776846830371340399960018503553645247165141598369089276272909152778232497473312835297 (91 digits) Sun Feb 15 14:55:04 2009 searching for 15-digit factors Sun Feb 15 14:55:06 2009 commencing quadratic sieve (91-digit input) Sun Feb 15 14:55:06 2009 using multiplier of 1 Sun Feb 15 14:55:06 2009 using 32kb Intel Core sieve core Sun Feb 15 14:55:06 2009 sieve interval: 36 blocks of size 32768 Sun Feb 15 14:55:06 2009 processing polynomials in batches of 6 Sun Feb 15 14:55:06 2009 using a sieve bound of 1652513 (62308 primes) Sun Feb 15 14:55:06 2009 using large prime bound of 145421144 (27 bits) Sun Feb 15 14:55:06 2009 using double large prime bound of 492866721827128 (42-49 bits) Sun Feb 15 14:55:06 2009 using trial factoring cutoff of 49 bits Sun Feb 15 14:55:06 2009 polynomial 'A' values have 12 factors Sun Feb 15 14:55:25 2009 Sun Feb 15 14:55:25 2009 Sun Feb 15 16:49:40 2009 Sun Feb 15 16:49:40 2009 Msieve v. 1.39 Sun Feb 15 16:49:40 2009 random seeds: 2c38db48 15232584 Sun Feb 15 16:49:40 2009 factoring 1455447776846830371340399960018503553645247165141598369089276272909152778232497473312835297 (91 digits) Sun Feb 15 16:49:41 2009 searching for 15-digit factors Sun Feb 15 16:49:43 2009 commencing quadratic sieve (91-digit input) Sun Feb 15 16:49:43 2009 using multiplier of 1 Sun Feb 15 16:49:43 2009 using 32kb Intel Core sieve core Sun Feb 15 16:49:43 2009 sieve interval: 36 blocks of size 32768 Sun Feb 15 16:49:43 2009 processing polynomials in batches of 6 Sun Feb 15 16:49:43 2009 using a sieve bound of 1652513 (62308 primes) Sun Feb 15 16:49:43 2009 using large prime bound of 145421144 (27 bits) Sun Feb 15 16:49:43 2009 using double large prime bound of 492866721827128 (42-49 bits) Sun Feb 15 16:49:43 2009 using trial factoring cutoff of 49 bits Sun Feb 15 16:49:43 2009 polynomial 'A' values have 12 factors Sun Feb 15 16:49:44 2009 restarting with 17030 full and 725896 partial relations Sun Feb 15 16:49:44 2009 68855 relations (17030 full + 51825 combined from 725896 partial), need 62404 Sun Feb 15 16:49:44 2009 begin with 742926 relations Sun Feb 15 16:49:45 2009 reduce to 170003 relations in 10 passes Sun Feb 15 16:49:45 2009 attempting to read 170003 relations Sun Feb 15 16:49:50 2009 recovered 168835 relations Sun Feb 15 16:49:50 2009 recovered 142934 polynomials Sun Feb 15 16:49:51 2009 attempting to build 67691 cycles Sun Feb 15 16:49:51 2009 found 67691 cycles in 6 passes Sun Feb 15 16:49:51 2009 distribution of cycle lengths: Sun Feb 15 16:49:51 2009 length 1 : 16909 Sun Feb 15 16:49:51 2009 length 2 : 12702 Sun Feb 15 16:49:51 2009 length 3 : 12004 Sun Feb 15 16:49:51 2009 length 4 : 9263 Sun Feb 15 16:49:51 2009 length 5 : 6880 Sun Feb 15 16:49:51 2009 length 6 : 4239 Sun Feb 15 16:49:51 2009 length 7 : 2643 Sun Feb 15 16:49:51 2009 length 9+: 3051 Sun Feb 15 16:49:51 2009 largest cycle: 18 relations Sun Feb 15 16:49:51 2009 matrix is 62308 x 67691 (16.6 MB) with weight 4091641 (60.45/col) Sun Feb 15 16:49:51 2009 sparse part has weight 4091641 (60.45/col) Sun Feb 15 16:49:52 2009 filtering completed in 4 passes Sun Feb 15 16:49:52 2009 matrix is 57681 x 57745 (13.2 MB) with weight 3241565 (56.14/col) Sun Feb 15 16:49:52 2009 sparse part has weight 3241565 (56.14/col) Sun Feb 15 16:49:52 2009 saving the first 48 matrix rows for later Sun Feb 15 16:49:52 2009 matrix is 57633 x 57745 (8.2 MB) with weight 2515473 (43.56/col) Sun Feb 15 16:49:52 2009 sparse part has weight 1794001 (31.07/col) Sun Feb 15 16:49:52 2009 matrix includes 64 packed rows Sun Feb 15 16:49:52 2009 using block size 23098 for processor cache size 2048 kB Sun Feb 15 16:49:52 2009 commencing Lanczos iteration Sun Feb 15 16:49:52 2009 memory use: 8.2 MB Sun Feb 15 16:50:09 2009 lanczos halted after 913 iterations (dim = 57631) Sun Feb 15 16:50:09 2009 recovered 15 nontrivial dependencies Sun Feb 15 16:50:10 2009 prp32 factor: 14226811194310956229338618806873 Sun Feb 15 16:50:10 2009 prp60 factor: 102303162456309080732822575209405595505437738286521037113289 Sun Feb 15 16:50:10 2009 elapsed time 00:00:30
(43·10¹²²-61)/9 = 4(7)₁₂₁1_<123> = 3 · 19² · 389 · 41673733 · 17391826414699782103_<20> · C91
C91 = P41 · P50
P41 = 28184184763523821836019790432528482078337_<41>
P50 = 55518128008771743119102762930430142616557897671791_<50>

Sun Feb 15 15:16:02 2009 Msieve v. 1.38 Sun Feb 15 15:16:02 2009 random seeds: 7f02d460 f08de5ca Sun Feb 15 15:16:02 2009 factoring 1564733177524189700508302751567064458781574081944760784627626700487602371134391481177091567 (91 digits) Sun Feb 15 15:16:03 2009 searching for 15-digit factors Sun Feb 15 15:16:05 2009 commencing quadratic sieve (91-digit input) Sun Feb 15 15:16:05 2009 using multiplier of 7 Sun Feb 15 15:16:05 2009 using 64kb Pentium 4 sieve core Sun Feb 15 15:16:05 2009 sieve interval: 18 blocks of size 65536 Sun Feb 15 15:16:05 2009 processing polynomials in batches of 6 Sun Feb 15 15:16:05 2009 using a sieve bound of 1645421 (62353 primes) Sun Feb 15 15:16:05 2009 using large prime bound of 144797048 (27 bits) Sun Feb 15 15:16:05 2009 using double large prime bound of 489065930136608 (42-49 bits) Sun Feb 15 15:16:05 2009 using trial factoring cutoff of 49 bits Sun Feb 15 15:16:05 2009 polynomial 'A' values have 12 factors Sun Feb 15 17:32:30 2009 62641 relations (16533 full + 46108 combined from 696963 partial), need 62449 Sun Feb 15 17:32:33 2009 begin with 713496 relations Sun Feb 15 17:32:34 2009 reduce to 154230 relations in 10 passes Sun Feb 15 17:32:34 2009 attempting to read 154230 relations Sun Feb 15 17:32:40 2009 recovered 154230 relations Sun Feb 15 17:32:40 2009 recovered 134193 polynomials Sun Feb 15 17:32:40 2009 attempting to build 62641 cycles Sun Feb 15 17:32:40 2009 found 62641 cycles in 5 passes Sun Feb 15 17:32:40 2009 distribution of cycle lengths: Sun Feb 15 17:32:40 2009 length 1 : 16533 Sun Feb 15 17:32:40 2009 length 2 : 11802 Sun Feb 15 17:32:40 2009 length 3 : 10893 Sun Feb 15 17:32:40 2009 length 4 : 8380 Sun Feb 15 17:32:40 2009 length 5 : 6072 Sun Feb 15 17:32:40 2009 length 6 : 3885 Sun Feb 15 17:32:40 2009 length 7 : 2327 Sun Feb 15 17:32:40 2009 length 9+: 2749 Sun Feb 15 17:32:40 2009 largest cycle: 17 relations Sun Feb 15 17:32:40 2009 matrix is 62353 x 62641 (15.4 MB) with weight 3792217 (60.54/col) Sun Feb 15 17:32:40 2009 sparse part has weight 3792217 (60.54/col) Sun Feb 15 17:32:41 2009 filtering completed in 3 passes Sun Feb 15 17:32:41 2009 matrix is 58535 x 58599 (14.5 MB) with weight 3566489 (60.86/col) Sun Feb 15 17:32:41 2009 sparse part has weight 3566489 (60.86/col) Sun Feb 15 17:32:42 2009 saving the first 48 matrix rows for later Sun Feb 15 17:32:42 2009 matrix is 58487 x 58599 (9.2 MB) with weight 2813987 (48.02/col) Sun Feb 15 17:32:42 2009 sparse part has weight 2071367 (35.35/col) Sun Feb 15 17:32:42 2009 matrix includes 64 packed rows Sun Feb 15 17:32:42 2009 using block size 21845 for processor cache size 512 kB Sun Feb 15 17:32:42 2009 commencing Lanczos iteration Sun Feb 15 17:32:42 2009 memory use: 9.0 MB Sun Feb 15 17:33:16 2009 lanczos halted after 926 iterations (dim = 58485) Sun Feb 15 17:33:16 2009 recovered 16 nontrivial dependencies Sun Feb 15 17:33:17 2009 prp41 factor: 28184184763523821836019790432528482078337 Sun Feb 15 17:33:17 2009 prp50 factor: 55518128008771743119102762930430142616557897671791 Sun Feb 15 17:33:17 2009 elapsed time 02:17:15
(43·10¹²¹-61)/9 = 4(7)₁₂₀1_<122> = 41 · 937 · 11969 · 25429687427_<11> · C103
C103 = P35 · P68
P35 = 90194248637814352047759031494690479_<35>
P68 = 45302770742221875681422612444030225099879253011075410319280004436519_<68>

Number: 47771_121 N=4086049368305861293153821232230387164334742283566132179392795643464068457934791786218016782912709202601 ( 103 digits) SNFS difficulty: 122 digits. Divisors found: r1=90194248637814352047759031494690479 r2=45302770742221875681422612444030225099879253011075410319280004436519 Version: Total time: 2.37 hours. Scaled time: 2.36 units (timescale=0.994). Factorization parameters were as follows: n: 4086049368305861293153821232230387164334742283566132179392795643464068457934791786218016782912709202601 m: 1000000000000000000000000 deg: 5 c5: 430 c0: -61 skew: 0.68 type: snfs lss: 1 rlim: 770000 alim: 770000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 770000/770000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [385000, 685001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 86738 x 86983 Total sieving time: 2.37 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,770000,770000,25,25,46,46,2.2,2.2,50000 total time: 2.37 hours. --------- CPU info (if available) ----------
Feb 16, 2009 (3rd): By Serge Batalov / GMP-ECM / Feb 15, 2009
(64·10³¹³-1)/9 = 7(1)₃₁₃_<314> = 21311665559_<11> · C304
C304 = P32 · C272
P32 = 56869355183867970524925233480563_<32>
C272 = [58673469295479689569217613095246308254466564622209413268305902989491810201228240723973260931840271019115647539071466078885025309304572271657870575907588919118705280718254174488336225167199496315865486233581672561101987944769670437830049389779045700170933931843777556163883_<272>]

Input number is (64*10^313-1)/9/21311665559 (304 digits) Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=586813494 Step 1 took 11294ms Step 2 took 8312ms ********** Factor found in step 2: 56869355183867970524925233480563 Found probable prime factor of 32 digits: 56869355183867970524925233480563 Composite cofactor has 272 digits
(64·10³²⁹-1)/9 = 7(1)₃₂₉_<330> = 3 · 25391 · 229689721 · 699955539929_<12> · 1124527993523090279_<19> · C287
C287 = P29 · C259
P29 = 40704154126759059654594607763_<29>
C259 = [1268572766450642491152425150378294135396957255234847563295739922893453854657476574671444949567558350482770410510695204806721172358758008154803977106461792779271742602837417211283835274253110616197477675473057655924764392013624354984613370223714600952428428599_<259>]

Input number is (64*10^329-1)/9/17496155117733/699955539929/1124527993523090279 (287 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1652848252 Step 1 took 10096ms Step 2 took 5695ms ********** Factor found in step 2: 40704154126759059654594607763 Found probable prime factor of 29 digits: 40704154126759059654594607763 Composite cofactor has 259 digits
(64·10³²⁵-1)/9 = 7(1)₃₂₅_<326> = 2351 · 2693 · 559369 · 409481053 · C305
C305 = P37 · C269
P37 = 2055038511900243647232933024391865987_<37>
C269 = [23861421436245432814856204502196893138753855465286917828862029055337849688154013987993558266773941682867659577131547642497160767247096986685566754254247968589257517588732393442403635800292178906992890301105723560177433653333434641150265701045469843517957678137021325403_<269>]

Input number is (64*10^325-1)/9/2351/2693/559369/409481053 (305 digits) Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4209806395 Step 1 took 34082ms Step 2 took 25836ms ********** Factor found in step 2: 2055038511900243647232933024391865987 Found probable prime factor of 37 digits: 2055038511900243647232933024391865987 Composite cofactor ((64*10^325-1)/9/2351/2693/559369/409481053)/2055038511900243647232933024391865987 has 269 digits
By Serge Batalov / GMP-ECM, Msieve-1.39 / Feb 16, 2009
(64·10³⁰⁹-1)/9 = 7(1)₃₀₉_<310> = 13 · 31 · 67 · 199 · 2332951 · 1107465757_<10> · 231408998480608427_<18> · 2433987702761838793853_<22> · 5870493298900966567934867_<25> · 9972146931819828646905779951_<28> · C197
C197 = P30 · P42 · P60 · P67
P30 = 175215362685043374193444272439_<30>
P42 = 135881099877537704102527393172637763005001_<42>
P60 = 455143980801337770203718698452650780386906760272814860845717_<60>
P60 = 1433595695421525345160288214513093277763500173335894023645075916027_<67>

Input number is (64*10^309-1)/(4*10^103-1)/3/31/1107465757 (197 digits) Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1837215423 Step 1 took 6099ms Step 2 took 5093ms ********** Factor found in step 2: 175215362685043374193444272439 Found probable prime factor of 30 digits: 175215362685043374193444272439 Composite cofactor has 167 digits Input number is (64*10^309-1)/(4*10^103-1)/3/31/1107465757/175215362685043374193444272439 (167 digits) Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2067577463 Step 1 took 50538ms Step 2 took 33888ms ********** Factor found in step 2: 135881099877537704102527393172637763005001 Found probable prime factor of 42 digits: 135881099877537704102527393172637763005001 Composite cofactor ((64*10^309-1)/(4*10^103-1)/3/31/1107465757/175215362685043374193444272439)/135881099877537704102527393172637763005001 has 126 digits N=652492451673815201209861895168404601709647029326303666607615459828522384455586028292649098275637500812719004235320429694606359 ( 126 digits) Divisors found: r1=455143980801337770203718698452650780386906760272814860845717 (pp60) r2=1433595695421525345160288214513093277763500173335894023645075916027 (pp67) Version: Msieve-1.39 Total time: 61 hours. Scaled time: 179.19 units (timescale=2.948). Factorization parameters were as follows: name: t n: 652492451673815201209861895168404601709647029326303666607615459828522384455586028292649098275637500812719004235320429694606359 skew: 208560.13 # norm 3.79e+17 c5: 20520 c4: -39040291878 c3: -1815988380632129 c2: 1418998931057512282898 c1: 52248932385834119347087434 c0: -8322878027540642438038865640480 # alpha -7.33 Y1: 10998909987373 Y0: -1997471249591076947964299 # Murphy_E 1.51e-10 # M 440071143724497757575898699709739009936761701217522723178112120106975840417089773780803036670841879485242795129300641371276230 type: gnfs rlim: 8000000 alim: 8000000 lpbr: 27 lpba: 27 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved algebraic special-q in [4000000, 7500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1019394 x 1019642 Total sieving time: 50.61 hours. Total relation processing time: 0.00 hours. Matrix solve time: 1.50 hours. x 4 cpus Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,27,27,54,54,2.5,2.5,200000 total time: 61 hours.
Feb 16, 2009 (2nd): Factorizations of 711...11 have been extended up to n=350.
Feb 16, 2009: By Serge Batalov / PFGW / Feb 16, 2009
(43·10¹⁵⁹⁵⁵-61)/9 = 4(7)₁₅₉₅₄1_<15956> is PRP.
(43·10¹⁶⁰⁹⁸-61)/9 = 4(7)₁₆₀₉₇1_<16099> is PRP.
Feb 15, 2009 (6th): By Erik Branger / GGNFS, Msieve / Feb 15, 2009
(85·10¹⁸⁶+41)/9 = 9(4)₁₈₅9_<187> = 7² · 73 · 2963 · 13879 · 15569 · 249311 · 13535091039564671486279847232684736987_<38> · C130
C130 = P60 · P70
P60 = 292843897769971100638716964000406879520058047538234610226607_<60>
P70 = 4173189726567027680792291651364686867194792560382788150602958007405151_<70>

