News and updates, March 2009

Home > Math > Factorizations >

News and updates, March 2009

Mar 31, 2009 (6th): By Sinkiti Sibata / GGNFS / Mar 31, 2009
(17·10¹⁴³+7)/3 = 5(6)₁₄₂9_<144> = C144
C144 = P50 · P95
P50 = 27982756612723364391161873357402661413921623326919_<50>
P95 = 20250566250825028908340470371472117580789090434207731128039313703339686354231140442904863190251_<95>

Number: 56669_143 N=566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 ( 144 digits) SNFS difficulty: 145 digits. Divisors found: r1=27982756612723364391161873357402661413921623326919 (pp50) r2=20250566250825028908340470371472117580789090434207731128039313703339686354231140442904863190251 (pp95) Version: GGNFS-0.77.1-20060513-k8 Total time: 17.71 hours. Scaled time: 35.25 units (timescale=1.991). Factorization parameters were as follows: name: 56669_143 n: 566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 m: 50000000000000000000000000000 deg: 5 c5: 136 c0: 175 skew: 1.05 type: snfs lss: 1 rlim: 1870000 alim: 1870000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1870000/1870000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [935000, 2435001) Primes: RFBsize:139952, AFBsize:140182, largePrimes:4117559 encountered Relations: rels:4277564, finalFF:355683 Max relations in full relation-set: 28 Initial matrix: 280201 x 355683 with sparse part having weight 38073609. Pruned matrix : 254929 x 256394 with weight 25011096. Total sieving time: 16.72 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.74 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1870000,1870000,26,26,49,49,2.3,2.3,100000 total time: 17.71 hours. --------- CPU info (if available) ----------
(17·10¹³²-11)/3 = 5(6)₁₃₁3_<133> = 11927 · 12241 · C125
C125 = P59 · P66
P59 = 52284820891276381659708546870688803399267075582265861157609_<59>
P66 = 742341815766471509352216623789785937342597231924390451309162340601_<66>

Number: 56663_132 N=38813208877454852412647671331555464620012372235449573546831005263411310143039209096758615090003459192994254154202289800783009 ( 125 digits) SNFS difficulty: 134 digits. Divisors found: r1=52284820891276381659708546870688803399267075582265861157609 (pp59) r2=742341815766471509352216623789785937342597231924390451309162340601 (pp66) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 8.62 hours. Scaled time: 4.08 units (timescale=0.473). Factorization parameters were as follows: name: 56663_132 n: 38813208877454852412647671331555464620012372235449573546831005263411310143039209096758615090003459192994254154202289800783009 m: 200000000000000000000000000 deg: 5 c5: 425 c0: -88 skew: 0.73 type: snfs lss: 1 rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [600000, 1350001) Primes: RFBsize:92938, AFBsize:92785, largePrimes:3089925 encountered Relations: rels:3013509, finalFF:213784 Max relations in full relation-set: 28 Initial matrix: 185790 x 213784 with sparse part having weight 19355847. Pruned matrix : 178577 x 179569 with weight 14186814. Total sieving time: 7.78 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.64 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000 total time: 8.62 hours. --------- CPU info (if available) ----------
(17·10¹³³+7)/3 = 5(6)₁₃₂9_<134> = 1585523 · C128
C128 = P61 · P67
P61 = 6354900264814491244184743748128071268238350143265482183046067_<61>
P67 = 5624013846139737478130811647155975800741681473273243786489905382309_<67>

Number: 56669_133 N=35740047080153783115518769936901998057843794550231479875515313664113776127288387911538758294056072770099624330058073371793828703 ( 128 digits) SNFS difficulty: 135 digits. Divisors found: r1=6354900264814491244184743748128071268238350143265482183046067 (pp61) r2=5624013846139737478130811647155975800741681473273243786489905382309 (pp67) Version: GGNFS-0.77.1-20060513-nocona Total time: 6.47 hours. Scaled time: 16.65 units (timescale=2.575). Factorization parameters were as follows: name: 56669_133 n: 35740047080153783115518769936901998057843794550231479875515313664113776127288387911538758294056072770099624330058073371793828703 m: 500000000000000000000000000 deg: 5 c5: 136 c0: 175 skew: 1.05 type: snfs lss: 1 rlim: 1280000 alim: 1280000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1280000/1280000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [640000, 1315001) Primes: RFBsize:98610, AFBsize:98755, largePrimes:3463453 encountered Relations: rels:3624793, finalFF:411535 Max relations in full relation-set: 28 Initial matrix: 197432 x 411535 with sparse part having weight 40428850. Pruned matrix : 153381 x 154432 with weight 13499290. Total sieving time: 6.23 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1280000,1280000,26,26,47,47,2.3,2.3,75000 total time: 6.47 hours. --------- CPU info (if available) ----------
(17·10¹³⁴+7)/3 = 5(6)₁₃₃9_<135> = 3187 · 1526387 · 124908761 · C117
C117 = P39 · P79
P39 = 177690045721539954255192188637430523827_<39>
P79 = 5248376050110084584175551640517401731912747171702980190279975114064593981426783_<79>

Number: 56669_134 N=932584180307896199826436755725362816413786179614293760112655727894376981585212686153454842386632332266149796537458541 ( 117 digits) SNFS difficulty: 136 digits. Divisors found: r1=177690045721539954255192188637430523827 (pp39) r2=5248376050110084584175551640517401731912747171702980190279975114064593981426783 (pp79) Version: GGNFS-0.77.1-20060513-nocona Total time: 10.06 hours. Scaled time: 25.81 units (timescale=2.564). Factorization parameters were as follows: name: 56669_134 n: 932584180307896199826436755725362816413786179614293760112655727894376981585212686153454842386632332266149796537458541 m: 1000000000000000000000000000 deg: 5 c5: 17 c0: 70 skew: 1.33 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: RFBsize:100021, AFBsize:100398, largePrimes:4120790 encountered Relations: rels:5006144, finalFF:1098798 Max relations in full relation-set: 28 Initial matrix: 200484 x 1098798 with sparse part having weight 104332057. Pruned matrix : 130458 x 131524 with weight 15361620. Total sieving time: 9.84 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.10 hours. Time per square root: 0.05 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: 10.06 hours. --------- CPU info (if available) ----------
(17·10¹⁴⁷-11)/3 = 5(6)₁₄₆3_<148> = 7 · 59 · 14797 · 65029 · 332207 · 171783755123_<12> · C120
C120 = P35 · P85
P35 = 86544108390160860576618609111824549_<35>
P85 = 2887144271562123331708866792687322803919554408546240280625249905275715279143834477443_<85>

Number: 56663_147 N=249865326776104423930264688962865431115384646336343536218983974506030500463312084659865793670525610032092933357714148207 ( 120 digits) SNFS difficulty: 149 digits. Divisors found: r1=86544108390160860576618609111824549 (pp35) r2=2887144271562123331708866792687322803919554408546240280625249905275715279143834477443 (pp85) Version: GGNFS-0.77.1-20060513-k8 Total time: 28.69 hours. Scaled time: 55.23 units (timescale=1.925). Factorization parameters were as follows: name: 56663_147 n: 249865326776104423930264688962865431115384646336343536218983974506030500463312084659865793670525610032092933357714148207 m: 200000000000000000000000000000 deg: 5 c5: 425 c0: -88 skew: 0.73 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 3550001) Primes: RFBsize:155805, AFBsize:156018, largePrimes:4577116 encountered Relations: rels:4946005, finalFF:377828 Max relations in full relation-set: 28 Initial matrix: 311890 x 377828 with sparse part having weight 46231365. Pruned matrix : 289754 x 291377 with weight 34207449. Total sieving time: 27.11 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.28 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 28.69 hours. --------- CPU info (if available) ----------
Mar 31, 2009 (5th): By Ignacio Santos / GGNFS, Msieve / Mar 31, 2009
(17·10¹⁴⁶+7)/3 = 5(6)₁₄₅9_<147> = 2753 · 191602500378467_<15> · 348303469429687_<15> · C115
C115 = P43 · P73
P43 = 3057392239329248851492355041710477577863419_<43>
P73 = 1008814518216364144881525304100909685341593542436645633932512347413758923_<73>

Number: 56669_146 N=3084341678917386880850198417534629193145857975643907546729705176891505592880992672853761482215266377566809886537737 ( 115 digits) SNFS difficulty: 148 digits. Divisors found: r1=3057392239329248851492355041710477577863419 (pp43) r2=1008814518216364144881525304100909685341593542436645633932512347413758923 (pp73) Version: Msieve-1.39 Total time: 10.06 hours. Scaled time: 17.50 units (timescale=1.739). Factorization parameters were as follows: n: 3084341678917386880850198417534629193145857975643907546729705176891505592880992672853761482215266377566809886537737 m: 200000000000000000000000000000 deg: 5 c5: 85 c0: 112 skew: 1.06 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 373222 x 373467 Total sieving time: 10.06 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 10.06 hours. --------- CPU info (if available) ----------
(17·10¹⁵⁶+7)/3 = 5(6)₁₅₅9_<157> = 15870103 · C150
C150 = P40 · P111
P40 = 2367635701915964097724774454907252952361_<40>
P111 = 150811007437796566561181108281747578101194546138167998981260017491864192266868547474304779267945342162030780643_<111>

Number: 56669_156 N=357065525451641156120200774164267658922356500563774958906483887764727592925305315703790118228386209381669839613937393264975448909604850495719319948123 ( 150 digits) SNFS difficulty: 158 digits. Divisors found: r1=2367635701915964097724774454907252952361 (pp40) r2=150811007437796566561181108281747578101194546138167998981260017491864192266868547474304779267945342162030780643 (pp111) Version: Msieve-1.39 Total time: 25.77 hours. Scaled time: 66.27 units (timescale=2.571). Factorization parameters were as follows: n: 357065525451641156120200774164267658922356500563774958906483887764727592925305315703790118228386209381669839613937393264975448909604850495719319948123 m: 20000000000000000000000000000000 deg: 5 c5: 85 c0: 112 skew: 1.06 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor 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 : 606794 x 607042 Total sieving time: 25.77 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,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 25.77 hours. --------- CPU info (if available) ----------
(17·10¹⁶²+7)/3 = 5(6)₁₆₁9_<163> = 151 · 883 · C158
C158 = P60 · P98
P60 = 938555543805634759258867025023469462009038450912147151697593_<60>
P98 = 45282462535927402072019537780515353914840639175316981835821290735171335483580567771222872954596801_<98>

Number: 56669_162 N=42500106250265625664064160160400401001002502506256265640664101660254150635376588441471103677759194397985994964987412468531171327928319820799551998879997199993 ( 158 digits) SNFS difficulty: 164 digits. Divisors found: r1=938555543805634759258867025023469462009038450912147151697593 (pp60) r2=45282462535927402072019537780515353914840639175316981835821290735171335483580567771222872954596801 (pp98) Version: Msieve-1.39 Total time: 31.25 hours. Scaled time: 54.35 units (timescale=1.739). Factorization parameters were as follows: n: 42500106250265625664064160160400401001002502506256265640664101660254150635376588441471103677759194397985994964987412468531171327928319820799551998879997199993 m: 200000000000000000000000000000000 deg: 5 c5: 425 c0: 56 skew: 0.67 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1900000, 3700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 662969 x 663217 Total sieving time: 31.25 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,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 31.25 hours. --------- CPU info (if available) ----------
(49·10¹⁵²+41)/9 = 5(4)₁₅₁9_<153> = 3 · 19 · 71 · 27067 · 54454587301_<11> · C134
C134 = P50 · P85
P50 = 71383023650434742673540327947729791872255675161503_<50>
P85 = 1278647495690664764624201577118918428375254439965018372226597323792892389586504540967_<85>

Number: 54449_152 N=91273724425455878608183269099983069058428866640355708824581369879911159793711223544499072175584234280081660305868836764124980604793401 ( 134 digits) SNFS difficulty: 154 digits. Divisors found: r1=71383023650434742673540327947729791872255675161503 (pp50) r2=1278647495690664764624201577118918428375254439965018372226597323792892389586504540967 (pp85) Version: Msieve-1.39 Total time: 14.99 hours. Scaled time: 26.07 units (timescale=1.739). Factorization parameters were as follows: n: 91273724425455878608183269099983069058428866640355708824581369879911159793711223544499072175584234280081660305868836764124980604793401 m: 2000000000000000000000000000000 deg: 5 c5: 1225 c0: 328 skew: 0.77 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor 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, 2200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 418620 x 418868 Total sieving time: 14.99 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: snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 14.99 hours. --------- CPU info (if available) ----------
(17·10¹⁶⁸-11)/3 = 5(6)₁₆₇3_<169> = 157 · 2833506191_<10> · C158
C158 = P48 · P55 · P56
P48 = 483474821596767408759082695358090165964391803959_<48>
P55 = 1837726659308304398305992928336713542412055109386752587_<55>
P56 = 14336695821349312910842315435438406296777782235007995553_<56>

Number: 56663_168 N=12738076371128477468978940600870901594686948017709240282640546203307075948320395285636508081077478314865146941533419891948955009115764013722423058628275173949 ( 158 digits) SNFS difficulty: 170 digits. Divisors found: r1=483474821596767408759082695358090165964391803959 (pp48) r2=1837726659308304398305992928336713542412055109386752587 (pp55) r3=14336695821349312910842315435438406296777782235007995553 (pp56) Version: Msieve-1.39 Total time: 55.51 hours. Scaled time: 142.10 units (timescale=2.560). Factorization parameters were as follows: n: 12738076371128477468978940600870901594686948017709240282640546203307075948320395285636508081077478314865146941533419891948955009115764013722423058628275173949 m: 5000000000000000000000000000000000 deg: 5 c5: 136 c0: -275 skew: 1.15 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor 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, 5150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 884260 x 884508 Total sieving time: 55.51 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: 55.51 hours. --------- CPU info (if available) ----------
Mar 31, 2009 (4th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 31, 2009
(16·10¹⁵⁷+17)/3 = 5(3)₁₅₆9_<158> = 17169989 · 6719426025889_<13> · C138
C138 = P57 · P82
P57 = 151415726802733836070298952223999025939393684802019324559_<57>
P82 = 3052991170776104521524354567572988782090802728355355198184479556190327131801237201_<82>

Number: n N=462270877045393163584348333685350086843161288349162181866585708605048711534748880933255975279236570378999265058357048501718512986563719359 ( 138 digits) SNFS difficulty: 158 digits. Divisors found: Tue Mar 31 10:09:36 2009 prp57 factor: 151415726802733836070298952223999025939393684802019324559 Tue Mar 31 10:09:36 2009 prp82 factor: 3052991170776104521524354567572988782090802728355355198184479556190327131801237201 Tue Mar 31 10:09:36 2009 elapsed time 00:45:07 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 17.44 hours. Scaled time: 46.39 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_3_156_9 n: 462270877045393163584348333685350086843161288349162181866585708605048711534748880933255975279236570378999265058357048501718512986563719359 skew: 0.81 deg: 5 c5: 50 c0: 17 m: 20000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2250000, 3240409) Primes: RFBsize:315948, AFBsize:316401, largePrimes:14457525 encountered Relations: rels:13441122, finalFF:589292 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 934151 hash collisions in 15350882 relations Msieve: matrix is 569049 x 569297 (151.8 MB) Total sieving time: 17.16 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000 total time: 17.44 hours. --------- CPU info (if available) ----------
(17·10²⁰²-11)/3 = 5(6)₂₀₁3_<203> = 25508661453125273_<17> · 1409768013786543156259_<22> · 1513242066470195178659029_<25> · 6533393411141674191648447518542097_<34> · C108
C108 = P43 · P65
P43 = 8533119906049968013405927966076339919424151_<43>
P65 = 18678297133149696415319508843765989670835661272807507536836918743_<65>

Number: n N=159384149077995724360968874191338336220570220714108819627737775487450405265340226750529863760307117738762193 ( 108 digits) Divisors found: Tue Mar 31 14:05:24 2009 prp43 factor: 8533119906049968013405927966076339919424151 Tue Mar 31 14:05:24 2009 prp65 factor: 18678297133149696415319508843765989670835661272807507536836918743 Tue Mar 31 14:05:24 2009 elapsed time 00:25:39 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 8.88 hours. Scaled time: 23.35 units (timescale=2.629). Factorization parameters were as follows: name: KA_5_6_201_3 n: 159384149077995724360968874191338336220570220714108819627737775487450405265340226750529863760307117738762193 skew: 21605.08 # norm 6.21e+14 c5: 25380 c4: -660213150 c3: -24921912202565 c2: 707460791442207938 c1: 7580049824717362649974 c0: 756794256944768577900120 # alpha -5.93 Y1: 259070668967 Y0: -362737383380765073881 # Murphy_E 1.36e-09 # M 109100457503249211478622374976003187991088526352527265693883999034580980374613343265241024834765793558473934 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1250000, 2306641) Primes: RFBsize:183072, AFBsize:183136, largePrimes:15477607 encountered Relations: rels:13629014, finalFF:405215 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1107998 hash collisions in 14538239 relations Msieve: matrix is 358515 x 358763 (98.6 MB) Total sieving time: 8.41 hours. Total relation processing time: 0.48 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000 total time: 8.88 hours. --------- CPU info (if available) ----------
(17·10¹⁴⁰-11)/3 = 5(6)₁₃₉3_<141> = 23 · 1988582244189483800485209843958743589043_<40> · C101
C101 = P49 · P52
P49 = 3005579956989595830896695132357111722799545705839_<49>
P52 = 4122189828877880282767943433686839636744205235978853_<52>

Number: n N=12389571128581728818477254444904148656371225081269043431614820414039285832831268485708657579962622667 ( 101 digits) Divisors found: r1=3005579956989595830896695132357111722799545705839 (pp49) r2=4122189828877880282767943433686839636744205235978853 (pp52) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.57 hours. Scaled time: 8.33 units (timescale=1.823). Factorization parameters were as follows: name: KA_5_6_139_3 n: 12389571128581728818477254444904148656371225081269043431614820414039285832831268485708657579962622667 skew: 4651.48 # norm 9.89e+13 c5: 69300 c4: 571486905 c3: -12839315526392 c2: -9622006559641436 c1: 57287478236820850868 c0: 2430459791125601077760 # alpha -5.44 Y1: 15320936839 Y0: -11232169038330410541 # Murphy_E 3.14e-09 # M 4060843220027718992330198455824508205853740189188640325603580098901770979732502745137967010543083242 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [900000, 1400001) Primes: RFBsize:135072, AFBsize:135518, largePrimes:10265150 encountered Relations: rels:8908522, finalFF:341461 Max relations in full relation-set: 48 Initial matrix: 270671 x 341461 with sparse part having weight 36163373. Pruned matrix : 227834 x 229251 with weight 18117846. Total sieving time: 3.78 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.40 hours. Total square root time: 0.19 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,28,28,56,56,2.5,2.5,100000 total time: 4.57 hours. --------- CPU info (if available) ----------
(17·10¹⁴⁵+7)/3 = 5(6)₁₄₄9_<146> = 239 · 677 · 1049 · 292118833 · 29674305301143700049_<20> · C110
C110 = P41 · P70
P41 = 18183749665123138488743833669798206342683_<41>
P70 = 2118078478457350688003065996325803900532514144740988502378387478125357_<70>

Number: n N=38514608823353377272641347653420217491397580608502431726839383981631414778701495850403463655142317875973712831 ( 110 digits) Divisors found: Tue Mar 31 17:40:48 2009 prp41 factor: 18183749665123138488743833669798206342683 Tue Mar 31 17:40:48 2009 prp70 factor: 2118078478457350688003065996325803900532514144740988502378387478125357 Tue Mar 31 17:40:48 2009 elapsed time 00:33:50 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 13.42 hours. Scaled time: 35.42 units (timescale=2.639). Factorization parameters were as follows: name: KA_5_6_144_9 n: 38514608823353377272641347653420217491397580608502431726839383981631414778701495850403463655142317875973712831 skew: 37739.22 # norm 4.10e+15 c5: 20580 c4: -3779595533 c3: -179745057398388 c2: 4385492615468670600 c1: 77526627803213528726734 c0: -311510180055772786998885888 # alpha -6.59 Y1: 159942219547 Y0: -1133543719479839699269 # Murphy_E 9.84e-10 # M 33740392465434260340494028499491057358071137137340339477433159730462287355555309704189306725907028187501742996 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1600000, 2200141) Primes: RFBsize:230209, AFBsize:230131, largePrimes:16112914 encountered Relations: rels:14158601, finalFF:468589 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 786233 hash collisions in 14611703 relations Msieve: matrix is 452695 x 452943 (125.8 MB) Total sieving time: 12.98 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: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000 total time: 13.42 hours. --------- CPU info (if available) ----------
(17·10¹⁴⁵-11)/3 = 5(6)₁₄₄3_<146> = 352357 · 50632934702653297795467724997_<29> · C112
C112 = P39 · P73
P39 = 464627234444086771952257423350409216049_<39>
P73 = 6836077856706214117788292473821556206302849788523878355659660833037097103_<73>

Number: n N=3176227949005868364358693738547790942522693886423918740391964916137466084652121419130404718461305044596919006047 ( 112 digits) Divisors found: Tue Mar 31 20:15:07 2009 prp39 factor: 464627234444086771952257423350409216049 Tue Mar 31 20:15:07 2009 prp73 factor: 6836077856706214117788292473821556206302849788523878355659660833037097103 Tue Mar 31 20:15:07 2009 elapsed time 00:42:53 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 15.08 hours. Scaled time: 39.96 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_6_144_3 n: 3176227949005868364358693738547790942522693886423918740391964916137466084652121419130404718461305044596919006047 skew: 54953.55 # norm 5.48e+15 c5: 11520 c4: 1446373908 c3: 134262196311763 c2: -3817045765264157060 c1: -243283989464720815205980 c0: 4747964505240438282057733040 # alpha -6.74 Y1: 316846995377 Y0: -3076739404819159933737 # Murphy_E 8.00e-10 # M 205874714480015875367168626463213627297291540683003617802622108955885926000947565141870728968097023688519563551 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1750000, 2450083) Primes: RFBsize:250150, AFBsize:249829, largePrimes:16312727 encountered Relations: rels:14195956, finalFF:521565 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 815780 hash collisions in 14679846 relations Msieve: matrix is 566775 x 567023 (158.2 MB) Total sieving time: 14.67 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000 total time: 15.08 hours. --------- CPU info (if available) ----------
(17·10¹⁴⁹-11)/3 = 5(6)₁₄₈3_<150> = 31 · 11382247123588637_<17> · C133
C133 = P40 · P93
P40 = 7590405178178339305402471611491947851643_<40>
P93 = 211579215767037376360039653308037412309227402033175342484760722035903386871514912511485607703_<93>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 1605971974953032633620272892291686979162820217563299946643348773906039149427150458389421453602769051062426587033402865804805142006029 (133 digits) Using B1=2564000, B2=3568033570, polynomial Dickson(6), sigma=1582264560 Step 1 took 31746ms Step 2 took 10951ms ********** Factor found in step 2: 7590405178178339305402471611491947851643 Found probable prime factor of 40 digits: 7590405178178339305402471611491947851643 Probable prime cofactor 211579215767037376360039653308037412309227402033175342484760722035903386871514912511485607703 has 93 digits
Mar 31, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 31, 2009
(8·10¹⁸²+1)/9 = (8)₁₈₁9_<182> = 15236737 · C175
C175 = P52 · P124
P52 = 2110195633562623203363788636409114570248983488203027_<52>
P124 = 2764603071590345234203219159089774679474933517069560468037418091215396508782747937036376125151482683214742185677398930843011_<124>

Number: 88889_182 N=5833853330203762714345524825222676540842628502998305272899892469686186017970178843993230892473164621066104172362421750069512185508543521417275161269036073070558931934631994297 ( 175 digits) SNFS difficulty: 182 digits. Divisors found: r1=2110195633562623203363788636409114570248983488203027 r2=2764603071590345234203219159089774679474933517069560468037418091215396508782747937036376125151482683214742185677398930843011 Version: Total time: 78.73 hours. Scaled time: 187.62 units (timescale=2.383). Factorization parameters were as follows: n: 5833853330203762714345524825222676540842628502998305272899892469686186017970178843993230892473164621066104172362421750069512185508543521417275161269036073070558931934631994297 m: 2000000000000000000000000000000000000 deg: 5 c5: 25 c0: 1 skew: 0.53 type: snfs lss: 1 rlim: 6600000 alim: 6600000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6600000/6600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3300000, 5400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 18294595 Max relations in full relation-set: Initial matrix: Pruned matrix : 1201370 x 1201618 Total sieving time: 72.82 hours. Total relation processing time: 2.03 hours. Matrix solve time: 3.56 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,6600000,6600000,28,28,53,53,2.5,2.5,100000 total time: 78.73 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)
Mar 31, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Mar 31, 2009
(17·10¹³⁸+7)/3 = 5(6)₁₃₇9_<139> = 239 · C137
C137 = P40 · P98
P40 = 2098112473379109578751455496357626967749_<40>
P98 = 11300586918872044831776718863224420912853578411193077140307922192223698599776702875788745176999879_<98>

Number: 56669_138 N=23709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902371 ( 137 digits) SNFS difficulty: 140 digits. Divisors found: r1=2098112473379109578751455496357626967749 r2=11300586918872044831776718863224420912853578411193077140307922192223698599776702875788745176999879 Version: Total time: 8.22 hours. Scaled time: 8.60 units (timescale=1.046). Factorization parameters were as follows: n: 23709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902371 m: 5000000000000000000000000000 deg: 5 c5: 136 c0: 175 skew: 1.05 type: snfs lss: 1 rlim: 1540000 alim: 1540000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1540000/1540000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [770000, 1770001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 234388 x 234636 Total sieving time: 8.22 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,140,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000 total time: 8.22 hours. --------- CPU info (if available) ----------
(17·10¹³⁷-11)/3 = 5(6)₁₃₆3_<138> = 89 · C136
C136 = P32 · P105
P32 = 30786338087936362186389460909151_<32>
P105 = 206813852960212896386184499990362608712079715902907975666006921434264383142752261316006717304525197630817_<105>

Number: 56663_137 N=6367041198501872659176029962546816479400749063670411985018726591760299625468164794007490636704119850187265917602996254681647940074906367 ( 136 digits) SNFS difficulty: 139 digits. Divisors found: r1=30786338087936362186389460909151 r2=206813852960212896386184499990362608712079715902907975666006921434264383142752261316006717304525197630817 Version: Total time: 9.54 hours. Scaled time: 7.45 units (timescale=0.781). Factorization parameters were as follows: n: 6367041198501872659176029962546816479400749063670411985018726591760299625468164794007490636704119850187265917602996254681647940074906367 m: 2000000000000000000000000000 deg: 5 c5: 425 c0: -88 skew: 0.73 type: snfs lss: 1 rlim: 1460000 alim: 1460000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1460000/1460000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [730000, 1705001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 261625 x 261873 Total sieving time: 9.54 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,139,5,0,0,0,0,0,0,0,0,1460000,1460000,26,26,48,48,2.3,2.3,75000 total time: 9.54 hours. --------- CPU info (if available) ----------
Mar 31, 2009: By Jo Yeong Uk / GMP-ECM / Mar 31, 2009
(17·10¹⁷⁶+7)/3 = 5(6)₁₇₅9_<177> = C177
C177 = P37 · P141
P37 = 1332900038363680881394620148129664059_<37>
P141 = 425138157668843915788962204505688086610791867911821343666941015479820678943431096734573619034309056634425509765000685116141894382558408244791_<141>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 (177 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3212400340 Step 1 took 19100ms Step 2 took 7720ms ********** Factor found in step 2: 1332900038363680881394620148129664059 Found probable prime factor of 37 digits: 1332900038363680881394620148129664059 Probable prime cofactor 425138157668843915788962204505688086610791867911821343666941015479820678943431096734573619034309056634425509765000685116141894382558408244791 has 141 digits
Mar 30, 2009 (7th): By Sinkiti Sibata / GGNFS
(17·10¹²⁸-11)/3 = 5(6)₁₂₇3_<129> = 29 · 17021 · 5505469367639_<13> · C111
C111 = P50 · P61
P50 = 24820327977021975378256090284946693494883960699649_<50>
P61 = 8401227213587191514482424464656102094826473116869647302619337_<61>

Number: 56663_128 N=208521214850716544221599058555411701945808374634706100934515675276173697928018386423321266670848732764836512713 ( 111 digits) SNFS difficulty: 130 digits. Divisors found: r1=24820327977021975378256090284946693494883960699649 (pp50) r2=8401227213587191514482424464656102094826473116869647302619337 (pp61) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 4.83 hours. Scaled time: 2.28 units (timescale=0.473). Factorization parameters were as follows: name: 56663_128 n: 208521214850716544221599058555411701945808374634706100934515675276173697928018386423321266670848732764836512713 m: 50000000000000000000000000 deg: 5 c5: 136 c0: -275 skew: 1.15 type: snfs lss: 1 rlim: 1050000 alim: 1050000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1050000/1050000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [525000, 925001) Primes: RFBsize:82134, AFBsize:82353, largePrimes:2798952 encountered Relations: rels:2768491, finalFF:272749 Max relations in full relation-set: 28 Initial matrix: 164554 x 272749 with sparse part having weight 20623329. Pruned matrix : 132835 x 133721 with weight 7226487. Total sieving time: 4.43 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.24 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1050000,1050000,26,26,47,47,2.3,2.3,50000 total time: 4.83 hours. --------- CPU info (if available) ----------
(17·10¹²⁹+7)/3 = 5(6)₁₂₈9_<130> = 31 · 73571 · 3748847 · 5887939 · C111
C111 = P31 · P81
P31 = 1124466814397827153397456968673_<31>
P81 = 100104050957610405407547844556194856347545057379087033154669977098606751781653141_<81>

Number: 56663_129 N=112563683288621931257893820232631592344395789058017227723897905579838046080414432892570091892364372398589051893 ( 111 digits) SNFS difficulty: 131 digits. Divisors found: r1=1124466814397827153397456968673 (pp31) r2=100104050957610405407547844556194856347545057379087033154669977098606751781653141 (pp81) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 4.52 hours. Scaled time: 2.14 units (timescale=0.473). Factorization parameters were as follows: name: 56663_129 n: 112563683288621931257893820232631592344395789058017227723897905579838046080414432892570091892364372398589051893 m: 100000000000000000000000000 deg: 5 c5: 17 c0: 70 skew: 1.33 type: snfs lss: 1 rlim: 1080000 alim: 1080000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor 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: RFBsize:84270, AFBsize:84768, largePrimes:2723010 encountered Relations: rels:2604917, finalFF:205337 Max relations in full relation-set: 28 Initial matrix: 169103 x 205337 with sparse part having weight 14878093. Pruned matrix : 154361 x 155270 with weight 8821894. Total sieving time: 4.04 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.33 hours. Time per square root: 0.05 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: 4.52 hours. --------- CPU info (if available) ----------
Mar 30, 2009 (6th): By Wataru Sakai / Msieve / Mar 30, 2009
(14·10¹⁸⁵-11)/3 = 4(6)₁₈₄3_<186> = 5003 · C182
C182 = P51 · P53 · P79
P51 = 472028819964297438740806605192579205630100803128437_<51>
P53 = 24871243197390234627509331406490531115713301860364091_<53>
P79 = 7945299421360233896153427606410291300881548381778500398649648806810791075311763_<79>

Number: 46663_185 N=93277366913185422080085282164034912385901792257978546205609967352921580385102271970151242587780664934372709707508828036511426477446865214204810447065094276767272969551602371910187221 ( 182 digits) SNFS difficulty: 186 digits. Divisors found: r1=472028819964297438740806605192579205630100803128437 r2=24871243197390234627509331406490531115713301860364091 r3=7945299421360233896153427606410291300881548381778500398649648806810791075311763 Version: Total time: 280.59 hours. Scaled time: 564.54 units (timescale=2.012). Factorization parameters were as follows: n: 93277366913185422080085282164034912385901792257978546205609967352921580385102271970151242587780664934372709707508828036511426477446865214204810447065094276767272969551602371910187221 m: 10000000000000000000000000000000000000 deg: 5 c5: 14 c0: -11 skew: 0.95 type: snfs lss: 1 rlim: 8900000 alim: 8900000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 8900000/8900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4450000, 7350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1165764 x 1166012 Total sieving time: 280.59 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,186,5,0,0,0,0,0,0,0,0,8900000,8900000,28,28,54,54,2.5,2.5,100000 total time: 280.59 hours. --------- CPU info (if available) ----------
Mar 30, 2009 (5th): By Ignacio Santos / GGNFS, Msieve / Mar 30, 2009
(17·10¹⁰¹-11)/3 = 5(6)₁₀₀3_<102> = 67912517003_<11> · C91
C91 = P40 · P52
P40 = 5123831568700026011372584628954576029969_<40>
P52 = 1628482120734270536821075988987892173086356834821509_<52>

Number: 56663_101 N=8344068099281822559585314721701608004037927833753428446267223188442051074345256757949803221 ( 91 digits) SNFS difficulty: 103 digits. Divisors found: r1=5123831568700026011372584628954576029969 (pp40) r2=1628482120734270536821075988987892173086356834821509 (pp52) Version: Msieve-1.39 Total time: 0.27 hours. Scaled time: 0.32 units (timescale=1.196). Factorization parameters were as follows: n: 8344068099281822559585314721701608004037927833753428446267223188442051074345256757949803221 m: 20000000000000000000000000 deg: 4 c4: 85 c0: -88 skew: 1.01 type: snfs lss: 1 rlim: 370000 alim: 370000 lpbr: 25 lpba: 25 mfbr: 43 mfba: 43 rlambda: 2.2 alambda: 2.2 Factor base limits: 370000/370000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [185000, 235001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 36875 x 37111 Total sieving time: 0.27 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,103,4,0,0,0,0,0,0,0,0,370000,370000,25,25,43,43,2.2,2.2,10000 total time: 0.27 hours. --------- CPU info (if available) ----------
(17·10¹¹⁵+7)/3 = 5(6)₁₁₄9_<116> = 67 · 21061 · C110
C110 = P41 · P69
P41 = 95290352109099817535683452296597792913083_<41>
P69 = 421429510891924613323930011380750009408902662687024674204055392048089_<69>

Number: 56669_115 N=40158166482057213103562478193525038971138325749345480942469646922313554491442885283945402846647064756933248387 ( 110 digits) SNFS difficulty: 116 digits. Divisors found: r1=95290352109099817535683452296597792913083 (pp41) r2=421429510891924613323930011380750009408902662687024674204055392048089 (pp69) Version: Msieve-1.39 Total time: 0.77 hours. Scaled time: 0.92 units (timescale=1.198). Factorization parameters were as follows: n: 40158166482057213103562478193525038971138325749345480942469646922313554491442885283945402846647064756933248387 m: 100000000000000000000000 deg: 5 c5: 17 c0: 7 skew: 0.84 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: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 64735 x 64965 Total sieving time: 0.77 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,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) ----------
(17·10¹¹⁸+7)/3 = 5(6)₁₁₇9_<119> = 101917 · 8323537 · C107
C107 = P48 · P60
P48 = 601885235402110792210900200078722304656813123651_<48>
P60 = 110983759173059900845424929359819040363022947328137613794411_<60>

Number: 56669_118 N=66799486015688331413048161090075435589653725608566758691907701831234347207760026800744726843636555435714561 ( 107 digits) SNFS difficulty: 120 digits. Divisors found: r1=601885235402110792210900200078722304656813123651 (pp48) r2=110983759173059900845424929359819040363022947328137613794411 (pp60) Version: Msieve-1.39 Total time: 1.43 hours. Scaled time: 1.71 units (timescale=1.198). Factorization parameters were as follows: n: 66799486015688331413048161090075435589653725608566758691907701831234347207760026800744726843636555435714561 m: 500000000000000000000000 deg: 5 c5: 136 c0: 175 skew: 1.05 type: snfs lss: 1 rlim: 720000 alim: 720000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2Factor 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, 660001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 83421 x 83653 Total sieving time: 1.43 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,120,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000 total time: 1.43 hours. --------- CPU info (if available) ----------
(17·10¹²²+7)/3 = 5(6)₁₂₁9_<123> = 13725133 · C116
C116 = P47 · P69
P47 = 74312416334972309488106373427432495350587766049_<47>
P69 = 555583989609428877329491732475831696278630005512381518127600113742657_<69>