Number: 94449_186 N=1222093145661488304689087334206869992908799364801631751346153045069664958899170583005647688332917002870930209205870065660169052657 ( 130 digits) Divisors found: r1=292843897769971100638716964000406879520058047538234610226607 r2=4173189726567027680792291651364686867194792560382788150602958007405151 Version: Total time: 270.00 hours. Factorization parameters were as follows: name: 94449_186 n: 1222093145661488304689087334206869992908799364801631751346153045069664958899170583005647688332917002870930209205870065660169052657 skew: 510698.00 Y0: -7656719028100712519179654 Y1: 142321670357531 c0: 1167978539070622701566323783130925 c1: 5304559839315764477186444265 c2: -3710644512753648335949 c3: -35176895023575725 c4: -8370219004 c5: 46440 type: gnfs Factor base limits: 11000000/11000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [5500000, 13300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1252951 x 1253199 Total sieving time: 99.99 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,129,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,11000000,11000000,27,27,51,51,2.6,2.6,100000 total time: 270.00 hours. --------- CPU info (if available) ----------
Feb 15, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 15, 2009
(14·10¹⁵⁴+1)/3 = 4(6)₁₅₃7_<155> = 293 · 7512655541259282306331650654533633_<34> · C119
C119 = P41 · P78
P41 = 54231808989727239423216603755622960161369_<41>
P78 = 390923332769930875603107034278747100755856831370854327511895410945686871799847_<78>

Number: 46667_154 N=21200479512406470387486737841689387728256616761959944459277057188240292447586447134939384922724107131176462502589510543 ( 119 digits) SNFS difficulty: 155 digits. Divisors found: r1=54231808989727239423216603755622960161369 r2=390923332769930875603107034278747100755856831370854327511895410945686871799847 Version: Total time: 8.87 hours. Scaled time: 21.14 units (timescale=2.384). Factorization parameters were as follows: n: 21200479512406470387486737841689387728256616761959944459277057188240292447586447134939384922724107131176462502589510543 m: 10000000000000000000000000000000 deg: 5 c5: 7 c0: 5 skew: 0.93 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1100000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8302757 Max relations in full relation-set: Initial matrix: Pruned matrix : 366414 x 366662 Total sieving time: 8.12 hours. Total relation processing time: 0.34 hours. Matrix solve time: 0.30 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000 total time: 8.87 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(14·10¹⁷⁵-11)/3 = 4(6)₁₇₄3_<176> = 19 · 18637 · 883431433 · 1059339599_<10> · 163183031653807813_<18> · 387506515120886326479029_<24> · C112
C112 = P53 · P59
P53 = 39458651391662737560426731250115138746054521972087131_<53>
P59 = 56438163889499086885495949504388402747909851042790704623549_<59>

Number: 46663_175 N=2226973834101272806078695268331691820297865666351981094067120577496103583990954688153969172760108806003182447919 ( 112 digits) Divisors found: r1=39458651391662737560426731250115138746054521972087131 r2=56438163889499086885495949504388402747909851042790704623549 Version: Total time: 11.13 hours. Scaled time: 25.91 units (timescale=2.327). Factorization parameters were as follows: name: 46663_175 n: 2226973834101272806078695268331691820297865666351981094067120577496103583990954688153969172760108806003182447919 skew: 18558.79 # norm 2.18e+15 c5: 48300 c4: 154232447 c3: -77704578312477 c2: 1515535832638192026 c1: 6186317058615615263235 c0: -184906614236828287925975 # alpha -5.68 Y1: 1058921340037 Y0: -2151559993028487286086 # Murphy_E 8.38e-10 # M 1641793509583862624017536670586366418670310473889377820970417999873360158999715871821814994386591398598360466243 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1200000, 1980001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8230458 Max relations in full relation-set: Initial matrix: Pruned matrix : 408250 x 408498 Polynomial selection time: 0.93 hours. Total sieving time: 8.99 hours. Total relation processing time: 0.52 hours. Matrix solve time: 0.37 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000 total time: 11.13 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 15, 2009 (4th): By Sinkiti Sibata / Msieve / Feb 15, 2009
(14·10¹⁴⁷+1)/3 = 4(6)₁₄₆7_<148> = 13 · 71 · 10821683 · 415360308636593_<15> · C124
C124 = P53 · P71
P53 = 59211116240071953560041490929300702713976962338049427_<53>
P71 = 18996869093972672801989286866587901833146301492603126387978691101914233_<71>

Number: 46667_147 N=1124825824120646305023027673995572656480837216059662782981628272312007636368630268568362380512011078237498677112251068794491 ( 124 digits) SNFS difficulty: 150 digits. Divisors found: r1=59211116240071953560041490929300702713976962338049427 r2=18996869093972672801989286866587901833146301492603126387978691101914233 Version: Total time: 14.36 hours. Scaled time: 27.90 units (timescale=1.943). Factorization parameters were as follows: name: 46667_147 n: 1124825824120646305023027673995572656480837216059662782981628272312007636368630268568362380512011078237498677112251068794491 m: 500000000000000000000000000000 deg: 5 c5: 56 c0: 125 skew: 1.17 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 1600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 318450 x 318698 Total sieving time: 14.36 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000 total time: 14.36 hours. --------- CPU info (if available) ----------
(14·10¹⁹⁶+1)/3 = 4(6)₁₉₅7_<197> = 19 · 88125623503_<11> · 63724402211023850353_<20> · 174979598539031380917131233_<27> · 300304125643577097155478944475718909_<36> · C103
C103 = P35 · P69
P35 = 36569467023955655702572987728072281_<35>
P69 = 227602936992216342653791484918798807288750684295729520069400243313211_<69>

Sat Feb 14 08:07:36 2009 Msieve v. 1.39 Sat Feb 14 08:07:36 2009 random seeds: 54bcde54 f0c5251e Sat Feb 14 08:07:36 2009 factoring 8323318098892312395018467980900645024149797138390385911208071430477385229001986137257942282261530204291 (103 digits) Sat Feb 14 08:07:37 2009 searching for 15-digit factors Sat Feb 14 08:07:39 2009 commencing quadratic sieve (103-digit input) Sat Feb 14 08:07:39 2009 using multiplier of 3 Sat Feb 14 08:07:39 2009 using 32kb Intel Core sieve core Sat Feb 14 08:07:39 2009 sieve interval: 36 blocks of size 32768 Sat Feb 14 08:07:39 2009 processing polynomials in batches of 6 Sat Feb 14 08:07:39 2009 using a sieve bound of 3491867 (125000 primes) Sat Feb 14 08:07:39 2009 using large prime bound of 523780050 (28 bits) Sat Feb 14 08:07:39 2009 using double large prime bound of 4948437687597450 (44-53 bits) Sat Feb 14 08:07:39 2009 using trial factoring cutoff of 53 bits Sat Feb 14 08:07:39 2009 polynomial 'A' values have 14 factors Sun Feb 15 10:05:35 2009 125322 relations (29305 full + 96017 combined from 1879366 partial), need 125096 Sun Feb 15 10:05:38 2009 begin with 1908671 relations Sun Feb 15 10:05:40 2009 reduce to 331728 relations in 12 passes Sun Feb 15 10:05:40 2009 attempting to read 331728 relations Sun Feb 15 10:05:47 2009 recovered 331728 relations Sun Feb 15 10:05:47 2009 recovered 324855 polynomials Sun Feb 15 10:05:48 2009 attempting to build 125322 cycles Sun Feb 15 10:05:48 2009 found 125322 cycles in 6 passes Sun Feb 15 10:05:48 2009 distribution of cycle lengths: Sun Feb 15 10:05:48 2009 length 1 : 29305 Sun Feb 15 10:05:48 2009 length 2 : 21336 Sun Feb 15 10:05:48 2009 length 3 : 21156 Sun Feb 15 10:05:48 2009 length 4 : 17003 Sun Feb 15 10:05:48 2009 length 5 : 13040 Sun Feb 15 10:05:48 2009 length 6 : 9175 Sun Feb 15 10:05:48 2009 length 7 : 5943 Sun Feb 15 10:05:48 2009 length 9+: 8364 Sun Feb 15 10:05:48 2009 largest cycle: 22 relations Sun Feb 15 10:05:48 2009 matrix is 125000 x 125322 (36.0 MB) with weight 8946269 (71.39/col) Sun Feb 15 10:05:48 2009 sparse part has weight 8946269 (71.39/col) Sun Feb 15 10:05:51 2009 filtering completed in 3 passes Sun Feb 15 10:05:51 2009 matrix is 120297 x 120361 (34.8 MB) with weight 8630529 (71.71/col) Sun Feb 15 10:05:51 2009 sparse part has weight 8630529 (71.71/col) Sun Feb 15 10:05:51 2009 saving the first 48 matrix rows for later Sun Feb 15 10:05:51 2009 matrix is 120249 x 120361 (22.1 MB) with weight 6954167 (57.78/col) Sun Feb 15 10:05:51 2009 sparse part has weight 5074835 (42.16/col) Sun Feb 15 10:05:51 2009 matrix includes 64 packed rows Sun Feb 15 10:05:51 2009 using block size 43690 for processor cache size 1024 kB Sun Feb 15 10:05:52 2009 commencing Lanczos iteration Sun Feb 15 10:05:52 2009 memory use: 21.0 MB Sun Feb 15 10:07:37 2009 lanczos halted after 1904 iterations (dim = 120247) Sun Feb 15 10:07:37 2009 recovered 17 nontrivial dependencies Sun Feb 15 10:07:38 2009 prp35 factor: 36569467023955655702572987728072281 Sun Feb 15 10:07:38 2009 prp69 factor: 227602936992216342653791484918798807288750684295729520069400243313211 Sun Feb 15 10:07:38 2009 elapsed time 26:00:02
Feb 15, 2009 (3rd): By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Feb 15, 2009
(14·10¹⁷⁰+1)/3 = 4(6)₁₆₉7_<171> = 46743868447870267651_<20> · C151
C151 = P48 · P104
P48 = 104294166814274386903054982107897366760334221897_<48>
P104 = 95724280549876303733349614934130035922104058690830754970637258308603613525009196486295646799077246779761_<104>

SNFS difficulty: 171 digits. Divisors found: r1=104294166814274386903054982107897366760334221897 (pp48) r2=95724280549876303733349614934130035922104058690830754970637258308603613525009196486295646799077246779761 (pp104) Version: Msieve-1.39 Total time: 30.32 hours. Scaled time: units (timescale=2.950). Factorization parameters were as follows: n: 9983484083845200357518942533658895832376749692236922937893888318516337912293695221613470764610702632769022446093554356116181010244931137412628862626617 m: 10000000000000000000000000000000000 deg: 5 c5: 14 c0: 1 skew: 0.59 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 4500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 883374 x 883621 Total sieving time: 22.32 hours. Total relation processing time: 0.00 hours. Matrix solve time: 1.60 hours. * 4 Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,200000 total time: 30.32 hours.
7·10¹⁹⁵-3 = 6(9)₁₉₄7_<196> = 139 · 3067 · 17876051 · 24527621194063819800299250874272523_<35> · C149
C149 = P38 · P112
P38 = 10810175462712766378399682400374658337_<38>
P112 = 3464253826178025203451630850730623859360665647158270629727669693950603939546671253113435093020109567689734805669_<112>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=705256189 Step 1 took 58911ms Step 2 took 44658ms ********** Factor found in step 2: 10810175462712766378399682400374658337 Found probable prime factor of 38 digits: 10810175462712766378399682400374658337 probable prime cofactor
(8·10¹⁸¹-53)/9 = (8)₁₈₀3_<181> = 3 · 3373 · 104548979020861334868919_<24> · C154
C154 = P35 · P120
P35 = 12499821320686222156090511981140217_<35>
P120 = 672181074501094515150749049807572101902956191960026465193303607551381843935978711469108196973715165015264234761959682059_<120>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1439701945 Step 1 took 45437ms Step 2 took 35187ms ********** Factor found in step 2: 12499821320686222156090511981140217 Found probable prime factor of 35 digits: 12499821320686222156090511981140217 Probable prime cofactor has 120 digits
(28·10¹⁹⁰+71)/9 = 3(1)₁₈₉9_<191> = 3 · 11 · 19 · 118571561 · C180
C180 = P41 · C139
P41 = 72948732985607639943348271937061875858767_<41>
C139 = [5736535564946222076701029625873664000242757235671459219099940391735526356194060277001714023463867870843827613222563476713106720501742427331_<139>]

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=2901755410 Step 1 took 59001ms Step 2 took 44783ms ********** Factor found in step 2: 72948732985607639943348271937061875858767 Found probable prime factor of 41 digits: 72948732985607639943348271937061875858767 Composite cofactor has 139 digits
(8·10¹⁸⁹-53)/9 = (8)₁₈₈3_<189> = 67 · 3715079 · 3805037 · 5562883 · C168
C168 = P39 · P129
P39 = 264803101224449082168597348476311611311_<39>
P129 = 637122209537919103959346621143746198671213839806088223842581849059827407105588908456565553663175429328843741231582163026217491951_<129>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1970532011 Step 1 took 50602ms Step 2 took 39936ms ********** Factor found in step 2: 264803101224449082168597348476311611311 Found probable prime factor of 39 digits: 264803101224449082168597348476311611311 Probable prime cofactor has 129 digits
Feb 15, 2009 (2nd): Factorizations of 477...771 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Feb 15, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 15, 2009
(14·10¹⁵³+1)/3 = 4(6)₁₅₂7_<154> = 13² · 9187433068570610519_<19> · 85252816908018269189_<20> · C113
C113 = P54 · P59
P54 = 432646889532735937305204725920593650955996146661358049_<54>
P59 = 81486106008963007311412437866254747504214979242895064015777_<59>

Number: 46667_153 N=35254710304912628291403028187926064483943842176341801575918120849567564630525220153645723046212671844646381939073 ( 113 digits) SNFS difficulty: 155 digits. Divisors found: r1=432646889532735937305204725920593650955996146661358049 r2=81486106008963007311412437866254747504214979242895064015777 Version: Total time: 9.75 hours. Scaled time: 23.18 units (timescale=2.377). Factorization parameters were as follows: n: 35254710304912628291403028187926064483943842176341801575918120849567564630525220153645723046212671844646381939073 m: 10000000000000000000000000000000 deg: 5 c5: 7 c0: 50 skew: 1.48 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1100000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7765803 Max relations in full relation-set: Initial matrix: Pruned matrix : 459979 x 460227 Total sieving time: 8.90 hours. Total relation processing time: 0.34 hours. Matrix solve time: 0.47 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000 total time: 9.75 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 14, 2009 (5th): By matsui / GGNFS / Feb 14, 2009
2·10²⁰⁰-3 = 1(9)₁₉₉7_<201> = 3917 · C197
C197 = P52 · P60 · P87
P52 = 1353143889460780219324261867805948229627354629623799_<52>
P60 = 107421636386525513520653234479254640339061189356540018700131_<60>
P87 = 351269691736020689086731151005390507435230742784114223916529804772069637453814458555389_<87>

N=51059484299208577993362267041102884860862905284656624968087822312994638754148583099310696961960684197089609394945111054378350778657135562930814398774572376818994128159305591013530763339290273168241 ( 197 digits) SNFS difficulty: 200 digits. Divisors found: r1=1353143889460780219324261867805948229627354629623799 (pp52) r2=107421636386525513520653234479254640339061189356540018700131 (pp60) r3=351269691736020689086731151005390507435230742784114223916529804772069637453814458555389 (pp87) Version: GGNFS-0.77.1-20060722-nocona
Feb 14, 2009 (4th): By Sinkiti Sibata / Msieve / Feb 14, 2009
(14·10¹⁶⁶+1)/3 = 4(6)₁₆₅7_<167> = 227 · 93609576563291_<14> · 6410436491169121721_<19> · 8567432506482975511227306736847_<31> · C101
C101 = P48 · P54
P48 = 105837646301488096064392853135688270797190690443_<48>
P54 = 377817592382338625566553437445757380341481911272332791_<54>

Fri Feb 13 12:23:57 2009 Msieve v. 1.39 Fri Feb 13 12:23:57 2009 random seeds: c697f178 e036b717 Fri Feb 13 12:23:57 2009 factoring 39987324709041758691823561140139597659692108721927001185977095775180330550267978236047812260559216413 (101 digits) Fri Feb 13 12:23:58 2009 searching for 15-digit factors Fri Feb 13 12:23:59 2009 commencing quadratic sieve (101-digit input) Fri Feb 13 12:24:00 2009 using multiplier of 5 Fri Feb 13 12:24:00 2009 using 32kb Intel Core sieve core Fri Feb 13 12:24:00 2009 sieve interval: 36 blocks of size 32768 Fri Feb 13 12:24:00 2009 processing polynomials in batches of 6 Fri Feb 13 12:24:00 2009 using a sieve bound of 2974607 (107273 primes) Fri Feb 13 12:24:00 2009 using large prime bound of 446191050 (28 bits) Fri Feb 13 12:24:00 2009 using double large prime bound of 3707981036623950 (44-52 bits) Fri Feb 13 12:24:00 2009 using trial factoring cutoff of 52 bits Fri Feb 13 12:24:00 2009 polynomial 'A' values have 13 factors Sat Feb 14 03:55:15 2009 107440 relations (25168 full + 82272 combined from 1625467 partial), need 107369 Sat Feb 14 03:55:17 2009 begin with 1650635 relations Sat Feb 14 03:55:19 2009 reduce to 286005 relations in 11 passes Sat Feb 14 03:55:19 2009 attempting to read 286005 relations Sat Feb 14 03:55:25 2009 recovered 286005 relations Sat Feb 14 03:55:25 2009 recovered 278001 polynomials Sat Feb 14 03:55:25 2009 attempting to build 107440 cycles Sat Feb 14 03:55:25 2009 found 107440 cycles in 6 passes Sat Feb 14 03:55:25 2009 distribution of cycle lengths: Sat Feb 14 03:55:25 2009 length 1 : 25168 Sat Feb 14 03:55:25 2009 length 2 : 18101 Sat Feb 14 03:55:25 2009 length 3 : 17717 Sat Feb 14 03:55:25 2009 length 4 : 14669 Sat Feb 14 03:55:25 2009 length 5 : 11309 Sat Feb 14 03:55:25 2009 length 6 : 7873 Sat Feb 14 03:55:25 2009 length 7 : 5171 Sat Feb 14 03:55:25 2009 length 9+: 7432 Sat Feb 14 03:55:25 2009 largest cycle: 21 relations Sat Feb 14 03:55:26 2009 matrix is 107273 x 107440 (30.8 MB) with weight 7645489 (71.16/col) Sat Feb 14 03:55:26 2009 sparse part has weight 7645489 (71.16/col) Sat Feb 14 03:55:28 2009 filtering completed in 3 passes Sat Feb 14 03:55:28 2009 matrix is 103299 x 103363 (29.8 MB) with weight 7398436 (71.58/col) Sat Feb 14 03:55:28 2009 sparse part has weight 7398436 (71.58/col) Sat Feb 14 03:55:28 2009 saving the first 48 matrix rows for later Sat Feb 14 03:55:28 2009 matrix is 103251 x 103363 (19.5 MB) with weight 5997541 (58.02/col) Sat Feb 14 03:55:28 2009 sparse part has weight 4487591 (43.42/col) Sat Feb 14 03:55:28 2009 matrix includes 64 packed rows Sat Feb 14 03:55:28 2009 using block size 41345 for processor cache size 1024 kB Sat Feb 14 03:55:29 2009 commencing Lanczos iteration Sat Feb 14 03:55:29 2009 memory use: 18.2 MB Sat Feb 14 03:56:55 2009 lanczos halted after 1634 iterations (dim = 103249) Sat Feb 14 03:56:55 2009 recovered 17 nontrivial dependencies Sat Feb 14 03:56:56 2009 prp48 factor: 105837646301488096064392853135688270797190690443 Sat Feb 14 03:56:56 2009 prp54 factor: 377817592382338625566553437445757380341481911272332791 Sat Feb 14 03:56:56 2009 elapsed time 15:32:59
(14·10¹⁴⁴+1)/3 = 4(6)₁₄₃7_<145> = 34231 · 112734187101659502097272353_<27> · C115
C115 = P53 · P62
P53 = 41860487605074545822214730527238787086921508635630057_<53>
P62 = 28888651782642712901521098516490340221304589902980438590000517_<62>