Number: 56669_122 N=41286788744900808368608644205244981354036180681576394681688451883611376783501235774303000682519190645851422107652193 ( 116 digits) SNFS difficulty: 124 digits. Divisors found: r1=74312416334972309488106373427432495350587766049 (pp47) r2=555583989609428877329491732475831696278630005512381518127600113742657 (pp69) Version: Msieve-1.39 Total time: 1.80 hours. Scaled time: 2.14 units (timescale=1.188). Factorization parameters were as follows: n: 41286788744900808368608644205244981354036180681576394681688451883611376783501235774303000682519190645851422107652193 m: 2000000000000000000000000 deg: 5 c5: 425 c0: 56 skew: 0.67 type: snfs lss: 1 rlim: 820000 alim: 820000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2Factor base limits: 820000/820000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [410000, 760001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 92352 x 92600 Total sieving time: 1.80 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,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000 total time: 1.80 hours. --------- CPU info (if available) ----------
(17·10¹¹⁹-11)/3 = 5(6)₁₁₈3_<120> = 31 · 887 · 11731 · C112
C112 = P30 · P82
P30 = 239450380240083774854468268749_<30>
P82 = 7336548403427378900248248059735962221136819514321416423825489537237179273289440041_<82>

Number: 56663_119 N=1756739304850465415165792566407440251428414804190514777328834092497373475814356681431037481633768504216909578709 ( 112 digits) SNFS difficulty: 121 digits. Divisors found: r1=239450380240083774854468268749 (pp30) r2=7336548403427378900248248059735962221136819514321416423825489537237179273289440041 (pp82) Version: Msieve-1.39 Total time: 1.34 hours. Scaled time: 1.59 units (timescale=1.183). Factorization parameters were as follows: n: 1756739304850465415165792566407440251428414804190514777328834092497373475814356681431037481633768504216909578709 m: 1000000000000000000000000 deg: 5 c5: 17 c0: -110 skew: 1.45 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 565001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 84097 x 84345 Total sieving time: 1.34 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,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 1.34 hours. --------- CPU info (if available) ----------
(17·10¹²²-11)/3 = 5(6)₁₂₁3_<123> = 677 · C120
C120 = P39 · P82
P39 = 795291725793282443500552146174546722231_<39>
P82 = 1052476806148759029278464603331228114347816926127482451611939039647002492509057149_<82>

Number: 56663_122 N=837026095519448547513540128015755785327424913835548990645002461841457410142786804529788281634662727720334810438207779419 ( 120 digits) SNFS difficulty: 124 digits. Divisors found: r1=795291725793282443500552146174546722231 (pp39) r2=1052476806148759029278464603331228114347816926127482451611939039647002492509057149 (pp82) Version: Msieve-1.39 Total time: 2.21 hours. Scaled time: 2.65 units (timescale=1.198). Factorization parameters were as follows: n: 837026095519448547513540128015755785327424913835548990645002461841457410142786804529788281634662727720334810438207779419 m: 2000000000000000000000000 deg: 5 c5: 425 c0: -88 skew: 0.73 type: snfs lss: 1 rlim: 820000 alim: 820000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 820000/820000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [410000, 860001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 110779 x 111027 Total sieving time: 2.21 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,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000 total time: 2.21 hours. --------- CPU info (if available) ----------
(17·10¹²⁷-11)/3 = 5(6)₁₂₆3_<128> = 3631 · C125
C125 = P37 · P88
P37 = 3958394890072113977857155948035524349_<37>
P88 = 3942596213104646669262560616780369956388402140240085425022769072444304806099790128161277_<88>

Number: 56663_127 N=15606352703571100706875975397043973193794179748462315248324612136234278894703020288258514642430918938768016157165151932433673 ( 125 digits) SNFS difficulty: 129 digits. Divisors found: r1=3958394890072113977857155948035524349 (pp37) r2=3942596213104646669262560616780369956388402140240085425022769072444304806099790128161277 (pp88) Version: Msieve-1.39 Total time: 2.71 hours. Scaled time: 3.22 units (timescale=1.186). Factorization parameters were as follows: n: 15606352703571100706875975397043973193794179748462315248324612136234278894703020288258514642430918938768016157165151932433673 m: 20000000000000000000000000 deg: 5 c5: 425 c0: -88 skew: 0.73 type: snfs lss: 1 rlim: 990000 alim: 990000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 990000/990000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [495000, 995001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 154284 x 154529 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,129,5,0,0,0,0,0,0,0,0,990000,990000,26,26,47,47,2.3,2.3,50000 total time: 2.71 hours. --------- CPU info (if available) ----------
(17·10¹²⁵+7)/3 = 5(6)₁₂₄9_<126> = 23 · 2593 · 144228983586167_<15> · C107
C107 = P39 · P69
P39 = 589250921545742190593877958793077296379_<39>
P69 = 111800694279228050333176460851172320271408111898525575752334134383047_<69>

Number: 56669_125 N=65878662133488915633720942220528513751455616516752988633261898199458452664627642528077056373168179932086813 ( 107 digits) SNFS difficulty: 126 digits. Divisors found: r1=589250921545742190593877958793077296379 (pp39) r2=111800694279228050333176460851172320271408111898525575752334134383047 (pp69) Version: Msieve-1.39 Total time: 1.49 hours. Scaled time: 1.77 units (timescale=1.189). Factorization parameters were as follows: n: 65878662133488915633720942220528513751455616516752988633261898199458452664627642528077056373168179932086813 m: 10000000000000000000000000 deg: 5 c5: 17 c0: 7 skew: 0.84 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 : 115556 x 115804 Total sieving time: 1.49 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: 1.49 hours. --------- CPU info (if available) ----------
(49·10¹⁶⁸+23)/9 = 5(4)₁₆₇7_<169> = 269 · 491 · 8053 · 10253 · C156
C156 = P71 · P85
P71 = 69456425612216082029462188812207301586685011392460105683467565827546433_<71>
P85 = 7187845147472167912233172898770037011894826265333750517439708363073552108865016407969_<85>

Number: 54447_168 N=499242031797528964603322450116699697726570511429147637000037655432511436237498026365668367009829901398816139852650418300760547125611219115491032386218724577 ( 156 digits) SNFS difficulty: 171 digits. Divisors found: r1=69456425612216082029462188812207301586685011392460105683467565827546433 (pp71) r2=7187845147472167912233172898770037011894826265333750517439708363073552108865016407969 (pp85) Version: Msieve-1.39 Total time: 70.78 hours. Scaled time: 181.98 units (timescale=2.571). Factorization parameters were as follows: n: 499242031797528964603322450116699697726570511429147637000037655432511436237498026365668367009829901398816139852650418300760547125611219115491032386218724577 m: 5000000000000000000000000000000000 deg: 5 c5: 392 c0: 575 skew: 1.08 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, 5600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1006000 x 1006248 Total sieving time: 70.78 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 70.78 hours. --------- CPU info (if available) ----------
(17·10¹³¹-11)/3 = 5(6)₁₃₀3_<132> = 53 · 163 · 1657 · C125
C125 = P44 · P81
P44 = 57254393326442842901839185810365868132126073_<44>
P81 = 691405559039504718020667746214520013146066727040298897302914444029868559857781097_<81>

Number: 56663_131 N=39586005825336901941900830116213568736872727428531017579935614060101662917289767862771804210688924806591507744571250840242081 ( 125 digits) SNFS difficulty: 132 digits. Divisors found: r1=57254393326442842901839185810365868132126073 (pp44) r2=691405559039504718020667746214520013146066727040298897302914444029868559857781097 (pp81) Version: Msieve-1.39 Total time: 2.68 hours. Scaled time: 6.90 units (timescale=2.571). Factorization parameters were as follows: n: 39586005825336901941900830116213568736872727428531017579935614060101662917289767862771804210688924806591507744571250840242081 m: 100000000000000000000000000 deg: 5 c5: 170 c0: -11 skew: 0.58 type: snfs lss: 1 rlim: 1120000 alim: 1120000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1120000/1120000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [560000, 960001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 175868 x 176116 Total sieving time: 2.68 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,132,5,0,0,0,0,0,0,0,0,1120000,1120000,26,26,47,47,2.3,2.3,50000 total time: 2.68 hours. --------- CPU info (if available) ----------
(17·10¹⁴⁶-11)/3 = 5(6)₁₄₅3_<147> = 127 · 2678747 · C139
C139 = P38 · P101
P38 = 27811417659945137991544604657599424539_<38>
P101 = 59892042054550345949298752078376499404048130275627420744018974026631281026436704763054876687625491393_<101>

Number: 56663_146 N=1665682596086098376975829143654147064117777625860992926113503451005784075956215933906584661506748434163072836438482662037722974383897492827 ( 139 digits) SNFS difficulty: 147 digits. Divisors found: r1=27811417659945137991544604657599424539 (pp38) r2=59892042054550345949298752078376499404048130275627420744018974026631281026436704763054876687625491393 (pp101) Version: Msieve-1.39 Total time: 8.27 hours. Scaled time: 21.25 units (timescale=2.571). Factorization parameters were as follows: n: 1665682596086098376975829143654147064117777625860992926113503451005784075956215933906584661506748434163072836438482662037722974383897492827 m: 100000000000000000000000000000 deg: 5 c5: 170 c0: -11 skew: 0.58 type: snfs lss: 1 rlim: 1990000 alim: 1990000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 1990000/1990000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [995000, 2295001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 329154 x 329402 Total sieving time: 8.27 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,147,5,0,0,0,0,0,0,0,0,1990000,1990000,26,26,49,49,2.3,2.3,100000 total time: 8.27 hours. --------- CPU info (if available) ----------
(17·10¹³²+7)/3 = 5(6)₁₃₁9_<133> = 43 · 2067783733_<10> · C122
C122 = P52 · P70
P52 = 9908855818710071772279685922495241980372071557069529_<52>
P70 = 6431771211676737322956945474073996162358335807731917122684415567681219_<70>

Number: 56669_132 N=63731493595434967341012437950993608144671061585793864272607916454570032027829144609646555791788131891898934762993290475851 ( 122 digits) SNFS difficulty: 134 digits. Divisors found: r1=9908855818710071772279685922495241980372071557069529 (pp52) r2=6431771211676737322956945474073996162358335807731917122684415567681219 (pp70) Version: Msieve-1.39 Total time: 3.46 hours. Scaled time: 8.90 units (timescale=2.572). Factorization parameters were as follows: n: 63731493595434967341012437950993608144671061585793864272607916454570032027829144609646555791788131891898934762993290475851 m: 200000000000000000000000000 deg: 5 c5: 425 c0: 56 skew: 0.67 type: snfs lss: 1 rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 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: 47/47 Sieved rational special-q in [600000, 1125001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 165896 x 166141 Total sieving time: 3.46 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,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000 total time: 3.46 hours. --------- CPU info (if available) ----------
(25·10¹⁸¹-61)/9 = 2(7)₁₈₀1_<182> = 3 · 7 · 23 · C179
C179 = P65 · P114
P65 = 75510615435433520332094734482048406815014663397888447357329506169_<65>
P114 = 761627047329789607062080654255561176112224466344542541980790154090969468251343258094559369704529752173237377695073_<114>

Number: 27771_181 N=57510927076144467448815274902231423970554405337014032666206579250057510927076144467448815274902231423970554405337014032666206579250057510927076144467448815274902231423970554405337 ( 179 digits) SNFS difficulty: 182 digits. Divisors found: r1=75510615435433520332094734482048406815014663397888447357329506169 (pp65) r2=761627047329789607062080654255561176112224466344542541980790154090969468251343258094559369704529752173237377695073 (pp114) Version: Msieve-1.39 Total time: 164.24 hours. Scaled time: 284.96 units (timescale=1.735). Factorization parameters were as follows: n: 57510927076144467448815274902231423970554405337014032666206579250057510927076144467448815274902231423970554405337014032666206579250057510927076144467448815274902231423970554405337 m: 1000000000000000000000000000000000000 deg: 5 c5: 250 c0: -61 skew: 0.75 type: snfs lss: 1 rlim: 7700000 alim: 7700000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7700000/7700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3850000, 6650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1525062 x 1525310 Total sieving time: 164.24 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,182,5,0,0,0,0,0,0,0,0,7700000,7700000,28,28,53,53,2.5,2.5,100000 total time: 164.24 hours. --------- CPU info (if available) ----------
Mar 30, 2009 (4th): By Erik Branger / GGNFS, Msieve / Mar 30, 2009
(17·10¹¹²-11)/3 = 5(6)₁₁₁3_<113> = 5827 · 252383 · C104
C104 = P44 · P60
P44 = 81164110798176097423933218771319343515292509_<44>
P60 = 474742940179331324463463707253091559418247960492922361378927_<60>

Number: 56663_112 N=38532088597367134617100718665769640550757338534360199985556223923342460549288844372419388022112993557843 ( 104 digits) SNFS difficulty: 114 digits. Divisors found: r1=81164110798176097423933218771319343515292509 r2=474742940179331324463463707253091559418247960492922361378927 Version: Total time: 1.43 hours. Scaled time: 1.51 units (timescale=1.058). Factorization parameters were as follows: n: 38532088597367134617100718665769640550757338534360199985556223923342460549288844372419388022112993557843 m: 20000000000000000000000 deg: 5 c5: 425 c0: -88 skew: 0.73 type: snfs lss: 1 rlim: 560000 alim: 560000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 560000/560000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [280000, 530001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 64327 x 64554 Total sieving time: 1.43 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,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000 total time: 1.43 hours. --------- CPU info (if available) ----------
(17·10¹¹⁶-11)/3 = 5(6)₁₁₅3_<117> = 61 · 83 · 2147371619171101_<16> · C98
C98 = P43 · P56
P43 = 4828924233309463931619182770068478624306471_<43>
P56 = 10793496102454005499202825484190161769189847553433786531_<56>

Number: 56663_116 N=52120974891271395662797528266595552975220418579988058726081993476367737739647564816301019335942101 ( 98 digits) SNFS difficulty: 117 digits. Divisors found: r1=4828924233309463931619182770068478624306471 r2=10793496102454005499202825484190161769189847553433786531 Version: Total time: 1.35 hours. Scaled time: 1.40 units (timescale=1.036). Factorization parameters were as follows: n: 52120974891271395662797528266595552975220418579988058726081993476367737739647564816301019335942101 m: 100000000000000000000000 deg: 5 c5: 170 c0: -11 skew: 0.58 type: snfs lss: 1 rlim: 630000 alim: 630000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 630000/630000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [315000, 515001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 66128 x 66354 Total sieving time: 1.35 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,117,5,0,0,0,0,0,0,0,0,630000,630000,25,25,45,45,2.2,2.2,50000 total time: 1.35 hours. --------- CPU info (if available) ----------
(17·10¹²⁵-11)/3 = 5(6)₁₂₄3_<126> = C126
C126 = P59 · P67
P59 = 71785287581807633716076980461443991324728287066807910129827_<59>
P67 = 7893910935731566057306717859770778813519376767106692139028677261869_<67>

Number: 56663_125 N=566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 126 digits) SNFS difficulty: 126 digits. Divisors found: r1=71785287581807633716076980461443991324728287066807910129827 r2=7893910935731566057306717859770778813519376767106692139028677261869 Version: Total time: 1.96 hours. Scaled time: 2.03 units (timescale=1.034). Factorization parameters were as follows: n: 566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 m: 10000000000000000000000000 deg: 5 c5: 17 c0: -11 skew: 0.92 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor 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 : 118757 x 119002 Total sieving time: 1.96 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,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 1.96 hours. --------- CPU info (if available) ----------
(17·10¹²⁴-11)/3 = 5(6)₁₂₃3_<125> = 19 · 26981 · 248309 · 310614151 · C106
C106 = P39 · P67
P39 = 804449340177554271459153452597709920213_<39>
P67 = 1781573013452190413442256085833160667959483917129251044909137802551_<67>

Number: 56663_124 N=1433185235149751598102742298752877358386848046087618306723849826450082955179103739767073691849380357863363 ( 106 digits) SNFS difficulty: 126 digits. Divisors found: r1=804449340177554271459153452597709920213 r2=1781573013452190413442256085833160667959483917129251044909137802551 Version: Total time: 2.02 hours. Scaled time: 2.14 units (timescale=1.058). Factorization parameters were as follows: n: 1433185235149751598102742298752877358386848046087618306723849826450082955179103739767073691849380357863363 m: 10000000000000000000000000 deg: 5 c5: 17 c0: -110 skew: 1.45 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor 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 : 109917 x 110165 Total sieving time: 2.02 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,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 2.02 hours. --------- CPU info (if available) ----------
(17·10¹²⁷+7)/3 = 5(6)₁₂₆9_<128> = 227 · 6569 · C122
C122 = P44 · P79
P44 = 25921348302963192499630665485734572989144837_<44>
P79 = 1466037096889321752043564176958402615677429746334965177187281480617951278229099_<79>

Number: 56669_127 N=38001658213533105815170217251009223449526756408700233754905846420992652491153996354970359824289273987261397088491779011863 ( 122 digits) SNFS difficulty: 129 digits. Divisors found: r1=25921348302963192499630665485734572989144837 r2=1466037096889321752043564176958402615677429746334965177187281480617951278229099 Version: Total time: 2.72 hours. Scaled time: 1.08 units (timescale=0.397). Factorization parameters were as follows: n: 38001658213533105815170217251009223449526756408700233754905846420992652491153996354970359824289273987261397088491779011863 m: 20000000000000000000000000 deg: 5 c5: 425 c0: 56 skew: 0.67 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 139261 x 139499 Total sieving time: 2.72 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 2.72 hours. --------- CPU info (if available) ----------
(17·10¹⁴²+7)/3 = 5(6)₁₄₁9_<143> = 208001 · 8641465134611_<13> · 27133063997213638003_<20> · C106
C106 = P42 · P64
P42 = 227233283820335395527908096833051840478717_<42>
P64 = 5113333015204387993644768090944545112606409701910513354681529129_<64>

Number: 56669_142 N=1161919452311830061295286320108968874314420959924846927818658944252231072336726982590444060540124940047493 ( 106 digits) SNFS difficulty: 144 digits. Divisors found: r1=227233283820335395527908096833051840478717 r2=5113333015204387993644768090944545112606409701910513354681529129 Version: Total time: 9.28 hours. Scaled time: 3.70 units (timescale=0.398). Factorization parameters were as follows: n: 1161919452311830061295286320108968874314420959924846927818658944252231072336726982590444060540124940047493 m: 20000000000000000000000000000 deg: 5 c5: 425 c0: 56 skew: 0.67 type: snfs lss: 1 rlim: 1770000 alim: 1770000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 1770000/1770000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [885000, 1985001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 270587 x 270828 Total sieving time: 9.28 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,144,5,0,0,0,0,0,0,0,0,1770000,1770000,26,26,49,49,2.3,2.3,100000 total time: 9.28 hours. --------- CPU info (if available) ----------
Mar 30, 2009 (3rd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Mar 30, 2009
(17·10¹³⁸-11)/3 = 5(6)₁₃₇3_<139> = 169006200297797685527_<21> · 2300927100902701975264719427_<28> · C92
C92 = P35 · P57
P35 = 31468010786775134148962698036356169_<35>
P57 = 463076646059587584495461971854363692884207025602098484963_<57>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 14572100893306753029562782655749178686780912853468794144718369748167302877578129447958786747 (92 digits) Using B1=1734000, B2=2140281790, polynomial Dickson(6), sigma=3753322 Step 1 took 10719ms Step 2 took 5000ms ********** Factor found in step 2: 31468010786775134148962698036356169 Found probable prime factor of 35 digits: 31468010786775134148962698036356169 Probable prime cofactor 463076646059587584495461971854363692884207025602098484963 has 57 digits
(10²⁰⁷+17)/9 = (1)₂₀₆3_<207> = 1607 · C203
C203 = P54 · P67 · P83
P54 = 115951269499650019696884731749121224100590303382217461_<54>
P67 = 8291114615663811786913421243762707131703902669337013526581555333831_<67>
P83 = 71920580989461300167938721656900149535458931816276322011236571042026371770244374549_<83>

Number: n N=69141948420106478600566963977044873124524649104611767959621102122657816497268893037405794095277604922906727511581276360367835165594966466155016248357878725022471133236534605545184263292539583765470510959 ( 203 digits) SNFS difficulty: 207 digits. Divisors found: Mon Mar 30 09:50:31 2009 prp54 factor: 115951269499650019696884731749121224100590303382217461 Mon Mar 30 09:50:31 2009 prp67 factor: 8291114615663811786913421243762707131703902669337013526581555333831 Mon Mar 30 09:50:31 2009 prp83 factor: 71920580989461300167938721656900149535458931816276322011236571042026371770244374549 Mon Mar 30 09:50:31 2009 elapsed time 18:58:17 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 107.71 hours. Scaled time: 216.94 units (timescale=2.014). Factorization parameters were as follows: name: KA_1_206_3 n: 69141948420106478600566963977044873124524649104611767959621102122657816497268893037405794095277604922906727511581276360367835165594966466155016248357878725022471133236534605545184263292539583765470510959 deg: 5 c5: 100 c0: 17 m: 100000000000000000000000000000000000000000 skew: 0.70 type: snfs rlim: 12000000 alim: 12000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [6000000, 31599990) Primes: RFBsize:788060, AFBsize:787814, largePrimes:36906914 encountered Relations: rels:32333155, finalFF:131025 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7543613 hash collisions in 42811934 relations Msieve: matrix is 3331182 x 3331430 (903.7 MB) Total sieving time: 106.65 hours. Total relation processing time: 1.06 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,207,5,0,0,0,0,0,0,0,0,12000000,12000000,29,29,58,58,2.5,2.5,100000 total time: 107.71 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: 3368972k/3407296k available (2746k kernel code, 36964k reserved, 1423k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830497) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447) Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Total of 4 processors activated (22643.71 BogoMIPS).
(49·10¹⁵⁸-13)/9 = 5(4)₁₅₇3_<159> = 3 · 29 · 922489 · 715570943 · C142
C142 = P46 · P97
P46 = 1933753263829273755790956506822876419039373431_<46>
P97 = 4902519898348793797289993772044717042707344704118234633885033167780703243173321590976815042695197_<97>

Number: n N=9480263854419939406567288559368136851958668930098235963980024426324338005691026094222629647173171716995999099228114115163173665542864393110907 ( 142 digits) SNFS difficulty: 161 digits. Divisors found: Mon Mar 30 12:48:36 2009 prp46 factor: 1933753263829273755790956506822876419039373431 Mon Mar 30 12:48:36 2009 prp97 factor: 4902519898348793797289993772044717042707344704118234633885033167780703243173321590976815042695197 Mon Mar 30 12:48:36 2009 elapsed time 01:32:15 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 28.69 hours. Scaled time: 76.31 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_4_157_3 n: 9480263854419939406567288559368136851958668930098235963980024426324338005691026094222629647173171716995999099228114115163173665542864393110907 skew: 1.92 deg: 5 c5: 49 c0: -1300 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2250000, 4049990) Primes: RFBsize:315948, AFBsize:315681, largePrimes:15059121 encountered Relations: rels:14210576, finalFF:560178 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1302492 hash collisions in 15864309 relations Msieve: matrix is 683824 x 684072 (181.8 MB) Total sieving time: 28.34 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000 total time: 28.69 hours. --------- CPU info (if available) ----------
(49·10¹⁵⁸+23)/9 = 5(4)₁₅₇7_<159> = 2039647062871998809149_<22> · C138
C138 = P40 · P42 · P56
P40 = 7561107105557510584961327966551236839939_<40>
P42 = 487659925013640987505028384915301079926139_<42>
P56 = 72392919040279406746095501779506808157490294988149843643_<56>

Number: n N=266930712844907468956210745438042353032837564638417938008625283292057659396759594420765443389292001623725450501654132366788120505688933003 ( 138 digits) SNFS difficulty: 161 digits. Divisors found: Mon Mar 30 12:55:35 2009 prp40 factor: 7561107105557510584961327966551236839939 Mon Mar 30 12:55:35 2009 prp42 factor: 487659925013640987505028384915301079926139 Mon Mar 30 12:55:35 2009 prp56 factor: 72392919040279406746095501779506808157490294988149843643 Mon Mar 30 12:55:35 2009 elapsed time 01:38:38 (Msieve 1.39 - dependency 5) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 28.25 hours. Scaled time: 75.15 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_4_157_7 n: 266930712844907468956210745438042353032837564638417938008625283292057659396759594420765443389292001623725450501654132366788120505688933003 skew: 2.16 deg: 5 c5: 49 c0: 2300 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2250000, 10000000 ) Primes: RFBsize:315948, AFBsize:316501, largePrimes:15420747 encountered Relations: rels:14977241, finalFF:765435 Max relations in full relation-set: 28 Initial matrix: 632513 x 765435 with sparse part having weight 77547461. Pruned matrix : 547396 x 550622 with weight 58136808. Msieve: found 1271426 hash collisions in 15912073 relations Msieve: matrix is 656971 x 657219 (174.5 MB) Total sieving time: 27.27 hours. Total relation processing time: 0.42 hours. Matrix solve time: 0.56 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000 total time: 28.25 hours. --------- CPU info (if available) ----------
(17·10¹³⁰-11)/3 = 5(6)₁₂₉3_<131> = 821 · 957659 · 10929609074387850346393_<23> · C100
C100 = P39 · P62
P39 = 275500419214459207522978242754423626131_<39>
P62 = 23935732489875274791493269824915507905526696732420120893398499_<62>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 6594304335165789684057187749729952168894186892873528185290466032084721385086046044161848915572577369 (100 digits) Using B1=1960000, B2=2853920170, polynomial Dickson(6), sigma=2249210397 Step 1 took 13500ms Step 2 took 6625ms ********** Factor found in step 2: 275500419214459207522978242754423626131 Found probable prime factor of 39 digits: 275500419214459207522978242754423626131 Probable prime cofactor 23935732489875274791493269824915507905526696732420120893398499 has 62 digits
(49·10¹⁴⁸+23)/9 = 5(4)₁₄₇7_<149> = 3 · 461 · 683 · 1273580364222764178583_<22> · C122
C122 = P59 · P63
P59 = 50942162569083495932825063490147390786014622365694977329219_<59>
P63 = 888396736999855975410516186125965281921713380681765300530218399_<63>

Number: n N=45256851002089977943223127636832110629196301893626535842317331291752486970739396762669811086799587838896573702539794100381 ( 122 digits) SNFS difficulty: 151 digits. Divisors found: Mon Mar 30 15:05:52 2009 prp59 factor: 50942162569083495932825063490147390786014622365694977329219 Mon Mar 30 15:05:52 2009 prp63 factor: 888396736999855975410516186125965281921713380681765300530218399 Mon Mar 30 15:05:52 2009 elapsed time 00:31:22 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 12.12 hours. Scaled time: 32.24 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_4_147_7 n: 45256851002089977943223127636832110629196301893626535842317331291752486970739396762669811086799587838896573702539794100381 skew: 2.16 deg: 5 c5: 49 c0: 2300 m: 1000000000000000000000000000000 type: snfs rlim: 2400000 alim: 2400000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.4 alambda: 2.4 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 [1200000, 1956533) Primes: RFBsize:176302, AFBsize:176533, largePrimes:13701058 encountered Relations: rels:12036131, finalFF:290665 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 887013 hash collisions in 12698429 relations Msieve: matrix is 431379 x 431627 (115.5 MB) Total sieving time: 11.77 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,29,29,58,58,2.4,2.4,100000 total time: 12.12 hours. --------- CPU info (if available) ----------
Mar 30, 2009 (2nd): By Jo Yeong Uk / GMP-ECM / Mar 30, 2009
(16·10¹⁹⁷+17)/3 = 5(3)₁₉₆9_<198> = C198
C198 = P34 · P164
P34 = 8330730914910739494869962789866397_<34>
P164 = 64019992817046568864072386610912369178865900873939871107157058564192119869482424687933582394044661175526797445218338045141217468977459877568210571489380832289734487_<164>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 533333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339 (198 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4195428485 Step 1 took 21881ms Step 2 took 8593ms ********** Factor found in step 2: 8330730914910739494869962789866397 Found probable prime factor of 34 digits: 8330730914910739494869962789866397 Probable prime cofactor 64019992817046568864072386610912369178865900873939871107157058564192119869482424687933582394044661175526797445218338045141217468977459877568210571489380832289734487 has 164 digits
Mar 30, 2009: By Serge Batalov / GMP-ECM 6.2.2 / Mar 30, 2009
(17·10¹⁵²+7)/3 = 5(6)₁₅₁9_<153> = 239 · 13513006159_<11> · 34315669240219_<14> · 17652303027868178773_<20> · C108
C108 = P29 · P80
P29 = 21420174711076672817390171047_<29>
P80 = 13522622829796860710833630636754411679637874455069340439451980743975628136252621_<80>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=588125940 Step 1 took 6860ms Step 2 took 5964ms ********** Factor found in step 2: 21420174711076672817390171047 Found probable prime factor of 29 digits: 21420174711076672817390171047 Probable prime cofactor has 80 digits
(17·10¹⁷²-11)/3 = 5(6)₁₇₁3_<173> = 4955881256811199723_<19> · 11290582017638819227_<20> · C136
C136 = P32 · C104
P32 = 11112034900286103762642201273601_<32>
C104 = [91137444731686262774627615616319827328697194596617503688409426242033418216434046022033424397591326427503_<104>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3570570968 Step 1 took 9005ms Step 2 took 7596ms ********** Factor found in step 2: 11112034900286103762642201273601 Found probable prime factor of 32 digits: 11112034900286103762642201273601 Composite cofactor has 104 digits
(17·10²⁰⁰+7)/3 = 5(6)₁₉₉9_<201> = 139 · 1319 · 4091 · 5953 · 4583407129440823_<16> · 1454913548016373279_<19> · C155
C155 = P32 · C124
P32 = 16235484672840827305747235427721_<32>
C124 = [1172227287557431664659229679610875208906271615395435937554333020682862854689618819963973299985339269262349249624933994874019_<124>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1267963406 Step 1 took 10029ms Step 2 took 8524ms ********** Factor found in step 2: 16235484672840827305747235427721 Found probable prime factor of 32 digits: 16235484672840827305747235427721 Composite cofactor has 124 digits
(17·10¹⁹⁹+7)/3 = 5(6)₁₉₈9_<200> = 853 · 49108949 · 4690843055178469916009_<22> · C168
C168 = P33 · C136
P33 = 139439575860152525764642907000219_<33>
C136 = [2068145264829021522693134837565772375255413534314070907056190048608030188897413343095857160841289014207680735432647902934113992020248887_<136>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1353002088 Step 1 took 9940ms Step 2 took 8913ms ********** Factor found in step 2: 139439575860152525764642907000219 Found probable prime factor of 33 digits: 139439575860152525764642907000219 Composite cofactor has 136 digits
(17·10¹⁷³+7)/3 = 5(6)₁₇₂9_<174> = 239 · 3719 · C168
C168 = P28 · P140
P28 = 7509372153663948212960430553_<28>
P140 = 84898488730764227478927360584223002525621599992773503802613527890415688576632781607023486143938568208272345414025486917663448442946997504653_<140>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1914745003 Step 1 took 9889ms Step 2 took 8913ms ********** Factor found in step 2: 7509372153663948212960430553 Found probable prime factor of 28 digits: 7509372153663948212960430553 Probable prime cofactor has 140 digits
(17·10¹⁹⁴+7)/3 = 5(6)₁₉₃9_<195> = 239 · 2460564151_<10> · C183
C183 = P36 · C148
P36 = 159720630294001366032944725330382413_<36>
C148 = [6033010178949490073361316871767491374941752999300200709376915162995870293743735197054524436589368399019120045621934770911807822296559368927412793417_<148>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3496528567 Step 1 took 11805ms Step 2 took 9992ms ********** Factor found in step 2: 159720630294001366032944725330382413 Found probable prime factor of 36 digits: 159720630294001366032944725330382413 Composite cofactor has 148 digits
(17·10¹⁴⁰-11)/3 = 5(6)₁₃₉3_<141> = 23 · C140
C140 = P40 · C101
P40 = 1988582244189483800485209843958743589043_<40>
C101 = [12389571128581728818477254444904148656371225081269043431614820414039285832831268485708657579962622667_<101>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1248108625 Step 1 took 9168ms Step 2 took 7753ms ********** Factor found in step 2: 1988582244189483800485209843958743589043 Found probable prime factor of 40 digits: 1988582244189483800485209843958743589043 Composite cofactor has 101 digits
Mar 29, 2009 (6th): By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Mar 29, 2009
(49·10¹⁵⁵+23)/9 = 5(4)₁₅₄7_<156> = 17 · 106319 · 42741631 · C142
C142 = P36 · P46 · P61
P36 = 409065749093004214423575760361672489_<36>
P46 = 6534980153883198524785693798616329050629060233_<46>
P61 = 2636363466388369334313208869093679303721597028944419656356687_<61>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 7047623182591198721228603674492812887560618947204801559116644732177071109244426383906311382987479237879253592111943827457642510612559750138719 (142 digits) Using B1=1354000, B2=1426564240, polynomial Dickson(6), sigma=3350466869 Step 1 took 18766ms Step 2 took 6552ms ********** Factor found in step 2: 409065749093004214423575760361672489 Found probable prime factor of 36 digits: 409065749093004214423575760361672489 Composite cofactor 17228582931270708514083747678543048612110301217622656613888747449097910949597250515490753732934867455328071 has 107 digits Number: n N=17228582931270708514083747678543048612110301217622656613888747449097910949597250515490753732934867455328071 ( 107 digits) Divisors found: Sun Mar 29 21:30:54 2009 prp46 factor: 6534980153883198524785693798616329050629060233 Sun Mar 29 21:30:54 2009 prp61 factor: 2636363466388369334313208869093679303721597028944419656356687 Sun Mar 29 21:30:54 2009 elapsed time 00:26:54 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 7.17 hours. Scaled time: 17.91 units (timescale=2.498). Factorization parameters were as follows: name: KA_5_4_154_7 n: 17228582931270708514083747678543048612110301217622656613888747449097910949597250515490753732934867455328071 skew: 18099.40 # norm 8.35e+14 c5: 23100 c4: 3113741728 c3: -31044755523147 c2: -1261698035532545324 c1: 7240654224891409569948 c0: -7973236351116161462387888 # alpha -6.39 Y1: 226421965439 Y0: -236873416973092157223 # Murphy_E 1.53e-09 # M 12147195532541688516625504347878815099683545814935576793611958648061402688146723638257757268267574761915608 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2099990) Primes: RFBsize:183072, AFBsize:183296, largePrimes:14448958 encountered Relations: rels:12209996, finalFF:372024 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 863448 hash collisions in 13117547 relations Msieve: matrix is 384782 x 385030 (105.4 MB) Total sieving time: 6.79 hours. Total relation processing time: 0.38 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000 total time: 7.17 hours. --------- CPU info (if available) ----------
Mar 29, 2009 (5th): By Sinkiti Sibata / Msieve / Mar 29, 2009
(13·10¹⁶⁷-31)/9 = 1(4)₁₆₆1_<168> = 3² · 11² · 17 · 173 · 1459 · 452853659 · 155695384417_<12> · C138
C138 = P67 · P71
P67 = 5417590935726697778181429215751858994416076969577660845369964579189_<67>
P71 = 80925020418520285456515411888513924913719814105591957988967280127650553_<71>

Number: 14441_167 N=438418657092873437140255716613415047002897640850210659821001335171971975493968967373742325714372536553148432048435029807813404043888141517 ( 138 digits) SNFS difficulty: 169 digits. Divisors found: r1=5417590935726697778181429215751858994416076969577660845369964579189 r2=80925020418520285456515411888513924913719814105591957988967280127650553 Version: Total time: 40.05 hours. Scaled time: 133.72 units (timescale=3.339). Factorization parameters were as follows: name: 14441_167 n: 438418657092873437140255716613415047002897640850210659821001335171971975493968967373742325714372536553148432048435029807813404043888141517 m: 2000000000000000000000000000000000 deg: 5 c5: 325 c0: -248 skew: 0.95 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [2300000, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 842418 x 842665 Total sieving time: 40.05 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,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000 total time: 40.05 hours. --------- CPU info (if available) ----------
(49·10¹⁷²-13)/9 = 5(4)₁₇₁3_<173> = C173
C173 = P50 · P123
P50 = 90457133252859086370797452249079159362984754582263_<50>
P123 = 601881161679680073414733529094278946019249854432828112732618999568591744333440032921249761043945003829360819175126160932861_<123>

Number: 54443_172 N=54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 ( 173 digits) SNFS difficulty: 174 digits. Divisors found: r1=90457133252859086370797452249079159362984754582263 r2=601881161679680073414733529094278946019249854432828112732618999568591744333440032921249761043945003829360819175126160932861 Version: Total time: 134.18 hours. Scaled time: 342.69 units (timescale=2.554). Factorization parameters were as follows: name: 54443_172 n: 54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 m: 20000000000000000000000000000000000 deg: 5 c5: 1225 c0: -104 skew: 0.61 type: snfs 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 algebraic special-q in [2500000, 8700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1086216 x 1086464 Total sieving time: 134.18 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,174,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 134.18 hours. --------- CPU info (if available) ----------
Mar 29, 2009 (4th): By Jo Yeong Uk / GMP-ECM / Mar 29, 2009
(46·10¹⁷⁸+71)/9 = 5(1)₁₇₇9_<179> = C179
C179 = P30 · P150
P30 = 301987358663348695516213202159_<30>
P150 = 169249174327489206034164467968894139877111470560964098347821869949162177687945915103723675787020585299769888419146145185091773482803832289761745201441_<150>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 51111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119 (179 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2958435836 Step 1 took 6314ms Step 2 took 3302ms ********** Factor found in step 2: 301987358663348695516213202159 Found probable prime factor of 30 digits: 301987358663348695516213202159 Probable prime cofactor 169249174327489206034164467968894139877111470560964098347821869949162177687945915103723675787020585299769888419146145185091773482803832289761745201441 has 150 digits
Mar 29, 2009 (3rd): By Ignacio Santos / GGNFS, Msieve / Mar 29, 2009
(49·10¹⁶⁷+23)/9 = 5(4)₁₆₆7_<168> = 10559587231972013_<17> · C152
C152 = P69 · P83
P69 = 767767536287199542101945167997849215441525824338148173132657698090917_<69>
P83 = 67154772717526357740761695015258839151705607000361615191854608560565425792519343007_<83>

Number: 54447_167 N=51559254399262055672112903247669280513372718601182176087537408205257236885136324117744525371190925777657136066754141731545354083503744691559498994167419 ( 152 digits) SNFS difficulty: 169 digits. Divisors found: r1=767767536287199542101945167997849215441525824338148173132657698090917 (pp69) r2=67154772717526357740761695015258839151705607000361615191854608560565425792519343007 (pp83) Version: Msieve-1.39 Total time: 76.49 hours. Scaled time: 196.65 units (timescale=2.571). Factorization parameters were as follows: n: 51559254399262055672112903247669280513372718601182176087537408205257236885136324117744525371190925777657136066754141731545354083503744691559498994167419 m: 2000000000000000000000000000000000 deg: 5 c5: 1225 c0: 184 skew: 0.68 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, 5750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 936316 x 936564 Total sieving time: 76.49 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000 total time: 76.49 hours. --------- CPU info (if available) ----------
Mar 29, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Mar 29, 2009
(49·10¹⁴⁶+23)/9 = 5(4)₁₄₅7_<147> = 367937719 · 4152854718155167_<16> · C123
C123 = P41 · P82
P41 = 42507220291575390569061312126266571436511_<41>
P82 = 8382427676288048262413847664914236679385164784376828071942780399395127187230556249_<82>

Number: 54447_146 N=356313699814174474491639870463144151088608729515701630864241104069885188680083539616515109540850294506582375609049517807239 ( 123 digits) SNFS difficulty: 148 digits. Divisors found: r1=42507220291575390569061312126266571436511 r2=8382427676288048262413847664914236679385164784376828071942780399395127187230556249 Version: Total time: 18.38 hours. Scaled time: 14.08 units (timescale=0.766). Factorization parameters were as follows: n: 356313699814174474491639870463144151088608729515701630864241104069885188680083539616515109540850294506582375609049517807239 m: 200000000000000000000000000000 deg: 5 c5: 245 c0: 368 skew: 1.08 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 373502 x 373745 Total sieving time: 18.38 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 18.38 hours. --------- CPU info (if available) ----------
Mar 29, 2009: Factorizations of 566...663 and Factorizations of 566...669 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.
Mar 28, 2009 (3rd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 28, 2009
(49·10¹⁵⁶+23)/9 = 5(4)₁₅₅7_<157> = 17707721075698273_<17> · 2033817327775288969990595237689_<31> · C111
C111 = P51 · P60
P51 = 454500693687026425426203190166113666052452088501549_<51>
P60 = 332616971158229236983081432079825089338499648979568233502899_<60>

Number: n N=151174644123492849592600496381704676212629009609146369177302522320081362468179705521001158149486074548257490551 ( 111 digits) Divisors found: Sat Mar 28 03:43:11 2009 prp51 factor: 454500693687026425426203190166113666052452088501549 Sat Mar 28 03:43:11 2009 prp60 factor: 332616971158229236983081432079825089338499648979568233502899 Sat Mar 28 03:43:11 2009 elapsed time 00:58:49 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 17.89 hours. Scaled time: 32.72 units (timescale=1.829). Factorization parameters were as follows: name: KA_5_4_155_7 n: 151174644123492849592600496381704676212629009609146369177302522320081362468179705521001158149486074548257490551 skew: 19769.16 # norm 3.26e+14 c5: 22800 c4: -583278862 c3: -30993018703825 c2: 215141010662061476 c1: 6053494876806255768132 c0: 15710288339883256330285332 # alpha -4.64 Y1: 611596749247 Y0: -1459855103768153476979 # Murphy_E 9.39e-10 # M 86602127258112390202379596066607795227983754583130173412703693163778176060001927693573246820648690457463833676 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1600000, 10000000 ) Primes: RFBsize:230209, AFBsize:229831, largePrimes:15089378 encountered Relations: rels:13636040, finalFF:864157 Max relations in full relation-set: 28 Initial matrix: 460118 x 864157 with sparse part having weight 109034210. Pruned matrix : 275917 x 278281 with weight 43207207. Msieve: found 1625564 hash collisions in 15085140 relations Msieve: matrix is 367792 x 368040 (99.3 MB) Total sieving time: 17.53 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000 total time: 17.89 hours. --------- CPU info (if available) ----------
(49·10¹⁵⁸-31)/9 = 5(4)₁₅₇1_<159> = 23 · 2422087 · 99603367 · C143
C143 = P42 · P102
P42 = 338983214914643563511308571161310372441779_<42>
P102 = 289456816972690351532668866002715672964035429516916062876460836624896725733021164280118302721885812837_<102>

Number: n N=98121002396362140147876046516105890668748182387245599073687682895032770426853914253252119806488821693256356417565016168442322595430837873317023 ( 143 digits) SNFS difficulty: 161 digits. Divisors found: Sat Mar 28 03:48:39 2009 prp42 factor: 338983214914643563511308571161310372441779 Sat Mar 28 03:48:39 2009 prp102 factor: 289456816972690351532668866002715672964035429516916062876460836624896725733021164280118302721885812837 Sat Mar 28 03:48:39 2009 elapsed time 01:18:48 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 30.21 hours. Scaled time: 59.06 units (timescale=1.955). Factorization parameters were as follows: name: KA_5_4_157_1 n: 98121002396362140147876046516105890668748182387245599073687682895032770426853914253252119806488821693256356417565016168442322595430837873317023 skew: 2.29 deg: 5 c5: 49 c0: -3100 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 10000000 ) Primes: RFBsize:315948, AFBsize:316122, largePrimes:15660913 encountered Relations: rels:15286806, finalFF:766542 Max relations in full relation-set: 28 Initial matrix: 632134 x 766542 with sparse part having weight 79728896. Pruned matrix : 555964 x 559188 with weight 59562732. Msieve: found 1378570 hash collisions in 16322804 relations Msieve: matrix is 666431 x 666679 (176.6 MB) Total sieving time: 29.43 hours. Total relation processing time: 0.48 hours. Matrix solve time: 0.30 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000 total time: 30.21 hours. --------- CPU info (if available) ----------
(47·10¹⁶¹-11)/9 = 5(2)₁₆₀1_<162> = 7² · 17 · 89 · 36112890957281_<14> · C144
C144 = P58 · P86
P58 = 5659520845447040182541664681416062365985670446984129683683_<58>
P86 = 34465010887937013645516458746347821551770956037600985349479839853501589174635796347271_<86>

Number: n N=195055447558838732532493662392781748112699080604895365658760154519007772407120895016155495442547256068767076944538986843466920758834616050279093 ( 144 digits) SNFS difficulty: 162 digits. Divisors found: Sat Mar 28 04:25:58 2009 prp58 factor: 5659520845447040182541664681416062365985670446984129683683 Sat Mar 28 04:25:58 2009 prp86 factor: 34465010887937013645516458746347821551770956037600985349479839853501589174635796347271 Sat Mar 28 04:25:58 2009 elapsed time 01:22:01 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 30.24 hours. Scaled time: 80.45 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_2_160_1 n: 195055447558838732532493662392781748112699080604895365658760154519007772407120895016155495442547256068767076944538986843466920758834616050279093 skew: 0.47 deg: 5 c5: 470 c0: -11 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 4250261) Primes: RFBsize:315948, AFBsize:315892, largePrimes:15787994 encountered Relations: rels:15298505, finalFF:692461 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1375752 hash collisions in 16329518 relations Msieve: matrix is 696166 x 696414 (184.1 MB) Total sieving time: 29.66 hours. Total relation processing time: 0.59 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000 total time: 30.24 hours. --------- CPU info (if available) ----------
(46·10¹⁶⁸+71)/9 = 5(1)₁₆₇9_<169> = 13 · 131 · 269 · 811 · 359987 · C155
C155 = P38 · P54 · P65
P38 = 17471464129836365814931789218571329749_<38>
P54 = 141275887934387088918433822407219888328785550169645917_<54>
P65 = 15482581541185975084705285429391126016253950713185106907656310157_<65>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 38215603508259411274979741248363330838097261366926042069863624871097160809685140681287477149915512645041996754268125206269981445882823582837890494768348781 (155 digits) Using B1=1902000, B2=2853920170, polynomial Dickson(6), sigma=2699684377 Step 1 took 32479ms Step 2 took 11388ms ********** Factor found in step 2: 17471464129836365814931789218571329749 Found probable prime factor of 38 digits: 17471464129836365814931789218571329749 Composite cofactor 2187315454747599957262681204066632824538375447374393308106855746227320684871358623712175018680473014032220407420678969 has 118 digits Number: n N=2187315454747599957262681204066632824538375447374393308106855746227320684871358623712175018680473014032220407420678969 ( 118 digits) Divisors found: Sat Mar 28 05:28:03 2009 prp54 factor: 141275887934387088918433822407219888328785550169645917 Sat Mar 28 05:28:03 2009 prp65 factor: 15482581541185975084705285429391126016253950713185106907656310157 Sat Mar 28 05:28:03 2009 elapsed time 01:18:32 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 28.53 hours. Scaled time: 75.89 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_1_167_9 n: 2187315454747599957262681204066632824538375447374393308106855746227320684871358623712175018680473014032220407420678969 skew: 43271.35 # norm 2.74e+16 c5: 56880 c4: 18038371314 c3: -333026503155184 c2: -7470405842608349126 c1: -136619444764706775747779 c0: -3058100909330477201165739940 # alpha -6.32 Y1: 864609803699 Y0: -32884378819716757892421 # Murphy_E 3.76e-10 # M 1118767806770688025859182493513034584215833027743594558217465092282461308752967594068423351362471169988009929142135920 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 4011467) Primes: RFBsize:315948, AFBsize:315599, largePrimes:10805214 encountered Relations: rels:9805383, finalFF:628669 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 824513 hash collisions in 10764421 relations Msieve: matrix is 654424 x 654672 (181.7 MB) Total sieving time: 27.92 hours. Total relation processing time: 0.61 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000 total time: 28.53 hours. --------- CPU info (if available) ----------
(49·10¹⁶³+23)/9 = 5(4)₁₆₂7_<164> = 3 · 19³ · 697475003 · C151
C151 = P36 · P116
P36 = 281771363630732629031583706433092583_<36>
P116 = 13463129146711053496034967138964031226984131523252406266924392904522707992604894585783077441626599518226160500296939_<116>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 3793524258405435352440492779960415544269989551997559007185731146851143361170035411115019941709401493203830929177424803532593017727945863322107578503437 (151 digits) Using B1=320000, B2=215159500, polynomial Dickson(3), sigma=1451542920 Step 1 took 4914ms Step 2 took 2230ms ********** Factor found in step 2: 281771363630732629031583706433092583 Found probable prime factor of 36 digits: 281771363630732629031583706433092583 Probable prime cofactor 13463129146711053496034967138964031226984131523252406266924392904522707992604894585783077441626599518226160500296939 has 116 digits
(49·10¹⁶⁹+41)/9 = 5(4)₁₆₈9_<170> = 1633987 · 222842116547_<12> · 4309002319101724709_<19> · 12626797757710355343920087032327_<32> · C103
C103 = P42 · P62
P42 = 161726317463004925294893739483643455711403_<42>
P62 = 16992491013336792208581860510277455208049350422509007698567129_<62>

Number: n N=2748132996110164316692394787675034756341704156057136951873517972369944327740468903886111422774446271987 ( 103 digits) Divisors found: Sat Mar 28 06:32:51 2009 prp42 factor: 161726317463004925294893739483643455711403 Sat Mar 28 06:32:51 2009 prp62 factor: 16992491013336792208581860510277455208049350422509007698567129 Sat Mar 28 06:32:51 2009 elapsed time 00:21:51 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 5.76 hours. Scaled time: 15.26 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_4_168_9 n: 2748132996110164316692394787675034756341704156057136951873517972369944327740468903886111422774446271987 skew: 6018.30 # norm 9.19e+13 c5: 33540 c4: 684589501 c3: 5791283135574 c2: -28206819817534566 c1: -38476561442250937966 c0: -33218737564069799087307 # alpha -5.31 Y1: 74270204899 Y0: -38255289751789543670 # Murphy_E 2.39e-09 # M 2118835397043999855895382204736405261545507460993547449580085793519358158855105205632886183942560675358 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1751117) Primes: RFBsize:169511, AFBsize:169243, largePrimes:13837185 encountered Relations: rels:11629589, finalFF:365377 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 666886 hash collisions in 12075964 relations Msieve: matrix is 347056 x 347304 (95.4 MB) Total sieving time: 5.33 hours. Total relation processing time: 0.43 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,28,28,56,56,2.6,2.6,100000 total time: 5.76 hours. --------- CPU info (if available) ----------
(49·10¹⁶⁴+41)/9 = 5(4)₁₆₃9_<165> = 3² · 2999 · 14383957318464271_<17> · C145
C145 = P36 · P49 · P60
P36 = 610669137960733395685042251722807251_<36>
P49 = 7186553173058630799368238546006774398260215801703_<49>
P60 = 319543210483475316340708907207542706196386873040108707971853_<60>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 1402349324633698256140012135543458744822102593646541812746298229673535472139910433762013003100546995491089384322899717818288966583222385504693409 (145 digits) Using B1=2770000, B2=4281513610, polynomial Dickson(6), sigma=648140982 Step 1 took 38376ms ********** Factor found in step 1: 610669137960733395685042251722807251 Found probable prime factor of 36 digits: 610669137960733395685042251722807251 Composite cofactor 2296414273229361472578839807470333744690001646782988120596944464494727792347492919926882269338661235553465659 has 109 digits GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 2296414273229361472578839807470333744690001646782988120596944464494727792347492919926882269338661235553465659 (109 digits) Using B1=3316000, B2=5707206970, polynomial Dickson(6), sigma=27217913 Step 1 took 32510ms Step 2 took 10920ms ********** Factor found in step 2: 7186553173058630799368238546006774398260215801703 Found probable prime factor of 49 digits: 7186553173058630799368238546006774398260215801703 Probable prime cofactor 319543210483475316340708907207542706196386873040108707971853 has 60 digits
Mar 28, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Mar 28, 2009
(49·10¹⁴⁶+41)/9 = 5(4)₁₄₅9_<147> = 3² · 401 · 37781 · 246975928358611_<15> · C125
C125 = P36 · P89
P36 = 635631229052462147884290094903460557_<36>
P89 = 25435096336658932336705167917031068008789759084152689170327716094934210451817361767116803_<89>

Number: 54449_146 N=16167341545538294700472713844287897030163776178300163755670307640173965598426295954889076267540032446185900158239333122439271 ( 125 digits) SNFS difficulty: 147 digits. Divisors found: r1=635631229052462147884290094903460557 (pp36) r2=25435096336658932336705167917031068008789759084152689170327716094934210451817361767116803 (pp89) Version: Msieve-1.39 Total time: 12.37 hours. Scaled time: 31.80 units (timescale=2.571). Factorization parameters were as follows: n: 16167341545538294700472713844287897030163776178300163755670307640173965598426295954889076267540032446185900158239333122439271 m: 100000000000000000000000000000 deg: 5 c5: 490 c0: 41 skew: 0.61 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, 2800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 360372 x 360618 Total sieving time: 12.37 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,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000 total time: 12.37 hours. --------- CPU info (if available) ----------
(14·10¹⁸⁰+1)/3 = 4(6)₁₇₉7_<181> = 23 · 19477 · C176
C176 = P82 · P94
P82 = 1172452363816037728649885943412504699468920569755011261533521576093947543910089989_<82>
P94 = 8885086784734578588942035780312830751406596097560532726566468481627824418076932918133587209093_<94>

Number: 46667_180 N=10417341003472695033086219122815241760441338092569980348430292734723155442353783317818936196018641087629928425426348282961769102613041171563933081977776835256448892152989069977 ( 176 digits) SNFS difficulty: 181 digits. Divisors found: r1=1172452363816037728649885943412504699468920569755011261533521576093947543910089989 (pp82) r2=8885086784734578588942035780312830751406596097560532726566468481627824418076932918133587209093 (pp94) Version: Msieve-1.39 Total time: 102.09 hours. Scaled time: 177.54 units (timescale=1.739). Factorization parameters were as follows: n: 10417341003472695033086219122815241760441338092569980348430292734723155442353783317818936196018641087629928425426348282961769102613041171563933081977776835256448892152989069977 m: 1000000000000000000000000000000000000 deg: 5 c5: 14 c0: 1 skew: 0.59 type: snfs lss: 1 rlim: 7300000 alim: 7300000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7300000/7300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3650000, 5350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1247235 x 1247483 Total sieving time: 102.09 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,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000 total time: 102.09 hours. --------- CPU info (if available) ----------
Mar 28, 2009: By Erik Branger / GGNFS, Msieve / Mar 28, 2009
(49·10¹⁴³+41)/9 = 5(4)₁₄₂9_<144> = 3 · 17 · 19413661 · 14241432483999782428669_<23> · C113
C113 = P50 · P63
P50 = 48208737729702173551817182097623439690535527340379_<50>
P63 = 800933607368938839181048674491588864161303805763605741405443609_<63>

Number: 54449_143 N=38611998216553428634976880852884532742105214703709972979595744163625655295796044808871492594795432863440433187811 ( 113 digits) SNFS difficulty: 146 digits. Divisors found: r1=48208737729702173551817182097623439690535527340379 r2=800933607368938839181048674491588864161303805763605741405443609 Version: Total time: 16.54 hours. Scaled time: 12.92 units (timescale=0.781). Factorization parameters were as follows: n: 38611998216553428634976880852884532742105214703709972979595744163625655295796044808871492594795432863440433187811 m: 50000000000000000000000000000 deg: 5 c5: 392 c0: 1025 skew: 1.21 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, 2550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 321094 x 321333 Total sieving time: 16.54 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,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 16.54 hours. --------- CPU info (if available) ----------
(49·10¹⁴⁹+41)/9 = 5(4)₁₄₈9_<150> = 3 · 23 · 5059 · 7663491709_<10> · C135
C135 = P33 · P47 · P56
P33 = 131534588641078345566638760776333_<33>
P47 = 25803421214234640523206313517076073590238151873_<47>
P56 = 59964724923190813318774664569029690764738692093753141799_<56>

Number: 54449_149 N=203522818590634280245075835535627462874181435936750438917137494088318261455309665736275011729733172064884678791543045626662602717314491 ( 135 digits) SNFS difficulty: 151 digits. Divisors found: r1=131534588641078345566638760776333 r2=25803421214234640523206313517076073590238151873 r3=59964724923190813318774664569029690764738692093753141799 Version: Total time: 21.59 hours. Scaled time: 21.70 units (timescale=1.005). Factorization parameters were as follows: n: 203522818590634280245075835535627462874181435936750438917137494088318261455309665736275011729733172064884678791543045626662602717314491 m: 1000000000000000000000000000000 deg: 5 c5: 49 c0: 410 skew: 1.53 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, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 444856 x 445104 Total sieving time: 21.59 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: 21.59 hours. --------- CPU info (if available) ----------
Mar 27, 2009 (7th): By Andreas Tete / Yafu v1.08 / Mar 27, 2009
(49·10¹⁵⁸+41)/9 = 5(4)₁₅₇9_<159> = 3 · 1109 · 2017 · 103231 · 1192853 · 395872333 · 3669428891409834705930932488771_<31> · C102
C102 = P51 · P52
P51 = 145182403511774248585192727630916578243588995294079_<51>
P52 = 3124137943097999819298035626042740374316930537111941_<52>

03/26/09 16:03:31 v1.08 @ LAPPIE, 03/26/09 16:03:31 v1.08 @ LAPPIE, **************************** 03/26/09 16:03:31 v1.08 @ LAPPIE, Starting factorization of 453569855481298226564723037610642262164563210989868695838728271565250333688282786216554526112637497339 03/26/09 16:03:31 v1.08 @ LAPPIE, **************************** 03/26/09 16:03:32 v1.08 @ LAPPIE, Rho method, input has 338 bits, 1000 max iterations per poly 03/26/09 16:03:32 v1.08 @ LAPPIE, poly x^2 + 1: 0.0780 sec 03/26/09 16:03:32 v1.08 @ LAPPIE, poly x^2 + 3: 0.1360 sec 03/26/09 16:03:32 v1.08 @ LAPPIE, poly x^2 + 2: 0.1960 sec 03/26/09 16:03:32 v1.08 @ LAPPIE, Williams P+1 method, input has 338 bits, B1 = 20000, B2 = 1000000 03/26/09 16:03:32 v1.08 @ LAPPIE, base 752376243: 0.1660 sec 03/26/09 16:03:32 v1.08 @ LAPPIE, base 352856595: 0.3250 sec 03/26/09 16:03:32 v1.08 @ LAPPIE, base 2326730079: 0.4830 sec 03/26/09 16:03:32 v1.08 @ LAPPIE, Pollard P-1 method, input has 338 bits, B1 = 100000, B2 = 5000000 03/26/09 16:03:33 v1.08 @ LAPPIE, base 2045834211: 0.4800 sec 03/26/09 16:03:33 v1.08 @ LAPPIE, 25 curves using Lenstra ECM method, input has 338 bits, B1 = 2000, B2 = 200000 03/26/09 16:03:35 v1.08 @ LAPPIE, 90 curves using Lenstra ECM method, input has 338 bits, B1 = 11000, B2 = 1100000 03/26/09 16:04:12 v1.08 @ LAPPIE, 200 curves using Lenstra ECM method, input has 338 bits, B1 = 50000, B2 = 5000000 03/26/09 16:08:48 v1.08 @ LAPPIE, 400 curves using Lenstra ECM method, input has 338 bits, B1 = 250000, B2 = 25000000 03/26/09 16:51:46 v1.08 @ LAPPIE, 1000 curves using Lenstra ECM method, input has 338 bits, B1 = 1000000, B2 = 100000000 03/26/09 23:42:56 v1.08 @ LAPPIE, starting SIQS on c102: 453569855481298226564723037610642262164563210989868695838728271565250333688282786216554526112637497339 03/26/09 23:42:56 v1.08 @ LAPPIE, random seeds: 2459799540, 1414896784 03/26/09 23:42:57 v1.08 @ LAPPIE, ==== sieve params ==== 03/26/09 23:42:57 v1.08 @ LAPPIE, n = 102 digits, 342 bits 03/26/09 23:42:57 v1.08 @ LAPPIE, factor base: 121000 primes (max prime = 3375233) 03/26/09 23:42:57 v1.08 @ LAPPIE, single large prime cutoff: 506284950 (150 * pmax) 03/26/09 23:42:57 v1.08 @ LAPPIE, double large prime range from 45 to 53 bits 03/26/09 23:42:57 v1.08 @ LAPPIE, double large prime cutoff: 4654907246467955 03/26/09 23:42:57 v1.08 @ LAPPIE, using 6 large prime slices of factor base 03/26/09 23:42:57 v1.08 @ LAPPIE, buckets hold 2048 elements 03/26/09 23:42:57 v1.08 @ LAPPIE, sieve interval: 40 blocks of size 32768 03/26/09 23:42:57 v1.08 @ LAPPIE, polynomial A has ~ 13 factors 03/26/09 23:42:57 v1.08 @ LAPPIE, using multiplier of 19 03/26/09 23:42:57 v1.08 @ LAPPIE, using small prime variation correction of 21 bits 03/26/09 23:42:57 v1.08 @ LAPPIE, using x128 sieve scanning 03/26/09 23:42:57 v1.08 @ LAPPIE, trial factoring cutoff at 98 bits 03/26/09 23:42:57 v1.08 @ LAPPIE, ==== sieving started ==== 03/27/09 13:27:40 v1.08 @ LAPPIE, sieve time = 14761.2410, relation time = 11943.4010, poly_time = 22714.0660 03/27/09 13:27:40 v1.08 @ LAPPIE, 121065 relations found: 27879 full + 93186 from 1844469 partial, using 2695059 polys (609 A polys) 03/27/09 13:27:40 v1.08 @ LAPPIE, trial division touched 561952386 sieve locations out of 7064935464960 03/27/09 13:27:40 v1.08 @ LAPPIE, ==== post processing stage (msieve-1.38) ==== 03/27/09 13:27:47 v1.08 @ LAPPIE, begin with 1872348 relations 03/27/09 13:27:48 v1.08 @ LAPPIE, reduce to 326294 relations in 15 passes 03/27/09 13:27:51 v1.08 @ LAPPIE, failed to read relation 94436 03/27/09 13:27:51 v1.08 @ LAPPIE, failed to read relation 126269 03/27/09 13:27:54 v1.08 @ LAPPIE, failed to read relation 236788 03/27/09 13:27:56 v1.08 @ LAPPIE, failed to read relation 291206 03/27/09 13:27:57 v1.08 @ LAPPIE, recovered 326290 relations 03/27/09 13:27:57 v1.08 @ LAPPIE, recovered 307271 polynomials 03/27/09 13:27:57 v1.08 @ LAPPIE, attempting to build 121061 cycles 03/27/09 13:27:57 v1.08 @ LAPPIE, found 121061 cycles in 7 passes 03/27/09 13:27:57 v1.08 @ LAPPIE, distribution of cycle lengths: 03/27/09 13:27:57 v1.08 @ LAPPIE, length 1 : 27879 03/27/09 13:27:57 v1.08 @ LAPPIE, length 2 : 19652 03/27/09 13:27:57 v1.08 @ LAPPIE, length 3 : 19792 03/27/09 13:27:57 v1.08 @ LAPPIE, length 4 : 16536 03/27/09 13:27:57 v1.08 @ LAPPIE, length 5 : 12912 03/27/09 13:27:57 v1.08 @ LAPPIE, length 6 : 9112 03/27/09 13:27:57 v1.08 @ LAPPIE, length 7 : 6125 03/27/09 13:27:57 v1.08 @ LAPPIE, length 9+: 9053 03/27/09 13:27:57 v1.08 @ LAPPIE, largest cycle: 21 relations 03/27/09 13:27:57 v1.08 @ LAPPIE, matrix is 121000 x 121061 (36.0 MB) with weight 8959249 (74.01/col) 03/27/09 13:27:57 v1.08 @ LAPPIE, sparse part has weight 8959249 (74.01/col) 03/27/09 13:27:58 v1.08 @ LAPPIE, filtering completed in 3 passes 03/27/09 13:27:58 v1.08 @ LAPPIE, matrix is 116549 x 116613 (34.9 MB) with weight 8691415 (74.53/col) 03/27/09 13:27:58 v1.08 @ LAPPIE, sparse part has weight 8691415 (74.53/col) 03/27/09 13:27:59 v1.08 @ LAPPIE, saving the first 48 matrix rows for later 03/27/09 13:27:59 v1.08 @ LAPPIE, matrix is 116501 x 116613 (24.3 MB) with weight 7166912 (61.46/col) 03/27/09 13:27:59 v1.08 @ LAPPIE, sparse part has weight 5671030 (48.63/col) 03/27/09 13:27:59 v1.08 @ LAPPIE, matrix includes 64 packed rows 03/27/09 13:27:59 v1.08 @ LAPPIE, using block size 46645 for processor cache size 3072 kB 03/27/09 13:28:00 v1.08 @ LAPPIE, commencing Lanczos iteration 03/27/09 13:28:00 v1.08 @ LAPPIE, memory use: 21.8 MB 03/27/09 13:29:28 v1.08 @ LAPPIE, lanczos halted after 1844 iterations (dim = 116501) 03/27/09 13:29:28 v1.08 @ LAPPIE, recovered 18 nontrivial dependencies 03/27/09 13:29:29 v1.08 @ LAPPIE, prp52 = 3124137943097999819298035626042740374316930537111941 03/27/09 13:29:32 v1.08 @ LAPPIE, prp51 = 145182403511774248585192727630916578243588995294079 03/27/09 13:29:32 v1.08 @ LAPPIE, Lanczos elapsed time = 107.5710 seconds. 03/27/09 13:29:32 v1.08 @ LAPPIE, Sqrt elapsed time = 4.3410 seconds. 03/27/09 13:29:32 v1.08 @ LAPPIE, SIQS elapsed time = 49596.1740 seconds. 03/27/09 13:29:32 v1.08 @ LAPPIE, 03/27/09 13:29:32 v1.08 @ LAPPIE, 03/27/09 13:29:32 v1.08 @ LAPPIE, Total factoring time = 77160.9650 seconds
Mar 27, 2009 (6th): By Robert Backstrom / GGNFS, Msieve / Mar 27, 2009
(49·10¹⁴⁵+23)/9 = 5(4)₁₄₄7_<146> = 3 · 19 · 1433 · 1637 · 13441 · 19121 · 843689909 · 12546029357_<11> · C111
C111 = P41 · P70
P41 = 28099096755963360760156147612476659621363_<41>
P70 = 5326723434107357287126667494376808424483238382966320913407508042003889_<70>

Number: n N=149676117167240055804949774649484580128526423564024288653847340628041533707950209508991314055486019230513480707 ( 111 digits) Divisors found: Fri Mar 27 20:38:02 2009 prp41 factor: 28099096755963360760156147612476659621363 Fri Mar 27 20:38:02 2009 prp70 factor: 5326723434107357287126667494376808424483238382966320913407508042003889 Fri Mar 27 20:38:02 2009 elapsed time 00:28:45 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 11.59 hours. Scaled time: 30.31 units (timescale=2.616). Factorization parameters were as follows: name: KA_5_4_144_7 n: 149676117167240055804949774649484580128526423564024288653847340628041533707950209508991314055486019230513480707 skew: 54054.23 # norm 5.58e+14 c5: 4080 c4: 104162355 c3: -24151431615492 c2: -413790679185675356 c1: 24983205633200245884864 c0: 600209768239263810987355997 # alpha -5.44 Y1: 213617932927 Y0: -2055408927863635415646 # Murphy_E 1.01e-09 # M 47036110769373571685223730777806106190142807887105667390924714824160485749629030815867038979515447120817685924 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2310157) Primes: RFBsize:230209, AFBsize:230174, largePrimes:10909616 encountered Relations: rels:9252464, finalFF:462617 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 479607 hash collisions in 9905449 relations Msieve: matrix is 456373 x 456621 (126.1 MB) Total sieving time: 11.29 hours. Total relation processing time: 0.30 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000 total time: 11.59 hours. --------- CPU info (if available) ----------
Mar 27, 2009 (5th): By Sinkiti Sibata / Msieve, GGNFS / Mar 27, 2009
(49·10¹³⁹+23)/9 = 5(4)₁₃₈7_<140> = 3 · 17 · 2207 · 1904082082311853_<16> · 6244544042098850789167_<22> · C98
C98 = P49 · P50
P49 = 2072759047416221070534804488754052236069702934877_<49>
P50 = 19626634850383055370477280716473069938045234782973_<50>

hu Mar 26 18:13:36 2009 Msieve v. 1.39 Thu Mar 26 18:13:36 2009 random seeds: 1860eb28 af6a59ad Thu Mar 26 18:13:36 2009 factoring 40681284956465988403080857946319072263186432526101152628954576776813427435085598802385742247449321 (98 digits) Thu Mar 26 18:13:37 2009 searching for 15-digit factors Thu Mar 26 18:13:39 2009 commencing quadratic sieve (98-digit input) Thu Mar 26 18:13:39 2009 using multiplier of 1 Thu Mar 26 18:13:39 2009 using 32kb Intel Core sieve core Thu Mar 26 18:13:39 2009 sieve interval: 36 blocks of size 32768 Thu Mar 26 18:13:39 2009 processing polynomials in batches of 6 Thu Mar 26 18:13:39 2009 using a sieve bound of 2508151 (91735 primes) Thu Mar 26 18:13:39 2009 using large prime bound of 376222650 (28 bits) Thu Mar 26 18:13:39 2009 using double large prime bound of 2727726703072350 (43-52 bits) Thu Mar 26 18:13:39 2009 using trial factoring cutoff of 52 bits Thu Mar 26 18:13:39 2009 polynomial 'A' values have 13 factors Fri Mar 27 02:30:51 2009 92021 relations (21823 full + 70198 combined from 1396079 partial), need 91831 Fri Mar 27 02:30:53 2009 begin with 1417902 relations Fri Mar 27 02:30:54 2009 reduce to 243523 relations in 10 passes Fri Mar 27 02:30:54 2009 attempting to read 243523 relations Fri Mar 27 02:30:59 2009 recovered 243523 relations Fri Mar 27 02:30:59 2009 recovered 232972 polynomials Fri Mar 27 02:30:59 2009 attempting to build 92021 cycles Fri Mar 27 02:30:59 2009 found 92021 cycles in 6 passes Fri Mar 27 02:30:59 2009 distribution of cycle lengths: Fri Mar 27 02:30:59 2009 length 1 : 21823 Fri Mar 27 02:30:59 2009 length 2 : 15568 Fri Mar 27 02:30:59 2009 length 3 : 15478 Fri Mar 27 02:30:59 2009 length 4 : 12640 Fri Mar 27 02:30:59 2009 length 5 : 9600 Fri Mar 27 02:30:59 2009 length 6 : 6545 Fri Mar 27 02:30:59 2009 length 7 : 4289 Fri Mar 27 02:30:59 2009 length 9+: 6078 Fri Mar 27 02:30:59 2009 largest cycle: 21 relations Fri Mar 27 02:31:00 2009 matrix is 91735 x 92021 (24.9 MB) with weight 6171846 (67.07/col) Fri Mar 27 02:31:00 2009 sparse part has weight 6171846 (67.07/col) Fri Mar 27 02:31:01 2009 filtering completed in 3 passes Fri Mar 27 02:31:01 2009 matrix is 88169 x 88233 (24.0 MB) with weight 5942491 (67.35/col) Fri Mar 27 02:31:01 2009 sparse part has weight 5942491 (67.35/col) Fri Mar 27 02:31:01 2009 saving the first 48 matrix rows for later Fri Mar 27 02:31:01 2009 matrix is 88121 x 88233 (15.1 MB) with weight 4742704 (53.75/col) Fri Mar 27 02:31:01 2009 sparse part has weight 3440666 (39.00/col) Fri Mar 27 02:31:01 2009 matrix includes 64 packed rows Fri Mar 27 02:31:01 2009 using block size 35293 for processor cache size 1024 kB Fri Mar 27 02:31:02 2009 commencing Lanczos iteration Fri Mar 27 02:31:02 2009 memory use: 14.6 MB Fri Mar 27 02:31:57 2009 lanczos halted after 1395 iterations (dim = 88118) Fri Mar 27 02:31:57 2009 recovered 15 nontrivial dependencies Fri Mar 27 02:31:58 2009 prp49 factor: 2072759047416221070534804488754052236069702934877 Fri Mar 27 02:31:58 2009 prp50 factor: 19626634850383055370477280716473069938045234782973 Fri Mar 27 02:31:58 2009 elapsed time 08:18:22
(49·10¹³²+23)/9 = 5(4)₁₃₁7_<133> = 16980584111_<11> · C123
C123 = P53 · P70
P53 = 65594212145907328803824064243879179779552967931235427_<53>
P70 = 4888047585303310525809787280229165861700492433207353199793648310838651_<70>