Number: 46667_144 N=1209293049874629965857509671889586266473728920998546232084066695052908898286693988441135423590198309266664250739469 ( 115 digits) SNFS difficulty: 145 digits. Divisors found: r1=41860487605074545822214730527238787086921508635630057 r2=28888651782642712901521098516490340221304589902980438590000517 Version: Total time: 9.39 hours. Scaled time: 18.52 units (timescale=1.972). Factorization parameters were as follows: name: 46667_144 n: 1209293049874629965857509671889586266473728920998546232084066695052908898286693988441135423590198309266664250739469 m: 100000000000000000000000000000 deg: 5 c5: 7 c0: 5 skew: 0.93 type: snfs lss: 1 rlim: 1890000 alim: 1890000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1890000/1890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [945000, 1845001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 267507 x 267755 Total sieving time: 9.39 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,145,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000 total time: 9.39 hours. --------- CPU info (if available) ----------
Feb 14, 2009 (3rd): By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Feb 14, 2009
(14·10¹⁶⁵-11)/3 = 4(6)₁₆₄3_<166> = 1187 · C163
C163 = P53 · P110
P53 = 75273344314006455047373618700306263254729554245011119_<53>
P110 = 52229377573155775722074013780922150979377281646505623065824363308585613892793884921603674014013584366953471971_<110>

SNFS difficulty: 166 digits. Divisors found: r1=75273344314006455047373618700306263254729554245011119 (pp53) r2=52229377573155775722074013780922150979377281646505623065824363308585613892793884921603674014013584366953471971 (pp110) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.917). Factorization parameters were as follows: n: 3931479921370401572591968548160629036787419264251614714967705700645885987082280258354394832912103341757933164841336703173265936534681269306374613872507722549845549 m: 1000000000000000000000000000000000 deg: 5 c5: 14 c0: -11 skew: 0.95 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2050000, 3650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 739970 x 740218 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,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.4,2.4,200000 total time: 29.00 hours.
(10¹⁹⁵+17)/9 = (1)₁₉₄3_<195> = 89 · 839 · 46337 · C185
C185 = P39 · P147
P39 = 180219932950749045834203315868394030019_<39>
P147 = 178186495547831158629886584868040389093978707544314165250237649071872527239633949856494301323944055336016195990546166140103456946868516762554689901_<147>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=410370439 Step 1 took 58922ms Step 2 took 44850ms ********** Factor found in step 2: 180219932950749045834203315868394030019 Found probable prime factor of 39 digits: 180219932950749045834203315868394030019 Probable prime cofactor has 147 digits
(10¹⁹⁹+17)/9 = (1)₁₉₈3_<199> = 3 · 53 · 61 · 5261569 · 14429307007535652733_<20> · 28953978442052238625370216321_<29> · C140
C140 = P44 · P47 · P50
P44 = 22030472258797275743537418347333146628457907_<44>
P47 = 34282597905119932900091785459591793403348759523_<47>
P50 = 69002370162380621152740212076872714098090972363351_<50>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1005177743 Step 1 took 43500ms Step 2 took 35167ms ********** Factor found in step 2: 34282597905119932900091785459591793403348759523 Found probable prime factor of 47 digits: 34282597905119932900091785459591793403348759523 Composite cofactor has 94 digits N=1520154801653587145519307402953669982384665387658339424932743614496399400375403119312412966357 ( 94 digits) Divisors found: r1=22030472258797275743537418347333146628457907 (pp44) r2=69002370162380621152740212076872714098090972363351 (pp50) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: name: t n: 1520154801653587145519307402953669982384665387658339424932743614496399400375403119312412966357 m: 2670485256132997099992 deg: 4 c4: 29890080 c3: -13117314349 c2: -242242966401244948 c1: 324114490938892144 c0: 357487177208619254665813 skew: 1635.250 type: gnfs # adj. I(F,S) = 53.124 # E(F1,F2) = 6.714689e-05 # GGNFS version 0.77.1-20060722-k8 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1234577083. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 140362 x 140589 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,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 3.00 hours.
(4·10¹⁹¹+41)/9 = (4)₁₉₀9_<191> = 9445455512599_<13> · 568330868941154509_<18> · 18527367251974270369_<20> · C141
C141 = P39 · P103
P39 = 335732563467571075947367193609809575347_<39>
P103 = 1331024816574415178535198740376933736414450937292699184327359822630102869705402231438438248290257348273_<103>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=152571016 Step 1 took 43365ms Step 2 took 29504ms ********** Factor found in step 2: 335732563467571075947367193609809575347 Found probable prime factor of 39 digits: 335732563467571075947367193609809575347 Probable prime cofactor has 103 digits
7·10¹⁸⁶-3 = 6(9)₁₈₅7_<187> = 887 · 439823 · 1196059 · 1026017623085007713_<19> · C155
C155 = P32 · P123
P32 = 92337907616891958329226316547999_<32>
P123 = 158346705035860066410666443177431638272396001523007818205086265361406331827017357270653495045419576915774032335665253102209_<123>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2080995158 Step 1 took 52056ms Step 2 took 32746ms ********** Factor found in step 2: 92337907616891958329226316547999 Found probable prime factor of 32 digits: 92337907616891958329226316547999 Probable prime cofactor 158346705035860066410666443177431638272396001523007818205086265361406331827017357270653495045419576915774032335665253102209 has 123 digits
5·10¹⁸⁴-7 = 4(9)₁₈₃3_<185> = 59 · 2381 · 3823 · 6566081 · 31425551790847_<14> · C156
C156 = P41 · P115
P41 = 80039443926543333426030393619033027817759_<41>
P115 = 5637169435779042518564618258869429332554961926507393446662237475156718430440794073039044584353258208612957374372233_<115>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2736760227 Step 1 took 51483ms Step 2 took 33748ms ********** Factor found in step 2: 80039443926543333426030393619033027817759 Found probable prime factor of 41 digits: 80039443926543333426030393619033027817759 Probable prime cofactor 5637169435779042518564618258869429332554961926507393446662237475156718430440794073039044584353258208612957374372233 has 115 digits
7·10¹⁹⁵-3 = 6(9)₁₉₄7_<196> = 139 · 3067 · 17876051 · C183
C183 = P35 · C149
P35 = 24527621194063819800299250874272523_<35>
C149 = [37449191708358504951512531418661234354118514299816902412910533299054998461221910284706013330562360986172625399055406703880777217563744499862965712453_<149>]

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=2507872870 Step 1 took 59190ms Step 2 took 46541ms ********** Factor found in step 2: 24527621194063819800299250874272523 Found probable prime factor of 35 digits: 24527621194063819800299250874272523 Composite cofactor has 149 digits
(4·10¹⁸⁴+41)/9 = (4)₁₈₃9_<184> = 3 · 493859316479_<12> · C172
C172 = P40 · C133
P40 = 1028468656901316025194870592631166453493_<40>
C133 = [2916768192185476209130600299020222703251001859873551312550186038537008789362831619096830736907690865140108164330933656050977865580289_<133>]

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1065531543 Step 1 took 50760ms Step 2 took 41555ms ********** Factor found in step 2: 1028468656901316025194870592631166453493 Found probable prime factor of 40 digits: 1028468656901316025194870592631166453493 Composite cofactor has 133 digits
8·10¹⁷⁰-7 = 7(9)₁₆₉3_<171> = 13 · 167 · 173 · 3527 · 1164843975864664079_<19> · C144
C144 = P39 · P106
P39 = 267225671577587886263333427818158723483_<39>
P106 = 1940138194737605546964094210184209125694364459325237602677778591219159584108616662614835144171508335314589_<106>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=4243394023 Step 1 took 43630ms Step 2 took 10886ms ********** Factor found in step 2: 267225671577587886263333427818158723483 Found probable prime factor of 39 digits: 267225671577587886263333427818158723483 Probable prime cofactor has 106 digits
(28·10¹⁹⁴+71)/9 = 3(1)₁₉₃9_<195> = 11² · 41 · 1674922471_<10> · 1474538095136372480044028131_<28> · C155
C155 = P36 · C119
P36 = 267407641043367558042632242380571217_<36>
C119 = [94955860921945704007355546974800936804246583000431312236385646536971406882241375331831813631952300999296434499069136387_<119>]

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=710368225 Step 1 took 55001ms Step 2 took 37692ms ********** Factor found in step 2: 267407641043367558042632242380571217 Found probable prime factor of 36 digits: 267407641043367558042632242380571217 Composite cofactor has 119 digits
8·10¹⁹⁶-7 = 7(9)₁₉₅3_<197> = 5531 · 358990876536924989546737_<24> · C170
C170 = P36 · P135
P36 = 214605166213413649753799079575549309_<36>
P135 = 187742563889361910433535169521129458961729353440826580401787271210018504832215823551155968418007570578866423270571979403524548052497991_<135>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1664096161 Step 1 took 50439ms Step 2 took 41184ms ********** Factor found in step 2: 214605166213413649753799079575549309 Found probable prime factor of 36 digits: 214605166213413649753799079575549309 Probable prime cofactor has 135 digits
(8·10¹⁸²-53)/9 = (8)₁₈₁3_<182> = 157 · 499 · 22385351 · C170
C170 = P38 · P133
P38 = 20927507877603562216772481531959930821_<38>
P133 = 2421953813812902991229062272111059316848736284277459734782495754095937631298254836200644777053879601560333590388382682997464506923911_<133>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=2787302746 Step 1 took 50683ms Step 2 took 40992ms ********** Factor found in step 2: 20927507877603562216772481531959930821 Found probable prime factor of 38 digits: 20927507877603562216772481531959930821 Probable prime cofactor has 133 digits
Feb 14, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Feb 14, 2009
(14·10¹⁴³+1)/3 = 4(6)₁₄₂7_<144> = 9020890114447567_<16> · C128
C128 = P45 · P84
P45 = 260954755813331551484629836671841329424589369_<45>
P84 = 198240403140835028113695300828948914392004001895842843502933578491559379460150732429_<84>

Number: 46667_143 N=51731775993953009910301308419212924796902674648198394769006101620615186310053836176840364665870571890912291010439718267916947301 ( 128 digits) SNFS difficulty: 145 digits. Divisors found: r1=260954755813331551484629836671841329424589369 r2=198240403140835028113695300828948914392004001895842843502933578491559379460150732429 Version: Total time: 12.09 hours. Scaled time: 9.46 units (timescale=0.782). Factorization parameters were as follows: n: 51731775993953009910301308419212924796902674648198394769006101620615186310053836176840364665870571890912291010439718267916947301 m: 100000000000000000000000000000 deg: 5 c5: 7 c0: 50 skew: 1.48 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [950000, 2050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 309798 x 310046 Total sieving time: 12.09 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,145,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 12.09 hours. --------- CPU info (if available) ----------
Feb 14, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 14, 2009
(14·10¹⁴⁹+1)/3 = 4(6)₁₄₈7_<150> = 17 · 1433 · 88848637 · 29178780371701_<14> · C124
C124 = P59 · P66
P59 = 52085636918944088812203312210504732508023447832895818013441_<59>
P66 = 141865170733330080376212873778627147222277396429992237445479582291_<66>

Number: 46669_149 N=7389137774260243688053830273352604246508616558218557111613676233755812817641078542381629932217207801812449835065450103573331 ( 124 digits) SNFS difficulty: 150 digits. Divisors found: r1=52085636918944088812203312210504732508023447832895818013441 r2=141865170733330080376212873778627147222277396429992237445479582291 Version: Total time: 5.45 hours. Scaled time: 12.87 units (timescale=2.360). Factorization parameters were as follows: n: 7389137774260243688053830273352604246508616558218557111613676233755812817641078542381629932217207801812449835065450103573331 m: 1000000000000000000000000000000 deg: 5 c5: 7 c0: 5 skew: 0.93 type: snfs lss: 1 rlim: 1800000 alim: 1800000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [900000, 1400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6346214 Max relations in full relation-set: Initial matrix: Pruned matrix : 348304 x 348552 Total sieving time: 4.98 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.27 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,27,27,49,49,2.4,2.4,100000 total time: 5.45 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(14·10¹⁵²+1)/3 = 4(6)₁₅₁7_<153> = 1259 · 4449581879_<10> · 31680660311933_<14> · C127
C127 = P51 · P77
P51 = 164419801792715399978720014469178894785688300264421_<51>
P77 = 15992394807860943672501515269727850107518587694312563080621071031105148189079_<77>

Number: 46667_152 N=2629466384499347241036001490457162666115412103509341476457525842912585465822458952893668770251581037113343323667412465004458259 ( 127 digits) SNFS difficulty: 153 digits. Divisors found: r1=164419801792715399978720014469178894785688300264421 r2=15992394807860943672501515269727850107518587694312563080621071031105148189079 Version: Total time: 7.86 hours. Scaled time: 18.80 units (timescale=2.392). Factorization parameters were as follows: n: 2629466384499347241036001490457162666115412103509341476457525842912585465822458952893668770251581037113343323667412465004458259 m: 2000000000000000000000000000000 deg: 5 c5: 175 c0: 4 skew: 0.47 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1100000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8279462 Max relations in full relation-set: Initial matrix: Pruned matrix : 340575 x 340823 Total sieving time: 7.23 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.25 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000 total time: 7.86 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 13, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 13, 2009
(13·10¹⁹⁵+17)/3 = 4(3)₁₉₄9_<196> = C196
C196 = P44 · P49 · P104
P44 = 43038594302076212180404662503389491920977571_<44>
P49 = 6396895104394665782573448096012043723085976503681_<49>
P104 = 15739639826095135291644801789933718287314134718487647918772287020703181372193969444606666771292347715689_<104>

Number: 43339_195 N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339 ( 196 digits) SNFS difficulty: 196 digits. Divisors found: r1=43038594302076212180404662503389491920977571 r2=6396895104394665782573448096012043723085976503681 r3=15739639826095135291644801789933718287314134718487647918772287020703181372193969444606666771292347715689 Version: Total time: 283.07 hours. Scaled time: 674.00 units (timescale=2.381). Factorization parameters were as follows: n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339 m: 1000000000000000000000000000000000000000 deg: 5 c5: 13 c0: 17 skew: 1.06 type: snfs lss: 1 rlim: 15000000 alim: 15000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 15000000/15000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [7500000, 14100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 23478985 Max relations in full relation-set: Initial matrix: Pruned matrix : 2445387 x 2445635 Total sieving time: 256.46 hours. Total relation processing time: 8.45 hours. Matrix solve time: 17.08 hours. Time per square root: 1.08 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,15000000,15000000,28,28,55,55,2.5,2.5,100000 total time: 283.07 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 13, 2009 (4th): By Erik Branger / Msieve / Feb 13, 2009
(14·10¹⁶²+1)/3 = 4(6)₁₆₁7_<163> = 139 · 599 · 37243 · 1143529 · 521121781 · 85455939917603_<14> · 399007013662755691469737714633_<30> · C95
C95 = P42 · P53
P42 = 780810284493164937541387674186542177655467_<42>
P53 = 94856213196199882289140137695997617853942491092295137_<53>