Number: 54447_132 N=320627630289675401169387043145423187759765541815903934922327033514639056249155459010608144823931872365992041959176892088977 ( 123 digits) SNFS difficulty: 134 digits. Divisors found: r1=65594212145907328803824064243879179779552967931235427 (pp53) r2=4888047585303310525809787280229165861700492433207353199793648310838651 (pp70) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 8.87 hours. Scaled time: 4.20 units (timescale=0.473). Factorization parameters were as follows: name: 5444_132 n: 320627630289675401169387043145423187759765541815903934922327033514639056249155459010608144823931872365992041959176892088977 m: 200000000000000000000000000 deg: 5 c5: 1225 c0: 184 skew: 0.68 type: snfs lss: 1 rlim: 1230000 alim: 1230000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1230000/1230000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [615000, 1365001) Primes: RFBsize:95051, AFBsize:94798, largePrimes:3188611 encountered Relations: rels:3164491, finalFF:263511 Max relations in full relation-set: 28 Initial matrix: 189914 x 263511 with sparse part having weight 23975523. Pruned matrix : 170528 x 171541 with weight 12559364. Total sieving time: 8.10 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.56 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1230000,1230000,26,26,47,47,2.3,2.3,75000 total time: 8.87 hours. --------- CPU info (if available) ----------
(49·10¹³⁶+23)/9 = 5(4)₁₃₅7_<137> = 3 · C137
C137 = P47 · P91
P47 = 11469748045393866785079980234484149679778904849_<47>
P91 = 1582262145281932184224557733322428115520702729873734992229974599729019302327043912919001701_<91>

Number: 54447_136 N=18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149 ( 137 digits) SNFS difficulty: 138 digits. Divisors found: r1=11469748045393866785079980234484149679778904849 r2=1582262145281932184224557733322428115520702729873734992229974599729019302327043912919001701 Version: Total time: 4.53 hours. Scaled time: 15.13 units (timescale=3.339). Factorization parameters were as follows: name: 54447_136 n: 18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149 m: 2000000000000000000000000000 deg: 5 c5: 245 c0: 368 skew: 1.08 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, 1550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 222076 x 222324 Total sieving time: 4.53 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,138,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000 total time: 4.53 hours. --------- CPU info (if available) ----------
(49·10¹⁴¹+23)/9 = 5(4)₁₄₀7_<142> = 13 · 417717737 · 237649169221_<12> · 75672693320024537909317_<23> · C98
C98 = P41 · P58
P41 = 25422400608002178538937352091939883519719_<41>
P58 = 2192982932771281359086104058811103715388491439096170268589_<58>

Fri Mar 27 04:05:55 2009 Msieve v. 1.39 Fri Mar 27 04:05:55 2009 random seeds: b36ff260 c126c954 Fri Mar 27 04:05:55 2009 factoring 55750890643423023846877628970441753098432966504896865465627005857047479051479338805773750907806491 (98 digits) Fri Mar 27 04:05:56 2009 searching for 15-digit factors Fri Mar 27 04:05:58 2009 commencing quadratic sieve (98-digit input) Fri Mar 27 04:05:58 2009 using multiplier of 19 Fri Mar 27 04:05:58 2009 using 32kb Intel Core sieve core Fri Mar 27 04:05:58 2009 sieve interval: 36 blocks of size 32768 Fri Mar 27 04:05:58 2009 processing polynomials in batches of 6 Fri Mar 27 04:05:58 2009 using a sieve bound of 2508139 (91605 primes) Fri Mar 27 04:05:58 2009 using large prime bound of 376220850 (28 bits) Fri Mar 27 04:05:58 2009 using double large prime bound of 2727703118350350 (43-52 bits) Fri Mar 27 04:05:58 2009 using trial factoring cutoff of 52 bits Fri Mar 27 04:05:58 2009 polynomial 'A' values have 13 factors Fri Mar 27 11:32:05 2009 91986 relations (22361 full + 69625 combined from 1374307 partial), need 91701 Fri Mar 27 11:32:07 2009 begin with 1396668 relations Fri Mar 27 11:32:09 2009 reduce to 240128 relations in 13 passes Fri Mar 27 11:32:09 2009 attempting to read 240128 relations Fri Mar 27 11:32:13 2009 recovered 240128 relations Fri Mar 27 11:32:13 2009 recovered 228608 polynomials Fri Mar 27 11:32:13 2009 attempting to build 91986 cycles Fri Mar 27 11:32:13 2009 found 91986 cycles in 6 passes Fri Mar 27 11:32:13 2009 distribution of cycle lengths: Fri Mar 27 11:32:13 2009 length 1 : 22361 Fri Mar 27 11:32:13 2009 length 2 : 16061 Fri Mar 27 11:32:13 2009 length 3 : 15438 Fri Mar 27 11:32:13 2009 length 4 : 12603 Fri Mar 27 11:32:13 2009 length 5 : 9395 Fri Mar 27 11:32:13 2009 length 6 : 6325 Fri Mar 27 11:32:13 2009 length 7 : 4184 Fri Mar 27 11:32:13 2009 length 9+: 5619 Fri Mar 27 11:32:13 2009 largest cycle: 21 relations Fri Mar 27 11:32:14 2009 matrix is 91605 x 91986 (24.2 MB) with weight 5976920 (64.98/col) Fri Mar 27 11:32:14 2009 sparse part has weight 5976920 (64.98/col) Fri Mar 27 11:32:15 2009 filtering completed in 3 passes Fri Mar 27 11:32:15 2009 matrix is 87537 x 87601 (23.1 MB) with weight 5707780 (65.16/col) Fri Mar 27 11:32:15 2009 sparse part has weight 5707780 (65.16/col) Fri Mar 27 11:32:15 2009 saving the first 48 matrix rows for later Fri Mar 27 11:32:16 2009 matrix is 87489 x 87601 (13.3 MB) with weight 4351256 (49.67/col) Fri Mar 27 11:32:16 2009 sparse part has weight 2973209 (33.94/col) Fri Mar 27 11:32:16 2009 matrix includes 64 packed rows Fri Mar 27 11:32:16 2009 using block size 35040 for processor cache size 1024 kB Fri Mar 27 11:32:16 2009 commencing Lanczos iteration Fri Mar 27 11:32:16 2009 memory use: 13.6 MB Fri Mar 27 11:33:06 2009 lanczos halted after 1385 iterations (dim = 87487) Fri Mar 27 11:33:06 2009 recovered 17 nontrivial dependencies Fri Mar 27 11:33:07 2009 prp41 factor: 25422400608002178538937352091939883519719 Fri Mar 27 11:33:07 2009 prp58 factor: 2192982932771281359086104058811103715388491439096170268589 Fri Mar 27 11:33:07 2009 elapsed time 07:27:12
Mar 27, 2009 (4th): By Jo Yeong Uk / GMP-ECM / Mar 27, 2009
(49·10¹⁸⁵+23)/9 = 5(4)₁₈₄7_<186> = C186
C186 = P33 · P153
P33 = 806733444214685110818405149979937_<33>
P153 = 674875261895748026104835169072656059803931384591054243173189832904384059405927583278464754459983266422994151032177491844598621496960454629394526600967231_<153>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 544444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 (186 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1723084161 Step 1 took 6221ms Step 2 took 3400ms ********** Factor found in step 2: 806733444214685110818405149979937 Found probable prime factor of 33 digits: 806733444214685110818405149979937 Probable prime cofactor 674875261895748026104835169072656059803931384591054243173189832904384059405927583278464754459983266422994151032177491844598621496960454629394526600967231 has 153 digits
Mar 27, 2009 (3rd): By Ignacio Santos / GGNFS, Msieve / Mar 27, 2009
(49·10¹³⁷+41)/9 = 5(4)₁₃₆9_<138> = 3² · 233 · 36097 · 5517307 · 160828175857_<12> · C112
C112 = P49 · P64
P49 = 2425727394160925168973174009150207745849594329787_<49>
P64 = 3341586837971065273981699845466591967077869497074885030760101097_<64>

Number: 54449_137 N=8105778732833997840998552688220217168092181072232097955983824590327356982459028278624705999411103235686078476339 ( 112 digits) SNFS difficulty: 139 digits. Divisors found: r1=2425727394160925168973174009150207745849594329787 (pp49) r2=3341586837971065273981699845466591967077869497074885030760101097 (pp64) Version: Msieve-1.39 Total time: 3.99 hours. Scaled time: 6.93 units (timescale=1.739). Factorization parameters were as follows: n: 8105778732833997840998552688220217168092181072232097955983824590327356982459028278624705999411103235686078476339 m: 2000000000000000000000000000 deg: 5 c5: 1225 c0: 328 skew: 0.77 type: snfs lss: 1 rlim: 1480000 alim: 1480000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1480000/1480000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [740000, 1490001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 226080 x 226328 Total sieving time: 3.99 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: snfs,139,5,0,0,0,0,0,0,0,0,1480000,1480000,26,26,48,48,2.3,2.3,75000 total time: 3.99 hours. --------- CPU info (if available) ----------
(49·10¹³⁸+41)/9 = 5(4)₁₃₇9_<139> = 15595643090259138670909471_<26> · C114
C114 = P47 · P68
P47 = 18533989362828478542555461551240462977930149887_<47>
P68 = 18835683030031066796183322332961649164918753989445572020809159395137_<68>

Number: 54449_138 N=349100348920204677754729896469469518001250723946393823346871892322067135526799095817938294302315163602800668899519 ( 114 digits) SNFS difficulty: 141 digits. Divisors found: r1=18533989362828478542555461551240462977930149887 (pp47) r2=18835683030031066796183322332961649164918753989445572020809159395137 (pp68) Version: Msieve-1.39 Total time: 5.77 hours. Scaled time: 10.04 units (timescale=1.739). Factorization parameters were as follows: n: 349100348920204677754729896469469518001250723946393823346871892322067135526799095817938294302315163602800668899519 m: 5000000000000000000000000000 deg: 5 c5: 392 c0: 1025 skew: 1.21 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, 1885001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 267184 x 267432 Total sieving time: 5.77 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,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 5.77 hours. --------- CPU info (if available) ----------
(49·10¹⁶⁶+41)/9 = 5(4)₁₆₅9_<167> = 2151847 · C161
C161 = P39 · P122
P39 = 403475196715413542945185597203831441517_<39>
P122 = 62708345080053725423367577282775798846310717380281419671758144564588907556000849612451063415371641841328324130172173742451_<122>

Number: 54449_166 N=25301261866872711881673950073794486524573747317743521934619164115499124447251335454818323256460354497529073602558380983612889041109541916523082005572164026738167 ( 161 digits) SNFS difficulty: 167 digits. Divisors found: r1=403475196715413542945185597203831441517 (pp39) r2=62708345080053725423367577282775798846310717380281419671758144564588907556000849612451063415371641841328324130172173742451 (pp122) Version: Msieve-1.39 Total time: 51.88 hours. Scaled time: 90.22 units (timescale=1.739). Factorization parameters were as follows: n: 25301261866872711881673950073794486524573747317743521934619164115499124447251335454818323256460354497529073602558380983612889041109541916523082005572164026738167 m: 1000000000000000000000000000000000 deg: 5 c5: 490 c0: 41 skew: 0.61 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, 5200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 874003 x 874251 Total sieving time: 51.88 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 51.88 hours. --------- CPU info (if available) ----------
(8·10¹⁷⁰-53)/9 = (8)₁₆₉3_<170> = 320125693285593749063_<21> · C150
C150 = P47 · P104
P47 = 23559899128668130997812153260935382432418417441_<47>
P104 = 11785649435366880973726668861597007737603372223460325079320068596433820581085450083045755315594565351701_<104>

Number: 88883_170 N=277668711863088229130098651489614886471886915528918772949629453601534389737903588995330059164196819694470193153548947465023028184980242144797997417141 ( 150 digits) SNFS difficulty: 170 digits. Divisors found: r1=23559899128668130997812153260935382432418417441 (pp47) r2=11785649435366880973726668861597007737603372223460325079320068596433820581085450083045755315594565351701 (pp104) Version: Msieve-1.39 Total time: 49.08 hours. Scaled time: 126.18 units (timescale=2.571). Factorization parameters were as follows: n: 277668711863088229130098651489614886471886915528918772949629453601534389737903588995330059164196819694470193153548947465023028184980242144797997417141 m: 10000000000000000000000000000000000 deg: 5 c5: 8 c0: -53 skew: 1.46 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, 4450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 866303 x 866551 Total sieving time: 49.08 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: 49.08 hours. --------- CPU info (if available) ----------
(49·10¹⁴⁴+23)/9 = 5(4)₁₄₃7_<145> = 4463 · 5084335385724661558411_<22> · C120
C120 = P44 · P77
P44 = 18587922413311078500682008656078799844857539_<44>
P77 = 12908079806624081195761137810924158501690725662669177809379445232500203387761_<77>

Number: 54447_144 N=239934385950355890837148625513788087364983744889451972553265266567739880538425926972922707561318526301372830222221180179 ( 120 digits) SNFS difficulty: 146 digits. Divisors found: r1=18587922413311078500682008656078799844857539 (pp44) r2=12908079806624081195761137810924158501690725662669177809379445232500203387761 (pp77) Version: Msieve-1.39 Total time: 9.88 hours. Scaled time: 25.40 units (timescale=2.571). Factorization parameters were as follows: n: 239934385950355890837148625513788087364983744889451972553265266567739880538425926972922707561318526301372830222221180179 m: 100000000000000000000000000000 deg: 5 c5: 49 c0: 230 skew: 1.36 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 : 327912 x 328160 Total sieving time: 9.88 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: 9.88 hours. --------- CPU info (if available) ----------
Mar 27, 2009 (2nd): By Serge Batalov / Msieve-1.40, Msieve-1.40/1.39sqrt / Mar 27, 2009
(47·10¹⁵⁷+43)/9 = 5(2)₁₅₆7_<158> = 3² · C157
C157 = P63 · P94
P63 = 863739116053015826056476279862601665119897672463708354914661277_<63>
P94 = 6717849206966234942139994623500961571684454208649571846255616026490064023572030489723138698039_<94>

SNFS difficulty: 159 digits. Divisors found: r1=863739116053015826056476279862601665119897672463708354914661277 (pp63) r2=6717849206966234942139994623500961571684454208649571846255616026490064023572030489723138698039 (pp94) Version: Msieve-1.40 Total time: 12.45 hours. Scaled time: 35.34 units (timescale=2.840). Factorization parameters were as follows: n: 5802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803 m: 20000000000000000000000000000000 deg: 5 c5: 1175 c0: 344 skew: 0.78 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1600000, 3100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 600280 x 600528 Total sieving time: 12.45 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,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,52,52,2.4,2.4,100000 total time: 12.45 hours.
(49·10¹⁵⁶-13)/9 = 5(4)₁₅₅3_<157> = 1885805722707991669898771533_<28> · C130
C130 = P55 · P76
P55 = 2210524998163295381088357432294324394655053936779965711_<55>
P76 = 1306054171647590876958690600009006792110053639951158724187114943389454925961_<76>

SNFS difficulty: 158 digits. Divisors found: r1=2210524998163295381088357432294324394655053936779965711 (pp55) r2=1306054171647590876958690600009006792110053639951158724187114943389454925961 (pp76) Version: Msieve-1.40 Total time: 10.84 hours. Scaled time: 30.78 units (timescale=2.839). Factorization parameters were as follows: n: 2887065395382455093675160127696693984232235070487908532313326863483666488669758862609112195172261282961921826638822593725623723271 m: 20000000000000000000000000000000 deg: 5 c5: 245 c0: -208 skew: 0.97 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1600000, 2900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 585235 x 585482 Total sieving time: 10.84 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,158,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,52,52,2.4,2.4,100000 total time: 10.84 hours.
(49·10¹⁷⁵+23)/9 = 5(4)₁₇₄7_<176> = 3 · C176
C176 = P64 · P113
P64 = 1495137986198626713891034616766476860505226920685712498786743139_<64>
P113 = 12138109201739721837657904196381001857689869557081702922551111410234045319431624045172325499708883925960213827591_<113>

SNFS difficulty: 176 digits. Divisors found: r1=1495137986198626713891034616766476860505226920685712498786743139 (pp64) r2=12138109201739721837657904196381001857689869557081702922551111410234045319431624045172325499708883925960213827591 (pp113) Version: Msieve-1.40/1.39 Total time: 46.80 hours. Scaled time: 132.91 units (timescale=2.840). Factorization parameters were as follows: n: 18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149 m: 100000000000000000000000000000000000 deg: 5 c5: 49 c0: 23 skew: 0.86 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved special-q in [3100000, 3100000) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1425483 x 1425729 Total sieving time: 38.80 hours. Total relation processing time: 0.00 hours. Matrix solve time: 2.10 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,55,55,2.5,2.5,100000 total time: 46.80 hours.
Mar 27, 2009: By Erik Branger / GGNFS, Msieve / Mar 27, 2009
(49·10¹³⁷+23)/9 = 5(4)₁₃₆7_<138> = 367 · 41519 · C131
C131 = P48 · P84
P48 = 111686516686440099713105228891396349952349160121_<48>
P84 = 319918883357687655326884373101551813841497448613417153161897436456980513663260915959_<84>

Number: 54447_137 N=35730625704435666231824951843684608625357002729024979696071943454432663765471114826221148640883199231555287707118132018638815271039 ( 131 digits) SNFS difficulty: 139 digits. Divisors found: r1=111686516686440099713105228891396349952349160121 r2=319918883357687655326884373101551813841497448613417153161897436456980513663260915959 Version: Total time: 9.81 hours. Scaled time: 7.65 units (timescale=0.780). Factorization parameters were as follows: n: 35730625704435666231824951843684608625357002729024979696071943454432663765471114826221148640883199231555287707118132018638815271039 m: 2000000000000000000000000000 deg: 5 c5: 1225 c0: 184 skew: 0.68 type: snfs lss: 1 rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 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: 48/48 Sieved rational special-q in [750000, 1725001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 245198 x 245446 Total sieving time: 9.81 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,48,48,2.3,2.3,75000 total time: 9.81 hours. --------- CPU info (if available) ----------
(49·10¹⁴⁴+41)/9 = 5(4)₁₄₃9_<145> = 179 · 94593921041_<11> · C132
C132 = P65 · P67
P65 = 34618114200346796804140356391786401986013866968419090798524170021_<65>
P67 = 9288250196524313420503337155642549167984865224535302935187999437071_<67>

Number: 54449_144 N=321541706024672260551787816221255298649921458882378056825433992581094497126329589535485981556862183103890401989612491476535494248491 ( 132 digits) SNFS difficulty: 146 digits. Divisors found: r1=34618114200346796804140356391786401986013866968419090798524170021 r2=9288250196524313420503337155642549167984865224535302935187999437071 Version: Total time: 13.63 hours. Scaled time: 13.89 units (timescale=1.019). Factorization parameters were as follows: n: 321541706024672260551787816221255298649921458882378056825433992581094497126329589535485981556862183103890401989612491476535494248491 m: 100000000000000000000000000000 deg: 5 c5: 49 c0: 410 skew: 1.53 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, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 369163 x 369411 Total sieving time: 13.63 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: 13.63 hours. --------- CPU info (if available) ----------
Mar 26, 2009 (7th): By Ignacio Santos / GGNFS, Msieve / Mar 26, 2009
(49·10¹¹¹+41)/9 = 5(4)₁₁₀9_<112> = 17² · 949631 · C104
C104 = P33 · P34 · P37
P33 = 971722182165766413416910057805321_<33>
P34 = 2903609920526649428880059207607911_<34>
P37 = 7031054367157515839501298639415675681_<37>

Number: 54449_111 N=19838135141191171779982639129717270529561053960298031640271697900492627494930363552518843950035039632511 ( 104 digits) SNFS difficulty: 112 digits. Divisors found: r1=971722182165766413416910057805321 (pp33) r2=2903609920526649428880059207607911 (pp34) r3=7031054367157515839501298639415675681 (pp37) Version: Msieve-1.39 Total time: 0.94 hours. Scaled time: 1.12 units (timescale=1.190). Factorization parameters were as follows: n: 19838135141191171779982639129717270529561053960298031640271697900492627494930363552518843950035039632511 m: 10000000000000000000000 deg: 5 c5: 490 c0: 41 skew: 0.61 type: snfs lss: 1 rlim: 530000 alim: 530000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 530000/530000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [265000, 465001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 58703 x 58941 Total sieving time: 0.94 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,112,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000 total time: 0.94 hours. --------- CPU info (if available) ----------
(49·10¹¹⁵+41)/9 = 5(4)₁₁₄9_<116> = 4794897909653311_<16> · C101
C101 = P32 · P35 · P35
P32 = 10186924979578406583472433052629_<32>
P35 = 16338425213924652585496712373192443_<35>
P35 = 68221443328719721898218651146386297_<35>

Number: 54449_115 N=11354661865653982362261839676089086822686511351795352067983241640600745659167261885722919030896288159 ( 101 digits) SNFS difficulty: 116 digits. Divisors found: r1=10186924979578406583472433052629 (pp32) r2=16338425213924652585496712373192443 (pp35) r3=68221443328719721898218651146386297 (pp35) Version: Msieve-1.39 Total time: 1.04 hours. Scaled time: 1.24 units (timescale=1.193). Factorization parameters were as follows: n: 11354661865653982362261839676089086822686511351795352067983241640600745659167261885722919030896288159 m: 100000000000000000000000 deg: 5 c5: 49 c0: 41 skew: 0.96 type: snfs lss: 1 rlim: 620000 alim: 620000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 620000/620000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [310000, 510001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 64279 x 64517 Total sieving time: 1.04 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,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000 total time: 1.04 hours. --------- CPU info (if available) ----------
(49·10¹¹⁸+23)/9 = 5(4)₁₁₇7_<119> = 3 · 163 · 1593269 · C110
C110 = P47 · P64
P47 = 15910289293665460540700312777954637144135377863_<47>
P64 = 4392153693257523977981110166469894720194709254490343305931044509_<64>

Number: 54447_118 N=69880435881968395010117652457418567106228712803245272656360783554090757226655078402541147914901942326986304267 ( 110 digits) SNFS difficulty: 121 digits. Divisors found: r1=15910289293665460540700312777954637144135377863 (pp47) r2=4392153693257523977981110166469894720194709254490343305931044509 (pp64) Version: Msieve-1.39 Total time: 1.50 hours. Scaled time: 1.78 units (timescale=1.190). Factorization parameters were as follows: n: 69880435881968395010117652457418567106228712803245272656360783554090757226655078402541147914901942326986304267 m: 500000000000000000000000 deg: 5 c5: 392 c0: 575 skew: 1.08 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 665001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 80344 x 80581 Total sieving time: 1.50 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,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 1.50 hours. --------- CPU info (if available) ----------
(49·10¹²²+41)/9 = 5(4)₁₂₁9_<123> = 3 · 61 · 16421 · 269527 · C111
C111 = P39 · P73
P39 = 194427825632112280839477791635994595997_<39>
P73 = 3457340734650925945845897206191168163665361420064678013468291084068546497_<73>

Number: 54449_122 N=672203241507509203306318147571058464803415911356671337559948980034010718106973978089196178664520519414524572509 ( 111 digits) SNFS difficulty: 124 digits. Divisors found: r1=194427825632112280839477791635994595997 (pp39) r2=3457340734650925945845897206191168163665361420064678013468291084068546497 (pp73) Version: Msieve-1.39 Total time: 1.69 hours. Scaled time: 2.02 units (timescale=1.194). Factorization parameters were as follows: n: 672203241507509203306318147571058464803415911356671337559948980034010718106973978089196178664520519414524572509 m: 2000000000000000000000000 deg: 5 c5: 1225 c0: 328 skew: 0.77 type: snfs lss: 1 rlim: 830000 alim: 830000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 830000/830000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [415000, 765001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 92849 x 93096 Total sieving time: 1.69 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,124,5,0,0,0,0,0,0,0,0,830000,830000,25,25,46,46,2.2,2.2,50000 total time: 1.69 hours. --------- CPU info (if available) ----------
(16·10¹⁷⁰+17)/3 = 5(3)₁₆₉9_<171> = 7⁴ · 11² · 3277640053_<10> · C156
C156 = P36 · P121
P36 = 132352806904194982440252584077327919_<36>
P121 = 4231816069054994431419448863751815900867250965737302061112758210469770212260400845121738062490712318340173811038583094537_<121>

Number: 53339_170 N=560092735041705137562298026759894588633998295834374639822117020159143485878569329742355372234945155356505826309236855960429115016162119308543393017126478503 ( 156 digits) SNFS difficulty: 171 digits. Divisors found: r1=132352806904194982440252584077327919 (pp36) r2=4231816069054994431419448863751815900867250965737302061112758210469770212260400845121738062490712318340173811038583094537 (pp121) Version: Msieve-1.39 Total time: 36.83 hours. Scaled time: 64.05 units (timescale=1.739). Factorization parameters were as follows: n: 560092735041705137562298026759894588633998295834374639822117020159143485878569329742355372234945155356505826309236855960429115016162119308543393017126478503 m: 10000000000000000000000000000000000 deg: 5 c5: 16 c0: 17 skew: 1.01 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, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 812802 x 813050 Total sieving time: 36.83 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,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 36.83 hours. --------- CPU info (if available) ----------
(49·10¹²⁹+41)/9 = 5(4)₁₂₈9_<130> = 103 · C128
C128 = P34 · P38 · P57
P34 = 1933030102714732371359649944976571_<34>
P38 = 67460989330069140041565000686446989847_<38>
P57 = 405345188912107832212622449426391920980159997852887421459_<57>

Number: 54449_129 N=52858683926645091693635382955771305285868392664509169363538295577130528586839266450916936353829557713052858683926645091693635383 ( 128 digits) SNFS difficulty: 131 digits. Divisors found: r1=1933030102714732371359649944976571 (pp34) r2=67460989330069140041565000686446989847 (pp38) r3=405345188912107832212622449426391920980159997852887421459 (pp57) Version: Msieve-1.39 Total time: 2.74 hours. Scaled time: 4.75 units (timescale=1.735). Factorization parameters were as follows: n: 52858683926645091693635382955771305285868392664509169363538295577130528586839266450916936353829557713052858683926645091693635383 m: 100000000000000000000000000 deg: 5 c5: 49 c0: 410 skew: 1.53 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 168168 x 168416 Total sieving time: 2.74 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,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 2.74 hours. --------- CPU info (if available) ----------
(49·10¹²⁴+41)/9 = 5(4)₁₂₃9_<125> = 116538371 · 204661783981_<12> · C106
C106 = P41 · P65
P41 = 37428052363683529029244596049442228725609_<41>
P65 = 60988877974397866287182423059627153170887298299087679623642765311_<65>

Number: 54449_124 N=2282694918428068381348693425024345271947221342778726134596358771658935004775994118288821273088756202549399 ( 106 digits) SNFS difficulty: 126 digits. Divisors found: r1=37428052363683529029244596049442228725609 (pp41) r2=60988877974397866287182423059627153170887298299087679623642765311 (pp65) Version: Msieve-1.39 Total time: 1.93 hours. Scaled time: 3.35 units (timescale=1.739). Factorization parameters were as follows: n: 2282694918428068381348693425024345271947221342778726134596358771658935004775994118288821273088756202549399 m: 10000000000000000000000000 deg: 5 c5: 49 c0: 410 skew: 1.53 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor 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, 850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 130255 x 130496 Total sieving time: 1.93 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: 1.93 hours. --------- CPU info (if available) ----------
(49·10¹³¹+41)/9 = 5(4)₁₃₀9_<132> = 3 · 127 · 151 · C127
C127 = P48 · P80
P48 = 495966937574525418753568714951542682334528456989_<48>
P80 = 19080902894169119340618115193581337119237563669324766720592482700362221956219311_<80>

Number: 54449_131 N=9463496974577957004822520805208399722661598867470484511731839259606897923631510741069066145981200473561113911533685220914714579 ( 127 digits) SNFS difficulty: 132 digits. Divisors found: r1=495966937574525418753568714951542682334528456989 (pp48) r2=19080902894169119340618115193581337119237563669324766720592482700362221956219311 (pp80) Version: Msieve-1.39 Total time: 2.75 hours. Scaled time: 4.78 units (timescale=1.735). Factorization parameters were as follows: n: 9463496974577957004822520805208399722661598867470484511731839259606897923631510741069066145981200473561113911533685220914714579 m: 100000000000000000000000000 deg: 5 c5: 490 c0: 41 skew: 0.61 type: snfs lss: 1 rlim: 1140000 alim: 1140000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1140000/1140000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [570000, 1120001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 191855 x 192103 Total sieving time: 2.75 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,132,5,0,0,0,0,0,0,0,0,1140000,1140000,26,26,47,47,2.3,2.3,50000 total time: 2.75 hours. --------- CPU info (if available) ----------
(35·10¹⁶⁹-71)/9 = 3(8)₁₆₈1_<170> = 8143481792871063619_<19> · C151
C151 = P75 · P77
P75 = 118340978066617131616605003668155243043376160853287972504030188576447929869_<75>
P77 = 40353411013219617905735168316884121943560908269453282029870176563425168687271_<77>

Number: 38881_169 N=4775462127628609004397620791239844944136870989009288523975169563758497738965996401945642214198142722452627484918282805662237004596874406817488200997499 ( 151 digits) SNFS difficulty: 170 digits. Divisors found: r1=118340978066617131616605003668155243043376160853287972504030188576447929869 (pp75) r2=40353411013219617905735168316884121943560908269453282029870176563425168687271 (pp77) Version: Msieve-1.39 Total time: 48.10 hours. Scaled time: 123.68 units (timescale=2.571). Factorization parameters were as follows: n: 4775462127628609004397620791239844944136870989009288523975169563758497738965996401945642214198142722452627484918282805662237004596874406817488200997499 m: 5000000000000000000000000000000000 deg: 5 c5: 112 c0: -71 skew: 0.91 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor 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, 4750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 929709 x 929957 Total sieving time: 48.10 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,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 48.10 hours. --------- CPU info (if available) ----------
(49·10¹³⁰+41)/9 = 5(4)₁₂₉9_<131> = 980924498657_<12> · C119
C119 = P26 · P93
P26 = 91157362108708740542600653_<26>
P93 = 608872332910711521932266724140424623918336615769247686425689983577184398681484932263575936069_<93>

Number: 54449_130 N=55503195729115988344309084736747369696542559541433720850677021062175206889975474460757689960075441138258614086125653057 ( 119 digits) SNFS difficulty: 131 digits. Divisors found: r1=91157362108708740542600653 (pp26) r2=608872332910711521932266724140424623918336615769247686425689983577184398681484932263575936069 (pp93) Version: Msieve-1.39 Total time: 2.09 hours. Scaled time: 3.63 units (timescale=1.735). Factorization parameters were as follows: n: 55503195729115988344309084736747369696542559541433720850677021062175206889975474460757689960075441138258614086125653057 m: 100000000000000000000000000 deg: 5 c5: 49 c0: 41 skew: 0.96 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 164089 x 164337 Total sieving time: 2.09 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,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 2.09 hours. --------- CPU info (if available) ----------
(49·10¹⁶²+41)/9 = 5(4)₁₆₁9_<163> = 1062458317_<10> · C154
C154 = P71 · P84
P71 = 34363196394391077614856507380930780469359185367467522330450410543511411_<71>
P84 = 149124196210808318999806998432402432647174526275866338390959675701508450716087029127_<84>

Number: 54449_162 N=5124384041547716026250886268364017564036297571233982296968027259034995576625943476373054214083058888082895438847079442124075766865538541823513669613868197 ( 154 digits) SNFS difficulty: 164 digits. Divisors found: r1=34363196394391077614856507380930780469359185367467522330450410543511411 (pp71) r2=149124196210808318999806998432402432647174526275866338390959675701508450716087029127 (pp84) Version: Msieve-1.39 Total time: 40.66 hours. Scaled time: 104.54 units (timescale=2.571). Factorization parameters were as follows: n: 5124384041547716026250886268364017564036297571233982296968027259034995576625943476373054214083058888082895438847079442124075766865538541823513669613868197 m: 200000000000000000000000000000000 deg: 5 c5: 1225 c0: 328 skew: 0.77 type: snfs lss: 1 rlim: 3900000 alim: 3900000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor 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, 3850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 679933 x 680181 Total sieving time: 40.66 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,164,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000 total time: 40.66 hours. --------- CPU info (if available) ----------
Mar 26, 2009 (6th): By Andreas Tete / Msieve v1.40beta2, GGNFS / Mar 26, 2009
(25·10¹⁹⁰-7)/9 = 2(7)₁₉₀_<191> = 3³ · 2797 · 32987 · 126410761 · 1898586340075031513_<19> · 41055377346413536886441_<23> · C133
C133 = P45 · P88
P45 = 795128268408707329677455854041947365447846189_<45>
P88 = 1423235633423252778206479630683161968045089225219334698844656222491689510969378337996137_<88>

Wed Mar 25 16:28:21 2009 Wed Mar 25 16:28:21 2009 Wed Mar 25 16:28:21 2009 Msieve v. 1.40 Wed Mar 25 16:28:21 2009 random seeds: 205c5d10 e64a3f8d Wed Mar 25 16:28:21 2009 factoring 1131654884741400727699726376138663572315929999578565409629799410879508529632871965546762957227601037045689888661925111699728852171893 (133 digits) Wed Mar 25 16:28:22 2009 searching for 15-digit factors Wed Mar 25 16:28:24 2009 commencing number field sieve (133-digit input) Wed Mar 25 16:28:24 2009 R0: -28472200377097373513764874 Wed Mar 25 16:28:24 2009 R1: 468852546756907 Wed Mar 25 16:28:24 2009 A0: 3540594829011056504452269227293095 Wed Mar 25 16:28:24 2009 A1: 37878618697434955116910807726 Wed Mar 25 16:28:24 2009 A2: 37056681488483502513677 Wed Mar 25 16:28:24 2009 A3: -141162992671673610 Wed Mar 25 16:28:24 2009 A4: -24837161256 Wed Mar 25 16:28:24 2009 A5: 60480 Wed Mar 25 16:28:24 2009 skew 821183.19, size 9.199391e-013, alpha -7.661392, combined = 5.642171e-011 Wed Mar 25 16:28:24 2009 Wed Mar 25 16:28:24 2009 commencing relation filtering Wed Mar 25 16:28:24 2009 commencing duplicate removal, pass 1 Wed Mar 25 16:28:59 2009 error -15 reading relation 3007155 Wed Mar 25 16:28:59 2009 error -15 reading relation 3007384 Wed Mar 25 16:29:22 2009 error -15 reading relation 5139341 Wed Mar 25 16:31:29 2009 found 3944235 hash collisions in 16830320 relations Wed Mar 25 16:32:12 2009 added 106165 free relations Wed Mar 25 16:32:12 2009 commencing duplicate removal, pass 2 Wed Mar 25 16:33:20 2009 found 4190313 duplicates and 12746171 unique relations Wed Mar 25 16:33:20 2009 memory use: 106.6 MB Wed Mar 25 16:33:20 2009 reading rational ideals above 12255232 Wed Mar 25 16:33:20 2009 reading algebraic ideals above 12255232 Wed Mar 25 16:33:20 2009 commencing singleton removal, pass 1 Wed Mar 25 16:35:52 2009 relations with 0 large ideals: 482609 Wed Mar 25 16:35:52 2009 relations with 1 large ideals: 3067106 Wed Mar 25 16:35:52 2009 relations with 2 large ideals: 5577151 Wed Mar 25 16:35:52 2009 relations with 3 large ideals: 2996424 Wed Mar 25 16:35:52 2009 relations with 4 large ideals: 502027 Wed Mar 25 16:35:52 2009 relations with 5 large ideals: 21449 Wed Mar 25 16:35:52 2009 relations with 6 large ideals: 99405 Wed Mar 25 16:35:52 2009 relations with 7+ large ideals: 0 Wed Mar 25 16:35:52 2009 12746171 relations and about 11981739 large ideals Wed Mar 25 16:35:52 2009 commencing singleton removal, pass 2 Wed Mar 25 16:38:27 2009 found 5973933 singletons Wed Mar 25 16:38:27 2009 current dataset: 6772238 relations and about 4800496 large ideals Wed Mar 25 16:38:27 2009 commencing singleton removal, pass 3 Wed Mar 25 16:40:07 2009 found 1081690 singletons Wed Mar 25 16:40:07 2009 current dataset: 5690548 relations and about 3657854 large ideals Wed Mar 25 16:40:07 2009 commencing singleton removal, pass 4 Wed Mar 25 16:41:38 2009 found 253805 singletons Wed Mar 25 16:41:38 2009 current dataset: 5436743 relations and about 3399748 large ideals Wed Mar 25 16:41:38 2009 commencing singleton removal, final pass Wed Mar 25 16:43:11 2009 memory use: 77.7 MB Wed Mar 25 16:43:11 2009 commencing in-memory singleton removal Wed Mar 25 16:43:11 2009 begin with 5436743 relations and 3712401 unique ideals Wed Mar 25 16:43:16 2009 reduce to 4643827 relations and 2899656 ideals in 13 passes Wed Mar 25 16:43:16 2009 max relations containing the same ideal: 24 Wed Mar 25 16:43:18 2009 reading rational ideals above 720000 Wed Mar 25 16:43:18 2009 reading algebraic ideals above 720000 Wed Mar 25 16:43:18 2009 commencing singleton removal, final pass Wed Mar 25 16:44:51 2009 keeping 4349772 ideals with weight <= 20, new excess is 364446 Wed Mar 25 16:44:58 2009 memory use: 130.1 MB Wed Mar 25 16:44:58 2009 commencing in-memory singleton removal Wed Mar 25 16:44:59 2009 begin with 4680910 relations and 4349772 unique ideals Wed Mar 25 16:45:07 2009 reduce to 4548935 relations and 4035647 ideals in 12 passes Wed Mar 25 16:45:07 2009 max relations containing the same ideal: 20 Wed Mar 25 16:45:10 2009 removing 383563 relations and 338298 ideals in 45265 cliques Wed Mar 25 16:45:10 2009 commencing in-memory singleton removal Wed Mar 25 16:45:11 2009 begin with 4165372 relations and 4035647 unique ideals Wed Mar 25 16:45:15 2009 reduce to 4146785 relations and 3678522 ideals in 8 passes Wed Mar 25 16:45:15 2009 max relations containing the same ideal: 20 Wed Mar 25 16:45:18 2009 removing 284996 relations and 239731 ideals in 45265 cliques Wed Mar 25 16:45:19 2009 commencing in-memory singleton removal Wed Mar 25 16:45:19 2009 begin with 3861789 relations and 3678522 unique ideals Wed Mar 25 16:45:23 2009 reduce to 3849829 relations and 3426710 ideals in 7 passes Wed Mar 25 16:45:23 2009 max relations containing the same ideal: 20 Wed Mar 25 16:45:26 2009 relations with 0 large ideals: 9503 Wed Mar 25 16:45:26 2009 relations with 1 large ideals: 90848 Wed Mar 25 16:45:26 2009 relations with 2 large ideals: 396535 Wed Mar 25 16:45:26 2009 relations with 3 large ideals: 914667 Wed Mar 25 16:45:26 2009 relations with 4 large ideals: 1186000 Wed Mar 25 16:45:26 2009 relations with 5 large ideals: 853357 Wed Mar 25 16:45:26 2009 relations with 6 large ideals: 327220 Wed Mar 25 16:45:26 2009 relations with 7+ large ideals: 71699 Wed Mar 25 16:45:26 2009 commencing 2-way merge Wed Mar 25 16:45:30 2009 reduce to 2378718 relation sets and 1955599 unique ideals Wed Mar 25 16:45:30 2009 commencing full merge Wed Mar 25 16:46:08 2009 memory use: 176.4 MB Wed Mar 25 16:46:09 2009 found 1217257 cycles, need 1159799 Wed Mar 25 16:46:09 2009 weight of 1159799 cycles is about 81408641 (70.19/cycle) Wed Mar 25 16:46:09 2009 distribution of cycle lengths: Wed Mar 25 16:46:09 2009 1 relations: 114539 Wed Mar 25 16:46:09 2009 2 relations: 137131 Wed Mar 25 16:46:09 2009 3 relations: 143480 Wed Mar 25 16:46:09 2009 4 relations: 133059 Wed Mar 25 16:46:09 2009 5 relations: 119083 Wed Mar 25 16:46:09 2009 6 relations: 102704 Wed Mar 25 16:46:09 2009 7 relations: 86519 Wed Mar 25 16:46:09 2009 8 relations: 73187 Wed Mar 25 16:46:09 2009 9 relations: 61798 Wed Mar 25 16:46:09 2009 10+ relations: 188299 Wed Mar 25 16:46:09 2009 heaviest cycle: 17 relations Wed Mar 25 16:46:09 2009 commencing cycle optimization Wed Mar 25 16:46:12 2009 start with 6536252 relations Wed Mar 25 16:46:29 2009 pruned 174023 relations Wed Mar 25 16:46:29 2009 memory use: 172.4 MB Wed Mar 25 16:46:29 2009 distribution of cycle lengths: Wed Mar 25 16:46:29 2009 1 relations: 114539 Wed Mar 25 16:46:29 2009 2 relations: 140634 Wed Mar 25 16:46:29 2009 3 relations: 149409 Wed Mar 25 16:46:29 2009 4 relations: 137047 Wed Mar 25 16:46:29 2009 5 relations: 122430 Wed Mar 25 16:46:29 2009 6 relations: 103915 Wed Mar 25 16:46:29 2009 7 relations: 87256 Wed Mar 25 16:46:29 2009 8 relations: 73271 Wed Mar 25 16:46:29 2009 9 relations: 60820 Wed Mar 25 16:46:29 2009 10+ relations: 170478 Wed Mar 25 16:46:29 2009 heaviest cycle: 17 relations Wed Mar 25 16:46:31 2009 RelProcTime: 935 Wed Mar 25 16:46:31 2009 Wed Mar 25 16:46:31 2009 commencing linear algebra Wed Mar 25 16:46:31 2009 read 1159799 cycles Wed Mar 25 16:46:34 2009 cycles contain 3561496 unique relations Wed Mar 25 16:47:39 2009 read 3561496 relations Wed Mar 25 16:47:45 2009 using 20 quadratic characters above 268431422 Wed Mar 25 16:48:08 2009 building initial matrix Wed Mar 25 16:49:06 2009 memory use: 417.3 MB Wed Mar 25 16:49:11 2009 read 1159799 cycles Wed Mar 25 16:49:13 2009 matrix is 1159583 x 1159799 (333.0 MB) with weight 110624004 (95.38/col) Wed Mar 25 16:49:13 2009 sparse part has weight 78015465 (67.27/col) Wed Mar 25 16:49:32 2009 filtering completed in 2 passes Wed Mar 25 16:49:33 2009 matrix is 1155802 x 1156002 (332.5 MB) with weight 110419103 (95.52/col) Wed Mar 25 16:49:33 2009 sparse part has weight 77923718 (67.41/col) Wed Mar 25 16:49:37 2009 read 1156002 cycles Wed Mar 25 16:49:38 2009 matrix is 1155802 x 1156002 (332.5 MB) with weight 110419103 (95.52/col) Wed Mar 25 16:49:38 2009 sparse part has weight 77923718 (67.41/col) Wed Mar 25 16:49:38 2009 saving the first 48 matrix rows for later Wed Mar 25 16:49:39 2009 matrix is 1155754 x 1156002 (318.0 MB) with weight 87730479 (75.89/col) Wed Mar 25 16:49:39 2009 sparse part has weight 76424675 (66.11/col) Wed Mar 25 16:49:39 2009 matrix includes 64 packed rows Wed Mar 25 16:49:39 2009 using block size 65536 for processor cache size 3072 kB Wed Mar 25 16:49:49 2009 commencing Lanczos iteration Wed Mar 25 16:49:49 2009 memory use: 315.4 MB Wed Mar 25 20:18:27 2009 lanczos halted after 18278 iterations (dim = 1155754) Wed Mar 25 20:18:30 2009 recovered 29 nontrivial dependencies Wed Mar 25 20:18:30 2009 BLanczosTime: 12586 Wed Mar 25 20:18:30 2009 Wed Mar 25 20:18:30 2009 commencing square root phase Wed Mar 25 20:18:30 2009 reading relations for dependency 1 Wed Mar 25 20:18:31 2009 read 578022 cycles Wed Mar 25 20:18:33 2009 cycles contain 2175074 unique relations Wed Mar 25 20:19:35 2009 read 2175074 relations Wed Mar 25 20:19:49 2009 multiplying 1779100 relations Wed Mar 25 20:26:58 2009 multiply complete, coefficients have about 84.98 million bits Wed Mar 25 20:27:01 2009 initial square root is modulo 1258819 Wed Mar 25 20:35:30 2009 sqrtTime: 1020 Wed Mar 25 20:35:30 2009 prp45 factor: 795128268408707329677455854041947365447846189 Wed Mar 25 20:35:30 2009 prp88 factor: 1423235633423252778206479630683161968045089225219334698844656222491689510969378337996137 Wed Mar 25 20:35:30 2009 elapsed time 04:07:09 Msieve v1.40beta2 Polynomial Search take elapsed time 23:28:43 GGNFS for Sieving need 206.94 hours Final Factorization with Msieve v1.40 need 04:07:09 Total time ~ 234 hours
Mar 26, 2009 (5th): By Sinkiti Sibata / GGNFS / Mar 26, 2009
(49·10¹³¹+23)/9 = 5(4)₁₃₀7_<132> = 1663 · 23449818043019_<14> · C116
C116 = P40 · P77
P40 = 1155209557118607634866301603249630313369_<40>
P77 = 12085401163911818634847149173022128361640247401446141329665954189440760421179_<77>

Number: 54447_131 N=13961170926163277240688149356007896284655518876882225973901486035584422030375138157157355587292818264737566194442051 ( 116 digits) SNFS difficulty: 133 digits. Divisors found: r1=1155209557118607634866301603249630313369 (pp40) r2=12085401163911818634847149173022128361640247401446141329665954189440760421179 (pp77) Version: GGNFS-0.77.1-20060513-nocona Total time: 3.30 hours. Scaled time: 11.02 units (timescale=3.339). Factorization parameters were as follows: name: 54447_131 n: 13961170926163277240688149356007896284655518876882225973901486035584422030375138157157355587292818264737566194442051 m: 200000000000000000000000000 deg: 5 c5: 245 c0: 368 skew: 1.08 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, 1195001) Primes: RFBsize:92225, AFBsize:92072, largePrimes:3029635 encountered Relations: rels:2969240, finalFF:249592 Max relations in full relation-set: 28 Initial matrix: 184363 x 249592 with sparse part having weight 20809548. Pruned matrix : 166372 x 167357 with weight 10744253. Total sieving time: 3.15 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 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: 3.30 hours. --------- CPU info (if available) ----------
Mar 26, 2009 (4th): By Erik Branger / GGNFS, Msieve / Mar 26, 2009
(47·10¹⁵⁵+7)/9 = 5(2)₁₅₄3_<156> = 13 · 19 · 48779 · 1340071 · 49118467 · C135
C135 = P37 · P37 · P63
P37 = 1057730668417200572838874936212859657_<37>
P37 = 5105488992144329951453710753573117397_<37>
P63 = 121938387829153761107662905698626411651559749568993099534450107_<63>

Number: 52223_155 N=658495618645305733221984821404460863586812480725034488110267055018883740631864279001729002904992935850854797600803454626685203897402703 ( 135 digits) SNFS difficulty: 156 digits. Divisors found: r1=1057730668417200572838874936212859657 r2=5105488992144329951453710753573117397 r3=121938387829153761107662905698626411651559749568993099534450107 Version: Total time: 25.04 hours. Scaled time: 25.71 units (timescale=1.027). Factorization parameters were as follows: n: 658495618645305733221984821404460863586812480725034488110267055018883740631864279001729002904992935850854797600803454626685203897402703 m: 10000000000000000000000000000000 deg: 5 c5: 47 c0: 7 skew: 0.68 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1450000, 2350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 521816 x 522064 Total sieving time: 25.04 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,156,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000 total time: 25.04 hours. --------- CPU info (if available) ----------
(49·10¹²⁶+41)/9 = 5(4)₁₂₅9_<127> = C127
C127 = P50 · P77
P50 = 89509726479899433582217775103987526302712114761893_<50>
P77 = 60825171280878227682314694429796797662398614282260359785768606811199736018893_<77>

Number: 54449_126 N=5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 ( 127 digits) SNFS difficulty: 127 digits. Divisors found: r1=89509726479899433582217775103987526302712114761893 r2=60825171280878227682314694429796797662398614282260359785768606811199736018893 Version: Total time: 3.13 hours. Scaled time: 2.97 units (timescale=0.948). Factorization parameters were as follows: n: 5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 m: 10000000000000000000000000 deg: 5 c5: 490 c0: 41 skew: 0.61 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [500000, 900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 149326 x 149573 Total sieving time: 3.13 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,127,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,46,46,2.3,2.3,50000 total time: 3.13 hours. --------- CPU info (if available) ----------
(49·10¹⁰⁷+23)/9 = 5(4)₁₀₆7_<108> = 17 · 412784461 · C98
C98 = P47 · P52
P47 = 63256444323242069473713196879638132828513180833_<47>
P52 = 1226525361201857409856065873971323956702057027360907_<52>

Number: 54447_107 N=77585633221909661959427244730918590129384517933033400072176771385787737729509559518669570045895531 ( 98 digits) SNFS difficulty: 109 digits. Divisors found: r1=63256444323242069473713196879638132828513180833 r2=1226525361201857409856065873971323956702057027360907 Version: Total time: 1.22 hours. Scaled time: 0.96 units (timescale=0.787). Factorization parameters were as follows: n: 77585633221909661959427244730918590129384517933033400072176771385787737729509559518669570045895531 m: 2000000000000000000000 deg: 5 c5: 1225 c0: 184 skew: 0.68 type: snfs lss: 1 rlim: 470000 alim: 470000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 470000/470000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [235000, 385001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 50478 x 50708 Total sieving time: 1.22 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,109,5,0,0,0,0,0,0,0,0,470000,470000,25,25,44,44,2.2,2.2,50000 total time: 1.22 hours. --------- CPU info (if available) ----------
(49·10¹⁴²+23)/9 = 5(4)₁₄₁7_<143> = 3³ · 59 · 347 · 883 · 2606809451_<10> · 10974894967_<11> · C115
C115 = P48 · P67
P48 = 422487548822494189048430737716463004689438550629_<48>
P67 = 9228349684211586458646457759478541784731866561768689933021851095303_<67>

Number: 54447_142 N=3898862837759391465874496029507318729058503037759396950405744980149335186198631726209810851867165775544356469595587 ( 115 digits) SNFS difficulty: 144 digits. Divisors found: r1=422487548822494189048430737716463004689438550629 r2=9228349684211586458646457759478541784731866561768689933021851095303 Version: Total time: 10.83 hours. Scaled time: 10.74 units (timescale=0.992). Factorization parameters were as follows: n: 3898862837759391465874496029507318729058503037759396950405744980149335186198631726209810851867165775544356469595587 m: 20000000000000000000000000000 deg: 5 c5: 1225 c0: 184 skew: 0.68 type: snfs lss: 1 rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [900000, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 298355 x 298603 Total sieving time: 10.83 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,144,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,100000 total time: 10.83 hours. --------- CPU info (if available) ----------
(49·10¹³⁶+41)/9 = 5(4)₁₃₅9_<137> = 9257 · C133
C133 = P47 · P86
P47 = 71304781245914521607230391735935498351049913551_<47>
P86 = 82483039249126102767427949027373155037745463880624218563063734706630914560237529727607_<86>

Number: 54449_136 N=5881435070157118336874197304142210699410656200112827529917299821156362152365177103213184016900123630165760445548713886188229928102457 ( 133 digits) SNFS difficulty: 137 digits. Divisors found: r1=71304781245914521607230391735935498351049913551 r2=82483039249126102767427949027373155037745463880624218563063734706630914560237529727607 Version: Total time: 8.16 hours. Scaled time: 6.41 units (timescale=0.786). Factorization parameters were as follows: n: 5881435070157118336874197304142210699410656200112827529917299821156362152365177103213184016900123630165760445548713886188229928102457 m: 1000000000000000000000000000 deg: 5 c5: 490 c0: 41 skew: 0.61 type: snfs lss: 1 rlim: 1380000 alim: 1380000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1380000/1380000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [690000, 1515001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 242546 x 242794 Total sieving time: 8.16 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,137,5,0,0,0,0,0,0,0,0,1380000,1380000,26,26,48,48,2.3,2.3,75000 total time: 8.16 hours. --------- CPU info (if available) ----------
Mar 26, 2009 (3rd): By Robert Backstrom / Msieve, GGNFS, GMP-ECM / Mar 26, 2009
(49·10¹⁵⁴+41)/9 = 5(4)₁₅₃9_<155> = 111227 · 30989490023981_<14> · 19438696293455187099283_<23> · 4709579273971574805918139_<25> · C90
C90 = P35 · P55
P35 = 85398388677124700509979518851635059_<35>
P55 = 2020365738813114803260409765581225522390963662391877669_<55>

Thu Mar 26 03:57:27 2009 Thu Mar 26 03:57:27 2009 Thu Mar 26 03:57:27 2009 Msieve v. 1.39 Thu Mar 26 03:57:27 2009 random seeds: 3388a570 6268f5cc Thu Mar 26 03:57:27 2009 factoring 172535978633108583271830002807599001693998076198225974666984044214182960439546361759597471 (90 digits) Thu Mar 26 03:57:28 2009 searching for 15-digit factors Thu Mar 26 03:57:29 2009 commencing quadratic sieve (90-digit input) Thu Mar 26 03:57:29 2009 using multiplier of 21 Thu Mar 26 03:57:29 2009 using 64kb Opteron sieve core Thu Mar 26 03:57:29 2009 sieve interval: 18 blocks of size 65536 Thu Mar 26 03:57:29 2009 processing polynomials in batches of 6 Thu Mar 26 03:57:29 2009 using a sieve bound of 1573577 (59667 primes) Thu Mar 26 03:57:29 2009 using large prime bound of 125886160 (26 bits) Thu Mar 26 03:57:29 2009 using double large prime bound of 380154676666640 (42-49 bits) Thu Mar 26 03:57:29 2009 using trial factoring cutoff of 49 bits Thu Mar 26 03:57:29 2009 polynomial 'A' values have 12 factors Thu Mar 26 04:57:17 2009 60155 relations (15845 full + 44310 combined from 635792 partial), need 59763 Thu Mar 26 04:57:18 2009 begin with 651637 relations Thu Mar 26 04:57:19 2009 reduce to 146951 relations in 10 passes Thu Mar 26 04:57:19 2009 attempting to read 146951 relations Thu Mar 26 04:57:20 2009 recovered 146951 relations Thu Mar 26 04:57:20 2009 recovered 127740 polynomials Thu Mar 26 04:57:20 2009 attempting to build 60155 cycles Thu Mar 26 04:57:20 2009 found 60155 cycles in 5 passes Thu Mar 26 04:57:21 2009 distribution of cycle lengths: Thu Mar 26 04:57:21 2009 length 1 : 15845 Thu Mar 26 04:57:21 2009 length 2 : 11577 Thu Mar 26 04:57:21 2009 length 3 : 10639 Thu Mar 26 04:57:21 2009 length 4 : 8071 Thu Mar 26 04:57:21 2009 length 5 : 5683 Thu Mar 26 04:57:21 2009 length 6 : 3657 Thu Mar 26 04:57:21 2009 length 7 : 2161 Thu Mar 26 04:57:21 2009 length 9+: 2522 Thu Mar 26 04:57:21 2009 largest cycle: 18 relations Thu Mar 26 04:57:21 2009 matrix is 59667 x 60155 (15.0 MB) with weight 3692255 (61.38/col) Thu Mar 26 04:57:21 2009 sparse part has weight 3692255 (61.38/col) Thu Mar 26 04:57:22 2009 filtering completed in 3 passes Thu Mar 26 04:57:22 2009 matrix is 55810 x 55874 (13.9 MB) with weight 3430899 (61.40/col) Thu Mar 26 04:57:22 2009 sparse part has weight 3430899 (61.40/col) Thu Mar 26 04:57:22 2009 saving the first 48 matrix rows for later Thu Mar 26 04:57:22 2009 matrix is 55762 x 55874 (8.9 MB) with weight 2702698 (48.37/col) Thu Mar 26 04:57:22 2009 sparse part has weight 1988182 (35.58/col) Thu Mar 26 04:57:22 2009 matrix includes 64 packed rows Thu Mar 26 04:57:22 2009 using block size 22349 for processor cache size 1024 kB Thu Mar 26 04:57:22 2009 commencing Lanczos iteration Thu Mar 26 04:57:22 2009 memory use: 8.5 MB Thu Mar 26 04:57:40 2009 lanczos halted after 883 iterations (dim = 55760) Thu Mar 26 04:57:40 2009 recovered 18 nontrivial dependencies Thu Mar 26 04:57:40 2009 prp35 factor: 85398388677124700509979518851635059 Thu Mar 26 04:57:40 2009 prp55 factor: 2020365738813114803260409765581225522390963662391877669 Thu Mar 26 04:57:40 2009 elapsed time 01:00:13
(49·10¹¹⁷+41)/9 = 5(4)₁₁₆9_<118> = 59 · 71 · 863 · 2411 · 3142187 · 11039507 · C95
C95 = P42 · P53
P42 = 336604968389700345229006632632467724043359_<42>
P53 = 53497436933044664478816389244926048170274046484553327_<53>

Thu Mar 26 12:17:04 2009 Thu Mar 26 12:17:04 2009 Thu Mar 26 12:17:04 2009 Msieve v. 1.39 Thu Mar 26 12:17:04 2009 random seeds: 51e810a4 dba85ca5 Thu Mar 26 12:17:04 2009 factoring 18007503067777487071137242913972238984183195788228068696022682661075151599635220265841495705393 (95 digits) Thu Mar 26 12:17:04 2009 searching for 15-digit factors Thu Mar 26 12:17:05 2009 commencing quadratic sieve (95-digit input) Thu Mar 26 12:17:05 2009 using multiplier of 17 Thu Mar 26 12:17:05 2009 using 64kb Opteron sieve core Thu Mar 26 12:17:05 2009 sieve interval: 18 blocks of size 65536 Thu Mar 26 12:17:05 2009 processing polynomials in batches of 6 Thu Mar 26 12:17:05 2009 using a sieve bound of 2117273 (78824 primes) Thu Mar 26 12:17:05 2009 using large prime bound of 309121858 (28 bits) Thu Mar 26 12:17:05 2009 using double large prime bound of 1915285337885478 (43-51 bits) Thu Mar 26 12:17:05 2009 using trial factoring cutoff of 51 bits Thu Mar 26 12:17:05 2009 polynomial 'A' values have 12 factors Thu Mar 26 14:53:41 2009 78965 relations (19422 full + 59543 combined from 1158503 partial), need 78920 Thu Mar 26 14:53:43 2009 begin with 1177925 relations Thu Mar 26 14:53:44 2009 reduce to 204547 relations in 11 passes Thu Mar 26 14:53:44 2009 attempting to read 204547 relations Thu Mar 26 14:53:47 2009 recovered 204547 relations Thu Mar 26 14:53:47 2009 recovered 189076 polynomials Thu Mar 26 14:53:47 2009 attempting to build 78965 cycles Thu Mar 26 14:53:47 2009 found 78965 cycles in 5 passes Thu Mar 26 14:53:48 2009 distribution of cycle lengths: Thu Mar 26 14:53:48 2009 length 1 : 19422 Thu Mar 26 14:53:48 2009 length 2 : 13884 Thu Mar 26 14:53:48 2009 length 3 : 13302 Thu Mar 26 14:53:48 2009 length 4 : 10834 Thu Mar 26 14:53:48 2009 length 5 : 8180 Thu Mar 26 14:53:48 2009 length 6 : 5355 Thu Mar 26 14:53:48 2009 length 7 : 3494 Thu Mar 26 14:53:48 2009 length 9+: 4494 Thu Mar 26 14:53:48 2009 largest cycle: 20 relations Thu Mar 26 14:53:48 2009 matrix is 78824 x 78965 (21.3 MB) with weight 5257190 (66.58/col) Thu Mar 26 14:53:48 2009 sparse part has weight 5257190 (66.58/col) Thu Mar 26 14:53:49 2009 filtering completed in 4 passes Thu Mar 26 14:53:49 2009 matrix is 75072 x 75136 (20.4 MB) with weight 5039369 (67.07/col) Thu Mar 26 14:53:49 2009 sparse part has weight 5039369 (67.07/col) Thu Mar 26 14:53:49 2009 saving the first 48 matrix rows for later Thu Mar 26 14:53:49 2009 matrix is 75024 x 75136 (13.8 MB) with weight 4076805 (54.26/col) Thu Mar 26 14:53:49 2009 sparse part has weight 3163131 (42.10/col) Thu Mar 26 14:53:49 2009 matrix includes 64 packed rows Thu Mar 26 14:53:49 2009 using block size 30054 for processor cache size 1024 kB Thu Mar 26 14:53:50 2009 commencing Lanczos iteration Thu Mar 26 14:53:50 2009 memory use: 12.7 MB Thu Mar 26 14:54:31 2009 lanczos halted after 1188 iterations (dim = 75022) Thu Mar 26 14:54:32 2009 recovered 16 nontrivial dependencies Thu Mar 26 14:54:33 2009 prp42 factor: 336604968389700345229006632632467724043359 Thu Mar 26 14:54:33 2009 prp53 factor: 53497436933044664478816389244926048170274046484553327 Thu Mar 26 14:54:33 2009 elapsed time 02:37:29
(49·10¹⁶⁶-13)/9 = 5(4)₁₆₅3_<167> = 3392460707_<10> · C158
C158 = P39 · P119
P39 = 228606663332069098898658208677726772027_<39>
P119 = 70202060540836190435027353842202723932903383646206976045490228370900250805488572773763887061548507188806030834957521387_<119>

Number: n N=16048658819276471709608645570215131881391734700037144584809613962743075168193670826338164701532811134323462171331921176012737955182584357769083055276325841449 ( 158 digits) SNFS difficulty: 167 digits. Divisors found: Thu Mar 26 15:24:14 2009 prp39 factor: 228606663332069098898658208677726772027 Thu Mar 26 15:24:14 2009 prp119 factor: 70202060540836190435027353842202723932903383646206976045490228370900250805488572773763887061548507188806030834957521387 Thu Mar 26 15:24:14 2009 elapsed time 01:17:51 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 46.22 hours. Scaled time: 122.94 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_4_165_3 n: 16048658819276471709608645570215131881391734700037144584809613962743075168193670826338164701532811134323462171331921176012737955182584357769083055276325841449 skew: 0.48 deg: 5 c5: 490 c0: -13 m: 1000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 5400709) Primes: RFBsize:348513, AFBsize:347801, largePrimes:16583950 encountered Relations: rels:15857481, finalFF:721908 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1654776 hash collisions in 17166877 relations Msieve: matrix is 879243 x 879491 (235.5 MB) Total sieving time: 45.64 hours. Total relation processing time: 0.58 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 46.22 hours. --------- CPU info (if available) ----------
(49·10¹⁷⁷+41)/9 = 5(4)₁₇₆9_<178> = 131 · 191 · 449 · 331391 · 472840087 · 726941215300706671579_<21> · 2433838839766455950342062363_<28> · C109
C109 = P35 · P74
P35 = 83034203406922062183051715629104539_<35>
P74 = 21052294409786281603774327103314927783566223455754104095544829887091074031_<74>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 1748060496204602348217928342045955454659092137537713587969915638714670667753586844090191544518365344287126709 (109 digits) Using B1=720000, B2=696728352, polynomial Dickson(3), sigma=2714175444 Step 1 took 7176ms Step 2 took 2964ms ********** Factor found in step 2: 83034203406922062183051715629104539 Found probable prime factor of 35 digits: 83034203406922062183051715629104539 Probable prime cofactor 21052294409786281603774327103314927783566223455754104095544829887091074031 has 74 digits
(49·10¹³³+41)/9 = 5(4)₁₃₂9_<134> = 1847 · 17191 · 15928399 · 2569725611564596134156953_<25> · C95
C95 = P38 · P58
P38 = 31123736301946053601072239401392732729_<38>
P58 = 1345968600983785417249315598989980743105211831323133158399_<58>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 41891571807718584945127829778318507717751879939979549720467854224774931298243603645127428540871 (95 digits) Using B1=1538000, B2=2140123450, polynomial Dickson(6), sigma=100538867 Step 1 took 9438ms Step 2 took 5125ms ********** Factor found in step 2: 31123736301946053601072239401392732729 Found probable prime factor of 38 digits: 31123736301946053601072239401392732729 Probable prime cofactor 1345968600983785417249315598989980743105211831323133158399 has 58 digits
Mar 26, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.40 / Mar 26, 2009
(49·10¹⁷⁹+23)/9 = 5(4)₁₇₈7_<180> = 31 · 263 · C176
C176 = P32 · C145
P32 = 49019269914862359235884231368959_<32>
C145 = [1362289124694138590647084383486475677068698804342845520947990557153490588446492978754390220171132857402672722825249805305208753255232760139820361_<145>]

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=2685186263 Step 1 took 7737ms Step 2 took 5812ms ********** Factor found in step 2: 49019269914862359235884231368959 Found probable prime factor of 32 digits: 49019269914862359235884231368959 Composite cofactor has 145 digits
(49·10¹⁸⁰+23)/9 = 5(4)₁₇₉7_<181> = 14699 · 1856297 · 10162351 · 176396963 · 395885210069_<12> · 93495456952771_<14> · C130
C130 = P32 · P99
P32 = 19570989095089334341692051382711_<32>
P99 = 153659870377095098863641301496034790203531138412155043393272991554591626364446428220183087152397057_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=148828922 Step 1 took 7357ms Step 2 took 7044ms ********** Factor found in step 2: 19570989095089334341692051382711 Found probable prime factor of 32 digits: 19570989095089334341692051382711 Probable prime cofactor has 99 digits
(49·10¹⁶⁹+23)/9 = 5(4)₁₆₈7_<170> = 3³ · 7757 · C165
C165 = P33 · P133
P33 = 124536554543997314979024046350781_<33>
P133 = 2087368708499167158827513265956753940583325925005520026107942223059166689438339761676704306516497762484131504693365842596878578550933_<133>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=934136197 Step 1 took 9996ms Step 2 took 8941ms ********** Factor found in step 2: 124536554543997314979024046350781 Found probable prime factor of 33 digits: 124536554543997314979024046350781 Probable prime cofactor has 133 digits
(49·10¹⁸¹+23)/9 = 5(4)₁₈₀7_<182> = 3 · 19 · 25343 · 4898143973671943075533_<22> · C154
C154 = P30 · C125
P30 = 165703440094533134905772423687_<30>
C125 = [46436301276070201899460398906248605364338025400814138874003744066901307471773211792610214257185020149990475282233636591208907_<125>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=946105213 Step 1 took 9201ms Step 2 took 7804ms ********** Factor found in step 2: 165703440094533134905772423687 Found probable prime factor of 30 digits: 165703440094533134905772423687 Composite cofactor has 125 digits
(49·10¹⁹⁰+23)/9 = 5(4)₁₈₉7_<191> = 3 · 64109 · 4225530117516618479761_<22> · C164
C164 = P39 · P126
P39 = 220761939500028598302869393980575061631_<39>
P126 = 303464512073770648945878490978300439558503103582063123665138950766375927106303506145444934484669950085539836507940085379564071_<126>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2573314229 Step 1 took 9876ms Step 2 took 8681ms ********** Factor found in step 2: 220761939500028598302869393980575061631 Found probable prime factor of 39 digits: 220761939500028598302869393980575061631 Probable prime cofactor has 126 digits
(49·10¹²⁵+41)/9 = 5(4)₁₂₄9_<126> = 3 · 661439 · 3876997 · 4170227 · C107
C107 = P32 · P75
P32 = 74576531666662530089711767310951_<32>
P75 = 227554367291850453101197310205051455465156475107583107302535931180466407613_<75>

SNFS difficulty: 126 digits. Divisors found: r1=74576531666662530089711767310951 (pp32) r2=227554367291850453101197310205051455465156475107583107302535931180466407613 (pp75) Version: Msieve-1.39 Total time: 1.26 hours. Scaled time: 3.56 units (timescale=2.838). Factorization parameters were as follows: n: 16970215478228041594814063236791347986814014122707645679199223191602665685124329148314728537601692084669963 m: 10000000000000000000000000 deg: 5 c5: 49 c0: 41 skew: 0.96 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved special-q in [450000, 450000) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 112947 x 113192 Total sieving time: 1.26 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,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 1.26 hours.
(49·10¹²¹+23)/9 = 5(4)₁₂₀7_<122> = 3 · 15083 · 52627 · 1866461 · 2198407 · C100
C100 = P37 · P63
P37 = 7124603840479919365732898437556681717_<37>
P63 = 782074692248656594203654067738974568526834648445247639018273171_<63>

SNFS difficulty: 123 digits. Divisors found: r1=7124603840479919365732898437556681717 (pp37) r2=782074692248656594203654067738974568526834648445247639018273171 (pp63) Version: Msieve-1.39 Total time: 1.06 hours. Scaled time: 3.02 units (timescale=2.840). Factorization parameters were as follows: n: 5571972355936929796164402527839661785202415009775857808001397525490794471008880872643822230207314607 m: 2000000000000000000000000 deg: 5 c5: 245 c0: 368 skew: 1.08 type: snfs lss: 1 rlim: 810000 alim: 810000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 810000/810000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [405000, 905001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 90728 x 90976 Total sieving time: 1.06 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,123,5,0,0,0,0,0,0,0,0,810000,810000,25,25,46,46,2.2,2.2,50000 total time: 1.06 hours.
(49·10¹²⁸+23)/9 = 5(4)₁₂₇7_<129> = 5791 · 16451 · C121
C121 = P38 · P84
P38 = 13430260892711496624143275808375396407_<38>
P84 = 425523210547380281621608549880770539602816541215414945259160078414911239467806700781_<84>

SNFS difficulty: 131 digits. Divisors found: r1=13430260892711496624143275808375396407 (pp38) r2=425523210547380281621608549880770539602816541215414945259160078414911239467806700781 (pp84) Version: Msieve-1.40 Total time: 1.50 hours. Scaled time: 4.25 units (timescale=2.840). Factorization parameters were as follows: n: 5714887733555521637113705093988157486010342624209431442742454074191225384933231957756240325300087092906343233691711493867 m: 50000000000000000000000000 deg: 5 c5: 392 c0: 575 skew: 1.08 type: snfs lss: 1 rlim: 1070000 alim: 1070000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor 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, 1135001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 134952 x 135200 Total sieving time: 1.50 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: 1.50 hours.
Mar 26, 2009: By 10metreh / GMP-ECM 6.2.1 / Mar 26, 2009
(49·10¹³⁵+23)/9 = 5(4)₁₃₄7_<136> = 13 · 15551 · C131
C131 = P34 · P98
P34 = 1005344693062810933520912027258803_<34>
P98 = 26787791325737202548916567410163297961651803940100230936923958001195768311232370875084900124086023_<98>

Factored with Markus Tervooren's wonderful database workers in just a few minutes! 26930963848203897075352287235767397814854570047162163424783192000734280973493885846789197056060923336339708277204258170112456010469 = 1005344693062810933520912027258803 * 26787791325737202548916567410163297961651803940100230936923958001195768311232370875084900124086023
Mar 25, 2009 (4th): By Robert Backstrom / GGNFS, Msieve / Mar 25, 2009
(49·10¹⁵⁹-13)/9 = 5(4)₁₅₈3_<160> = 2428024769_<10> · C151
C151 = P63 · P88
P63 = 601351575708202483414719598577935244714095030835679564985254607_<63>
P88 = 3728825024421394506143678851589601389969611659833649468122314998192459819730376930996021_<88>

Number: n N=2242334803975982192480032498566510482103094412231856620093830865052614479504284020936379683383882499612360603741618767829153247177786284125194788918747 ( 151 digits) SNFS difficulty: 161 digits. Divisors found: Wed Mar 25 17:13:26 2009 prp63 factor: 601351575708202483414719598577935244714095030835679564985254607 Wed Mar 25 17:13:26 2009 prp88 factor: 3728825024421394506143678851589601389969611659833649468122314998192459819730376930996021 Wed Mar 25 17:13:26 2009 elapsed time 00:56:02 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 25.50 hours. Scaled time: 67.54 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_4_158_3 n: 2242334803975982192480032498566510482103094412231856620093830865052614479504284020936379683383882499612360603741618767829153247177786284125194788918747 skew: 1.22 deg: 5 c5: 49 c0: -130 m: 100000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 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 [100000, 3700049) Primes: RFBsize:283146, AFBsize:283762, largePrimes:14472488 encountered Relations: rels:13551879, finalFF:611318 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1159398 hash collisions in 14440877 relations Msieve: matrix is 697476 x 697724 (187.1 MB) Total sieving time: 25.15 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.4,2.4,100000 total time: 25.50 hours. --------- CPU info (if available) ----------
(49·10¹⁶⁵-13)/9 = 5(4)₁₆₄3_<166> = 21685402247_<11> · C156
C156 = P77 · P80
P77 = 14324711689563372779335680404766103636224125956636359995327793344470127538869_<77>
P80 = 17526701832941984245416388922140767102049667569465043187924398853225270451740601_<80>