Thu Feb 12 17:48:12 2009 Msieve v. 1.38 Thu Feb 12 17:48:12 2009 random seeds: bd78225c 7d519f38 Thu Feb 12 17:48:12 2009 factoring 74064706811669136267266549263175661936240043622241422381737475862705723444971303591286665563979 (95 digits) Thu Feb 12 17:48:14 2009 searching for 15-digit factors Thu Feb 12 17:48:15 2009 commencing quadratic sieve (95-digit input) Thu Feb 12 17:48:16 2009 using multiplier of 35 Thu Feb 12 17:48:16 2009 using 64kb Pentium 4 sieve core Thu Feb 12 17:48:16 2009 sieve interval: 18 blocks of size 65536 Thu Feb 12 17:48:16 2009 processing polynomials in batches of 6 Thu Feb 12 17:48:16 2009 using a sieve bound of 2193701 (81176 primes) Thu Feb 12 17:48:16 2009 using large prime bound of 329055150 (28 bits) Thu Feb 12 17:48:16 2009 using double large prime bound of 2143303351966200 (43-51 bits) Thu Feb 12 17:48:16 2009 using trial factoring cutoff of 51 bits Thu Feb 12 17:48:16 2009 polynomial 'A' values have 12 factors Fri Feb 13 00:06:21 2009 81352 relations (19911 full + 61441 combined from 1214476 partial), need 81272 Fri Feb 13 00:06:27 2009 begin with 1234387 relations Fri Feb 13 00:06:29 2009 reduce to 211622 relations in 11 passes Fri Feb 13 00:06:29 2009 attempting to read 211622 relations Fri Feb 13 00:06:35 2009 recovered 211622 relations Fri Feb 13 00:06:35 2009 recovered 196858 polynomials Fri Feb 13 00:06:35 2009 attempting to build 81352 cycles Fri Feb 13 00:06:35 2009 found 81352 cycles in 6 passes Fri Feb 13 00:06:35 2009 distribution of cycle lengths: Fri Feb 13 00:06:35 2009 length 1 : 19911 Fri Feb 13 00:06:35 2009 length 2 : 14320 Fri Feb 13 00:06:35 2009 length 3 : 13518 Fri Feb 13 00:06:35 2009 length 4 : 11192 Fri Feb 13 00:06:35 2009 length 5 : 8350 Fri Feb 13 00:06:35 2009 length 6 : 5604 Fri Feb 13 00:06:35 2009 length 7 : 3538 Fri Feb 13 00:06:35 2009 length 9+: 4919 Fri Feb 13 00:06:35 2009 largest cycle: 20 relations Fri Feb 13 00:06:36 2009 matrix is 81176 x 81352 (22.7 MB) with weight 5613162 (69.00/col) Fri Feb 13 00:06:36 2009 sparse part has weight 5613162 (69.00/col) Fri Feb 13 00:06:37 2009 filtering completed in 3 passes Fri Feb 13 00:06:37 2009 matrix is 77351 x 77415 (21.7 MB) with weight 5377028 (69.46/col) Fri Feb 13 00:06:37 2009 sparse part has weight 5377028 (69.46/col) Fri Feb 13 00:06:38 2009 saving the first 48 matrix rows for later Fri Feb 13 00:06:38 2009 matrix is 77303 x 77415 (16.2 MB) with weight 4522122 (58.41/col) Fri Feb 13 00:06:38 2009 sparse part has weight 3771008 (48.71/col) Fri Feb 13 00:06:38 2009 matrix includes 64 packed rows Fri Feb 13 00:06:38 2009 using block size 21845 for processor cache size 512 kB Fri Feb 13 00:06:40 2009 commencing Lanczos iteration Fri Feb 13 00:06:40 2009 memory use: 14.1 MB Fri Feb 13 00:07:51 2009 lanczos halted after 1223 iterations (dim = 77301) Fri Feb 13 00:07:52 2009 recovered 18 nontrivial dependencies Fri Feb 13 00:07:53 2009 prp42 factor: 780810284493164937541387674186542177655467 Fri Feb 13 00:07:53 2009 prp53 factor: 94856213196199882289140137695997617853942491092295137 Fri Feb 13 00:07:53 2009 elapsed time 06:19:41
Feb 13, 2009 (3rd): By Sinkiti Sibata / GGNFS, Msieve / Feb 13, 2009
(14·10¹⁵²-11)/3 = 4(6)₁₅₁3_<153> = 599 · 2039 · 5201159 · 500019643 · 9330687712735106756107_<22> · C110
C110 = P45 · P65
P45 = 203620709236385827266419928602895446827412681_<45>
P65 = 77328562429293032074941586762299177146068262610310551977403790177_<65>

Number: 46663_152 N=15745696726082785761030779523873758778735086950631405227876971911156989281795370993215599311066355391913034537 ( 110 digits) SNFS difficulty: 153 digits. Divisors found: r1=203620709236385827266419928602895446827412681 (pp45) r2=77328562429293032074941586762299177146068262610310551977403790177 (pp65) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 45.55 hours. Scaled time: 21.50 units (timescale=0.472). Factorization parameters were as follows: name: 46663_152 n: 15745696726082785761030779523873758778735086950631405227876971911156989281795370993215599311066355391913034537 m: 2000000000000000000000000000000 deg: 5 c5: 175 c0: -44 skew: 0.76 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1300000, 2400001) Primes: RFBsize:189880, AFBsize:189466, largePrimes:7918447 encountered Relations: rels:7927369, finalFF:448114 Max relations in full relation-set: 28 Initial matrix: 379413 x 448114 with sparse part having weight 48120728. Pruned matrix : 354056 x 356017 with weight 35108498. Total sieving time: 39.99 hours. Total relation processing time: 0.38 hours. Matrix solve time: 5.03 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 45.55 hours. --------- CPU info (if available) ----------
(14·10¹²⁸+1)/3 = 4(6)₁₂₇7_<129> = C129
C129 = P47 · P82
P47 = 97442427809946115669704136955838175329000474229_<47>
P82 = 4789152704372922037448426573012625124657528365691003679694960030537882336201918623_<82>

Number: 46667_128 N=466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667 ( 129 digits) SNFS difficulty: 130 digits. Divisors found: r1=97442427809946115669704136955838175329000474229 r2=4789152704372922037448426573012625124657528365691003679694960030537882336201918623 Version: Total time: 3.58 hours. Scaled time: 7.10 units (timescale=1.985). Factorization parameters were as follows: name: 46667_128 n: 466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667 m: 100000000000000000000000000 deg: 5 c5: 7 c0: 50 skew: 1.48 type: snfs lss: 1 rlim: 1060000 alim: 1060000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1060000/1060000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [530000, 930001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 139335 x 139583 Total sieving time: 3.58 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,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000 total time: 3.58 hours. --------- CPU info (if available) ----------
(14·10¹³⁹+1)/3 = 4(6)₁₃₈7_<140> = 47 · 919 · 19207 · 320149 · 14326847864654454928200037_<26> · C101
C101 = P49 · P53
P49 = 1171756816497492817243664472564133432549308489139_<49>
P53 = 10466309853523263277601766588807565342572842167782031_<53>

Fri Feb 13 07:37:47 2009 Msieve v. 1.39 Fri Feb 13 07:37:47 2009 random seeds: d3312254 864c9447 Fri Feb 13 07:37:47 2009 factoring 12263969914440759335266783627234628457014011679040525685138368121008357742749535862197848991282861309 (101 digits) Fri Feb 13 07:37:48 2009 searching for 15-digit factors Fri Feb 13 07:37:49 2009 commencing quadratic sieve (101-digit input) Fri Feb 13 07:37:50 2009 using multiplier of 1 Fri Feb 13 07:37:50 2009 using 32kb Intel Core sieve core Fri Feb 13 07:37:50 2009 sieve interval: 36 blocks of size 32768 Fri Feb 13 07:37:50 2009 processing polynomials in batches of 6 Fri Feb 13 07:37:50 2009 using a sieve bound of 2823631 (102500 primes) Fri Feb 13 07:37:50 2009 using large prime bound of 423544650 (28 bits) Fri Feb 13 07:37:50 2009 using double large prime bound of 3376125230508000 (43-52 bits) Fri Feb 13 07:37:50 2009 using trial factoring cutoff of 52 bits Fri Feb 13 07:37:50 2009 polynomial 'A' values have 13 factors Fri Feb 13 07:37:53 2009 restarting with 15879 full and 1011164 partial relations Fri Feb 13 11:40:41 2009 102614 relations (24294 full + 78320 combined from 1548059 partial), need 102596 Fri Feb 13 11:40:43 2009 begin with 1572353 relations Fri Feb 13 11:40:45 2009 reduce to 272541 relations in 10 passes Fri Feb 13 11:40:45 2009 attempting to read 272541 relations Fri Feb 13 11:40:50 2009 recovered 272541 relations Fri Feb 13 11:40:50 2009 recovered 263021 polynomials Fri Feb 13 11:40:50 2009 attempting to build 102614 cycles Fri Feb 13 11:40:50 2009 found 102614 cycles in 6 passes Fri Feb 13 11:40:50 2009 distribution of cycle lengths: Fri Feb 13 11:40:50 2009 length 1 : 24294 Fri Feb 13 11:40:50 2009 length 2 : 17427 Fri Feb 13 11:40:50 2009 length 3 : 16759 Fri Feb 13 11:40:50 2009 length 4 : 14052 Fri Feb 13 11:40:50 2009 length 5 : 10897 Fri Feb 13 11:40:50 2009 length 6 : 7402 Fri Feb 13 11:40:50 2009 length 7 : 4908 Fri Feb 13 11:40:50 2009 length 9+: 6875 Fri Feb 13 11:40:50 2009 largest cycle: 20 relations Fri Feb 13 11:40:51 2009 matrix is 102500 x 102614 (27.8 MB) with weight 6875032 (67.00/col) Fri Feb 13 11:40:51 2009 sparse part has weight 6875032 (67.00/col) Fri Feb 13 11:40:52 2009 filtering completed in 3 passes Fri Feb 13 11:40:52 2009 matrix is 98568 x 98631 (26.9 MB) with weight 6647785 (67.40/col) Fri Feb 13 11:40:52 2009 sparse part has weight 6647785 (67.40/col) Fri Feb 13 11:40:53 2009 saving the first 48 matrix rows for later Fri Feb 13 11:40:53 2009 matrix is 98520 x 98631 (15.8 MB) with weight 5180923 (52.53/col) Fri Feb 13 11:40:53 2009 sparse part has weight 3562677 (36.12/col) Fri Feb 13 11:40:53 2009 matrix includes 64 packed rows Fri Feb 13 11:40:53 2009 using block size 39452 for processor cache size 1024 kB Fri Feb 13 11:40:53 2009 commencing Lanczos iteration Fri Feb 13 11:40:53 2009 memory use: 15.9 MB Fri Feb 13 11:42:06 2009 lanczos halted after 1559 iterations (dim = 98516) Fri Feb 13 11:42:06 2009 recovered 14 nontrivial dependencies Fri Feb 13 11:42:07 2009 prp49 factor: 1171756816497492817243664472564133432549308489139 Fri Feb 13 11:42:07 2009 prp53 factor: 10466309853523263277601766588807565342572842167782031 Fri Feb 13 11:42:07 2009 elapsed time 04:04:20
(14·10¹⁴²+1)/3 = 4(6)₁₄₁7_<143> = 19 · 631 · 8629 · 82279 · 654047 · 1261759 · 280607091209_<12> · C107
C107 = P51 · P56
P51 = 354652338619270676018346061231933256617627024018009_<51>
P56 = 66755569921628218018055123882044193969712077797446507941_<56>

Number: 46667_142 N=23675018988567691200233651263717779618750621657030298258543712888967462264993398109679892203846411745509469 ( 107 digits) SNFS difficulty: 145 digits. Divisors found: r1=354652338619270676018346061231933256617627024018009 r2=66755569921628218018055123882044193969712077797446507941 Version: Total time: 8.19 hours. Scaled time: 16.11 units (timescale=1.967). Factorization parameters were as follows: name: 46667_142 n: 23675018988567691200233651263717779618750621657030298258543712888967462264993398109679892203846411745509469 m: 50000000000000000000000000000 deg: 5 c5: 56 c0: 125 skew: 1.17 type: snfs lss: 1 rlim: 1840000 alim: 1840000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1840000/1840000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [920000, 1720001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 278300 x 278548 Total sieving time: 8.19 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,145,5,0,0,0,0,0,0,0,0,1840000,1840000,26,26,49,49,2.3,2.3,100000 total time: 8.19 hours. --------- CPU info (if available) ----------
Feb 13, 2009 (2nd): By Andreas Tete / Msieve-1.39 / Feb 13, 2009
(14·10¹⁷⁵+1)/3 = 4(6)₁₇₄7_<176> = 211 · 128977427 · 674809256778071_<15> · 2798171122344373_<16> · 169183188323265888376647544823_<30> · C106
C106 = P48 · P58
P48 = 645931821966020252623561182000975442691069658013_<48>
P58 = 8310199105822166266834778444707835250551130821474294358883_<58>