Number: n N=251064950625835833703382280840771182234664703586415536986577735970020000544583139843679582377840521338633043270402953869839020673640559582673460585332920269 ( 156 digits) SNFS difficulty: 166 digits. Divisors found: Wed Mar 25 22:46:33 2009 prp77 factor: 14324711689563372779335680404766103636224125956636359995327793344470127538869 Wed Mar 25 22:46:33 2009 prp80 factor: 17526701832941984245416388922140767102049667569465043187924398853225270451740601 Wed Mar 25 22:46:33 2009 elapsed time 01:28:09 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 30.41 hours. Scaled time: 80.57 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_4_164_3 n: 251064950625835833703382280840771182234664703586415536986577735970020000544583139843679582377840521338633043270402953869839020673640559582673460585332920269 skew: 0.77 deg: 5 c5: 49 c0: -13 m: 1000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 4400587) Primes: RFBsize:348513, AFBsize:348526, largePrimes:15470826 encountered Relations: rels:14467287, finalFF:713923 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1171408 hash collisions in 15321624 relations Msieve: matrix is 838936 x 839183 (226.7 MB) Total sieving time: 30.00 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 30.41 hours. --------- CPU info (if available) ----------
Mar 25, 2009 (3rd): By Erik Branger / GGNFS, Msieve / Mar 25, 2009
(47·10¹⁵⁴+43)/9 = 5(2)₁₅₃7_<155> = 3 · 7 · 217015951 · 23192531703414525073_<20> · C126
C126 = P49 · P78
P49 = 1465580419519146912565525021259863883123452963969_<49>
P78 = 337121603846980406888182918563839484405915367888409034254610751275644373799801_<78>

Number: 52227_154 N=494078821595025196408271508880661445720441071385869313691441666275744356652202763243018257244781008472892898153247400472370169 ( 126 digits) SNFS difficulty: 156 digits. Divisors found: r1=1465580419519146912565525021259863883123452963969 r2=337121603846980406888182918563839484405915367888409034254610751275644373799801 Version: Total time: 34.14 hours. Scaled time: 33.66 units (timescale=0.986). Factorization parameters were as follows: n: 494078821595025196408271508880661445720441071385869313691441666275744356652202763243018257244781008472892898153247400472370169 m: 10000000000000000000000000000000 deg: 5 c5: 47 c0: 430 skew: 1.56 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1450000, 2750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 556521 x 556769 Total sieving time: 34.14 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,156,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000 total time: 34.14 hours. --------- CPU info (if available) ----------
Mar 25, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Mar 25, 2009
(47·10¹⁶⁸-11)/9 = 5(2)₁₆₇1_<169> = 42953 · 632473 · C159
C159 = P77 · P82
P77 = 93041312338394025755066831403637404825315085178858933751516025618646156596093_<77>
P82 = 2066065228441269232877887311452109654918977329340570718751096746897800608390142513_<82>

Number: 52221_168 N=192229420230899534496995068580248964574999947142737668924522307723339501553382715800958683080724049548225892858355344941318481757986963936844497016735249001709 ( 159 digits) SNFS difficulty: 171 digits. Divisors found: r1=93041312338394025755066831403637404825315085178858933751516025618646156596093 (pp77) r2=2066065228441269232877887311452109654918977329340570718751096746897800608390142513 (pp82) Version: Msieve-1.39 Total time: 57.84 hours. Scaled time: 148.72 units (timescale=2.571). Factorization parameters were as follows: n: 192229420230899534496995068580248964574999947142737668924522307723339501553382715800958683080724049548225892858355344941318481757986963936844497016735249001709 m: 5000000000000000000000000000000000 deg: 5 c5: 376 c0: -275 skew: 0.94 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, 5300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 913109 x 913357 Total sieving time: 57.84 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 57.84 hours. --------- CPU info (if available) ----------
(4·10²⁴¹-1)/3 = 1(3)₂₄₁_<242> = 13 · 3784757 · 4646801 · 183261467 · 52651626410827_<14> · 3917565792818569_<16> · 9984057494986111353041_<22> · 423978422171785937525330791300274672892443_<42> · C126
C126 = P44 · P82
P44 = 56919955399919399921032613355018851582842693_<44>
P82 = 6403076371209830662961764899764369901555755044549161602051092579478800140181888067_<82>

Number: 13333_241 N=364462821471541316916182370125769150792316542042148094133332048440810743632250528660469332549245321864282313669340167794844431 ( 126 digits) Divisors found: r1=56919955399919399921032613355018851582842693 (pp44) r2=6403076371209830662961764899764369901555755044549161602051092579478800140181888067 (pp82) Version: Msieve-1.39 Total time: 90.96 hours. Scaled time: 158.17 units (timescale=1.739). Factorization parameters were as follows: name: 13333_241 n: 364462821471541316916182370125769150792316542042148094133332048440810743632250528660469332549245321864282313669340167794844431 skew: 104881.74 # norm 1.56e+017 c5: 68280 c4: 20246049836 c3: 1031581154766598 c2: -149265930358695771868 c1: 3984915003571139614187031 c0: -123380521066506364881614258895 # alpha -5.78 Y1: 13341754081406329 Y0: -1397095912174927126195306 # Murphy_E 1.34e-010 # M 234978542453448223942047299040150843515415198217211451624943835103861081502650739162475339104672263335331634329759394120672071 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, 8200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1001662 x 1001910 Total sieving time: 90.96 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: gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,27,27,51,51,2.5,2.5,100000 total time: 90.96 hours. --------- CPU info (if available) ----------
Mar 25, 2009: Factorizations of 544...447 and Factorizations of 544...449 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.
Mar 24, 2009 (5th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 24, 2009
(47·10¹⁷⁰+43)/9 = 5(2)₁₆₉7_<171> = 397² · 12821581 · 709741139417_<12> · 2301500138073341378612732863_<28> · C120
C120 = P51 · P69
P51 = 480083270638162015012277626457696051905424961830297_<51>
P69 = 329537769239250933349558669210841259940463368184107656991978047362249_<69>

Number: n N=158205570055183487273379513322996014641789534534660875883619430317468638627535936866361100062189469901987850488022257953 ( 120 digits) Divisors found: r1=480083270638162015012277626457696051905424961830297 (pp51) r2=329537769239250933349558669210841259940463368184107656991978047362249 (pp69) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 39.86 hours. Scaled time: 106.47 units (timescale=2.671). Factorization parameters were as follows: name: KA_5_2_169_7 n: 158205570055183487273379513322996014641789534534660875883619430317468638627535936866361100062189469901987850488022257953 skew: 55677.21 # norm 2.84e+16 c5: 59400 c4: -15665912550 c3: -807592077619909 c2: 33222887004005503474 c1: 931840140544419999583792 c0: -24071922341916760519440992512 # alpha -6.24 Y1: 242445705203 Y0: -76751546911839328392471 # Murphy_E 3.27e-10 # M 1685311989380475577265181398064331751532813417905642689191093594604343860789446220243040490401329161826299123753053845 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4230001) Primes: RFBsize:315948, AFBsize:315721, largePrimes:7686811 encountered Relations: rels:7783655, finalFF:763522 Max relations in full relation-set: 28 Initial matrix: 631751 x 763522 with sparse part having weight 65387348. Pruned matrix : 522836 x 526058 with weight 41896142. Polynomial selection time: 5.21 hours. Total sieving time: 32.60 hours. Total relation processing time: 0.29 hours. Matrix solve time: 1.50 hours. Total square root time: 0.27 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 39.86 hours. --------- CPU info (if available) ----------
(47·10²⁰⁴+7)/9 = 5(2)₂₀₃3_<205> = 3² · C204
C204 = P56 · P149
P56 = 32435427185289642780743836726941466290571494203044552823_<56>
P149 = 17889294636557302013414769601901685301211205126351365730228586586267267345613074310366048610450327741439568237044298792141368152216691075010970173089_<149>

Number: n N=580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247 ( 204 digits) SNFS difficulty: 206 digits. Divisors found: Tue Mar 24 14:41:42 2009 prp56 factor: 32435427185289642780743836726941466290571494203044552823 Tue Mar 24 14:41:42 2009 prp149 factor: 17889294636557302013414769601901685301211205126351365730228586586267267345613074310366048610450327741439568237044298792141368152216691075010970173089 Tue Mar 24 14:41:42 2009 elapsed time 25:05:37 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 157.28 hours. Scaled time: 317.07 units (timescale=2.016). Factorization parameters were as follows: name: KA_5_2_203_3 n: 580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247 deg: 5 c5: 47 c0: 70 m: 100000000000000000000000000000000000000000 skew: 1.08 type: snfs rlim: 12000000 alim: 12000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [6000000, 9099990) Primes: RFBsize:788060, AFBsize:788074, largePrimes:37054617 encountered Relations: rels:31751478, finalFF:79075 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 9063074 hash collisions in 46888137 relations Msieve: matrix is 3779800 x 3780048 (1027.0 MB) Total sieving time: 156.12 hours. Total relation processing time: 1.15 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,206,5,0,0,0,0,0,0,0,0,12000000,12000000,29,29,58,58,2.5,2.5,100000 total time: 157.28 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).
(47·10¹⁶²+7)/9 = 5(2)₁₆₁3_<163> = 3 · 83 · 28447 · 59910937 · C149
C149 = P33 · P37 · P79
P33 = 677169855882163806082378185483179_<33>
P37 = 5496731340466694320360386942697835693_<37>
P79 = 3306064243695495188858715370392906167979916663834620388391227511084523258179119_<79>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 12305900993670026619980338207680961830364582789630242898677969682151698305106408426947801975811893341357262263082403247088756161137232942831386070593 (149 digits) Using B1=1448000, B2=2140044280, polynomial Dickson(6), sigma=344506990 Step 1 took 22198ms Step 2 took 8736ms ********** Factor found in step 2: 677169855882163806082378185483179 Found probable prime factor of 33 digits: 677169855882163806082378185483179 Composite cofactor 18172546941917347226698165407954137115963849562056879758917105037777316590135405923860492225765462654110141425494467 has 116 digits GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 18172546941917347226698165407954137115963849562056879758917105037777316590135405923860492225765462654110141425494467 (116 digits) Using B1=3640000, B2=8561127130, polynomial Dickson(6), sigma=2816991832 Step 1 took 36332ms Step 2 took 14227ms ********** Factor found in step 2: 5496731340466694320360386942697835693 Found probable prime factor of 37 digits: 5496731340466694320360386942697835693 Probable prime cofactor 3306064243695495188858715370392906167979916663834620388391227511084523258179119 has 79 digits
Mar 24, 2009 (4th): By Ignacio Santos / GGNFS, Msieve / Mar 24, 2009
(49·10¹⁹⁹-13)/9 = 5(4)₁₉₈3_<200> = 1913 · 4583 · 5882926056937_<13> · 1218401765880031784578024309927_<31> · 4907818000181670992135063669683_<31> · C120
C120 = P54 · P66
P54 = 382862862267837988347685597468140406206315789449064437_<54>
P66 = 461076664664287937538598147921472880754573683407889104041697315173_<66>

Number: 54443_199 N=176529131558277395295848214656542631892093690847442977004772986008117440783537228870033700974644012582018395859574802601 ( 120 digits) Divisors found: r1=382862862267837988347685597468140406206315789449064437 (pp54) r2=461076664664287937538598147921472880754573683407889104041697315173 (pp66) Version: Msieve-1.39 Total time: 34.80 hours. Scaled time: 60.38 units (timescale=1.735). Factorization parameters were as follows: name: 54443_199 n: 176529131558277395295848214656542631892093690847442977004772986008117440783537228870033700974644012582018395859574802601 skew: 59649.00 # norm 2.13e+016 c5: 49140 c4: -7417611066 c3: -888921018349013 c2: 25278019887156247159 c1: 886039038126969350535769 c0: -11713735379912792142821591589 # alpha -5.96 Y1: 3967998397231 Y0: -81484852731824154537860 # Murphy_E 3.16e-010 # M 128248013014603672007157954630463537972435946001750055529136290548333258835222509238735059376381621761948624658563372549 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4170001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 637939 x 638187 Total sieving time: 34.80 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,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 34.80 hours. --------- CPU info (if available) ----------
(49·10¹⁵⁷-13)/9 = 5(4)₁₅₆3_<158> = 47 · 53² · 3067 · C150
C150 = P46 · P104
P46 = 3500992370764356766315734545757211678902724333_<46>
P104 = 38405996066735363768333922495487422849558454494069750646053519783449675603954475673158889673318407032931_<104>

Number: 54443_157 N=134459099221246402322816172819154065510441731566376235533720791826155841719807351755353346138400212316515559376872179170380656802454630653643146010023 ( 150 digits) SNFS difficulty: 159 digits. Divisors found: r1=3500992370764356766315734545757211678902724333 (pp46) r2=38405996066735363768333922495487422849558454494069750646053519783449675603954475673158889673318407032931 (pp104) Version: Msieve-1.39 Total time: 27.90 hours. Scaled time: 71.73 units (timescale=2.571). Factorization parameters were as follows: n: 134459099221246402322816172819154065510441731566376235533720791826155841719807351755353346138400212316515559376872179170380656802454630653643146010023 m: 20000000000000000000000000000000 deg: 5 c5: 1225 c0: -104 skew: 0.61 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1600000, 3100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 570062 x 570310 Total sieving time: 27.90 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,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000 total time: 27.90 hours. --------- CPU info (if available) ----------
(16·10¹⁶⁹+17)/3 = 5(3)₁₆₈9_<170> = 25717 · 4507879 · C159
C159 = P36 · P124
P36 = 117980842480867583939408945317682323_<36>
P124 = 3899372097972789414698208696244062153377248699113952186123882034637330975141875979630721018894931532069809165030022672431651_<124>

Number: 53339_169 N=460051205265217827867701313446325309642435347740758774579621175352669685683423258785786058802508686637912682582855982468213333463621214818058817838949948405273 ( 159 digits) SNFS difficulty: 170 digits. Divisors found: r1=117980842480867583939408945317682323 (pp36) r2=3899372097972789414698208696244062153377248699113952186123882034637330975141875979630721018894931532069809165030022672431651 (pp124) Version: Msieve-1.39 Total time: 42.98 hours. Scaled time: 110.50 units (timescale=2.571). Factorization parameters were as follows: n: 460051205265217827867701313446325309642435347740758774579621175352669685683423258785786058802508686637912682582855982468213333463621214818058817838949948405273 m: 10000000000000000000000000000000000 deg: 5 c5: 8 c0: 85 skew: 1.60 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor 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, 4450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 819069 x 819316 Total sieving time: 42.98 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: 42.98 hours. --------- CPU info (if available) ----------
Mar 24, 2009 (3rd): By Erik Branger / GGNFS, Msieve / Mar 24, 2009
(16·10¹⁵³+17)/3 = 5(3)₁₅₂9_<154> = 181 · 35354371022851_<14> · 7978261056929857142957_<22> · C117
C117 = P48 · P69
P48 = 264723415122518858514699565296543054555719138609_<48>
P69 = 394617588357467205736723452214598506058331081720963009624925936387913_<69>

Number: 53339_153 N=104464515657401055928513502186110775732201553600729263450936442463049596896934901716742173064842467251215741239233017 ( 117 digits) SNFS difficulty: 155 digits. Divisors found: r1=264723415122518858514699565296543054555719138609 r2=394617588357467205736723452214598506058331081720963009624925936387913 Version: Total time: 26.42 hours. Scaled time: 20.69 units (timescale=0.783). Factorization parameters were as follows: n: 104464515657401055928513502186110775732201553600729263450936442463049596896934901716742173064842467251215741239233017 m: 4000000000000000000000000000000 deg: 5 c5: 125 c0: 136 skew: 1.02 type: snfs lss: 1 rlim: 2700000 alim: 2700000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2700000/2700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1350000, 2050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 387890 x 388138 Total sieving time: 26.42 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,155,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,50,50,2.4,2.4,100000 total time: 26.42 hours. --------- CPU info (if available) ----------
Mar 24, 2009 (2nd): By Max Dettweiler / GGNFS, msieve v1.40beta2 / Mar 24, 2009
(49·10¹²⁹-13)/9 = 5(4)₁₂₈3_<130> = C130
C130 = P44 · P87
P44 = 20839062423751865311924060808738807499975091_<44>
P87 = 261261487380497348335111454787673218382349317230937862709249245977725305196403288090873_<87>

Number: 54443_129 N=5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 ( 130 digits) SNFS difficulty: 131 digits. Divisors found: r1=20839062423751865311924060808738807499975091 (pp44) r2=261261487380497348335111454787673218382349317230937862709249245977725305196403288090873 (pp87) Version: Msieve-1.39 Total time: 3.19 hours. Scaled time: 5.21 units (timescale=1.633). Factorization parameters were as follows: n: 5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 m: 100000000000000000000000000 deg: 5 c5: 49 c0: -130 skew: 1.22 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 157349 x 157597 Total sieving time: 3.19 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,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 3.19 hours. --------- CPU info (if available) ---------- [ 0.371579] CPU0: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.456481] CPU1: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem) [ 0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.12 BogoMIPS (lpj=8800256) [ 0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800811) [ 0.460049] Total of 2 processors activated (8800.53 BogoMIPS).
Mar 24, 2009: GMP-ECM 6.2.2 has been released
Mar 23, 2009 (5th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 23, 2009
(49·10¹³⁶-13)/9 = 5(4)₁₃₅3_<137> = 79 · 139 · 26881 · 84933809214398144209871_<23> · C106
C106 = P33 · P74
P33 = 125847487970644875553830835870751_<33>
P74 = 17256038650001398282032180042544723209657376815989641751284647004305394703_<74>

Number: n N=2171629116427034008262569406122406716652087870362523529087901011585934547193430581966660132012993748031953 ( 106 digits) SNFS difficulty: 137 digits. Divisors found: Mon Mar 23 03:16:52 2009 prp33 factor: 125847487970644875553830835870751 Mon Mar 23 03:16:52 2009 prp74 factor: 17256038650001398282032180042544723209657376815989641751284647004305394703 Mon Mar 23 03:16:52 2009 elapsed time 00:11:15 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 3.90 hours. Scaled time: 10.37 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_4_135_3 n: 2171629116427034008262569406122406716652087870362523529087901011585934547193430581966660132012993748031953 skew: 0.48 deg: 5 c5: 490 c0: -13 m: 1000000000000000000000000000 type: snfs rlim: 900000 alim: 900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1353901) Primes: RFBsize:71274, AFBsize:71505, largePrimes:6541331 encountered Relations: rels:6007484, finalFF:107350 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 727967 hash collisions in 6710840 relations Msieve: matrix is 176657 x 176893 (45.9 MB) Total sieving time: 3.80 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,137,5,0,0,0,0,0,0,0,0,900000,900000,28,28,56,56,2.4,2.4,75000 total time: 3.90 hours. --------- CPU info (if available) ----------
(49·10¹⁴⁶-13)/9 = 5(4)₁₄₅3_<147> = 3 · 23 · C145
C145 = P65 · P81
P65 = 73830498158509907022394810208166019095040149681165283254334567363_<65>
P81 = 106873167480281185337382613792493068629199332855411315792688634423552805727583669_<81>

Number: n N=7890499194847020933977455716586151368760064412238325281803542673107890499194847020933977455716586151368760064412238325281803542673107890499194847 ( 145 digits) SNFS difficulty: 147 digits. Divisors found: Mon Mar 23 13:37:42 2009 prp65 factor: 73830498158509907022394810208166019095040149681165283254334567363 Mon Mar 23 13:37:42 2009 prp81 factor: 106873167480281185337382613792493068629199332855411315792688634423552805727583669 Mon Mar 23 13:37:42 2009 elapsed time 00:16:47 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 9.42 hours. Scaled time: 25.05 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_4_145_3 n: 7890499194847020933977455716586151368760064412238325281803542673107890499194847020933977455716586151368760064412238325281803542673107890499194847 skew: 0.48 deg: 5 c5: 490 c0: -13 m: 100000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2849741) Primes: RFBsize:114155, AFBsize:114387, largePrimes:9440774 encountered Relations: rels:8881276, finalFF:237685 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1299095 hash collisions in 10127488 relations Msieve: matrix is 296878 x 297126 (77.5 MB) Total sieving time: 9.21 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,56,56,2.4,2.4,100000 total time: 9.42 hours. --------- CPU info (if available) ----------
(47·10¹⁶⁰-11)/9 = 5(2)₁₅₉1_<161> = 3² · 13² · 929 · 615289 · 1614723877096292986341793487631067_<34> · C116
C116 = P55 · P62
P55 = 3417337460494739626420771102558070436997856679143288723_<55>
P62 = 10885418609842797831468671827111280439846804963174619275986981_<62>

Number: n N=37199148788582365677151994359438136376925389872701302600149177581980521614758458078941790703622822529963458072115263 ( 116 digits) Divisors found: Mon Mar 23 18:21:00 2009 prp55 factor: 3417337460494739626420771102558070436997856679143288723 Mon Mar 23 18:21:00 2009 prp62 factor: 10885418609842797831468671827111280439846804963174619275986981 Mon Mar 23 18:21:00 2009 elapsed time 00:43:35 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 21.22 hours. Scaled time: 56.01 units (timescale=2.639). Factorization parameters were as follows: name: KA_5_2_159_1 n: 37199148788582365677151994359438136376925389872701302600149177581980521614758458078941790703622822529963458072115263 skew: 71051.95 # norm 1.50e+16 c5: 31020 c4: -4568203496 c3: -650994879945791 c2: 21226493527766243622 c1: 1134333360693395111011895 c0: -8668750557182613034144373155 # alpha -6.50 Y1: 646741172849 Y0: -16435341978766525421481 # Murphy_E 4.84e-10 # M 28697786502530949098227155344670279630021951848559771566053143617605185826843583689525558783262810034586906964477928 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 3510491) Primes: RFBsize:315948, AFBsize:315927, largePrimes:7299564 encountered Relations: rels:7154500, finalFF:669197 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 567717 hash collisions in 7651579 relations Msieve: matrix is 560477 x 560725 (154.2 MB) Total sieving time: 20.95 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 21.22 hours. --------- CPU info (if available) ----------
(46·10¹⁷⁴+53)/9 = 5(1)₁₇₃7_<175> = 11 · 110557 · 77883837686821_<14> · 111420482169715189_<18> · 2910487467143313244591_<22> · C117
C117 = P42 · P75
P42 = 536853205010070477751570463792644371118157_<42>
P75 = 309957915371554430586833991064591498214078894243423889658794630549706504457_<75>

Number: n N=166401900285459186183164258465440493370443079394472429719834326550583531484317913711130389138522747212789132994125749 ( 117 digits) Divisors found: Mon Mar 23 20:10:51 2009 prp42 factor: 536853205010070477751570463792644371118157 Mon Mar 23 20:10:51 2009 prp75 factor: 309957915371554430586833991064591498214078894243423889658794630549706504457 Mon Mar 23 20:10:51 2009 elapsed time 00:34:07 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 22.73 hours. Scaled time: 60.50 units (timescale=2.662). Factorization parameters were as follows: name: KA_5_1_173_7 n: 166401900285459186183164258465440493370443079394472429719834326550583531484317913711130389138522747212789132994125749 skew: 40828.59 # norm 4.82e+15 c5: 68640 c4: 381354376 c3: -346318543916472 c2: -1356621578298215941 c1: 235682672015256546584246 c0: 1514919480965173090953299231 # alpha -5.53 Y1: 1090532184019 Y0: -18919783983081763516780 # Murphy_E 4.53e-10 # M 111681274936674277178175601615880864336178708841231058862797851527797567703832190659576344088915678181723073994938108 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 3630281) Primes: RFBsize:315948, AFBsize:316486, largePrimes:7414964 encountered Relations: rels:7356594, finalFF:692768 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 607005 hash collisions in 7889899 relations Msieve: matrix is 528742 x 528990 (145.4 MB) Total sieving time: 22.42 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 22.73 hours. --------- CPU info (if available) ----------
(49·10²⁰⁵-31)/9 = 5(4)₂₀₄1_<206> = 3 · 47 · C204
C204 = P38 · P166
P38 = 63857407154518619099432007817527624871_<38>
P166 = 6046766207221483202200867690264664743792040332470375333789197689476780699012131797397027054060393163481932245065472333058710972868763794831723965812621141889670190331_<166>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 386130811662726556343577620173364854215918045705279747832939322301024428684003152088258471237194641449960598896769109535066981875492513790386130811662726556343577620173364854215918045705279747832939322301 (204 digits) Using B1=2254000, B2=3567637720, polynomial Dickson(6), sigma=1092356064 Step 1 took 44047ms Step 2 took 17234ms ********** Factor found in step 2: 63857407154518619099432007817527624871 Found probable prime factor of 38 digits: 63857407154518619099432007817527624871 Probable prime cofactor 6046766207221483202200867690264664743792040332470375333789197689476780699012131797397027054060393163481932245065472333058710972868763794831723965812621141889670190331 has 166 digits
Mar 23, 2009 (4th): By Erik Branger / GGNFS, Msieve / Mar 23, 2009
(16·10¹⁵⁵+17)/3 = 5(3)₁₅₄9_<156> = 269 · 857 · 5345787068339760725287117_<25> · C126
C126 = P36 · P40 · P52
P36 = 133580396914047305026081348186586773_<36>
P40 = 1641967491171100517839361762257277209237_<40>
P52 = 1973089047991938179155944152604719461286180910126899_<52>

Number: 53339_155 N=432766833624903841995769451831156239493595362335642487063658241830861851563850104811991408368391566906660453126060429189684699 ( 126 digits) SNFS difficulty: 156 digits. Divisors found: r1=133580396914047305026081348186586773 r2=1641967491171100517839361762257277209237 r3=1973089047991938179155944152604719461286180910126899 Version: Total time: 19.87 hours. Scaled time: 20.08 units (timescale=1.011). Factorization parameters were as follows: n: 432766833624903841995769451831156239493595362335642487063658241830861851563850104811991408368391566906660453126060429189684699 m: 10000000000000000000000000000000 deg: 5 c5: 16 c0: 17 skew: 1.01 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor 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, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 401024 x 401272 Total sieving time: 19.87 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: 19.87 hours. --------- CPU info (if available) ----------
Mar 23, 2009 (3rd): By Ignacio Santos / GGNFS, Msieve / Mar 23, 2009
(49·10¹⁴⁰-13)/9 = 5(4)₁₃₉3_<141> = 3 · 10501 · 22541 · 689699 · C127
C127 = P33 · P41 · P54
P33 = 207071850488006696795938318543661_<33>
P41 = 22474022215667142175693151054126926046513_<41>
P54 = 238872971288671773181147192316633901673882791915267263_<54>

Number: 54443_140 N=1111652072716786806280199894478985340144711508394996871064426887611081159266241363692668499358204687809656342000550329708807459 ( 127 digits) SNFS difficulty: 141 digits. Divisors found: r1=207071850488006696795938318543661 (pp33) r2=22474022215667142175693151054126926046513 (pp41) r3=238872971288671773181147192316633901673882791915267263 (pp54) Version: Msieve-1.39 Total time: 4.00 hours. Scaled time: 6.94 units (timescale=1.735). Factorization parameters were as follows: n: 1111652072716786806280199894478985340144711508394996871064426887611081159266241363692668499358204687809656342000550329708807459 m: 10000000000000000000000000000 deg: 5 c5: 49 c0: -13 skew: 0.77 type: snfs lss: 1 rlim: 1610000 alim: 1610000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1610000/1610000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [805000, 1505001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 220560 x 220808 Total sieving time: 4.00 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,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000 total time: 4.00 hours. --------- CPU info (if available) ----------
(49·10¹⁴⁵-13)/9 = 5(4)₁₄₄3_<146> = 1687354103_<10> · 3505546146359_<13> · C124
C124 = P40 · P85
P40 = 7140402236701543140617963582986208678971_<40>
P85 = 1289047654260669015173951513328700605459640910666217630944435952587966282067732957329_<85>

Number: 54443_145 N=9204318753697758502580249941200569767639330400560493094684823652953383377250635701260550464876367513699991278670232202628459 ( 124 digits) SNFS difficulty: 146 digits. Divisors found: r1=7140402236701543140617963582986208678971 (pp40) r2=1289047654260669015173951513328700605459640910666217630944435952587966282067732957329 (pp85) Version: Msieve-1.39 Total time: 5.93 hours. Scaled time: 10.31 units (timescale=1.739). Factorization parameters were as follows: n: 9204318753697758502580249941200569767639330400560493094684823652953383377250635701260550464876367513699991278670232202628459 m: 100000000000000000000000000000 deg: 5 c5: 49 c0: -13 skew: 0.77 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, 1975001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 285559 x 285807 Total sieving time: 5.93 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: 5.93 hours. --------- CPU info (if available) ----------
(49·10¹⁴⁴-31)/9 = 5(4)₁₄₃1_<145> = 173 · 2999 · 16657 · 951427 · 2585941 · C123
C123 = P55 · P68
P55 = 3257882588377989083926255526466788253796211702624682169_<55>
P68 = 78596770878296901617141918915241683753362330196819502016865089290893_<68>

Number: 54441_144 N=256059051347137664296684943791344848347371374573110192549585933050014669914539392291032586449386941150008047188499711186917 ( 123 digits) SNFS difficulty: 146 digits. Divisors found: r1=3257882588377989083926255526466788253796211702624682169 (pp55) r2=78596770878296901617141918915241683753362330196819502016865089290893 (pp68) Version: Msieve-1.39 Total time: 9.85 hours. Scaled time: 25.32 units (timescale=2.571). Factorization parameters were as follows: n: 256059051347137664296684943791344848347371374573110192549585933050014669914539392291032586449386941150008047188499711186917 m: 100000000000000000000000000000 deg: 5 c5: 49 c0: -310 skew: 1.45 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, 2575001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 330263 x 330511 Total sieving time: 9.85 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,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000 total time: 9.85 hours. --------- CPU info (if available) ----------
(49·10¹⁵²-13)/9 = 5(4)₁₅₁3_<153> = 3² · 491 · 632557 · 1592703598113809_<16> · C129
C129 = P55 · P74
P55 = 2146907550860162740600213632708655391877338081071796699_<55>
P74 = 56961523739466424569149913442650025242540002908402280547451425617956522631_<74>

Number: 54443_152 N=122291125424760880247517015235560595578717771861593788079807861507241681725560766919603504057041448257822793649727924561424595069 ( 129 digits) SNFS difficulty: 154 digits. Divisors found: r1=2146907550860162740600213632708655391877338081071796699 (pp55) r2=56961523739466424569149913442650025242540002908402280547451425617956522631 (pp74) Version: Msieve-1.39 Total time: 16.42 hours. Scaled time: 28.56 units (timescale=1.739). Factorization parameters were as follows: n: 122291125424760880247517015235560595578717771861593788079807861507241681725560766919603504057041448257822793649727924561424595069 m: 2000000000000000000000000000000 deg: 5 c5: 1225 c0: -104 skew: 0.61 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, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 534392 x 534640 Total sieving time: 16.42 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 16.42 hours. --------- CPU info (if available) ----------
(49·10¹⁶¹-13)/9 = 5(4)₁₆₀3_<162> = 3² · C161
C161 = P41 · P120
P41 = 89340062336934973963648121180445133883587_<41>
P120 = 677118703279485685836228095722187177748680567602212027120674408179765141637070828398608720395665830122030286741076835521_<120>

Number: 54443_161 N=60493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827 ( 161 digits) SNFS difficulty: 163 digits. Divisors found: r1=89340062336934973963648121180445133883587 (pp41) r2=677118703279485685836228095722187177748680567602212027120674408179765141637070828398608720395665830122030286741076835521 (pp120) Version: Msieve-1.39 Total time: 36.44 hours. Scaled time: 93.68 units (timescale=2.571). Factorization parameters were as follows: n: 60493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827 m: 200000000000000000000000000000000 deg: 5 c5: 245 c0: -208 skew: 0.97 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1900000, 3800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 705300 x 705548 Total sieving time: 36.44 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,163,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 36.44 hours. --------- CPU info (if available) ----------
Mar 23, 2009 (2nd): By Sinkiti Sibata / Msieve, GGNFS / Mar 23, 2009
(49·10¹²³-13)/9 = 5(4)₁₂₂3_<124> = 79 · 7854023 · 96574919997336701_<17> · C98
C98 = P39 · P60
P39 = 155032799336605825909522832709907573331_<39>
P60 = 586065780886139499566709891878394247094033801102050578861509_<60>

Sun Mar 22 22:14:39 2009 Msieve v. 1.39 Sun Mar 22 22:14:39 2009 random seeds: 13f8fae4 833acdc7 Sun Mar 22 22:14:39 2009 Msieve v. 1.39 Sun Mar 22 22:14:39 2009 factoring 90859418606172063134774748261539956958066980337601966602849256308594895491730641401085698910816479 (98 digits) Sun Mar 22 22:14:40 2009 searching for 15-digit factors Sun Mar 22 22:14:41 2009 commencing quadratic sieve (98-digit input) Sun Mar 22 22:14:42 2009 using multiplier of 1 Sun Mar 22 22:14:42 2009 using 32kb Intel Core sieve core Sun Mar 22 22:14:42 2009 sieve interval: 36 blocks of size 32768 Sun Mar 22 22:14:42 2009 processing polynomials in batches of 6 Sun Mar 22 22:14:42 2009 using a sieve bound of 2540407 (92941 primes) Sun Mar 22 22:14:42 2009 using large prime bound of 381061050 (28 bits) Sun Mar 22 22:14:42 2009 using double large prime bound of 2791194835856850 (43-52 bits) Sun Mar 22 22:14:42 2009 using trial factoring cutoff of 52 bits Sun Mar 22 22:14:42 2009 polynomial 'A' values have 13 factors Mon Mar 23 05:36:50 2009 93057 relations (22480 full + 70577 combined from 1401100 partial), need 93037 Mon Mar 23 05:36:52 2009 begin with 1423580 relations Mon Mar 23 05:36:53 2009 reduce to 244565 relations in 11 passes Mon Mar 23 05:36:53 2009 attempting to read 244565 relations Mon Mar 23 05:36:57 2009 recovered 244565 relations Mon Mar 23 05:36:57 2009 recovered 232392 polynomials Mon Mar 23 05:36:57 2009 attempting to build 93057 cycles Mon Mar 23 05:36:58 2009 found 93057 cycles in 5 passes Mon Mar 23 05:36:58 2009 distribution of cycle lengths: Mon Mar 23 05:36:58 2009 length 1 : 22480 Mon Mar 23 05:36:58 2009 length 2 : 16000 Mon Mar 23 05:36:58 2009 length 3 : 15708 Mon Mar 23 05:36:58 2009 length 4 : 12614 Mon Mar 23 05:36:58 2009 length 5 : 9517 Mon Mar 23 05:36:58 2009 length 6 : 6655 Mon Mar 23 05:36:58 2009 length 7 : 4213 Mon Mar 23 05:36:58 2009 length 9+: 5870 Mon Mar 23 05:36:58 2009 largest cycle: 22 relations Mon Mar 23 05:36:58 2009 matrix is 92941 x 93057 (25.3 MB) with weight 6271809 (67.40/col) Mon Mar 23 05:36:58 2009 sparse part has weight 6271809 (67.40/col) Mon Mar 23 05:37:00 2009 filtering completed in 3 passes Mon Mar 23 05:37:00 2009 matrix is 88962 x 89026 (24.4 MB) with weight 6046007 (67.91/col) Mon Mar 23 05:37:00 2009 sparse part has weight 6046007 (67.91/col) Mon Mar 23 05:37:00 2009 saving the first 48 matrix rows for later Mon Mar 23 05:37:00 2009 matrix is 88914 x 89026 (15.1 MB) with weight 4767098 (53.55/col) Mon Mar 23 05:37:00 2009 sparse part has weight 3421741 (38.44/col) Mon Mar 23 05:37:00 2009 matrix includes 64 packed rows Mon Mar 23 05:37:00 2009 using block size 35610 for processor cache size 1024 kB Mon Mar 23 05:37:01 2009 commencing Lanczos iteration Mon Mar 23 05:37:01 2009 memory use: 14.6 MB Mon Mar 23 05:37:56 2009 lanczos halted after 1407 iterations (dim = 88908) Mon Mar 23 05:37:56 2009 recovered 14 nontrivial dependencies Mon Mar 23 05:37:57 2009 prp39 factor: 155032799336605825909522832709907573331 Mon Mar 23 05:37:57 2009 prp60 factor: 586065780886139499566709891878394247094033801102050578861509 Mon Mar 23 05:37:57 2009 elapsed time 07:23:18
(49·10¹²⁷-13)/9 = 5(4)₁₂₆3_<128> = C128
C128 = P31 · P42 · P55
P31 = 6388426039807794712107618364273_<31>
P42 = 952116963596930070553655728861886818163819_<42>
P55 = 8950955467063706290214969828203183230927212987298134689_<55>

Number: 54443_127 N=54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 ( 128 digits) SNFS difficulty: 129 digits. Divisors found: r1=6388426039807794712107618364273 (pp31) r2=952116963596930070553655728861886818163819 (pp42) r3=8950955467063706290214969828203183230927212987298134689 (pp55) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 5.21 hours. Scaled time: 2.47 units (timescale=0.473). Factorization parameters were as follows: name: 54443_127 n: 54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 m: 20000000000000000000000000 deg: 5 c5: 1225 c0: -104 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, 955001) Primes: RFBsize:79251, AFBsize:79761, largePrimes:2639543 encountered Relations: rels:2518399, finalFF:189964 Max relations in full relation-set: 28 Initial matrix: 159077 x 189964 with sparse part having weight 14598093. Pruned matrix : 149777 x 150636 with weight 9259399. Total sieving time: 4.74 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.32 hours. Time per square root: 0.05 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: 5.21 hours. --------- CPU info (if available) ----------
(49·10¹⁴⁸-13)/9 = 5(4)₁₄₇3_<149> = C149
C149 = P43 · P107
P43 = 2400513117999809722405970619454289674628549_<43>
P107 = 22680336148218774284672959283888357977629962447175151940084971677874951003250148874102472003345354598125407_<107>

Number: 54443_148 N=54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 ( 149 digits) SNFS difficulty: 151 digits. Divisors found: r1=2400513117999809722405970619454289674628549 (pp43) r2=22680336148218774284672959283888357977629962447175151940084971677874951003250148874102472003345354598125407 (pp107) Version: GGNFS-0.77.1-20060513-nocona Total time: 24.37 hours. Scaled time: 62.76 units (timescale=2.575). Factorization parameters were as follows: name: 54443_148 n: 54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 m: 500000000000000000000000000000 deg: 5 c5: 392 c0: -325 skew: 0.96 type: snfs rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 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: 49/49 Sieved algebraic special-q in [1150000, 2050001) Primes: RFBsize:169511, AFBsize:169201, largePrimes:6871087 encountered Relations: rels:6772219, finalFF:417043 Max relations in full relation-set: 28 Initial matrix: 338777 x 417043 with sparse part having weight 43198668. Pruned matrix : 312178 x 313935 with weight 29224094. Total sieving time: 23.29 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.86 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 24.37 hours. --------- CPU info (if available) ----------
Mar 23, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 23, 2009
4·10¹⁸⁹+1 = 4(0)₁₈₈1_<190> = 53 · 18077 · 2643247 · 96964568413_<11> · 3643105412001703_<16> · C151
C151 = P65 · P87
P65 = 13506270059310058545933600271041349759458769588496747569910410889_<65>
P87 = 331054716915185039351115638053193982176316954185352183355312068630530447500029226468933_<87>

Number: 40001_189 N=4471314411064930883583891865633043659313970480829502358467553263209442083755243393829592046821388226901398045864511661002729970137066357369440623411437 ( 151 digits) SNFS difficulty: 190 digits. Divisors found: r1=13506270059310058545933600271041349759458769588496747569910410889 r2=331054716915185039351115638053193982176316954185352183355312068630530447500029226468933 Version: Total time: 141.02 hours. Scaled time: 336.91 units (timescale=2.389). Factorization parameters were as follows: n: 4471314411064930883583891865633043659313970480829502358467553263209442083755243393829592046821388226901398045864511661002729970137066357369440623411437 m: 100000000000000000000000000000000000000 deg: 5 c5: 2 c0: 5 skew: 1.20 type: snfs lss: 1 rlim: 10000000 alim: 10000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5000000, 8500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 20345343 Max relations in full relation-set: Initial matrix: Pruned matrix : 1869145 x 1869393 Total sieving time: 127.54 hours. Total relation processing time: 3.81 hours. Matrix solve time: 9.25 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,54,54,2.5,2.5,100000 total time: 141.02 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)
Mar 22, 2009 (7th): By Ignacio Santos / GGNFS, Msieve / Mar 22, 2009
(47·10¹⁵⁶+43)/9 = 5(2)₁₅₅7_<157> = 337 · 9491 · 51820057 · C143
C143 = P66 · P78
P66 = 113581577204809565513012062452451703276361480125789394032540587489_<66>
P78 = 277400789537348018726881092733478275821865326592097829516429044974540705826297_<78>

Number: 52227_156 N=31507619193511423542935436939709466487629251657249002190486601003992558407642434351504182852325940175227371864963648554636926509550429565398233 ( 143 digits) SNFS difficulty: 157 digits. Divisors found: r1=113581577204809565513012062452451703276361480125789394032540587489 (pp66) r2=277400789537348018726881092733478275821865326592097829516429044974540705826297 (pp78) Version: Msieve-1.39 Total time: 22.76 hours. Scaled time: 58.51 units (timescale=2.571). Factorization parameters were as follows: n: 31507619193511423542935436939709466487629251657249002190486601003992558407642434351504182852325940175227371864963648554636926509550429565398233 m: 10000000000000000000000000000000 deg: 5 c5: 470 c0: 43 skew: 0.62 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, 2700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 546997 x 547245 Total sieving time: 22.76 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,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 22.76 hours. --------- CPU info (if available) ----------
(11·10¹⁸⁰-17)/3 = 3(6)₁₇₉1_<181> = 29 · 160907 · C174
C174 = P60 · P115
P60 = 176325185615773625215171251016539484947995017242946993964977_<60>
P115 = 4456399789592708971102926999895272616391578598936752012977840464910707166020866224669377586464398546940798085854731_<115>

Number: 36661_180 N=785775520078028937826512051760605058579922192508001873574576418776634664887099416104497857654478645443012737635482879415817332622135053524528232878719334485280245767723756187 ( 174 digits) SNFS difficulty: 181 digits. Divisors found: r1=176325185615773625215171251016539484947995017242946993964977 (pp60) r2=4456399789592708971102926999895272616391578598936752012977840464910707166020866224669377586464398546940798085854731 (pp115) Version: Msieve-1.39 Total time: 125.86 hours. Scaled time: 218.88 units (timescale=1.739). Factorization parameters were as follows: n: 785775520078028937826512051760605058579922192508001873574576418776634664887099416104497857654478645443012737635482879415817332622135053524528232878719334485280245767723756187 m: 1000000000000000000000000000000000000 deg: 5 c5: 11 c0: -17 skew: 1.09 type: snfs lss: 1 rlim: 7300000 alim: 7300000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7300000/7300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3650000, 5750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1437252 x 1437500 Total sieving time: 125.86 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,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000 total time: 125.86 hours. --------- CPU info (if available) ----------
(11·10¹⁶⁷+1)/3 = 3(6)₁₆₆7_<168> = 7 · 36549260837_<11> · C157
C157 = P39 · P43 · P75
P39 = 759382237599703068226186568773861458713_<39>
P43 = 2871319944773339904197170463553741091654931_<43>
P75 = 657283560153017018445541294295980692946948772344737839113428718868371336571_<75>

Number: 36667_167 N=1433160375378246967538829528995992399920964573485346432325743080005051346816679054388297120909596040511367262821916323312932145259760301536419849988687539513 ( 157 digits) SNFS difficulty: 170 digits. Divisors found: r1=759382237599703068226186568773861458713 (pp39) r2=2871319944773339904197170463553741091654931 (pp43) r3=657283560153017018445541294295980692946948772344737839113428718868371336571 (pp75) Version: Msieve-1.39 Total time: 48.74 hours. Scaled time: 84.76 units (timescale=1.739). Factorization parameters were as follows: n: 1433160375378246967538829528995992399920964573485346432325743080005051346816679054388297120909596040511367262821916323312932145259760301536419849988687539513 m: 5000000000000000000000000000000000 deg: 5 c5: 44 c0: 125 skew: 1.23 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2400000, 5100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 953625 x 953873 Total sieving time: 48.74 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,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000 total time: 48.74 hours. --------- CPU info (if available) ----------
(49·10¹³⁴-13)/9 = 5(4)₁₃₃3_<135> = 3² · 419 · 7625281 · 10726355401104146640073_<23> · C103
C103 = P40 · P63
P40 = 3053575784592854265729449920832931528209_<40>
P63 = 578069825269579937655670787941745063303826005806320438808706249_<63>

Number: 54443_134 N=1765180020247011731278134277411512103003119124883459439773398747293564455928072644004637247393738078041 ( 103 digits) SNFS difficulty: 136 digits. Divisors found: r1=3053575784592854265729449920832931528209 (pp40) r2=578069825269579937655670787941745063303826005806320438808706249 (pp63) Version: Msieve-1.39 Total time: 3.55 hours. Scaled time: 6.18 units (timescale=1.739). Factorization parameters were as follows: n: 1765180020247011731278134277411512103003119124883459439773398747293564455928072644004637247393738078041 m: 1000000000000000000000000000 deg: 5 c5: 49 c0: -130 skew: 1.22 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, 1340001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 188447 x 188695 Total sieving time: 3.55 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,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 3.55 hours. --------- CPU info (if available) ----------
(16·10¹⁶⁸+17)/3 = 5(3)₁₆₇9_<169> = 11 · 227 · 5715255044861_<13> · C153
C153 = P57 · P97
P57 = 237162299947870602923360845817776486574128966845412187779_<57>
P97 = 1575792091453108964971588622205552962509706167218824000441526861593990073743591728636132377122173_<97>

Number: 53339_168 N=373718476648684572637694595120833703274454218519866059110650467541553477345097898834202957714009891476604066068299185279577128527994396935030163900523767 ( 153 digits) SNFS difficulty: 170 digits. Divisors found: r1=237162299947870602923360845817776486574128966845412187779 (pp57) r2=1575792091453108964971588622205552962509706167218824000441526861593990073743591728636132377122173 (pp97) Version: Msieve-1.39 Total time: 42.58 hours. Scaled time: 109.01 units (timescale=2.560). Factorization parameters were as follows: n: 373718476648684572637694595120833703274454218519866059110650467541553477345097898834202957714009891476604066068299185279577128527994396935030163900523767 m: 4000000000000000000000000000000000 deg: 5 c5: 125 c0: 136 skew: 1.02 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2400000, 4300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 836237 x 836485 Total sieving time: 42.58 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,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000 total time: 42.58 hours. --------- CPU info (if available) ----------
Mar 22, 2009 (6th): By Sinkiti Sibata / GGNFS, Msieve / Mar 22, 2009
(49·10¹⁴²-31)/9 = 5(4)₁₄₁1_<143> = 3 · 151 · 2023864397_<10> · 93445315257300767_<17> · C114
C114 = P43 · P72
P43 = 1716464456102413811533728553420001764417351_<43>
P72 = 370238527354276951849469480548758543807489129866387577784804649042444353_<72>

Number: 54441_142 N=635501272483317646192623949232245073819008743834263346476971567061448712480937188483427830079004753214351885168903 ( 114 digits) SNFS difficulty: 144 digits. Divisors found: r1=1716464456102413811533728553420001764417351 (pp43) r2=370238527354276951849469480548758543807489129866387577784804649042444353 (pp72) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 17.43 hours. Scaled time: 8.25 units (timescale=0.473). Factorization parameters were as follows: name: 54441_142 n: 635501272483317646192623949232245073819008743834263346476971567061448712480937188483427830079004753214351885168903 m: 20000000000000000000000000000 deg: 5 c5: 1225 c0: -248 skew: 0.73 type: snfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 2300001) Primes: RFBsize:135072, AFBsize:135069, largePrimes:3971918 encountered Relations: rels:4090853, finalFF:368042 Max relations in full relation-set: 28 Initial matrix: 270206 x 368042 with sparse part having weight 36737791. Pruned matrix : 237779 x 239194 with weight 21727203. Total sieving time: 15.54 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.60 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,100000 total time: 17.43 hours. --------- CPU info (if available) ----------
(49·10¹⁵¹-31)/9 = 5(4)₁₅₀1_<152> = 3 · 59 · 911 · 3407 · 339851027 · C135
C135 = P42 · P94
P42 = 286120041668600745533526907489500541024577_<42>
P94 = 1019184775083452183488830452860126346217069699358811608060108774820628340331919578837659937651_<94>

Number: 54441_151 N=291609190314880817618579760477553066552329881899773875289977893723653566933468795197023008294377682242284847777615153600283937478648627 ( 135 digits) SNFS difficulty: 152 digits. Divisors found: r1=286120041668600745533526907489500541024577 (pp42) r2=1019184775083452183488830452860126346217069699358811608060108774820628340331919578837659937651 (pp94) Version: GGNFS-0.77.1-20060513-nocona Total time: 33.36 hours. Scaled time: 85.21 units (timescale=2.554). Factorization parameters were as follows: name: 54441_151 n: 291609190314880817618579760477553066552329881899773875289977893723653566933468795197023008294377682242284847777615153600283937478648627 m: 1000000000000000000000000000000 deg: 5 c5: 490 c0: -31 skew: 0.58 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, 2150001) Primes: RFBsize:183072, AFBsize:183427, largePrimes:8957809 encountered Relations: rels:10343365, finalFF:1581511 Max relations in full relation-set: 28 Initial matrix: 366565 x 1581511 with sparse part having weight 194579687. Pruned matrix : 248031 x 249927 with weight 42723486. Total sieving time: 32.29 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.81 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000 total time: 33.36 hours. --------- CPU info (if available) ----------
(16·10¹²⁹+17)/3 = 5(3)₁₂₈9_<130> = 19 · 47 · 485858449 · C119
C119 = P39 · P80
P39 = 623219998062802938785799973843610813257_<39>
P80 = 19724051551602642903450015600131998699589330106576447898110400616964952612756111_<80>

Number: 53339_129 N=12292423369780424409286096691655132415558349762911633736102345174234635424394221190217084491352027704098652792906563527 ( 119 digits) SNFS difficulty: 130 digits. Divisors found: r1=623219998062802938785799973843610813257 (pp39) r2=19724051551602642903450015600131998699589330106576447898110400616964952612756111 (pp80) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.40 hours. Scaled time: 1.61 units (timescale=0.473). Factorization parameters were as follows: name: 53339_129 n: 12292423369780424409286096691655132415558349762911633736102345174234635424394221190217084491352027704098652792906563527 m: 100000000000000000000000000 deg: 5 c5: 8 c0: 85 skew: 1.60 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, 780001) Primes: RFBsize:82832, AFBsize:82838, largePrimes:2518222 encountered Relations: rels:2385744, finalFF:190256 Max relations in full relation-set: 28 Initial matrix: 165735 x 190256 with sparse part having weight 11939402. Pruned matrix : 153355 x 154247 with weight 7704026. Total sieving time: 2.98 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.30 hours. Time per square root: 0.04 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: 3.40 hours. --------- CPU info (if available) ----------
(49·10¹⁵⁹-31)/9 = 5(4)₁₅₈1_<160> = 19 · 47 · 292246842172269949747673873_<27> · 3567663311467094797752460691_<28> · C103
C103 = P31 · P36 · P37
P31 = 1286968891444224528016148245727_<31>
P36 = 827600391338879236747200546595124171_<36>
P37 = 5490092802033096484410654870220759027_<37>

Sat Mar 21 15:17:17 2009 Msieve v. 1.39 Sat Mar 21 15:17:17 2009 random seeds: 58f44c04 9e64a594 Sat Mar 21 15:17:17 2009 factoring 5847475653589482742496899192309564306665185208063887360339104592368359867530932457634445089863133120559 (103 digits) Sat Mar 21 15:17:18 2009 searching for 15-digit factors Sat Mar 21 15:17:19 2009 commencing quadratic sieve (103-digit input) Sat Mar 21 15:17:20 2009 using multiplier of 1 Sat Mar 21 15:17:20 2009 using 32kb Intel Core sieve core Sat Mar 21 15:17:20 2009 sieve interval: 36 blocks of size 32768 Sat Mar 21 15:17:20 2009 processing polynomials in batches of 6 Sat Mar 21 15:17:20 2009 using a sieve bound of 3499337 (124945 primes) Sat Mar 21 15:17:20 2009 using large prime bound of 524900550 (28 bits) Sat Mar 21 15:17:20 2009 using double large prime bound of 4967508683642700 (44-53 bits) Sat Mar 21 15:17:20 2009 using trial factoring cutoff of 53 bits Sat Mar 21 15:17:20 2009 polynomial 'A' values have 13 factors Sun Mar 22 13:17:00 2009 125221 relations (29552 full + 95669 combined from 1877452 partial), need 125041 Sun Mar 22 13:17:02 2009 begin with 1907004 relations Sun Mar 22 13:17:05 2009 reduce to 331621 relations in 12 passes Sun Mar 22 13:17:05 2009 attempting to read 331621 relations Sun Mar 22 13:17:11 2009 recovered 331621 relations Sun Mar 22 13:17:11 2009 recovered 323390 polynomials Sun Mar 22 13:17:12 2009 attempting to build 125221 cycles Sun Mar 22 13:17:12 2009 found 125221 cycles in 7 passes Sun Mar 22 13:17:12 2009 distribution of cycle lengths: Sun Mar 22 13:17:12 2009 length 1 : 29552 Sun Mar 22 13:17:12 2009 length 2 : 21309 Sun Mar 22 13:17:12 2009 length 3 : 20439 Sun Mar 22 13:17:12 2009 length 4 : 17242 Sun Mar 22 13:17:12 2009 length 5 : 13129 Sun Mar 22 13:17:12 2009 length 6 : 9202 Sun Mar 22 13:17:12 2009 length 7 : 6019 Sun Mar 22 13:17:12 2009 length 9+: 8329 Sun Mar 22 13:17:12 2009 largest cycle: 24 relations Sun Mar 22 13:17:12 2009 matrix is 124945 x 125221 (37.4 MB) with weight 9296264 (74.24/col) Sun Mar 22 13:17:12 2009 sparse part has weight 9296264 (74.24/col) Sun Mar 22 13:17:15 2009 filtering completed in 3 passes Sun Mar 22 13:17:15 2009 matrix is 120045 x 120109 (36.0 MB) with weight 8961886 (74.61/col) Sun Mar 22 13:17:15 2009 sparse part has weight 8961886 (74.61/col) Sun Mar 22 13:17:15 2009 saving the first 48 matrix rows for later Sun Mar 22 13:17:15 2009 matrix is 119997 x 120109 (26.3 MB) with weight 7548817 (62.85/col) Sun Mar 22 13:17:15 2009 sparse part has weight 6175038 (51.41/col) Sun Mar 22 13:17:15 2009 matrix includes 64 packed rows Sun Mar 22 13:17:15 2009 using block size 43690 for processor cache size 1024 kB Sun Mar 22 13:17:17 2009 commencing Lanczos iteration Sun Mar 22 13:17:17 2009 memory use: 23.0 MB Sun Mar 22 13:19:16 2009 lanczos halted after 1899 iterations (dim = 119995) Sun Mar 22 13:19:16 2009 recovered 17 nontrivial dependencies Sun Mar 22 13:19:18 2009 prp31 factor: 1286968891444224528016148245727 Sun Mar 22 13:19:18 2009 prp36 factor: 827600391338879236747200546595124171 Sun Mar 22 13:19:18 2009 prp37 factor: 5490092802033096484410654870220759027 Sun Mar 22 13:19:18 2009 elapsed time 22:02:01
(49·10¹³⁹-13)/9 = 5(4)₁₃₈3_<140> = 43² · 5879 · 6361 · 259993 · 2700760419073_<13> · 10123937678771113627_<20> · C93
C93 = P46 · P47
P46 = 1205299344754500667641838377887933065643674837_<46>
P47 = 91895808846580213792838373174075953576019739123_<47>

Sun Mar 22 13:51:54 2009 Msieve v. 1.39 Sun Mar 22 13:51:54 2009 random seeds: 1c254e34 3755ed4b Sun Mar 22 13:51:54 2009 factoring 110761958188467977456119371945228710724443759220876141066030782141391152874649874683779547951 (93 digits) Sun Mar 22 13:51:55 2009 searching for 15-digit factors Sun Mar 22 13:51:57 2009 commencing quadratic sieve (93-digit input) Sun Mar 22 13:51:57 2009 using multiplier of 1 Sun Mar 22 13:51:57 2009 using 32kb Intel Core sieve core Sun Mar 22 13:51:57 2009 sieve interval: 36 blocks of size 32768 Sun Mar 22 13:51:57 2009 processing polynomials in batches of 6 Sun Mar 22 13:51:57 2009 using a sieve bound of 1854599 (69412 primes) Sun Mar 22 13:51:57 2009 using large prime bound of 209569687 (27 bits) Sun Mar 22 13:51:57 2009 using double large prime bound of 951461467997464 (42-50 bits) Sun Mar 22 13:51:57 2009 using trial factoring cutoff of 50 bits Sun Mar 22 13:51:57 2009 polynomial 'A' values have 12 factors Sun Mar 22 16:03:41 2009 69822 relations (17555 full + 52267 combined from 897392 partial), need 69508 Sun Mar 22 16:03:42 2009 begin with 914947 relations Sun Mar 22 16:03:43 2009 reduce to 177819 relations in 9 passes Sun Mar 22 16:03:43 2009 attempting to read 177819 relations Sun Mar 22 16:03:45 2009 recovered 177819 relations Sun Mar 22 16:03:45 2009 recovered 158523 polynomials Sun Mar 22 16:03:46 2009 attempting to build 69822 cycles Sun Mar 22 16:03:46 2009 found 69822 cycles in 6 passes Sun Mar 22 16:03:46 2009 distribution of cycle lengths: Sun Mar 22 16:03:46 2009 length 1 : 17555 Sun Mar 22 16:03:46 2009 length 2 : 12647 Sun Mar 22 16:03:46 2009 length 3 : 12035 Sun Mar 22 16:03:46 2009 length 4 : 9404 Sun Mar 22 16:03:46 2009 length 5 : 7018 Sun Mar 22 16:03:46 2009 length 6 : 4605 Sun Mar 22 16:03:46 2009 length 7 : 2822 Sun Mar 22 16:03:46 2009 length 9+: 3736 Sun Mar 22 16:03:46 2009 largest cycle: 21 relations Sun Mar 22 16:03:46 2009 matrix is 69412 x 69822 (17.5 MB) with weight 4299783 (61.58/col) Sun Mar 22 16:03:46 2009 sparse part has weight 4299783 (61.58/col) Sun Mar 22 16:03:47 2009 filtering completed in 3 passes Sun Mar 22 16:03:47 2009 matrix is 65537 x 65601 (16.5 MB) with weight 4051076 (61.75/col) Sun Mar 22 16:03:47 2009 sparse part has weight 4051076 (61.75/col) Sun Mar 22 16:03:47 2009 saving the first 48 matrix rows for later Sun Mar 22 16:03:47 2009 matrix is 65489 x 65601 (9.7 MB) with weight 3112910 (47.45/col) Sun Mar 22 16:03:47 2009 sparse part has weight 2157274 (32.88/col) Sun Mar 22 16:03:47 2009 matrix includes 64 packed rows Sun Mar 22 16:03:47 2009 using block size 26240 for processor cache size 1024 kB Sun Mar 22 16:03:48 2009 commencing Lanczos iteration Sun Mar 22 16:03:48 2009 memory use: 9.8 MB Sun Mar 22 16:04:14 2009 lanczos halted after 1037 iterations (dim = 65489) Sun Mar 22 16:04:14 2009 recovered 18 nontrivial dependencies Sun Mar 22 16:04:14 2009 prp46 factor: 1205299344754500667641838377887933065643674837 Sun Mar 22 16:04:14 2009 prp47 factor: 91895808846580213792838373174075953576019739123 Sun Mar 22 16:04:14 2009 elapsed time 02:12:20
(49·10¹¹³-13)/9 = 5(4)₁₁₂3_<114> = 3 · C114
C114 = P47 · P67
P47 = 49270994758445485506745344522078417472249246961_<47>
P67 = 3683333011058680643342779360261730707241153817449805238013851687321_<67>

Number: 54443_113 N=181481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481 ( 114 digits) SNFS difficulty: 116 digits. Divisors found: r1=49270994758445485506745344522078417472249246961 (pp47) r2=3683333011058680643342779360261730707241153817449805238013851687321 (pp67) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.44 hours. Scaled time: 1.15 units (timescale=0.473). Factorization parameters were as follows: name: 54443_113 n: 181481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481 m: 50000000000000000000000 deg: 5 c5: 392 c0: -325 skew: 0.96 type: snfs lss: 1 rlim: 600000 alim: 600000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [300000, 550001) Primes: RFBsize:49098, AFBsize:49136, largePrimes:1303299 encountered Relations: rels:1299767, finalFF:165600 Max relations in full relation-set: 28 Initial matrix: 98299 x 165600 with sparse part having weight 8125362. Pruned matrix : 77886 x 78441 with weight 2834014. Total sieving time: 2.32 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000 total time: 2.44 hours. --------- CPU info (if available) ----------
(49·10¹⁴¹-13)/9 = 5(4)₁₄₀3_<142> = C142
C142 = P53 · P90
P53 = 29895894509244796665860680741717481942098627486442047_<53>
P90 = 182113448479049276921181897697664273046509544887453509951853505999576736492064061755845669_<90>

Number: 54443_141 N=5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 ( 142 digits) SNFS difficulty: 143 digits. Divisors found: r1=29895894509244796665860680741717481942098627486442047 (pp53) r2=182113448479049276921181897697664273046509544887453509951853505999576736492064061755845669 (pp90) Version: GGNFS-0.77.1-20060513-nocona Total time: 14.53 hours. Scaled time: 37.10 units (timescale=2.554). Factorization parameters were as follows: name: 54443_141 n: 5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 m: 20000000000000000000000000000 deg: 5 c5: 245 c0: -208 skew: 0.97 type: snfs lss: 1 rlim: 1750000 alim: 1750000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1750000/1750000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [875000, 2175001) Primes: RFBsize:131608, AFBsize:131782, largePrimes:4300365 encountered Relations: rels:4799866, finalFF:622644 Max relations in full relation-set: 28 Initial matrix: 263456 x 622644 with sparse part having weight 71808746. Pruned matrix : 194268 x 195649 with weight 27959680. Total sieving time: 14.09 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.29 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1750000,1750000,26,26,48,48,2.3,2.3,100000 total time: 14.53 hours. --------- CPU info (if available) ----------
(49·10¹²⁰-13)/9 = 5(4)₁₁₉3_<121> = 433 · 24517 · 1153799 · 1500979523_<10> · C99
C99 = P28 · P71
P28 = 9666149732721867133816317637_<28>
P71 = 30636553223357949753688263264707804811627036708515492327059389308255287_<71>

Number: 54443_120 N=296137510751480703017039742522270090064956369608944183048399620173500991977630933097560191476596819 ( 99 digits) SNFS difficulty: 121 digits. Divisors found: r1=9666149732721867133816317637 (pp28) r2=30636553223357949753688263264707804811627036708515492327059389308255287 (pp71) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.32 hours. Scaled time: 1.03 units (timescale=0.446). Factorization parameters were as follows: name: 54443_120 n: 296137510751480703017039742522270090064956369608944183048399620173500991977630933097560191476596819 m: 1000000000000000000000000 deg: 5 c5: 49 c0: -13 skew: 0.77 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, 575001) Primes: RFBsize:60238, AFBsize:59821, largePrimes:1299470 encountered Relations: rels:1274107, finalFF:150534 Max relations in full relation-set: 28 Initial matrix: 120123 x 150534 with sparse part having weight 6474460. Pruned matrix : 102811 x 103475 with weight 3409529. Total sieving time: 2.15 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 2.32 hours. --------- CPU info (if available) ----------
(49·10¹¹²-13)/9 = 5(4)₁₁₁3_<113> = 33751 · 713542013531_<12> · C97
C97 = P34 · P63
P34 = 3237808002986528818226382726266713_<34>
P63 = 698226429531598067180105615871883648384973706998991877568268031_<63>

Sun Mar 22 16:28:56 2009 Msieve v. 1.39 Sun Mar 22 16:28:56 2009 random seeds: d3015b48 7ed2183f Sun Mar 22 16:28:56 2009 factoring 2260723121434117828143713675810233409179298217736488423452589864962066789740202246598297977352103 (97 digits) Sun Mar 22 16:28:57 2009 searching for 15-digit factors Sun Mar 22 16:28:58 2009 commencing quadratic sieve (97-digit input) Sun Mar 22 16:28:59 2009 using multiplier of 7 Sun Mar 22 16:28:59 2009 using 32kb Intel Core sieve core Sun Mar 22 16:28:59 2009 sieve interval: 36 blocks of size 32768 Sun Mar 22 16:28:59 2009 processing polynomials in batches of 6 Sun Mar 22 16:28:59 2009 using a sieve bound of 2363903 (87059 primes) Sun Mar 22 16:28:59 2009 using large prime bound of 354585450 (28 bits) Sun Mar 22 16:28:59 2009 using double large prime bound of 2451870804143850 (43-52 bits) Sun Mar 22 16:28:59 2009 using trial factoring cutoff of 52 bits Sun Mar 22 16:28:59 2009 polynomial 'A' values have 13 factors Sun Mar 22 22:04:35 2009 87192 relations (21295 full + 65897 combined from 1307645 partial), need 87155 Sun Mar 22 22:04:37 2009 begin with 1328940 relations Sun Mar 22 22:04:38 2009 reduce to 227421 relations in 10 passes Sun Mar 22 22:04:38 2009 attempting to read 227421 relations Sun Mar 22 22:04:42 2009 recovered 227421 relations Sun Mar 22 22:04:42 2009 recovered 213881 polynomials Sun Mar 22 22:04:42 2009 attempting to build 87192 cycles Sun Mar 22 22:04:43 2009 found 87192 cycles in 5 passes Sun Mar 22 22:04:43 2009 distribution of cycle lengths: Sun Mar 22 22:04:43 2009 length 1 : 21295 Sun Mar 22 22:04:43 2009 length 2 : 15274 Sun Mar 22 22:04:43 2009 length 3 : 14822 Sun Mar 22 22:04:43 2009 length 4 : 11786 Sun Mar 22 22:04:43 2009 length 5 : 8794 Sun Mar 22 22:04:43 2009 length 6 : 5923 Sun Mar 22 22:04:43 2009 length 7 : 3909 Sun Mar 22 22:04:43 2009 length 9+: 5389 Sun Mar 22 22:04:43 2009 largest cycle: 20 relations Sun Mar 22 22:04:43 2009 matrix is 87059 x 87192 (23.4 MB) with weight 5778193 (66.27/col) Sun Mar 22 22:04:43 2009 sparse part has weight 5778193 (66.27/col) Sun Mar 22 22:04:45 2009 filtering completed in 3 passes Sun Mar 22 22:04:45 2009 matrix is 83157 x 83220 (22.4 MB) with weight 5551015 (66.70/col) Sun Mar 22 22:04:45 2009 sparse part has weight 5551015 (66.70/col) Sun Mar 22 22:04:45 2009 saving the first 48 matrix rows for later Sun Mar 22 22:04:45 2009 matrix is 83109 x 83220 (14.0 MB) with weight 4373772 (52.56/col) Sun Mar 22 22:04:45 2009 sparse part has weight 3161875 (37.99/col) Sun Mar 22 22:04:45 2009 matrix includes 64 packed rows Sun Mar 22 22:04:45 2009 using block size 33288 for processor cache size 1024 kB Sun Mar 22 22:04:46 2009 commencing Lanczos iteration Sun Mar 22 22:04:46 2009 memory use: 13.5 MB Sun Mar 22 22:05:32 2009 lanczos halted after 1315 iterations (dim = 83108) Sun Mar 22 22:05:32 2009 recovered 17 nontrivial dependencies Sun Mar 22 22:05:33 2009 prp34 factor: 3237808002986528818226382726266713 Sun Mar 22 22:05:33 2009 prp63 factor: 698226429531598067180105615871883648384973706998991877568268031 Sun Mar 22 22:05:33 2009 elapsed time 05:36:37
Mar 22, 2009 (5th): By Robert Backstrom / GGNFS, Msieve / Mar 22, 2009
(47·10¹⁵⁴+61)/9 = 5(2)₁₅₃9_<155> = 223 · 2041669007527_<13> · C141
C141 = P67 · P74
P67 = 6287405169625602502477237795484824113448923850663462083007464764063_<67>
P74 = 18242892600702144900224066166443686086519340119714997012668019979791537123_<74>

Number: n N=114700457246579318138478529527468263717968577260197719911362953388175243029481033280139922014098783960013610492455511266691921061547300810749 ( 141 digits) SNFS difficulty: 156 digits. Divisors found: Sun Mar 22 13:39:49 2009 prp67 factor: 6287405169625602502477237795484824113448923850663462083007464764063 Sun Mar 22 13:39:49 2009 prp74 factor: 18242892600702144900224066166443686086519340119714997012668019979791537123 Sun Mar 22 13:39:49 2009 elapsed time 01:25:39 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.36 hours. Scaled time: 44.42 units (timescale=1.823). Factorization parameters were as follows: name: KA_5_2_153_9 n: 114700457246579318138478529527468263717968577260197719911362953388175243029481033280139922014098783960013610492455511266691921061547300810749 deg: 5 c5: 47 c0: 610 m: 10000000000000000000000000000000 skew: 1.67 type: snfs rlim: 3000000 alim: 3000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [1500000, 10000000 ) Primes: RFBsize:216816, AFBsize:217102, largePrimes:24249774 encountered Relations: rels:22372236, finalFF:558517 Max relations in full relation-set: 28 Initial matrix: 433983 x 558517 with sparse part having weight 89057458. Pruned matrix : 399040 x 401273 with weight 56926209. Msieve: found 2110438 hash collisions in 23723689 relations Msieve: matrix is 535966 x 536214 (141.4 MB) Total sieving time: 23.82 hours. Total relation processing time: 0.54 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,29,29,58,58,2.5,2.5,100000 total time: 24.36 hours. --------- CPU info (if available) ----------
(47·10¹²²+43)/9 = 5(2)₁₂₁7_<123> = 31 · C122
C122 = P58 · P64
P58 = 3553753901649698354047921541097460083255890435040418905481_<58>
P64 = 4740305210324396166746716284276132282091713424142937278623424357_<64>

Number: n N=16845878136200716845878136200716845878136200716845878136200716845878136200716845878136200716845878136200716845878136200717 ( 122 digits) SNFS difficulty: 123 digits. Divisors found: r1=3553753901649698354047921541097460083255890435040418905481 (pp58) r2=4740305210324396166746716284276132282091713424142937278623424357 (pp64) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 1.59 hours. Scaled time: 4.23 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_2_121_7 n: 16845878136200716845878136200716845878136200716845878136200716845878136200716845878136200716845878136200716845878136200717 skew: 0.39 deg: 5 c5: 4700 c0: 43 m: 1000000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [300000, 660001) Primes: RFBsize:49098, AFBsize:49206, largePrimes:4778585 encountered Relations: rels:4334253, finalFF:160209 Max relations in full relation-set: 28 Initial matrix: 98371 x 160209 with sparse part having weight 17227502. Pruned matrix : 87616 x 88171 with weight 7733167. Total sieving time: 1.48 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.02 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,123,5,0,0,0,0,0,0,0,0,600000,600000,28,28,56,56,2.4,2.4,50000 total time: 1.59 hours. --------- CPU info (if available) ----------
(49·10¹¹⁷-13)/9 = 5(4)₁₁₆3_<118> = 223 · 185904631079077_<15> · C102
C102 = P47 · P55
P47 = 39440726016344745653943373742754827920013325257_<47>
P55 = 3329765108465687231084607438784113510264349945122473369_<55>

Number: n N=131328353341779614268153512653441448934258520553999210062837824880361345306679232117334355334117580833 ( 102 digits) SNFS difficulty: 121 digits. Divisors found: Sun Mar 22 20:10:43 2009 prp47 factor: 39440726016344745653943373742754827920013325257 Sun Mar 22 20:10:43 2009 prp55 factor: 3329765108465687231084607438784113510264349945122473369 Sun Mar 22 20:10:43 2009 elapsed time 00:04:08 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 1.08 hours. Scaled time: 2.88 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_4_116_3 n: 131328353341779614268153512653441448934258520553999210062837824880361345306679232117334355334117580833 skew: 3.05 deg: 5 c5: 49 c0: -13000 m: 1000000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 60000 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, 540613) Primes: RFBsize:49098, AFBsize:49661, largePrimes:3831306 encountered Relations: rels:3248478, finalFF:82968 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 187218 hash collisions in 3421566 relations Msieve: matrix is 111486 x 111726 (29.9 MB) Total sieving time: 1.04 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,28,28,56,56,2.4,2.4,50000 total time: 1.08 hours. --------- CPU info (if available) ----------
(49·10¹³⁰-13)/9 = 5(4)₁₂₉3_<131> = 29 · 8837 · C126
C126 = P38 · P89
P38 = 15365173779343757359334278547951668963_<38>
P89 = 13826531303417091869063585125914867774939884422495793079249247555637563832749104437904857_<89>