Thu Feb 12 22:34:57 2009 Msieve v. 1.39 Thu Feb 12 22:34:57 2009 random seeds: 9db02c00 3ef00dcd Thu Feb 12 22:34:57 2009 factoring 5367822049324104198459781648285230954004443945514259477635815794499811904007692354910681910349769898679479 (106 digits) Thu Feb 12 22:34:58 2009 searching for 15-digit factors Thu Feb 12 22:34:59 2009 commencing number field sieve (106-digit input) Thu Feb 12 22:34:59 2009 R0: -258172299182433160252 Thu Feb 12 22:34:59 2009 R1: 107981281439 Thu Feb 12 22:34:59 2009 A0: -82194652127860805641635 Thu Feb 12 22:34:59 2009 A1: 7033312543780076998983 Thu Feb 12 22:34:59 2009 A2: -87363472109491385 Thu Feb 12 22:34:59 2009 A3: -17887783854145 Thu Feb 12 22:34:59 2009 A4: 104218002 Thu Feb 12 22:34:59 2009 A5: 4680 Thu Feb 12 22:34:59 2009 skew 24498.05, size 6.764167e-011, alpha -5.840131, combined = 4.738707e-010 Thu Feb 12 22:35:00 2009 Thu Feb 12 22:35:00 2009 commencing relation filtering Thu Feb 12 22:35:00 2009 commencing duplicate removal, pass 1 Thu Feb 12 22:35:56 2009 found 323492 hash collisions in 4679360 relations Thu Feb 12 22:36:09 2009 added 31781 free relations Thu Feb 12 22:36:09 2009 commencing duplicate removal, pass 2 Thu Feb 12 22:36:16 2009 found 299722 duplicates and 4411418 unique relations Thu Feb 12 22:36:16 2009 memory use: 43.3 MB Thu Feb 12 22:36:16 2009 reading rational ideals above 2818048 Thu Feb 12 22:36:16 2009 reading algebraic ideals above 2818048 Thu Feb 12 22:36:16 2009 commencing singleton removal, pass 1 Thu Feb 12 22:37:03 2009 relations with 0 large ideals: 104413 Thu Feb 12 22:37:03 2009 relations with 1 large ideals: 664703 Thu Feb 12 22:37:03 2009 relations with 2 large ideals: 1546652 Thu Feb 12 22:37:03 2009 relations with 3 large ideals: 1511527 Thu Feb 12 22:37:03 2009 relations with 4 large ideals: 528095 Thu Feb 12 22:37:03 2009 relations with 5 large ideals: 25948 Thu Feb 12 22:37:03 2009 relations with 6 large ideals: 30080 Thu Feb 12 22:37:03 2009 relations with 7+ large ideals: 0 Thu Feb 12 22:37:03 2009 4411418 relations and about 4341436 large ideals Thu Feb 12 22:37:03 2009 commencing singleton removal, pass 2 Thu Feb 12 22:37:51 2009 found 1970017 singletons Thu Feb 12 22:37:51 2009 current dataset: 2441401 relations and about 1971541 large ideals Thu Feb 12 22:37:51 2009 commencing singleton removal, pass 3 Thu Feb 12 22:38:24 2009 found 459939 singletons Thu Feb 12 22:38:24 2009 current dataset: 1981462 relations and about 1477357 large ideals Thu Feb 12 22:38:24 2009 commencing singleton removal, final pass Thu Feb 12 22:39:07 2009 memory use: 37.3 MB Thu Feb 12 22:39:07 2009 commencing in-memory singleton removal Thu Feb 12 22:39:07 2009 begin with 1981462 relations and 1518445 unique ideals Thu Feb 12 22:39:09 2009 reduce to 1658341 relations and 1186258 ideals in 16 passes Thu Feb 12 22:39:09 2009 max relations containing the same ideal: 49 Thu Feb 12 22:39:10 2009 reading rational ideals above 720000 Thu Feb 12 22:39:10 2009 reading algebraic ideals above 720000 Thu Feb 12 22:39:10 2009 commencing singleton removal, final pass Thu Feb 12 22:39:32 2009 keeping 1441724 ideals with weight <= 20, new excess is 185015 Thu Feb 12 22:39:34 2009 memory use: 46.8 MB Thu Feb 12 22:39:34 2009 commencing in-memory singleton removal Thu Feb 12 22:39:34 2009 begin with 1663865 relations and 1441724 unique ideals Thu Feb 12 22:39:36 2009 reduce to 1646608 relations and 1397747 ideals in 11 passes Thu Feb 12 22:39:36 2009 max relations containing the same ideal: 20 Thu Feb 12 22:39:37 2009 removing 167614 relations and 150492 ideals in 17122 cliques Thu Feb 12 22:39:37 2009 commencing in-memory singleton removal Thu Feb 12 22:39:37 2009 begin with 1478994 relations and 1397747 unique ideals Thu Feb 12 22:39:38 2009 reduce to 1467517 relations and 1235600 ideals in 7 passes Thu Feb 12 22:39:38 2009 max relations containing the same ideal: 20 Thu Feb 12 22:39:39 2009 removing 123087 relations and 105965 ideals in 17122 cliques Thu Feb 12 22:39:39 2009 commencing in-memory singleton removal Thu Feb 12 22:39:39 2009 begin with 1344430 relations and 1235600 unique ideals Thu Feb 12 22:39:40 2009 reduce to 1336954 relations and 1122079 ideals in 8 passes Thu Feb 12 22:39:40 2009 max relations containing the same ideal: 20 Thu Feb 12 22:39:41 2009 relations with 0 large ideals: 16191 Thu Feb 12 22:39:41 2009 relations with 1 large ideals: 109998 Thu Feb 12 22:39:41 2009 relations with 2 large ideals: 306115 Thu Feb 12 22:39:41 2009 relations with 3 large ideals: 427806 Thu Feb 12 22:39:41 2009 relations with 4 large ideals: 318411 Thu Feb 12 22:39:41 2009 relations with 5 large ideals: 125538 Thu Feb 12 22:39:41 2009 relations with 6 large ideals: 29363 Thu Feb 12 22:39:41 2009 relations with 7+ large ideals: 3532 Thu Feb 12 22:39:41 2009 commencing 2-way merge Thu Feb 12 22:39:42 2009 reduce to 793256 relation sets and 578381 unique ideals Thu Feb 12 22:39:42 2009 commencing full merge Thu Feb 12 22:39:52 2009 memory use: 43.3 MB Thu Feb 12 22:39:52 2009 found 366573 cycles, need 340581 Thu Feb 12 22:39:52 2009 weight of 340581 cycles is about 24093365 (70.74/cycle) Thu Feb 12 22:39:52 2009 distribution of cycle lengths: Thu Feb 12 22:39:52 2009 1 relations: 38055 Thu Feb 12 22:39:52 2009 2 relations: 34114 Thu Feb 12 22:39:52 2009 3 relations: 33825 Thu Feb 12 22:39:52 2009 4 relations: 31479 Thu Feb 12 22:39:52 2009 5 relations: 29063 Thu Feb 12 22:39:52 2009 6 relations: 25710 Thu Feb 12 22:39:52 2009 7 relations: 23273 Thu Feb 12 22:39:52 2009 8 relations: 21000 Thu Feb 12 22:39:52 2009 9 relations: 18232 Thu Feb 12 22:39:52 2009 10+ relations: 85830 Thu Feb 12 22:39:52 2009 heaviest cycle: 20 relations Thu Feb 12 22:39:52 2009 commencing cycle optimization Thu Feb 12 22:39:52 2009 start with 2233449 relations Thu Feb 12 22:39:59 2009 pruned 71620 relations Thu Feb 12 22:39:59 2009 memory use: 56.8 MB Thu Feb 12 22:39:59 2009 distribution of cycle lengths: Thu Feb 12 22:39:59 2009 1 relations: 38055 Thu Feb 12 22:39:59 2009 2 relations: 35065 Thu Feb 12 22:39:59 2009 3 relations: 35335 Thu Feb 12 22:39:59 2009 4 relations: 32598 Thu Feb 12 22:39:59 2009 5 relations: 30086 Thu Feb 12 22:39:59 2009 6 relations: 26481 Thu Feb 12 22:39:59 2009 7 relations: 23791 Thu Feb 12 22:39:59 2009 8 relations: 21224 Thu Feb 12 22:39:59 2009 9 relations: 18440 Thu Feb 12 22:39:59 2009 10+ relations: 79506 Thu Feb 12 22:39:59 2009 heaviest cycle: 19 relations Thu Feb 12 22:40:00 2009 Thu Feb 12 22:40:00 2009 commencing linear algebra Thu Feb 12 22:40:00 2009 read 340581 cycles Thu Feb 12 22:40:00 2009 cycles contain 1166929 unique relations Thu Feb 12 22:40:14 2009 read 1166929 relations Thu Feb 12 22:40:16 2009 using 20 quadratic characters above 67107708 Thu Feb 12 22:40:23 2009 building initial matrix Thu Feb 12 22:40:38 2009 memory use: 137.7 MB Thu Feb 12 22:40:38 2009 read 340581 cycles Thu Feb 12 22:40:39 2009 matrix is 340340 x 340581 (96.0 MB) with weight 32664453 (95.91/col) Thu Feb 12 22:40:39 2009 sparse part has weight 22770201 (66.86/col) Thu Feb 12 22:40:44 2009 filtering completed in 3 passes Thu Feb 12 22:40:44 2009 matrix is 338226 x 338426 (95.6 MB) with weight 32510703 (96.06/col) Thu Feb 12 22:40:44 2009 sparse part has weight 22686610 (67.04/col) Thu Feb 12 22:40:45 2009 read 338426 cycles Thu Feb 12 22:40:46 2009 matrix is 338226 x 338426 (95.6 MB) with weight 32510703 (96.06/col) Thu Feb 12 22:40:46 2009 sparse part has weight 22686610 (67.04/col) Thu Feb 12 22:40:46 2009 saving the first 48 matrix rows for later Thu Feb 12 22:40:46 2009 matrix is 338178 x 338426 (92.3 MB) with weight 25662083 (75.83/col) Thu Feb 12 22:40:46 2009 sparse part has weight 22161269 (65.48/col) Thu Feb 12 22:40:46 2009 matrix includes 64 packed rows Thu Feb 12 22:40:46 2009 using block size 65536 for processor cache size 3072 kB Thu Feb 12 22:40:49 2009 commencing Lanczos iteration Thu Feb 12 22:40:49 2009 memory use: 90.3 MB Thu Feb 12 22:57:01 2009 lanczos halted after 5349 iterations (dim = 338176) Thu Feb 12 22:57:02 2009 recovered 28 nontrivial dependencies Thu Feb 12 22:57:02 2009 Thu Feb 12 22:57:02 2009 commencing square root phase Thu Feb 12 22:57:02 2009 reading relations for dependency 1 Thu Feb 12 22:57:02 2009 read 169394 cycles Thu Feb 12 22:57:03 2009 cycles contain 719905 unique relations Thu Feb 12 22:57:12 2009 read 719905 relations Thu Feb 12 22:57:16 2009 multiplying 582576 relations Thu Feb 12 22:58:47 2009 multiply complete, coefficients have about 23.47 million bits Thu Feb 12 22:58:48 2009 initial square root is modulo 5501819 Thu Feb 12 23:00:56 2009 prp48 factor: 645931821966020252623561182000975442691069658013 Thu Feb 12 23:00:56 2009 prp58 factor: 8310199105822166266834778444707835250551130821474294358883 Thu Feb 12 23:00:56 2009 elapsed time 00:25:59
Feb 13, 2009: By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Feb 13, 2009
(14·10¹⁵⁰+1)/3 = 4(6)₁₄₉7_<151> = 233 · 20231 · 9565063 · C138
C138 = P60 · P78
P60 = 278292037251093167192697707757978140015212683389508754823953_<60>
P78 = 371916027933907022212166087325008623133827796688636219284264407757441270101811_<78>

SNFS difficulty: 151 digits. Divisors found: r1=278292037251093167192697707757978140015212683389508754823953 (pp60) r2=371916027933907022212166087325008623133827796688636219284264407757441270101811 (pp78) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: n: 103501269100061459963680493576104709397584435573134197614576074461874816345074624925092291323443376939458487404792623379413862577691478883 m: 1000000000000000000000000000000 deg: 5 c5: 14 c0: 1 skew: 0.59 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1150000, 1650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 324486 x 324734 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,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,52,52,2.4,2.4,100000 total time: 10.00 hours.
(14·10¹³³+1)/3 = 4(6)₁₃₂7_<134> = 17 · 13769216033340347807_<20> · C114
C114 = P51 · P63
P51 = 447832221926721618206166623088373467276639957980131_<51>
P63 = 445177603722581126154064540081841356282753677680658453973442903_<63>

SNFS difficulty: 135 digits. Divisors found: r1=447832221926721618206166623088373467276639957980131 (pp51) r2=445177603722581126154064540081841356282753677680658453973442903 (pp63) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: n: 199364875427097082889189878762010012232418735432546046038860594807740900792360923025260503562375875979319736960293 m: 1000000000000000000000000000 deg: 5 c5: 7 c0: 50 skew: 1.48 type: snfs lss: 1 rlim: 1290000 alim: 1290000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1290000/1290000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [645000, 1320001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 161579 x 161825 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,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,49,49,2.3,2.3,75000 total time: 3.00 hours.
(8·10¹⁸⁴+7)/3 = 2(6)₁₈₃9_<185> = 23 · 3331 · 9974131 · 44534953 · 560165357 · C157
C157 = P32 · C126
P32 = 10490142307214064479640205122143_<32>
C126 = [133349862070778274177903595909790086247733391434306851920325896211332328606192378743990711854039144978397117642580702153728441_<126>]

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2422990683 Step 1 took 51122ms Step 2 took 33274ms ********** Factor found in step 2: 10490142307214064479640205122143 Found probable prime factor of 32 digits: 10490142307214064479640205122143 Composite cofactor has 126 digits
(8·10¹⁹⁵+7)/3 = 2(6)₁₉₄9_<196> = 17 · 15193 · 114861703391_<12> · 190185939589_<12> · C168
C168 = P41 · P128
P41 = 21361646902753773798774688972047426229999_<41>
P128 = 22125234476041939644861842402929543686459937107236436624986438920087136960016791042077082338659824729805893701781682408595537649_<128>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3406529621 Step 1 took 13669ms Step 2 took 317ms ********** Factor found in step 2: 21361646902753773798774688972047426229999 Found probable prime factor of 41 digits: 21361646902753773798774688972047426229999 Probable prime cofactor has 128 digits
(8·10¹⁸³+7)/3 = 2(6)₁₈₂9_<184> = 566794065586391351689_<21> · C163
C163 = P35 · P129
P35 = 30060400046075892826912630127724553_<35>
P129 = 156512375065718674354721548240702754368556888089823882809533087811465411008217641205470073242329288280820516388264024561842672157_<129>

Using B1=8000000, B2=46840406350, polynomial Dickson(12), sigma=215209419 Step 1 took 36590ms Step 2 took 28115ms ********** Factor found in step 2: 30060400046075892826912630127724553 Found probable prime factor of 35 digits: 30060400046075892826912630127724553 Probable prime cofactor has 129 digits
(5·10¹⁸⁰+7)/3 = 1(6)₁₇₉9_<181> = 709 · 2644933042766470246966192621_<28> · C150
C150 = P35 · P116
P35 = 31773102888110998286705529243790757_<35>
P116 = 27972301658995088320960956104735130981351338320881303986748486437792405387531996289545564795758198381632115477266953_<116>

Using B1=6000000, B2=35128842850, polynomial Dickson(12), sigma=1855914501 Step 1 took 23790ms Step 2 took 20738ms ********** Factor found in step 2: 31773102888110998286705529243790757 Found probable prime factor of 35 digits: 31773102888110998286705529243790757 Probable prime cofactor has 116 digits
6·10¹⁸²+1 = 6(0)₁₈₁1_<183> = 197 · 145547 · 1137803 · C170
C170 = P37 · P133
P37 = 3697766213694124457129202150295765873_<37>
P133 = 4973650241959479991177377391777452977902057601073658068611396750923243720787211361706581622604893959178219884712767066984209658142981_<133>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=1250300280 Step 1 took 50747ms Step 2 took 32902ms ********** Factor found in step 2: 3697766213694124457129202150295765873 Found probable prime factor of 37 digits: 3697766213694124457129202150295765873 Probable prime cofactor has 133 digits
4·10¹⁸¹+9 = 4(0)₁₈₀9_<182> = 7 · 4463 · 9013 · 44939 · 54440369 · 646495019927_<12> · C149
C149 = P38 · C112
P38 = 17375472304230114852745301318776299103_<38>
C112 = [5169153474928885848324348321675877484252277469106881063647738317793449445476644541605020599482510225817619276463_<112>]

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2640071409 Step 1 took 43398ms Step 2 took 30394ms ********** Factor found in step 2: 17375472304230114852745301318776299103 Found probable prime factor of 38 digits: 17375472304230114852745301318776299103 Composite cofactor has 112 digits
Feb 12, 2009 (5th): By Sinkiti Sibata / Msieve / Feb 12, 2009
(14·10¹¹²+1)/3 = 4(6)₁₁₁7_<113> = 71 · 79 · 1459060062993079_<16> · C94
C94 = P46 · P49
P46 = 2788605938735191414130857038217899259398483257_<46>
P49 = 2044847961067233264018846952173523758557643519821_<49>

Thu Feb 12 07:47:53 2009 Msieve v. 1.39 Thu Feb 12 07:47:53 2009 random seeds: 626506b0 94752051 Thu Feb 12 07:47:53 2009 factoring 5702275168042634161453697274977310092999593281419143237948608709452904758430079124662216136997 (94 digits) Thu Feb 12 07:47:54 2009 searching for 15-digit factors Thu Feb 12 07:47:56 2009 commencing quadratic sieve (94-digit input) Thu Feb 12 07:47:56 2009 using multiplier of 13 Thu Feb 12 07:47:56 2009 using 32kb Intel Core sieve core Thu Feb 12 07:47:56 2009 sieve interval: 36 blocks of size 32768 Thu Feb 12 07:47:56 2009 processing polynomials in batches of 6 Thu Feb 12 07:47:56 2009 using a sieve bound of 2055311 (76471 primes) Thu Feb 12 07:47:56 2009 using large prime bound of 283632918 (28 bits) Thu Feb 12 07:47:56 2009 using double large prime bound of 1640445722406174 (42-51 bits) Thu Feb 12 07:47:56 2009 using trial factoring cutoff of 51 bits Thu Feb 12 07:47:56 2009 polynomial 'A' values have 12 factors Thu Feb 12 10:18:24 2009 76601 relations (20440 full + 56161 combined from 1076215 partial), need 76567 Thu Feb 12 10:18:25 2009 begin with 1096655 relations Thu Feb 12 10:18:26 2009 reduce to 192800 relations in 10 passes Thu Feb 12 10:18:26 2009 attempting to read 192800 relations Thu Feb 12 10:18:29 2009 recovered 192800 relations Thu Feb 12 10:18:29 2009 recovered 170944 polynomials Thu Feb 12 10:18:29 2009 attempting to build 76601 cycles Thu Feb 12 10:18:30 2009 found 76601 cycles in 6 passes Thu Feb 12 10:18:30 2009 distribution of cycle lengths: Thu Feb 12 10:18:30 2009 length 1 : 20440 Thu Feb 12 10:18:30 2009 length 2 : 14239 Thu Feb 12 10:18:30 2009 length 3 : 13100 Thu Feb 12 10:18:30 2009 length 4 : 10074 Thu Feb 12 10:18:30 2009 length 5 : 7275 Thu Feb 12 10:18:30 2009 length 6 : 4693 Thu Feb 12 10:18:30 2009 length 7 : 2891 Thu Feb 12 10:18:30 2009 length 9+: 3889 Thu Feb 12 10:18:30 2009 largest cycle: 20 relations Thu Feb 12 10:18:30 2009 matrix is 76471 x 76601 (19.9 MB) with weight 4914996 (64.16/col) Thu Feb 12 10:18:30 2009 sparse part has weight 4914996 (64.16/col) Thu Feb 12 10:18:31 2009 filtering completed in 3 passes Thu Feb 12 10:18:31 2009 matrix is 71826 x 71890 (18.9 MB) with weight 4656393 (64.77/col) Thu Feb 12 10:18:31 2009 sparse part has weight 4656393 (64.77/col) Thu Feb 12 10:18:31 2009 saving the first 48 matrix rows for later Thu Feb 12 10:18:31 2009 matrix is 71778 x 71890 (12.7 MB) with weight 3753540 (52.21/col) Thu Feb 12 10:18:31 2009 sparse part has weight 2886411 (40.15/col) Thu Feb 12 10:18:31 2009 matrix includes 64 packed rows Thu Feb 12 10:18:31 2009 using block size 28756 for processor cache size 1024 kB Thu Feb 12 10:18:32 2009 commencing Lanczos iteration Thu Feb 12 10:18:32 2009 memory use: 11.8 MB Thu Feb 12 10:19:07 2009 lanczos halted after 1137 iterations (dim = 71778) Thu Feb 12 10:19:08 2009 recovered 18 nontrivial dependencies Thu Feb 12 10:19:09 2009 prp46 factor: 2788605938735191414130857038217899259398483257 Thu Feb 12 10:19:09 2009 prp49 factor: 2044847961067233264018846952173523758557643519821 Thu Feb 12 10:19:09 2009 elapsed time 02:31:16
(14·10¹¹⁹+1)/3 = 4(6)₁₁₈7_<120> = C120
C120 = P36 · P41 · P45
P36 = 342863294583316472753439512436141793_<36>
P41 = 10008884276539516247435781948737347856839_<41>
P45 = 135987853606852843149955196433161787992971421_<45>

Number: 46667_119 N=466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667 ( 120 digits) SNFS difficulty: 120 digits. Divisors found: r1=342863294583316472753439512436141793 r2=10008884276539516247435781948737347856839 r3=135987853606852843149955196433161787992971421 Version: Total time: 1.60 hours. Scaled time: 3.18 units (timescale=1.991). Factorization parameters were as follows: name: 46667_119 n: 466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667 m: 1000000000000000000000000 deg: 5 c5: 7 c0: 5 skew: 0.93 type: snfs lss: 1 rlim: 720000 alim: 720000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 720000/720000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [360000, 560001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 70783 x 71030 Total sieving time: 1.60 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,120,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000 total time: 1.60 hours. --------- CPU info (if available) ----------
(14·10¹⁵⁷+1)/3 = 4(6)₁₅₆7_<158> = 1229 · 14639 · 20570610787_<11> · 136089221564531_<15> · 6207025213840049369221560139_<28> · C99
C99 = P47 · P52
P47 = 69640697804905676650210740049288662547179405011_<47>
P52 = 2143512135664749341932732352584032738864120525449489_<52>

Thu Feb 12 11:55:17 2009 Msieve v. 1.39 Thu Feb 12 11:55:17 2009 random seeds: e96394ac 9a5ad5fa Thu Feb 12 11:55:17 2009 factoring 149275680880976788467660198622530779642196164017610224805481211436514278248616466484962074353989379 (99 digits) Thu Feb 12 11:55:18 2009 searching for 15-digit factors Thu Feb 12 11:55:20 2009 commencing quadratic sieve (99-digit input) Thu Feb 12 11:55:20 2009 using multiplier of 1 Thu Feb 12 11:55:20 2009 using 32kb Intel Core sieve core Thu Feb 12 11:55:20 2009 sieve interval: 36 blocks of size 32768 Thu Feb 12 11:55:20 2009 processing polynomials in batches of 6 Thu Feb 12 11:55:20 2009 using a sieve bound of 2577401 (94097 primes) Thu Feb 12 11:55:20 2009 using large prime bound of 386610150 (28 bits) Thu Feb 12 11:55:20 2009 using double large prime bound of 2864783531160900 (43-52 bits) Thu Feb 12 11:55:20 2009 using trial factoring cutoff of 52 bits Thu Feb 12 11:55:20 2009 polynomial 'A' values have 13 factors Thu Feb 12 18:39:39 2009 94622 relations (23309 full + 71313 combined from 1406727 partial), need 94193 Thu Feb 12 18:39:41 2009 begin with 1430036 relations Thu Feb 12 18:39:42 2009 reduce to 246673 relations in 12 passes Thu Feb 12 18:39:42 2009 attempting to read 246673 relations Thu Feb 12 18:39:46 2009 recovered 246673 relations Thu Feb 12 18:39:46 2009 recovered 233241 polynomials Thu Feb 12 18:39:47 2009 attempting to build 94622 cycles Thu Feb 12 18:39:47 2009 found 94622 cycles in 6 passes Thu Feb 12 18:39:47 2009 distribution of cycle lengths: Thu Feb 12 18:39:47 2009 length 1 : 23309 Thu Feb 12 18:39:47 2009 length 2 : 16347 Thu Feb 12 18:39:47 2009 length 3 : 15767 Thu Feb 12 18:39:47 2009 length 4 : 12855 Thu Feb 12 18:39:47 2009 length 5 : 9640 Thu Feb 12 18:39:47 2009 length 6 : 6630 Thu Feb 12 18:39:47 2009 length 7 : 4243 Thu Feb 12 18:39:47 2009 length 9+: 5831 Thu Feb 12 18:39:47 2009 largest cycle: 18 relations Thu Feb 12 18:39:47 2009 matrix is 94097 x 94622 (25.6 MB) with weight 6321039 (66.80/col) Thu Feb 12 18:39:47 2009 sparse part has weight 6321039 (66.80/col) Thu Feb 12 18:39:49 2009 filtering completed in 3 passes Thu Feb 12 18:39:49 2009 matrix is 89731 x 89795 (24.3 MB) with weight 6003460 (66.86/col) Thu Feb 12 18:39:49 2009 sparse part has weight 6003460 (66.86/col) Thu Feb 12 18:39:49 2009 saving the first 48 matrix rows for later Thu Feb 12 18:39:49 2009 matrix is 89683 x 89795 (14.6 MB) with weight 4679779 (52.12/col) Thu Feb 12 18:39:49 2009 sparse part has weight 3297305 (36.72/col) Thu Feb 12 18:39:49 2009 matrix includes 64 packed rows Thu Feb 12 18:39:49 2009 using block size 35918 for processor cache size 1024 kB Thu Feb 12 18:39:50 2009 commencing Lanczos iteration Thu Feb 12 18:39:50 2009 memory use: 14.4 MB Thu Feb 12 18:40:44 2009 lanczos halted after 1420 iterations (dim = 89681) Thu Feb 12 18:40:45 2009 recovered 16 nontrivial dependencies Thu Feb 12 18:40:46 2009 prp47 factor: 69640697804905676650210740049288662547179405011 Thu Feb 12 18:40:46 2009 prp52 factor: 2143512135664749341932732352584032738864120525449489 Thu Feb 12 18:40:46 2009 elapsed time 06:45:29
(14·10¹²²+1)/3 = 4(6)₁₂₁7_<123> = 181 · C121
C121 = P36 · P86
P36 = 233363571794395358732871502584131711_<36>
P86 = 11048291971135058539564418334874354567896531951537936403069323653753099323612883519137_<86>

Number: 46667_122 N=2578268876611418047882136279926335174953959484346224677716390423572744014732965009208103130755064456721915285451197053407 ( 121 digits) SNFS difficulty: 125 digits. Divisors found: r1=233363571794395358732871502584131711 r2=11048291971135058539564418334874354567896531951537936403069323653753099323612883519137 Version: Total time: 1.85 hours. Scaled time: 3.66 units (timescale=1.979). Factorization parameters were as follows: name: 46667_122 n: 2578268876611418047882136279926335174953959484346224677716390423572744014732965009208103130755064456721915285451197053407 m: 5000000000000000000000000 deg: 5 c5: 56 c0: 125 skew: 1.17 type: snfs lss: 1 rlim: 860000 alim: 860000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 860000/860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [430000, 630001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 100795 x 101040 Total sieving time: 1.85 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000 total time: 1.85 hours. --------- CPU info (if available) ----------
Feb 12, 2009 (4th): By Erik Branger / GGNFS, Msieve / Feb 12, 2009
(14·10¹⁶⁵-17)/3 = 4(6)₁₆₄1_<166> = 9488819 · 43588177743829_<14> · C146
C146 = P69 · P77
P69 = 192291543504650266312924830780127324976051701536760368444962051931847_<69>
P77 = 58676705241607330640162008428812640085749921181414466216785690293885780591613_<77>

Number: 46661_165 N=11283034218676076335450062104328480022556931502317869197767600548494780149843252727291425682419289464184378251077512205365756428650696865215799211 ( 146 digits) SNFS difficulty: 166 digits. Divisors found: r1=192291543504650266312924830780127324976051701536760368444962051931847 r2=58676705241607330640162008428812640085749921181414466216785690293885780591613 Version: Total time: 64.10 hours. Scaled time: 49.17 units (timescale=0.767). Factorization parameters were as follows: n: 11283034218676076335450062104328480022556931502317869197767600548494780149843252727291425682419289464184378251077512205365756428650696865215799211 m: 1000000000000000000000000000000000 deg: 5 c5: 14 c0: -17 skew: 1.04 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 3750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 751250 x 751498 Total sieving time: 64.10 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,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 64.10 hours. --------- CPU info (if available) ----------
Feb 12, 2009 (3rd): By Robert Backstrom / GGNFS, Msieve / Feb 12, 2009
(32·10¹⁹⁶+31)/9 = 3(5)₁₉₅9_<197> = 3 · C197
C197 = P49 · P148
P49 = 3559279910565634648793619648390695211930101119007_<49>
P148 = 3329845404029596513584266686001452221852005046336820091842356487673056284411726044805774754469766724250478115806325903135290063433358994107001192979_<148>

Number: n N=11851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853 ( 197 digits) SNFS difficulty: 197 digits. Divisors found: Thu Feb 12 05:19:50 2009 prp49 factor: 3559279910565634648793619648390695211930101119007 Thu Feb 12 05:19:50 2009 prp148 factor: 3329845404029596513584266686001452221852005046336820091842356487673056284411726044805774754469766724250478115806325903135290063433358994107001192979 Thu Feb 12 05:19:50 2009 elapsed time 10:06:12 (Msieve 1.39 - dependency 9) Version: GGNFS-0.77.1-20050930-k8 Total time: 40.90 hours. Scaled time: 82.20 units (timescale=2.010). Factorization parameters were as follows: name: KA_3_5_195_9 n: 11851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853 deg: 5 c5: 10 c0: 31 m: 2000000000000000000000000000000000000000 skew: 1.25 type: snfs rlim: 10000000 alim: 10000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 14052713) Primes: RFBsize:664579, AFBsize:664406, largePrimes:37099223 encountered Relations: rels:33783957, finalFF:423024 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 5477645 hash collisions in 39908701 relations Msieve: matrix is 2271192 x 2271440 (617.6 MB) Total sieving time: 40.07 hours. Total relation processing time: 0.82 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,197,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000 total time: 40.90 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830483) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Total of 4 processors activated (22643.68 BogoMIPS).
(14·10¹⁰¹+1)/3 = 4(6)₁₀₀7_<102> = 17 · 97 · C99
C99 = P37 · P62
P37 = 5033234758058990957431315127552236327_<37>
P62 = 56226226564171399584270023372840804616856797530190186799408429_<62>

Number: n N=282999797857287244794825146553466747523751768748736608045279967657165959167172023448554679603800283 ( 99 digits) SNFS difficulty: 102 digits. Divisors found: r1=5033234758058990957431315127552236327 (pp37) r2=56226226564171399584270023372840804616856797530190186799408429 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.71 hours. Scaled time: 1.25 units (timescale=1.752). Factorization parameters were as follows: name: KA_4_6_100_7 n: 282999797857287244794825146553466747523751768748736608045279967657165959167172023448554679603800283 deg: 5 c5: 140 c0: 1 m: 100000000000000000000 skew: 0.37 type: snfs rlim: 400000 alim: 400000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 10000 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved algebraic special-q in [200000, 230001) Primes: RFBsize:33860, AFBsize:33783, largePrimes:4654390 encountered Relations: rels:3905590, finalFF:116916 Max relations in full relation-set: 28 Initial matrix: 67710 x 116916 with sparse part having weight 9501067. Pruned matrix : 56212 x 56614 with weight 2878348. Total sieving time: 0.61 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.02 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,400000,400000,29,29,58,58,2.5,2.5,20000 total time: 0.71 hours. --------- CPU info (if available) ----------
Feb 12, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Feb 12, 2009
(14·10¹³¹+1)/3 = 4(6)₁₃₀7_<132> = 305947 · 159457726751_<12> · C115
C115 = P35 · P81
P35 = 46554278325090552516893199847461541_<35>
P81 = 205473308908773787368632582384091275114615193757427857138289590570000231197871171_<81>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=871041688 Step 1 took 8145ms Step 2 took 9102ms ********** Factor found in step 2: 46554278325090552516893199847461541 Found probable prime factor of 35 digits: 46554278325090552516893199847461541 Probable prime cofactor 205473308908773787368632582384091275114615193757427857138289590570000231197871171 has 81 digits
(14·10¹⁶²+1)/3 = 4(6)₁₆₁7_<163> = 139 · 599 · 37243 · 1143529 · 521121781 · 85455939917603_<14> · C125
C125 = P30 · C95
P30 = 399007013662755691469737714633_<30>
C95 = [74064706811669136267266549263175661936240043622241422381737475862705723444971303591286665563979_<95>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=953689393 Step 1 took 9805ms Step 2 took 10466ms ********** Factor found in step 2: 399007013662755691469737714633 Found probable prime factor of 30 digits: 399007013662755691469737714633 Composite cofactor has 95 digits
(14·10¹²⁹+1)/3 = 4(6)₁₂₈7_<130> = 13 · 89399 · C124
C124 = P35 · P90
P35 = 10192161599110403859711452399948989_<35>
P90 = 393971192375050542532099397791091062168385809913731410123886724602590737694211075449017269_<90>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=76032831 Step 1 took 3242ms Step 2 took 3943ms ********** Factor found in step 2: 10192161599110403859711452399948989 Found probable prime factor of 35 digits: 10192161599110403859711452399948989 Probable prime cofactor 393971192375050542532099397791091062168385809913731410123886724602590737694211075449017269 has 90 digits
(14·10¹⁵⁴+1)/3 = 4(6)₁₅₃7_<155> = 293 · C153
C153 = P34 · C119
P34 = 7512655541259282306331650654533633_<34>
C119 = [21200479512406470387486737841689387728256616761959944459277057188240292447586447134939384922724107131176462502589510543_<119>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3012614861 Step 1 took 3893ms Step 2 took 4707ms ********** Factor found in step 2: 7512655541259282306331650654533633 Found probable prime factor of 34 digits: 7512655541259282306331650654533633 Composite cofactor has 119 digits
(14·10¹⁶⁶+1)/3 = 4(6)₁₆₅7_<167> = 227 · 93609576563291_<14> · 6410436491169121721_<19> · C132
C132 = P31 · C101
P31 = 8567432506482975511227306736847_<31>
C101 = [39987324709041758691823561140139597659692108721927001185977095775180330550267978236047812260559216413_<101>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3502152376 Step 1 took 3243ms Step 2 took 4098ms ********** Factor found in step 2: 8567432506482975511227306736847 Found probable prime factor of 31 digits: 8567432506482975511227306736847 Composite cofactor has 101 digits
(14·10¹⁸⁶+1)/3 = 4(6)₁₈₅7_<187> = 10267 · 13219 · 4164360581_<10> · C169
C169 = P31 · C139
P31 = 1488247983280186098571489708637_<31>
C139 = [5548057925542539633876144788364042228068713112868763687008067831727809467689271994969198458381672917577464003883096593416056508405328606507_<139>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1804857347 Step 1 took 4577ms Step 2 took 5369ms ********** Factor found in step 2: 1488247983280186098571489708637 Found probable prime factor of 31 digits: 1488247983280186098571489708637 Composite cofactor has 139 digits
(14·10¹⁹³+1)/3 = 4(6)₁₉₂7_<194> = 162042457 · 20695762423014919_<17> · C170
C170 = P33 · P137
P33 = 462119935655791361486982051216493_<33>
P137 = 30112154280186876402133415618899951125050959464703518389615185245091234262257669146945323775268235498034779512356171484421776174648079993_<137>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3931416344 Step 1 took 4596ms Step 2 took 5150ms ********** Factor found in step 2: 462119935655791361486982051216493 Found probable prime factor of 33 digits: 462119935655791361486982051216493 Probable prime cofactor has 137 digits
(14·10¹⁸⁹+1)/3 = 4(6)₁₈₈7_<190> = 13 · 3089 · C186
C186 = P29 · C158
P29 = 10128992616845406650370872567_<29>
C158 = [11473060026002633862873187847428263852356990812032173801213368823063425357300143024973808939526542988293615478197607055708097005793552950139882721311441146193_<158>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=559243349 Step 1 took 5299ms Step 2 took 5887ms ********** Factor found in step 2: 10128992616845406650370872567 Found probable prime factor of 29 digits: 10128992616845406650370872567 Composite cofactor has 158 digits
(14·10¹⁹⁸+1)/3 = 4(6)₁₉₇7_<199> = 104241439 · 804275831676937_<15> · C176
C176 = P31 · C146
P31 = 2302547123295387084975840675017_<31>
C146 = [24174240446012188423303584163418618873580884672507283345705373054705879742773704017354755985074043014862200477183294129720127756212163374408552357_<146>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1926129916 Step 1 took 5350ms Step 2 took 5715ms ********** Factor found in step 2: 2302547123295387084975840675017 Found probable prime factor of 31 digits: 2302547123295387084975840675017 Composite cofactor has 146 digits
(14·10²⁰⁵+1)/3 = 4(6)₂₀₄7_<206> = 211 · 313883 · 166392511157_<12> · C187
C187 = P35 · C152
P35 = 85546395577581480397571844796656383_<35>
C152 = [49501805467225833449350459682062479620662966987145895723889560077810294783203738814482530345222472524750975100610029437647086129084137651615311158833889_<152>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3996907096 Step 1 took 16003ms Step 2 took 15084ms ********** Factor found in step 2: 85546395577581480397571844796656383 Found probable prime factor of 35 digits: 85546395577581480397571844796656383 Composite cofactor has 152 digits
(14·10¹⁹⁶+1)/3 = 4(6)₁₉₅7_<197> = 19 · 88125623503_<11> · 63724402211023850353_<20> · 174979598539031380917131233_<27> · C139
C139 = P36 · C103
P36 = 300304125643577097155478944475718909_<36>
C103 = [8323318098892312395018467980900645024149797138390385911208071430477385229001986137257942282261530204291_<103>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2390175780 Step 1 took 11879ms Step 2 took 11261ms ********** Factor found in step 2: 300304125643577097155478944475718909 Found probable prime factor of 36 digits: 300304125643577097155478944475718909 Composite cofactor has 103 digits
(14·10¹⁴⁵+1)/3 = 4(6)₁₄₄7_<146> = 211 · C144
C144 = P52 · P92
P52 = 8052958223086142680681622957815586168218929634167397_<52>
P92 = 27464321831555993887170069360422205207318039121738929888700795651176142159905108128526327701_<92>

SNFS difficulty: 146 digits. Divisors found: r1=8052958223086142680681622957815586168218929634167397 (pp52) r2=27464321831555993887170069360422205207318039121738929888700795651176142159905108128526327701 (pp92) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.301). Factorization parameters were as follows: n: 221169036334913112164296998420221169036334913112164296998420221169036334913112164296998420221169036334913112164296998420221169036334913112164297 m: 100000000000000000000000000000 deg: 5 c5: 14 c0: 1 skew: 0.59 type: snfs lss: 1 rlim: 1910000 alim: 1910000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1910000/1910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [955000, 1755001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 270750 x 270998 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000 total time: 6.00 hours.
(13·10¹⁷⁴+17)/3 = 4(3)₁₇₃9_<175> = 67 · 2339 · 145679 · 2299821779_<10> · C155
C155 = P37 · P119
P37 = 1541598869214810667584140500809981461_<37>
P119 = 53537064669212941145413465295673500930472498315861866176240448112515332806782940163632147043692072447594155558117056003_<119>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=3498946439 Step 1 took 53500ms Step 2 took 33290ms ********** Factor found in step 2: 1541598869214810667584140500809981461 Found probable prime factor of 37 digits: 1541598869214810667584140500809981461 Probable prime cofactor has 119 digits
Feb 12, 2009: Factorizations of 466...667 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Feb 11, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.1 / Feb 11, 2009
(10²⁴⁶-7)/3 = (3)₂₄₅1_<246> = 19 · 2573359 · 14760685190666539_<17> · 1961244970676841191_<19> · C204
C204 = P34 · C170
P34 = 3670527667049049608762094305631461_<34>
P38 = 32853358459821858604617750306149758051_<38>
P43 = 1346947706777778949523481608494225806440537_<43>
P91 = 1449864434985030623918793573325434152665912082226603904556877026696713336128758158707403277_<91>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=978534757 Step 1 took 68215ms Step 2 took 25543ms ********** Factor found in step 2: 3670527667049049608762094305631461 Found probable prime factor of 34 digits: 3670527667049049608762094305631461 Composite cofactor has 170 digits I temporarily created the _largest_ GNFS. 170 digits. 33331_246 So after some CPUs freed up I've restarted it's cracking and it is finished! Input number is 64159046974295305520723950792773478735297829893535629441057371436514358427793184945168214366306467643277111078191056438010184481010418240802535657701836153578260482169199 (170 digits) Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2339262197 Step 1 took 50772ms Step 2 took 34131ms ********** Factor found in step 2: 1346947706777778949523481608494225806440537 Found probable prime factor of 43 digits: 1346947706777778949523481608494225806440537 Composite cofactor has 128 digits Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=3044812234 Step 1 took 50698ms Step 2 took 33816ms ********** Factor found in step 2: 32853358459821858604617750306149758051 Found probable prime factor of 38 digits: 32853358459821858604617750306149758051 Done.
Feb 11, 2009: By Robert Backstrom / GGNFS, Msieve / Feb 11, 2009
(14·10¹⁵¹-11)/3 = 4(6)₁₅₀3_<152> = 71 · 8287 · 7636701967_<10> · C137
C137 = P48 · P89
P48 = 248786394540065217850357824605605247924193004817_<48>
P89 = 41746361077843051159101552049861320614361683800694094804506317570285200098139725783800321_<89>

Number: n N=10385926657724283585795401521825314336224352567336082740302586858895012580247310523831021187057343404423646960236022461931116166519146257 ( 137 digits) SNFS difficulty: 152 digits. Divisors found: Wed Feb 11 04:04:05 2009 prp48 factor: 248786394540065217850357824605605247924193004817 Wed Feb 11 04:04:05 2009 prp89 factor: 41746361077843051159101552049861320614361683800694094804506317570285200098139725783800321 Wed Feb 11 04:04:05 2009 elapsed time 01:11:10 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20051202-athlon Total time: 11.77 hours. Scaled time: 21.53 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_6_150_3 n: 10385926657724283585795401521825314336224352567336082740302586858895012580247310523831021187057343404423646960236022461931116166519146257 deg: 5 c5: 140 c0: -11 m: 1000000000000000000000000000000 skew: 0.60 type: snfs rlim: 2400000 alim: 2400000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 1900267) Primes: RFBsize:176302, AFBsize:176359, largePrimes:14958013 encountered Relations: rels:13357259, finalFF:360294 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 813924 hash collisions in 13880876 relations Msieve: matrix is 462992 x 463240 (125.6 MB) Total sieving time: 11.32 hours. Total relation processing time: 0.45 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,29,29,58,58,2.5,2.5,100000 total time: 11.77 hours. --------- CPU info (if available) ----------
Feb 10, 2009 (5th): By Wataru Sakai / Msieve / Feb 10, 2009
(38·10¹⁸⁰+43)/9 = 4(2)₁₇₉7_<181> = 3² · C180
C180 = P52 · P61 · P68
P52 = 4095157380675222708692130449535082586017393959914693_<52>
P61 = 4359068972382103688986139651920014643722275960934943125231403_<61>
P68 = 26280537309026180225728609426477728057761054472759357321451829916157_<68>

Number: 42227_180 N=469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803 ( 180 digits) SNFS difficulty: 181 digits. Divisors found: r1=4095157380675222708692130449535082586017393959914693 r2=4359068972382103688986139651920014643722275960934943125231403 r3=26280537309026180225728609426477728057761054472759357321451829916157 Version: Total time: 264.64 hours. Scaled time: 491.96 units (timescale=1.859). Factorization parameters were as follows: n: 469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803 m: 1000000000000000000000000000000000000 deg: 5 c5: 38 c0: 43 skew: 1.03 type: snfs lss: 1 rlim: 7400000 alim: 7400000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3700000, 6600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1187661 x 1187909 Total sieving time: 264.64 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,181,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,53,53,2.5,2.5,100000 total time: 264.64 hours. --------- CPU info (if available) ----------
(34·10¹⁹³+11)/9 = 3(7)₁₉₂9_<194> = 3 · 13 · C192
C192 = P65 · P128
P65 = 73872414964991438154457483704634845335532705457402330595616523903_<65>
P128 = 13112620849338994250152717854469097344358167518774155826832299075626325663630475733433075729484006608794021173456736425417519787_<128>

Number: 37779_193 N=968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968661 ( 192 digits) SNFS difficulty: 195 digits. Divisors found: r1=73872414964991438154457483704634845335532705457402330595616523903 r2=13112620849338994250152717854469097344358167518774155826832299075626325663630475733433075729484006608794021173456736425417519787 Version: Total time: 628.47 hours. Scaled time: 1191.57 units (timescale=1.896). Factorization parameters were as follows: n: 968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968661 m: 500000000000000000000000000000000000000 deg: 5 c5: 272 c0: 275 skew: 1.00 type: snfs lss: 1 rlim: 12900000 alim: 12900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 12900000/12900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6450000, 13550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2002769 x 2003017 Total sieving time: 628.47 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,195,5,0,0,0,0,0,0,0,0,12900000,12900000,28,28,55,55,2.5,2.5,100000 total time: 628.47 hours. --------- CPU info (if available) ----------
Feb 10, 2009 (4th): By Serge Batalov / GMP-ECM 6.2.1 / Feb 10, 2009
(10²¹⁴-7)/3 = (3)₂₁₃1_<214> = 199 · 3417523601_<10> · 146381644507781_<15> · 542863066827693324113_<21> · 3626441620130113046137_<22> · C146
C146 = P32 · C115
P32 = 16330057924125944094464094405083_<32>
C115 = [1041522875628824850206331401809802733379697364432095474461905180421216813505211719464595804937315371883591311059963_<115>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2876835942 Step 1 took 9988ms Step 2 took 9713ms ********** Factor found in step 2: 16330057924125944094464094405083 Found probable prime factor of 32 digits: 16330057924125944094464094405083 Composite cofactor has 115 digits submitted too soon!! http://hpcgi2.nifty.com/m_kamada/f/c.cgi?q=33331_214 Here's the 2nd factor and it is now done. Input number is 17008128888320931383354727108483414056951585774063347834284200331023442461936324048949309012574574088508559087429890500055997434344403526624991929 (146 digits) Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=113639890 Step 1 took 10005ms Step 2 took 9736ms ********** Factor found in step 2: 90101525598690239302205389921070183 Found probable prime factor of 35 digits: 90101525598690239302205389921070183 Probable prime cofactor... 1041522875628824850206331401809802733379697364432095474461905180421216813505211719464595804937315371883591311059963/90101525598690239302205389921070183 is 3-PRP! (0.0003s+0.0002s)
(10²⁰¹-7)/3 = (3)₂₀₀1_<201> = 17 · 179 · 89172847 · 59585840242305315008580382109_<29> · C161
C161 = P30 · P132
P30 = 113651646881442264198543362827_<30>
P132 = 181395019774523320920170919435768269521331834965340563969332201510128587969477158608084691969423902103319185187992483378214882686977_<132>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4223742160 Step 1 took 13927ms Step 2 took 7230ms ********** Factor found in step 2: 113651646881442264198543362827 Found probable prime factor of 30 digits: 113651646881442264198543362827 Probable prime cofactor has 132 digits
(10²²⁴-7)/3 = (3)₂₂₃1_<224> = 6217 · 41690693165187663091061923_<26> · C195
C195 = P31 · P164
P31 = 1910292367392025446273032520521_<31>
P164 = 67322296392159002608077001735383769255278175908017691909794326083950780784359539151524449036248700307859001497285459431557783174630917455064131629636899687902659521_<164>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=859583623 Step 1 took 15768ms Step 2 took 7621ms ********** Factor found in step 2: 1910292367392025446273032520521 Found probable prime factor of 31 digits: 1910292367392025446273032520521 Probable prime cofactor has 164 digits
(10²⁴¹-7)/3 = (3)₂₄₀1_<241> = 23 · 2213 · 23014650598801_<14> · 4338308440643575944982309_<25> · C198
C198 = P32 · P167
P32 = 33064576717718812538576350565093_<32>
P167 = 19837261401965769198527981065990686460477593452013812421089201511447713289236940228265964568859059864261224949749765633813634285773219174280863253840646720592135734937_<167>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1448815010 Step 1 took 18365ms Step 2 took 9100ms ********** Factor found in step 2: 33064576717718812538576350565093 Found probable prime factor of 32 digits: 33064576717718812538576350565093 Probable prime cofactor has 167 digits
(10²⁰³-7)/3 = (3)₂₀₂1_<203> = 61 · 137458709 · 74987928326523863886652073_<26> · C167
C167 = P35 · C133
P35 = 10610358077968123193638709904195047_<35>
C133 = [4996377606594178960305032917299180726132415750204707883244133191273381282972582184700185290354272608872569221264882363056206902082349_<133>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4042664593 Step 1 took 13716ms Step 2 took 7519ms ********** Factor found in step 2: 10610358077968123193638709904195047 Found probable prime factor of 35 digits: 10610358077968123193638709904195047 Composite cofactor
(10²⁴⁵-7)/3 = (3)₂₄₄1_<245> = 97 · 66751 · 3258371 · 1403863703183_<13> · 2249810655289_<13> · 81791825300240873_<17> · 145142221366577384926667_<24> · C167
C167 = P35 · C133
P35 = 31324445949473317700096188175894333_<35>
C133 = [1345211973340636127176790697467331273618032323820765030845459707299234006881987792073875316307596244915355092769177331580459819511583_<133>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3217281827 Step 1 took 13848ms Step 2 took 7475ms ********** Factor found in step 2: 31324445949473317700096188175894333 Found probable prime factor of 35 digits: 31324445949473317700096188175894333 Composite cofactor
(10²¹²-7)/3 = (3)₂₁₁1_<212> = 31 · 1093 · 100741 · 10606483 · 31419071 · 50412367 · C180
C180 = P39 · C142
P39 = 160369474887919636204031018406084819503_<39>
C142 = [3624658501922790512467951115480401502972941554455672341416503473005149627879493077221463061699864507739026825856828851938839116595131830375689_<142>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=983877145 Step 1 took 15973ms Step 2 took 8179ms ********** Factor found in step 2: 160369474887919636204031018406084819503 Found probable prime factor of 39 digits: 160369474887919636204031018406084819503 Composite cofactor has 142 digits
(10²³⁰-7)/3 = (3)₂₂₉1_<230> = 233 · 1297 · 393122956362713113380660433_<27> · C198
C198 = P34 · C164
P34 = 9303129115468200415617210160203863_<34>
C164 = [30159587312927400531121782459578573768168220812002239640548897386508114122444066628011920137122898396501255946521973488448971446636365589871978276114626319714707389_<164>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2889055076 Step 1 took 18352ms Step 2 took 9099ms ********** Factor found in step 2: 9303129115468200415617210160203863 Found probable prime factor of 34 digits: 9303129115468200415617210160203863 Composite cofactor has 164 digits
(10²³¹-7)/3 = (3)₂₃₀1_<231> = 1499 · 2482112511942529_<16> · C212
C212 = P34 · C179
P34 = 3446466606505865790664327219252139_<34>
C179 = [25994506314096885876158633451155888467704893043048927716803604951844879501178514759167485473233340925526490101735084270552747077029197942597564019662065791324161042138087343728699_<179>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2658315989 Step 1 took 22491ms Step 2 took 10133ms ********** Factor found in step 2: 3446466606505865790664327219252139 Found probable prime factor of 34 digits: 3446466606505865790664327219252139 Composite cofactor has 179 digits
Feb 10, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 10, 2009
(14·10¹⁹⁵-11)/3 = 4(6)₁₉₄3_<196> = 587 · 797 · 83773 · 1172713 · 178969457 · 846897031831_<12> · 8237203638149_<13> · 201492578685756587_<18> · 80127682289557157831_<20> · C109
C109 = P41 · P69
P41 = 22558276111077612412558862726288421629303_<41>
P69 = 223294318380324094025369972631450077795174647404248745282626852355461_<69>

Number: 46663_195 N=5037134888058223633450405039362530589056135098486725936090357273858295899885946655529213127422826484929673683 ( 109 digits) Divisors found: r1=22558276111077612412558862726288421629303 r2=223294318380324094025369972631450077795174647404248745282626852355461 Version: Total time: 7.96 hours. Scaled time: 19.01 units (timescale=2.389). Factorization parameters were as follows: name: 46663_195 n: 5037134888058223633450405039362530589056135098486725936090357273858295899885946655529213127422826484929673683 skew: 28245.07 # norm 9.99e+14 c5: 6720 c4: 193258244 c3: 36868640092844 c2: -461046821771144595 c1: -11402140141774968346118 c0: -51999097899030472876385888 # alpha -6.14 Y1: 297120973369 Y0: -943978439869455520635 # Murphy_E 1.16e-09 # M 3864773925994558014424622908664061302157833946497194619583286798249691747731010960060528393480808806337866640 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 51 mfba: 51 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: 51/51 Sieved algebraic special-q in [900000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 5208950 Max relations in full relation-set: Initial matrix: Pruned matrix : 360431 x 360679 Polynomial selection time: 0.58 hours. Total sieving time: 6.73 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.27 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,51,51,2.6,2.6,50000 total time: 7.96 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
(14·10¹⁵⁴-11)/3 = 4(6)₁₅₃3_<155> = 17 · 419 · 124219040700783859777_<21> · C131
C131 = P55 · P77
P55 = 1092016169384849798120897210779304049877673274452365493_<55>
P77 = 48297716353085503445307835642388754394984414013051487482307443167425362155721_<77>

Number: 46663_154 N=52741887201932449189966675575636064389669071230243083895140283552082454064592436345514785806933159360295226874178203392830272935453 ( 131 digits) SNFS difficulty: 155 digits. Divisors found: r1=1092016169384849798120897210779304049877673274452365493 r2=48297716353085503445307835642388754394984414013051487482307443167425362155721 Version: Total time: 8.85 hours. Scaled time: 21.11 units (timescale=2.387). Factorization parameters were as follows: n: 52741887201932449189966675575636064389669071230243083895140283552082454064592436345514785806933159360295226874178203392830272935453 m: 10000000000000000000000000000000 deg: 5 c5: 7 c0: -55 skew: 1.51 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1200000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8032928 Max relations in full relation-set: Initial matrix: Pruned matrix : 414630 x 414878 Total sieving time: 8.09 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.36 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 8.85 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: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)
Feb 10, 2009 (2nd): By Sinkiti Sibata / Msieve, GGNFS / Feb 10, 2009
(14·10¹⁴⁵-11)/3 = 4(6)₁₄₄3_<146> = 953 · 19463 · 313037 · 25299178511_<11> · 221211803957189523635743_<24> · C100
C100 = P49 · P51
P49 = 2776588592463035618167267446146966595973892341987_<49>
P51 = 517228173529495948025544277131777941326206753336991_<51>

Mon Feb 09 19:05:19 2009 Msieve v. 1.39 Mon Feb 09 19:05:19 2009 random seeds: 93e85930 5a9aa090 Mon Feb 09 19:05:19 2009 factoring 1436129846322489891861707997659023743610672331253254191596629561333123038998333422561982792429541117 (100 digits) Mon Feb 09 19:05:20 2009 searching for 15-digit factors Mon Feb 09 19:05:22 2009 commencing quadratic sieve (100-digit input) Mon Feb 09 19:05:22 2009 using multiplier of 5 Mon Feb 09 19:05:22 2009 using 32kb Intel Core sieve core Mon Feb 09 19:05:22 2009 sieve interval: 36 blocks of size 32768 Mon Feb 09 19:05:22 2009 processing polynomials in batches of 6 Mon Feb 09 19:05:22 2009 using a sieve bound of 2665589 (97647 primes) Mon Feb 09 19:05:22 2009 using large prime bound of 399838350 (28 bits) Mon Feb 09 19:05:22 2009 using double large prime bound of 3043630695467550 (43-52 bits) Mon Feb 09 19:05:22 2009 using trial factoring cutoff of 52 bits Mon Feb 09 19:05:22 2009 polynomial 'A' values have 13 factors Tue Feb 10 05:05:58 2009 97905 relations (23686 full + 74219 combined from 1461371 partial), need 97743 Tue Feb 10 05:06:00 2009 begin with 1485057 relations Tue Feb 10 05:06:01 2009 reduce to 256622 relations in 11 passes Tue Feb 10 05:06:01 2009 attempting to read 256622 relations Tue Feb 10 05:06:06 2009 recovered 256622 relations Tue Feb 10 05:06:06 2009 recovered 246902 polynomials Tue Feb 10 05:06:06 2009 attempting to build 97905 cycles Tue Feb 10 05:06:06 2009 found 97905 cycles in 7 passes Tue Feb 10 05:06:06 2009 distribution of cycle lengths: Tue Feb 10 05:06:06 2009 length 1 : 23686 Tue Feb 10 05:06:06 2009 length 2 : 16873 Tue Feb 10 05:06:06 2009 length 3 : 16230 Tue Feb 10 05:06:06 2009 length 4 : 13475 Tue Feb 10 05:06:06 2009 length 5 : 10092 Tue Feb 10 05:06:06 2009 length 6 : 6934 Tue Feb 10 05:06:06 2009 length 7 : 4403 Tue Feb 10 05:06:06 2009 length 9+: 6212 Tue Feb 10 05:06:06 2009 largest cycle: 27 relations Tue Feb 10 05:06:07 2009 matrix is 97647 x 97905 (26.2 MB) with weight 6485509 (66.24/col) Tue Feb 10 05:06:07 2009 sparse part has weight 6485509 (66.24/col) Tue Feb 10 05:06:09 2009 filtering completed in 3 passes Tue Feb 10 05:06:09 2009 matrix is 93535 x 93599 (25.2 MB) with weight 6227516 (66.53/col) Tue Feb 10 05:06:09 2009 sparse part has weight 6227516 (66.53/col) Tue Feb 10 05:06:09 2009 saving the first 48 matrix rows for later Tue Feb 10 05:06:09 2009 matrix is 93487 x 93599 (14.8 MB) with weight 4798306 (51.26/col) Tue Feb 10 05:06:09 2009 sparse part has weight 3306922 (35.33/col) Tue Feb 10 05:06:09 2009 matrix includes 64 packed rows Tue Feb 10 05:06:09 2009 using block size 37439 for processor cache size 1024 kB Tue Feb 10 05:06:10 2009 commencing Lanczos iteration Tue Feb 10 05:06:10 2009 memory use: 14.9 MB Tue Feb 10 05:07:16 2009 lanczos halted after 1480 iterations (dim = 93487) Tue Feb 10 05:07:17 2009 recovered 18 nontrivial dependencies Tue Feb 10 05:07:20 2009 prp49 factor: 2776588592463035618167267446146966595973892341987 Tue Feb 10 05:07:20 2009 prp51 factor: 517228173529495948025544277131777941326206753336991 Tue Feb 10 05:07:20 2009 elapsed time 10:02:01
(14·10¹²⁴-11)/3 = 4(6)₁₂₃3_<125> = 6481 · 461027756647_<12> · C110
C110 = P41 · P69
P41 = 46900919101739598763136250902750403061951_<41>
P69 = 333009277288341262475781822043827398097001339583286019035504156113359_<69>

Number: 46663_124 N=15618441174229263451452204214107669620027686965986696000061011132240544631265281382536562568528268909055703409 ( 110 digits) SNFS difficulty: 125 digits. Divisors found: r1=46900919101739598763136250902750403061951 (pp41) r2=333009277288341262475781822043827398097001339583286019035504156113359 (pp69) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.20 hours. Scaled time: 1.51 units (timescale=0.472). Factorization parameters were as follows: name: 46663_124 n: 15618441174229263451452204214107669620027686965986696000061011132240544631265281382536562568528268909055703409 m: 10000000000000000000000000 deg: 5 c5: 7 c0: -55 skew: 1.51 type: snfs lss: 1 rlim: 880000 alim: 880000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 880000/880000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [440000, 690001) Primes: RFBsize:69823, AFBsize:69849, largePrimes:2497100 encountered Relations: rels:2459152, finalFF:254174 Max relations in full relation-set: 28 Initial matrix: 139737 x 254174 with sparse part having weight 18212629. Pruned matrix : 105737 x 106499 with weight 5326069. Total sieving time: 2.96 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000 total time: 3.20 hours. --------- CPU info (if available) ----------
(14·10¹²⁵-11)/3 = 4(6)₁₂₄3_<126> = 197 · 373 · C121
C121 = P58 · P64
P58 = 5034932239666512615015060534000743855051033015105258165189_<58>
P64 = 1261357206557626066936205067924634248448443329495853791285540707_<64>

Number: 46663_125 N=6350848065032684185934686063971185295064937421464959195801182165004105369642038985134479207777067087637166977404589848623 ( 121 digits) SNFS difficulty: 126 digits. Divisors found: r1=5034932239666512615015060534000743855051033015105258165189 (pp58) r2=1261357206557626066936205067924634248448443329495853791285540707 (pp64) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.13 hours. Scaled time: 1.48 units (timescale=0.472). Factorization parameters were as follows: name: 46663_125 n: 6350848065032684185934686063971185295064937421464959195801182165004105369642038985134479207777067087637166977404589848623 m: 10000000000000000000000000 deg: 5 c5: 14 c0: -11 skew: 0.95 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 695001) Primes: RFBsize:70555, AFBsize:70714, largePrimes:2555662 encountered Relations: rels:2542004, finalFF:275929 Max relations in full relation-set: 28 Initial matrix: 141337 x 275929 with sparse part having weight 20282825. Pruned matrix : 103424 x 104194 with weight 5518508. Total sieving time: 2.88 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 3.13 hours. --------- CPU info (if available) ----------
(14·10¹²⁶-11)/3 = 4(6)₁₂₅3_<127> = 8297 · 158364175209281901057565131239_<30> · C94
C94 = P43 · P52
P43 = 3252180732294199220113691787392621500316407_<43>
P52 = 1092079048213714302920212100999726007741012258867823_<52>

Tue Feb 10 07:35:01 2009 Msieve v. 1.39 Tue Feb 10 07:35:01 2009 random seeds: 7830df1c 55440e32 Tue Feb 10 07:35:01 2009 factoring 3551638438742829478396902688411967033383524043930677957142978601586957545196084433786091271961 (94 digits) Tue Feb 10 07:35:02 2009 searching for 15-digit factors Tue Feb 10 07:35:03 2009 commencing quadratic sieve (94-digit input) Tue Feb 10 07:35:03 2009 using multiplier of 1 Tue Feb 10 07:35:03 2009 using 32kb Intel Core sieve core Tue Feb 10 07:35:03 2009 sieve interval: 36 blocks of size 32768 Tue Feb 10 07:35:03 2009 processing polynomials in batches of 6 Tue Feb 10 07:35:03 2009 using a sieve bound of 2017283 (75294 primes) Tue Feb 10 07:35:03 2009 using large prime bound of 270315922 (28 bits) Tue Feb 10 07:35:03 2009 using double large prime bound of 1504419205773942 (42-51 bits) Tue Feb 10 07:35:03 2009 using trial factoring cutoff of 51 bits Tue Feb 10 07:35:03 2009 polynomial 'A' values have 12 factors Tue Feb 10 10:04:55 2009 75815 relations (19619 full + 56196 combined from 1059430 partial), need 75390 Tue Feb 10 10:04:56 2009 begin with 1079049 relations Tue Feb 10 10:04:57 2009 reduce to 193123 relations in 11 passes Tue Feb 10 10:04:57 2009 attempting to read 193123 relations Tue Feb 10 10:05:00 2009 recovered 193123 relations Tue Feb 10 10:05:00 2009 recovered 172486 polynomials Tue Feb 10 10:05:00 2009 attempting to build 75815 cycles Tue Feb 10 10:05:00 2009 found 75815 cycles in 6 passes Tue Feb 10 10:05:00 2009 distribution of cycle lengths: Tue Feb 10 10:05:00 2009 length 1 : 19619 Tue Feb 10 10:05:00 2009 length 2 : 13612 Tue Feb 10 10:05:00 2009 length 3 : 12791 Tue Feb 10 10:05:00 2009 length 4 : 10175 Tue Feb 10 10:05:00 2009 length 5 : 7352 Tue Feb 10 10:05:00 2009 length 6 : 4997 Tue Feb 10 10:05:00 2009 length 7 : 3140 Tue Feb 10 10:05:00 2009 length 9+: 4129 Tue Feb 10 10:05:00 2009 largest cycle: 21 relations Tue Feb 10 10:05:00 2009 matrix is 75294 x 75815 (18.8 MB) with weight 4635779 (61.15/col) Tue Feb 10 10:05:00 2009 sparse part has weight 4635779 (61.15/col) Tue Feb 10 10:05:01 2009 filtering completed in 3 passes Tue Feb 10 10:05:01 2009 matrix is 71133 x 71197 (17.7 MB) with weight 4353762 (61.15/col) Tue Feb 10 10:05:01 2009 sparse part has weight 4353762 (61.15/col) Tue Feb 10 10:05:01 2009 saving the first 48 matrix rows for later Tue Feb 10 10:05:02 2009 matrix is 71085 x 71197 (10.5 MB) with weight 3344583 (46.98/col) Tue Feb 10 10:05:02 2009 sparse part has weight 2318253 (32.56/col) Tue Feb 10 10:05:02 2009 matrix includes 64 packed rows Tue Feb 10 10:05:02 2009 using block size 28478 for processor cache size 1024 kB Tue Feb 10 10:05:02 2009 commencing Lanczos iteration Tue Feb 10 10:05:02 2009 memory use: 10.6 MB Tue Feb 10 10:05:32 2009 lanczos halted after 1125 iterations (dim = 71085) Tue Feb 10 10:05:32 2009 recovered 17 nontrivial dependencies Tue Feb 10 10:05:34 2009 prp43 factor: 3252180732294199220113691787392621500316407 Tue Feb 10 10:05:34 2009 prp52 factor: 1092079048213714302920212100999726007741012258867823 Tue Feb 10 10:05:34 2009 elapsed time 02:30:33
(14·10¹²⁷-11)/3 = 4(6)₁₂₆3_<128> = 43 · C127
C127 = P52 · P75
P52 = 3202818108069289937646699055896780108615579936997021_<52>
P75 = 338848876586274922737750506772338476604603843678007719668492077103044148921_<75>

Number: 46663_127 N=1085271317829457364341085271317829457364341085271317829457364341085271317829457364341085271317829457364341085271317829457364341 ( 127 digits) SNFS difficulty: 128 digits. Divisors found: r1=3202818108069289937646699055896780108615579936997021 (pp52) r2=338848876586274922737750506772338476604603843678007719668492077103044148921 (pp75) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 5.12 hours. Scaled time: 2.42 units (timescale=0.472). Factorization parameters were as follows: name: 46663_127 n: 1085271317829457364341085271317829457364341085271317829457364341085271317829457364341085271317829457364341085271317829457364341 m: 20000000000000000000000000 deg: 5 c5: 175 c0: -44 skew: 0.76 type: snfs lss: 1 rlim: 980000 alim: 980000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 980000/980000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [490000, 940001) Primes: RFBsize:77067, AFBsize:76869, largePrimes:2752811 encountered Relations: rels:2682505, finalFF:229280 Max relations in full relation-set: 28 Initial matrix: 154003 x 229280 with sparse part having weight 19036918. Pruned matrix : 135193 x 136027 with weight 8277896. Total sieving time: 4.71 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.25 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,980000,980000,26,26,47,47,2.3,2.3,50000 total time: 5.12 hours. --------- CPU info (if available) ----------
Feb 10, 2009: Torbjörn Granlund's web page moved from http://swox.com/~tege/ to http://gmplib.org/~tege/.
Feb 9, 2009: By Robert Backstrom / GGNFS, Msieve
(31·10¹⁹⁶-13)/9 = 3(4)₁₉₅3_<197> = 3 · C197
C197 = P73 · P124
P73 = 1541538682997486108092462038285734433957144793058057857281416009722861673_<73>
P124 = 7448065759307452366876877828005306670204146180497540890101571996285418693550680753007022233010389291838968682804731542510497_<124>

Number: n N=11481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481 ( 197 digits) SNFS difficulty: 197 digits. Divisors found: Mon Feb 9 23:38:14 2009 prp73 factor: 1541538682997486108092462038285734433957144793058057857281416009722861673 Mon Feb 9 23:38:14 2009 prp124 factor: 7448065759307452366876877828005306670204146180497540890101571996285418693550680753007022233010389291838968682804731542510497 Mon Feb 9 23:38:14 2009 elapsed time 10:06:08 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20050930-k8 Total time: 44.75 hours. Scaled time: 89.95 units (timescale=2.010). Factorization parameters were as follows: name: KA_3_4_195_3 n: 11481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481 deg: 5 c5: 310 c0: -13 m: 1000000000000000000000000000000000000000 skew: 0.53 type: snfs rlim: 10000000 alim: 10000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 15503027) Primes: RFBsize:664579, AFBsize:664376, largePrimes:37285387 encountered Relations: rels:34226712, finalFF:440225 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 4998041 hash collisions in 37704766 relations Msieve: matrix is 2492067 x 2492312 (683.2 MB) Total sieving time: 43.87 hours. Total relation processing time: 0.88 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,197,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000 total time: 44.75 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830483) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Total of 4 processors activated (22643.68 BogoMIPS).
Feb 9, 2009 (5th): Factorizations of 33...331 have been extended up to n=250. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Feb 9, 2009 (4th): By Sinkiti Sibata / Msieve, GGNFS / Feb 9, 2009
(14·10¹¹³-11)/3 = 4(6)₁₁₂3_<114> = 1061 · 213765728522524457_<18> · C94
C94 = P33 · P61
P33 = 654530224410243311038137953434723_<33>
P61 = 3143573448517984282356294478527718100470179527192788309661953_<61>

Mon Feb 09 07:55:40 2009 Msieve v. 1.39 Mon Feb 09 07:55:40 2009 random seeds: 68aec570 31520c7c Mon Feb 09 07:55:40 2009 factoring 2057563834708558700370740045678726131547157359320251956209589653345623526539050521743382194019 (94 digits) Mon Feb 09 07:55:41 2009 searching for 15-digit factors Mon Feb 09 07:55:42 2009 commencing quadratic sieve (94-digit input) Mon Feb 09 07:55:43 2009 using multiplier of 19 Mon Feb 09 07:55:43 2009 using 32kb Intel Core sieve core Mon Feb 09 07:55:43 2009 sieve interval: 36 blocks of size 32768 Mon Feb 09 07:55:43 2009 processing polynomials in batches of 6 Mon Feb 09 07:55:43 2009 using a sieve bound of 1991609 (73895 primes) Mon Feb 09 07:55:43 2009 using large prime bound of 256917561 (27 bits) Mon Feb 09 07:55:43 2009 using double large prime bound of 1372868018887893 (42-51 bits) Mon Feb 09 07:55:43 2009 using trial factoring cutoff of 51 bits Mon Feb 09 07:55:43 2009 polynomial 'A' values have 12 factors Mon Feb 09 11:00:34 2009 74091 relations (18064 full + 56027 combined from 1032110 partial), need 73991 Mon Feb 09 11:00:35 2009 begin with 1050174 relations Mon Feb 09 11:00:36 2009 reduce to 192079 relations in 11 passes Mon Feb 09 11:00:36 2009 attempting to read 192079 relations Mon Feb 09 11:00:39 2009 recovered 192079 relations Mon Feb 09 11:00:39 2009 recovered 176068 polynomials Mon Feb 09 11:00:40 2009 attempting to build 74091 cycles Mon Feb 09 11:00:40 2009 found 74091 cycles in 5 passes Mon Feb 09 11:00:40 2009 distribution of cycle lengths: Mon Feb 09 11:00:40 2009 length 1 : 18064 Mon Feb 09 11:00:40 2009 length 2 : 13101 Mon Feb 09 11:00:40 2009 length 3 : 12529 Mon Feb 09 11:00:40 2009 length 4 : 9968 Mon Feb 09 11:00:40 2009 length 5 : 7638 Mon Feb 09 11:00:40 2009 length 6 : 5072 Mon Feb 09 11:00:40 2009 length 7 : 3333 Mon Feb 09 11:00:40 2009 length 9+: 4386 Mon Feb 09 11:00:40 2009 largest cycle: 22 relations Mon Feb 09 11:00:40 2009 matrix is 73895 x 74091 (19.5 MB) with weight 4822373 (65.09/col) Mon Feb 09 11:00:40 2009 sparse part has weight 4822373 (65.09/col) Mon Feb 09 11:00:41 2009 filtering completed in 3 passes Mon Feb 09 11:00:41 2009 matrix is 70504 x 70568 (18.7 MB) with weight 4617367 (65.43/col) Mon Feb 09 11:00:41 2009 sparse part has weight 4617367 (65.43/col) Mon Feb 09 11:00:41 2009 saving the first 48 matrix rows for later Mon Feb 09 11:00:41 2009 matrix is 70456 x 70568 (11.9 MB) with weight 3636187 (51.53/col) Mon Feb 09 11:00:41 2009 sparse part has weight 2704076 (38.32/col) Mon Feb 09 11:00:41 2009 matrix includes 64 packed rows Mon Feb 09 11:00:41 2009 using block size 28227 for processor cache size 1024 kB Mon Feb 09 11:00:42 2009 commencing Lanczos iteration Mon Feb 09 11:00:42 2009 memory use: 11.4 MB Mon Feb 09 11:01:15 2009 lanczos halted after 1116 iterations (dim = 70453) Mon Feb 09 11:01:15 2009 recovered 16 nontrivial dependencies Mon Feb 09 11:01:15 2009 prp33 factor: 654530224410243311038137953434723 Mon Feb 09 11:01:15 2009 prp61 factor: 3143573448517984282356294478527718100470179527192788309661953 Mon Feb 09 11:01:15 2009 elapsed time 03:05:35
(14·10¹³⁹-11)/3 = 4(6)₁₃₈3_<140> = 19 · 35603 · 822283639517_<12> · 230069536579690634739859_<24> · C99
C99 = P38 · P61
P38 = 98791777779310242924201001806786296129_<38>
P61 = 3691178247521975388576957842118369003602251665922839419914457_<61>

Number: 46663_139 N=364658061173014811940660341074139620063025883624393215828062415791310764890201996071076685050236953 ( 99 digits) SNFS difficulty: 140 digits. Divisors found: r1=98791777779310242924201001806786296129 (pp38) r2=3691178247521975388576957842118369003602251665922839419914457 (pp61) Version: GGNFS-0.77.1-