Number: n N=212447056242539964976585299444125773860080634496979566495278255783654323492698975094701527060768962959205395981802392153853291 ( 126 digits) SNFS difficulty: 131 digits. Divisors found: r1=15365173779343757359334278547951668963 (pp38) r2=13826531303417091869063585125914867774939884422495793079249247555637563832749104437904857 (pp89) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 1.87 hours. Scaled time: 4.96 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_4_129_3 n: 212447056242539964976585299444125773860080634496979566495278255783654323492698975094701527060768962959205395981802392153853291 skew: 0.77 deg: 5 c5: 49 c0: -13 m: 100000000000000000000000000 type: snfs rlim: 850000 alim: 850000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 850000/850000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [425000, 785001) Primes: RFBsize:67617, AFBsize:67170, largePrimes:5700028 encountered Relations: rels:5209170, finalFF:264753 Max relations in full relation-set: 28 Initial matrix: 134851 x 264753 with sparse part having weight 26750384. Pruned matrix : 109263 x 110001 with weight 8945134. Total sieving time: 1.74 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.03 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,850000,850000,28,28,56,56,2.4,2.4,50000 total time: 1.87 hours. --------- CPU info (if available) ----------
Mar 22, 2009 (4th): By Erik Branger / GMP-ECM, GGNFS, Msieve / Mar 22, 2009
(10²⁰⁴+17)/9 = (1)₂₀₃3_<204> = 23 · 773909 · 1540195883333_<13> · 1282146599377795849_<19> · 21676096960363463710282387103_<29> · C138
C138 = P37 · P101
P37 = 3563655936076273099916412456811109387_<37>
P101 = 40921284929194423257867202290995071601945357815830179626243613336714911803694463810877773792377543507_<101>

GMP-ECM 6.2 [powered by GMP 4.2.2] [ECM] Input number is 145829379949792239395107343637243079763628528658681310890575160988171862082801967137706829973725352350567726447106111950156737778528600209 (138 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=560508884 Step 1 took 46594ms ********** Factor found in step 1: 3563655936076273099916412456811109387 Found probable prime factor of 37 digits: 3563655936076273099916412456811109387 Probable prime cofactor 40921284929194423257867202290995071601945357815830179626243613336714911803694463810877773792377543507 has 101 digits
(49·10¹⁰²-13)/9 = 5(4)₁₀₁3_<103> = 23 · 29 · C100
C100 = P36 · P64
P36 = 856284975732961798770754067476869163_<36>
P64 = 9532557040362265696725320268206781344444145146303960880095399683_<64>

Number: 54443_102 N=8162585373979676828252540396468432450441445943694819257038147592870231550891221056138597367982675329 ( 100 digits) SNFS difficulty: 105 digits. Divisors found: r1=856284975732961798770754067476869163 r2=9532557040362265696725320268206781344444145146303960880095399683 Version: Total time: 0.67 hours. Scaled time: 0.52 units (timescale=0.774). Factorization parameters were as follows: n: 8162585373979676828252540396468432450441445943694819257038147592870231550891221056138597367982675329 m: 50000000000000000000000000 deg: 4 c4: 196 c0: -325 skew: 1.13 type: snfs lss: 1 rlim: 390000 alim: 390000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 390000/390000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [195000, 255001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 33044 x 33269 Total sieving time: 0.67 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,105,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,20000 total time: 0.67 hours. --------- CPU info (if available) ----------
(49·10¹²⁶-13)/9 = 5(4)₁₂₅3_<127> = 1935510386548969_<16> · C112
C112 = P33 · P34 · P46
P33 = 886472740761278554450087477716581_<33>
P34 = 1905222917172293197745705906814437_<34>
P46 = 1665508609598934955964817532355973948697940251_<46>

Number: 54443_126 N=2812924426694466797269053611378786655841506454604882955955606250617376556226484570126893360140540172447027234147 ( 112 digits) SNFS difficulty: 128 digits. Divisors found: r1=886472740761278554450087477716581 r2=1905222917172293197745705906814437 r3=1665508609598934955964817532355973948697940251 Version: Total time: 3.21 hours. Scaled time: 3.00 units (timescale=0.934). Factorization parameters were as follows: n: 2812924426694466797269053611378786655841506454604882955955606250617376556226484570126893360140540172447027234147 m: 20000000000000000000000000 deg: 5 c5: 245 c0: -208 skew: 0.97 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 137383 x 137631 Total sieving time: 3.21 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,128,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 3.21 hours. --------- CPU info (if available) ----------
Mar 22, 2009 (3rd): By Max Dettweiler / GGNFS, msieve v1.40beta2 / Mar 22, 2009
(49·10¹²⁹-31)/9 = 5(4)₁₂₈1_<130> = 17 · 1051 · 1223 · 188833 · C118
C118 = P34 · P84
P34 = 7162696482730668159103867263627691_<34>
P84 = 184213322171955253139200172783060241904468670066761404841591156427180089235354386967_<84>

Number: 54441_129 N=1319464114793195299715358693826383356772564901259144652368208640721475989621654185864368906977656604154533991830703197 ( 118 digits) SNFS difficulty: 131 digits. Divisors found: r1=7162696482730668159103867263627691 (pp34) r2=184213322171955253139200172783060241904468670066761404841591156427180089235354386967 (pp84) Version: Msieve-1.40 Total time: 3.93 hours. Scaled time: 6.40 units (timescale=1.631). Factorization parameters were as follows: n: 1319464114793195299715358693826383356772564901259144652368208640721475989621654185864368906977656604154533991830703197 m: 100000000000000000000000000 deg: 5 c5: 49 c0: -310 skew: 1.45 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 167913 x 168161 Total sieving time: 3.93 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,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 3.93 hours. --------- CPU info (if available) ---------- [ 0.371529] CPU0: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem) [ 0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.10 BogoMIPS (lpj=8800216) [ 0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821) [ 0.460049] Total of 2 processors activated (8800.51 BogoMIPS).
Mar 22, 2009 (2nd): By Serge Batalov / Msieve-1.40b2 / Mar 22, 2009
(47·10¹⁵⁸+7)/9 = 5(2)₁₅₇3_<159> = 103 · C157
C157 = P56 · P101
P56 = 71303755236789181010241436764968018401427992819337740943_<56>
P101 = 71105913643882583795061215112708628113247174708582329597976670564566008135825025418369512291553408087_<101>

SNFS difficulty: 161 digits. Divisors found: r1=71303755236789181010241436764968018401427992819337740943 (pp56) r2=71105913643882583795061215112708628113247174708582329597976670564566008135825025418369512291553408087 (pp101) Version: Msieve-1.40b2 Total time: 9.38 hours. Scaled time: 26.62 units (timescale=2.840). Factorization parameters were as follows: n: 5070118662351672060409924487594390507011866235167206040992448759439050701186623516720604099244875943905070118662351672060409924487594390507011866235167206041 m: 50000000000000000000000000000000 deg: 5 c5: 376 c0: 175 skew: 0.86 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, 2800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 655490 x 655738 Total sieving time: 9.38 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.55 hours. Time per square root: 0.10 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: 9.38 hours. --------- CPU info (if available) ---------- CPU0: AMD Phenom(tm) II X4 940 Processor stepping 02 CPU1: AMD Phenom(tm) II X4 940 Processor stepping 02 CPU2: AMD Phenom(tm) II X4 940 Processor stepping 02 CPU3: AMD Phenom(tm) II X4 940 Processor stepping 02 Memory: 8173900k/9175040k available (2699k kernel code, 213168k reserved, 3164k data, 788k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 6012.77 BogoMIPS (lpj=12025552) Calibrating delay using timer specific routine.. 6012.90 BogoMIPS (lpj=12025812) Calibrating delay using timer specific routine.. 6012.85 BogoMIPS (lpj=12025719) Calibrating delay using timer specific routine.. 6012.90 BogoMIPS (lpj=12025802) Total of 4 processors activated (24051.44 BogoMIPS).
Mar 22, 2009: Factorizations of 544...443 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.
Mar 21, 2009 (5th): By Sinkiti Sibata / GGNFS, Msieve / Mar 21, 2009
(16·10¹⁴⁶+17)/3 = 5(3)₁₄₅9_<147> = 7 · 11 · 114391987 · 10724771108770309319_<20> · C118
C118 = P41 · P77
P41 = 86647924148580878037180406898757962104657_<41>
P77 = 65157768781765977762053170572689023638293806097473705832942639134885363376267_<77>

Number: 53339_146 N=5645785407093229523450444930076978097985520970778427251742486562229340790332525704995666239342427900024865562723975419 ( 118 digits) SNFS difficulty: 147 digits. Divisors found: r1=86647924148580878037180406898757962104657 (pp41) r2=65157768781765977762053170572689023638293806097473705832942639134885363376267 (pp77) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 13.73 hours. Scaled time: 6.48 units (timescale=0.472). Factorization parameters were as follows: name: 53339_146 n: 5645785407093229523450444930076978097985520970778427251742486562229340790332525704995666239342427900024865562723975419 m: 200000000000000000000000000000 deg: 5 c5: 5 c0: 17 skew: 1.28 type: snfs rlim: 1990000 alim: 1990000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1990000/1990000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [995000, 1995001) Primes: RFBsize:148219, AFBsize:148151, largePrimes:3891517 encountered Relations: rels:3932779, finalFF:384477 Max relations in full relation-set: 28 Initial matrix: 296435 x 384477 with sparse part having weight 29846694. Pruned matrix : 262135 x 263681 with weight 17013240. Total sieving time: 11.83 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.65 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1990000,1990000,26,26,49,49,2.3,2.3,100000 total time: 13.73 hours. --------- CPU info (if available) ----------
(16·10¹⁴⁸+17)/3 = 5(3)₁₄₇9_<149> = 11³ · 13 · 53 · 8387 · C139
C139 = P52 · P88
P52 = 1970805129651612702855917094141798731030723421241267_<52>
P88 = 3518447892045144824283402589333190568229454329679224368597593827794731475863057750227249_<88>

Number: 53339_148 N=6934175154054475060038774393210973357889745590439477645571012428168544246773102249928479498122105298705396229221788410415615970922906684483 ( 139 digits) SNFS difficulty: 150 digits. Divisors found: r1=1970805129651612702855917094141798731030723421241267 (pp52) r2=3518447892045144824283402589333190568229454329679224368597593827794731475863057750227249 (pp88) Version: GGNFS-0.77.1-20060513-nocona Total time: 23.56 hours. Scaled time: 60.66 units (timescale=2.575). Factorization parameters were as follows: name: 53339_148 n: 6934175154054475060038774393210973357889745590439477645571012428168544246773102249928479498122105298705396229221788410415615970922906684483 m: 400000000000000000000000000000 deg: 5 c5: 125 c0: 136 skew: 1.02 type: snfs 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 algebraic special-q in [1100000, 1600001) Primes: RFBsize:162662, AFBsize:161875, largePrimes:8008307 encountered Relations: rels:9347537, finalFF:1756819 Max relations in full relation-set: 28 Initial matrix: 324603 x 1756819 with sparse part having weight 181642673. Pruned matrix : 188940 x 190627 with weight 44204690. Total sieving time: 22.89 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.46 hours. Time per square root: 0.07 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: 23.56 hours. --------- CPU info (if available) ----------
(49·10¹⁴⁶-31)/9 = 5(4)₁₄₅1_<147> = 643 · C144
C144 = P37 · P108
P37 = 3042106189827290624120844036782865833_<37>
P108 = 278335260575092870871504582135628218174720978379908946178727055375423453765822803874949132681646831312143739_<108>

Number: 54441_146 N=846725419042681873163988249524796958700535683428373941593226196647658545014688094003801624330395714532573008467254190426818731639882495247969587 ( 144 digits) SNFS difficulty: 147 digits. Divisors found: r1=3042106189827290624120844036782865833 (pp37) r2=278335260575092870871504582135628218174720978379908946178727055375423453765822803874949132681646831312143739 (pp108) Version: GGNFS-0.77.1-20060513-nocona Total time: 17.67 hours. Scaled time: 45.31 units (timescale=2.564). Factorization parameters were as follows: name:54441_146 n: 846725419042681873163988249524796958700535683428373941593226196647658545014688094003801624330395714532573008467254190426818731639882495247969587 m: 100000000000000000000000000000 deg: 5 c5: 490 c0: -31 skew: 0.58 type: snfs rlim: 2000000 alim: 2000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1000000, 2700001) Primes: RFBsize:148933, AFBsize:149076, largePrimes:4248112 encountered Relations: rels:4418526, finalFF:360963 Max relations in full relation-set: 28 Initial matrix: 298075 x 360963 with sparse part having weight 39507402. Pruned matrix : 276783 x 278337 with weight 28392277. Total sieving time: 16.91 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.59 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000 total time: 17.67 hours. --------- CPU info (if available) ----------
(16·10¹⁵⁹+17)/3 = 5(3)₁₅₈9_<160> = 4201 · 11369 · 20060626646968543458887062589_<29> · 181460042160288350794014941791_<30> · C95
C95 = P29 · P67
P29 = 16433336450614236706160575327_<29>
P67 = 1866691415650896562187704322494751573492502375255655246746456677447_<67>

Sat Mar 21 07:47:23 2009 Msieve v. 1.39 Sat Mar 21 07:47:23 2009 random seeds: 2dc22e14 ac7a317a Sat Mar 21 07:47:23 2009 factoring 30675968082864569337146521319456691256436797450754597199363823113423792359722327736654385550169 (95 digits) SSSat Mar 21 07:47:24 2009 searching for 15-digit factors Sat Mar 21 07:47:26 2009 commencing quadratic sieve (95-digit input) Sat Mar 21 07:47:26 2009 using multiplier of 5 Sat Mar 21 07:47:26 2009 using 32kb Intel Core sieve core Sat Mar 21 07:47:26 2009 sieve interval: 36 blocks of size 32768 Sat Mar 21 07:47:26 2009 processing polynomials in batches of 6 SSat Mar 21 07:47:26 2009 using a sieve bound of 2120351 (78824 primes) Sat Mar 21 07:47:26 2009 using large prime bound of 309571246 (28 bits) Sat Mar 21 07:47:26 2009 using double large prime bound of 1920299848206370 (43-51 bits) Sat Mar 21 07:47:26 2009 using trial factoring cutoff of 51 bits Sat Mar 21 07:47:26 2009 polynomial 'A' values have 12 factors Sat Mar 21 11:37:13 2009 79215 relations (19218 full + 59997 combined from 1172811 partial), need 78920 Sat Mar 21 11:37:14 2009 begin with 1192029 relations Sat Mar 21 11:37:16 2009 reduce to 207251 relations in 11 passes Sat Mar 21 11:37:16 2009 attempting to read 207251 relations Sat Mar 21 11:37:19 2009 recovered 207251 relations Sat Mar 21 11:37:19 2009 recovered 191354 polynomials Sat Mar 21 11:37:19 2009 attempting to build 79215 cycles Sat Mar 21 11:37:19 2009 found 79215 cycles in 5 passes Sat Mar 21 11:37:19 2009 distribution of cycle lengths: Sat Mar 21 11:37:19 2009 length 1 : 19218 Sat Mar 21 11:37:19 2009 length 2 : 13842 Sat Mar 21 11:37:19 2009 length 3 : 13308 Sat Mar 21 11:37:19 2009 length 4 : 10659 Sat Mar 21 11:37:19 2009 length 5 : 8146 Sat Mar 21 11:37:19 2009 length 6 : 5481 Sat Mar 21 11:37:19 2009 length 7 : 3649 Sat Mar 21 11:37:19 2009 length 9+: 4912 Sat Mar 21 11:37:19 2009 largest cycle: 20 relations Sat Mar 21 11:37:19 2009 matrix is 78824 x 79215 (21.5 MB) with weight 5319220 (67.15/col) Sat Mar 21 11:37:19 2009 sparse part has weight 5319220 (67.15/col) Sat Mar 21 11:37:21 2009 filtering completed in 3 passes Sat Mar 21 11:37:21 2009 matrix is 75158 x 75222 (20.5 MB) with weight 5063299 (67.31/col) Sat Mar 21 11:37:21 2009 sparse part has weight 5063299 (67.31/col) Sat Mar 21 11:37:21 2009 saving the first 48 matrix rows for later Sat Mar 21 11:37:21 2009 matrix is 75110 x 75222 (13.9 MB) with weight 4111085 (54.65/col) Sat Mar 21 11:37:21 2009 sparse part has weight 3194501 (42.47/col) Sat Mar 21 11:37:21 2009 matrix includes 64 packed rows Sat Mar 21 11:37:21 2009 using block size 30088 for processor cache size 1024 kB Sat Mar 21 11:37:22 2009 commencing Lanczos iteration Sat Mar 21 11:37:22 2009 memory use: 12.8 MB Sat Mar 21 11:38:01 2009 lanczos halted after 1189 iterations (dim = 75109) Sat Mar 21 11:38:01 2009 recovered 17 nontrivial dependencies Sat Mar 21 11:38:04 2009 prp29 factor: 16433336450614236706160575327 Sat Mar 21 11:38:04 2009 prp67 factor: 1866691415650896562187704322494751573492502375255655246746456677447 Sat Mar 21 11:38:04 2009 elapsed time 03:50:41
(49·10¹⁴⁸-31)/9 = 5(4)₁₄₇1_<149> = 3² · 1522307981_<10> · 32325361034799231983_<20> · C120
C120 = P47 · P73
P47 = 41174538329149687535593202758980475987623219157_<47>
P73 = 2985632945849170426739484835964697951250750532381210173726652975197022159_<73>

Number: 54441_148 N=122932058165638761226488241379896999017363022195995159595839729811725901694163162728063867754278449558440225991842299963 ( 120 digits) SNFS difficulty: 151 digits. Divisors found: r1=41174538329149687535593202758980475987623219157 (pp47) r2=2985632945849170426739484835964697951250750532381210173726652975197022159 (pp73) Version: GGNFS-0.77.1-20060513-nocona Total time: 24.50 hours. Scaled time: 63.09 units (timescale=2.575). Factorization parameters were as follows: name: 54441_148 n: 122932058165638761226488241379896999017363022195995159595839729811725901694163162728063867754278449558440225991842299963 m: 500000000000000000000000000000 deg: 5 c5: 392 c0: -775 skew: 1.15 type: snfs rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 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: 49/49 Sieved algebraic special-q in [1150000, 2050001) Primes: RFBsize:169511, AFBsize:169652, largePrimes:7433177 encountered Relations: rels:7869366, finalFF:804921 Max relations in full relation-set: 28 Initial matrix: 339228 x 804921 with sparse part having weight 96545322. Pruned matrix : 240416 x 242176 with weight 52494306. Total sieving time: 23.51 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.76 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 24.50 hours. --------- CPU info (if available) ----------
Mar 21, 2009 (4th): By Max Dettweiler / GGNFS, msieve v1.40beta2, Yafu v1.07 / Mar 21, 2009
(49·10¹⁰²-31)/9 = 5(4)₁₀₁1_<103> = 383 · 1877279 · C94
C94 = P39 · P56
P39 = 473755973482677914291347623099642100603_<39>
P56 = 15983477561793208607093630496325319497714439131327943771_<56>

Number: 54441_102 N=7572267971925880781094517844222788058246527492006759130638750213193534517648005235215109193913 ( 94 digits) SNFS difficulty: 105 digits. Divisors found: r1=473755973482677914291347623099642100603 (pp39) r2=15983477561793208607093630496325319497714439131327943771 (pp56) Version: GGNFS-0.77.1-20060722-prescott Total time: 0.66 hours. Scaled time: 1.07 units (timescale=1.608). Factorization parameters were as follows: n: 7572267971925880781094517844222788058246527492006759130638750213193534517648005235215109193913 m: 50000000000000000000000000 deg: 4 c4: 196 c0: -775 skew: 1.41 type: snfs lss: 1 rlim: 390000 alim: 390000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 390000/390000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [195000, 275001) Primes: RFBsize:33067, AFBsize:33072, largePrimes:1135645 encountered Relations: rels:1107071, finalFF:140559 Max relations in full relation-set: 32 Initial matrix: 66207 x 140559 with sparse part having weight 5846477. Pruned matrix : 43382 x 43777 with weight 1352172. Total sieving time: 0.63 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,105,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,20000 total time: 0.66 hours. --------- CPU info (if available) ---------- [ 0.371529] CPU0: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem) [ 0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.10 BogoMIPS (lpj=8800216) [ 0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821) [ 0.460049] Total of 2 processors activated (8800.51 BogoMIPS).
(49·10¹²¹-31)/9 = 5(4)₁₂₀1_<122> = 3² · 131 · 1275455269903484432893507007_<28> · C92
C92 = P41 · P51
P41 = 36277844381237430670455147233624365514761_<41>
P51 = 998005786686987798358882485633772896334040422474877_<51>

Number: 54441_121 N=36205498621004982089560554169086346790384341114722758168707702248023354316750849491695159397 ( 92 digits) SNFS difficulty: 122 digits. Divisors found: r1=36277844381237430670455147233624365514761 (pp41) r2=998005786686987798358882485633772896334040422474877 (pp51) Version: GGNFS-0.77.1-20060722-prescott Total time: 2.30 hours. Scaled time: 3.65 units (timescale=1.587). Factorization parameters were as follows: n: 36205498621004982089560554169086346790384341114722758168707702248023354316750849491695159397 m: 1000000000000000000000000 deg: 5 c5: 490 c0: -31 skew: 0.58 type: snfs lss: 1 rlim: 780000 alim: 780000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 780000/780000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [390000, 690001) Primes: RFBsize:62468, AFBsize:62381, largePrimes:1358161 encountered Relations: rels:1333530, finalFF:152464 Max relations in full relation-set: 32 Initial matrix: 124915 x 152464 with sparse part having weight 7336245. Pruned matrix : 112805 x 113493 with weight 4186936. Total sieving time: 2.17 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.05 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,780000,780000,25,25,46,46,2.2,2.2,50000 total time: 2.30 hours. --------- CPU info (if available) ---------- [ 0.371529] CPU0: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem) [ 0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.10 BogoMIPS (lpj=8800216) [ 0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821) [ 0.460049] Total of 2 processors activated (8800.51 BogoMIPS).
(49·10¹²⁸-31)/9 = 5(4)₁₂₇1_<129> = 157 · 653 · 1801003 · C118
C118 = P36 · P40 · P43
P36 = 334785113105198068383674639652573199_<36>
P40 = 2656934680962281058637638782134286920741_<40>
P43 = 3314967576878842350279855338342491270012073_<43>

Number: 54441_128 N=2948670878569275337440589887212647142554801661452814756709502398448268894092307014198822999294104956368884068184401507 ( 118 digits) SNFS difficulty: 131 digits. Divisors found: r1=334785113105198068383674639652573199 (pp36) r2=2656934680962281058637638782134286920741 (pp40) r3=3314967576878842350279855338342491270012073 (pp43) Version: Msieve-1.40 Total time: 4.04 hours. Scaled time: 6.58 units (timescale=1.630). Factorization parameters were as follows: n: 2948670878569275337440589887212647142554801661452814756709502398448268894092307014198822999294104956368884068184401507 m: 50000000000000000000000000 deg: 5 c5: 392 c0: -775 skew: 1.15 type: snfs lss: 1 rlim: 1070000 alim: 1070000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor 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, 1035001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 159940 x 160188 Total sieving time: 4.04 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: 4.04 hours. --------- CPU info (if available) ---------- [ 0.371529] CPU0: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem) [ 0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.10 BogoMIPS (lpj=8800216) [ 0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821) [ 0.460049] Total of 2 processors activated (8800.51 BogoMIPS).
(49·10¹⁴⁵-31)/9 = 5(4)₁₄₄1_<146> = 3 · 17 · 182773 · 1476511 · 1360874413_<10> · 49121077427_<11> · 215691204456149170031_<21> · C93
C93 = P39 · P54
P39 = 434960582530030125624174611913048830633_<39>
P54 = 630763272083566084158310359068270763055519969092874889_<54>

03/21/09 00:53:21 v1.07 @ Core2Duo, starting SIQS on c93: 274357160264015792942527616510918476292414957531453870300145327758573457549272898173619674737 03/21/09 00:53:21 v1.07 @ Core2Duo, random seeds: 1948697553, 1062661827 03/21/09 00:53:21 v1.07 @ Core2Duo, ==== sieve params ==== 03/21/09 00:53:21 v1.07 @ Core2Duo, n = 93 digits, 314 bits 03/21/09 00:53:21 v1.07 @ Core2Duo, factor base: 76080 primes (max prime = 2050033) 03/21/09 00:53:21 v1.07 @ Core2Duo, single large prime cutoff: 246003960 (120 * pmax) 03/21/09 00:53:21 v1.07 @ Core2Duo, double large prime range from 43 to 51 bits 03/21/09 00:53:21 v1.07 @ Core2Duo, double large prime cutoff: 1269684379467337 03/21/09 00:53:21 v1.07 @ Core2Duo, using 5 large prime slices of factor base 03/21/09 00:53:21 v1.07 @ Core2Duo, buckets hold 2048 elements 03/21/09 00:53:21 v1.07 @ Core2Duo, sieve interval: 22 blocks of size 32768 03/21/09 00:53:21 v1.07 @ Core2Duo, polynomial A has ~ 12 factors 03/21/09 00:53:21 v1.07 @ Core2Duo, using multiplier of 73 03/21/09 00:53:21 v1.07 @ Core2Duo, using small prime variation correction of 23 bits 03/21/09 00:53:21 v1.07 @ Core2Duo, using x128 sieve scanning 03/21/09 00:53:21 v1.07 @ Core2Duo, trial factoring cutoff at 98 bits 03/21/09 00:53:21 v1.07 @ Core2Duo, ==== sieving started ==== 03/21/09 02:55:00 v1.07 @ Core2Duo, sieve time = 2128.9600, relation time = 1238.0100, poly_time = 2958.2200 03/21/09 02:55:00 v1.07 @ Core2Duo, 76157 relations found: 20962 full + 55195 from 959290 partial, using 664939 polys (324 A polys) 03/21/09 02:55:00 v1.07 @ Core2Duo, trial division touched 46556240 sieve locations out of 958703730688 03/21/09 02:55:00 v1.07 @ Core2Duo, ==== post processing stage (msieve-1.38) ==== 03/21/09 02:55:01 v1.07 @ Core2Duo, begin with 980252 relations 03/21/09 02:55:02 v1.07 @ Core2Duo, reduce to 183836 relations in 9 passes 03/21/09 02:55:02 v1.07 @ Core2Duo, failed to read relation 27535 03/21/09 02:55:06 v1.07 @ Core2Duo, recovered 183835 relations 03/21/09 02:55:06 v1.07 @ Core2Duo, recovered 160637 polynomials 03/21/09 02:55:06 v1.07 @ Core2Duo, attempting to build 76156 cycles 03/21/09 02:55:06 v1.07 @ Core2Duo, found 76156 cycles in 6 passes 03/21/09 02:55:06 v1.07 @ Core2Duo, distribution of cycle lengths: 03/21/09 02:55:06 v1.07 @ Core2Duo, length 1 : 20962 03/21/09 02:55:06 v1.07 @ Core2Duo, length 2 : 15209 03/21/09 02:55:06 v1.07 @ Core2Duo, length 3 : 13707 03/21/09 02:55:06 v1.07 @ Core2Duo, length 4 : 10124 03/21/09 02:55:06 v1.07 @ Core2Duo, length 5 : 6651 03/21/09 02:55:06 v1.07 @ Core2Duo, length 6 : 4256 03/21/09 02:55:06 v1.07 @ Core2Duo, length 7 : 2395 03/21/09 02:55:06 v1.07 @ Core2Duo, length 9+: 2852 03/21/09 02:55:06 v1.07 @ Core2Duo, largest cycle: 21 relations 03/21/09 02:55:06 v1.07 @ Core2Duo, matrix is 76080 x 76156 (18.8 MB) with weight 4623885 (60.72/col) 03/21/09 02:55:06 v1.07 @ Core2Duo, sparse part has weight 4623885 (60.72/col) 03/21/09 02:55:07 v1.07 @ Core2Duo, filtering completed in 3 passes 03/21/09 02:55:07 v1.07 @ Core2Duo, matrix is 71114 x 71178 (17.8 MB) with weight 4370124 (61.40/col) 03/21/09 02:55:07 v1.07 @ Core2Duo, sparse part has weight 4370124 (61.40/col) 03/21/09 02:55:07 v1.07 @ Core2Duo, saving the first 48 matrix rows for later 03/21/09 02:55:07 v1.07 @ Core2Duo, matrix is 71066 x 71178 (11.9 MB) with weight 3488332 (49.01/col) 03/21/09 02:55:07 v1.07 @ Core2Duo, sparse part has weight 2684687 (37.72/col) 03/21/09 02:55:07 v1.07 @ Core2Duo, matrix includes 64 packed rows 03/21/09 02:55:07 v1.07 @ Core2Duo, using block size 28471 for processor cache size 2048 kB 03/21/09 02:55:08 v1.07 @ Core2Duo, commencing Lanczos iteration 03/21/09 02:55:08 v1.07 @ Core2Duo, memory use: 11.2 MB 03/21/09 02:55:37 v1.07 @ Core2Duo, lanczos halted after 1125 iterations (dim = 71065) 03/21/09 02:55:37 v1.07 @ Core2Duo, recovered 17 nontrivial dependencies 03/21/09 02:55:38 v1.07 @ Core2Duo, prp54 = 630763272083566084158310359068270763055519969092874889 03/21/09 02:55:40 v1.07 @ Core2Duo, prp39 = 434960582530030125624174611913048830633 03/21/09 02:55:40 v1.07 @ Core2Duo, Lanczos elapsed time = 34.4500 seconds. 03/21/09 02:55:40 v1.07 @ Core2Duo, Sqrt elapsed time = 2.8200 seconds. 03/21/09 02:55:40 v1.07 @ Core2Duo, SIQS elapsed time = 2099.7127 seconds. 03/21/09 02:55:40 v1.07 @ Core2Duo, 03/21/09 02:55:40 v1.07 @ Core2Duo, 03/21/09 02:55:40 v1.07 @ Core2Duo, Total factoring time = 2106.7827 seconds
Mar 21, 2009 (3rd): By Serge Batalov / GMP-ECM 6.2.2 / Mar 21, 2009
(49·10¹³⁶-31)/9 = 5(4)₁₃₅1_<137> = 3 · 23 · 665857 · 13972061 · 39460147 · 11671026512077_<14> · C102
C102 = P29 · P31 · P43
P29 = 18667939549767870850524668531_<29>
P31 = 3022782052436438642593509297659_<31>
P43 = 3263563458913913551196308954723352628160607_<43>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1100200419 Step 1 took 5688ms Step 2 took 6513ms ********** Factor found in step 2: 18667939549767870850524668531 Found probable prime factor of 29 digits: 18667939549767870850524668531 Composite cofactor has 73 digits 54441_136 Fri Mar 20 17:56:23 2009 Msieve v. 1.40 Fri Mar 20 17:56:23 2009 random seeds: 2779744d bad5cbc1 Fri Mar 20 17:56:23 2009 factoring 9865041050592362501661952318539719039996375986698139725961087645621119013 (73 digits) Fri Mar 20 17:56:23 2009 searching for 15-digit factors Fri Mar 20 17:56:23 2009 commencing quadratic sieve (73-digit input) Fri Mar 20 17:56:23 2009 using multiplier of 13 Fri Mar 20 17:56:23 2009 using 64kb Opteron sieve core Fri Mar 20 17:56:23 2009 sieve interval: 6 blocks of size 65536 Fri Mar 20 17:56:23 2009 processing polynomials in batches of 17 Fri Mar 20 17:56:23 2009 using a sieve bound of 497561 (20551 primes) Fri Mar 20 17:56:23 2009 using large prime bound of 49756100 (25 bits) Fri Mar 20 17:56:23 2009 using trial factoring cutoff of 26 bits Fri Mar 20 17:56:23 2009 polynomial 'A' values have 9 factors Fri Mar 20 17:57:54 2009 20938 relations (10558 full + 10380 combined from 114926 partial), need 20647 Fri Mar 20 17:57:54 2009 begin with 125484 relations Fri Mar 20 17:57:54 2009 reduce to 30024 relations in 2 passes Fri Mar 20 17:57:54 2009 attempting to read 30024 relations Fri Mar 20 17:57:55 2009 recovered 30024 relations Fri Mar 20 17:57:55 2009 recovered 23652 polynomials Fri Mar 20 17:57:55 2009 attempting to build 20938 cycles Fri Mar 20 17:57:55 2009 found 20938 cycles in 1 passes Fri Mar 20 17:57:55 2009 distribution of cycle lengths: Fri Mar 20 17:57:55 2009 length 1 : 10558 Fri Mar 20 17:57:55 2009 length 2 : 10380 Fri Mar 20 17:57:55 2009 largest cycle: 2 relations Fri Mar 20 17:57:55 2009 matrix is 20551 x 20938 (2.9 MB) with weight 602761 (28.79/col) Fri Mar 20 17:57:55 2009 sparse part has weight 602761 (28.79/col) Fri Mar 20 17:57:55 2009 filtering completed in 3 passes Fri Mar 20 17:57:55 2009 matrix is 15156 x 15220 (2.3 MB) with weight 484811 (31.85/col) Fri Mar 20 17:57:55 2009 sparse part has weight 484811 (31.85/col) Fri Mar 20 17:57:55 2009 saving the first 48 matrix rows for later Fri Mar 20 17:57:55 2009 matrix is 15108 x 15220 (1.7 MB) with weight 379916 (24.96/col) Fri Mar 20 17:57:55 2009 sparse part has weight 304295 (19.99/col) Fri Mar 20 17:57:55 2009 matrix includes 64 packed rows Fri Mar 20 17:57:55 2009 commencing Lanczos iteration Fri Mar 20 17:57:55 2009 memory use: 2.3 MB Fri Mar 20 17:57:57 2009 lanczos halted after 240 iterations (dim = 15106) Fri Mar 20 17:57:57 2009 recovered 16 nontrivial dependencies Fri Mar 20 17:57:57 2009 prp31 factor: 3022782052436438642593509297659 Fri Mar 20 17:57:57 2009 prp43 factor: 3263563458913913551196308954723352628160607 Fri Mar 20 17:57:57 2009 elapsed time 00:01:34
(49·10²⁰¹-31)/9 = 5(4)₂₀₀1_<202> = 1319 · 178067 · 5439093729791_<13> · C181
C181 = P33 · C149
P33 = 424468423345885433156577302198219_<33>
C149 = [10040455184883628723379516918972718663570880925820870748754105264964125669194550840151796264594212956524156346638928243460828919631807445780254353073_<149>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1761079087 Step 1 took 11284ms Step 2 took 10537ms ********** Factor found in step 2: 424468423345885433156577302198219 Found probable prime factor of 33 digits: 424468423345885433156577302198219 Composite cofactor has 149 digits
(49·10²⁰³-31)/9 = 5(4)₂₀₂1_<204> = 787 · 7433 · C197
C197 = P30 · P168
P30 = 250258947013949118526184405219_<30>
P168 = 371899070167657494778515770799102838016236456489920897993331203914363646004089375009102210345490410627952983442877093935149349822956554542662818169335938886868137369209_<168>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1435368007 Step 1 took 13265ms Step 2 took 12292ms ********** Factor found in step 2: 250258947013949118526184405219 Found probable prime factor of 30 digits: 250258947013949118526184405219 Probable prime cofactor has 168 digits
(49·10¹⁵²-31)/9 = 5(4)₁₅₁1_<153> = 139066913 · 143811039393017_<15> · C131
C131 = P30 · P101
P30 = 812352607758978810286632150707_<30>
P101 = 33511429361318384365714365555561437168521607903032200299203243906271811241705138132135209592480782203_<101>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1803878505 Step 1 took 6969ms Step 2 took 7556ms ********** Factor found in step 2: 812352607758978810286632150707 Found probable prime factor of 30 digits: 812352607758978810286632150707 Probable prime cofactor has 101 digits
(49·10¹⁹⁰-31)/9 = 5(4)₁₈₉1_<191> = 3 · 63389 · 8043221326363661_<16> · C170
C170 = P32 · C139
P32 = 10488120350258049738490426522001_<32>
C139 = [3393835074574017376539546445699521745886417441021383295473943155188861165490674176590119566336901074380489532848268861497947052610509364443_<139>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=135339706 Step 1 took 9849ms Step 2 took 9693ms ********** Factor found in step 2: 10488120350258049738490426522001 Found probable prime factor of 32 digits: 10488120350258049738490426522001 Composite cofactor has 139 digits
(49·10¹⁸⁶-31)/9 = 5(4)₁₈₅1_<187> = 4861 · C184
C184 = P31 · C153
P31 = 1241191640392313005099385818109_<31>
C153 = [902379265325329705591066395933044306860508809089952038926144254478684282445955327984884168429055650670735545558654745328579151448711225262133357429176209_<153>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1750105925 Step 1 took 11496ms Step 2 took 10725ms ********** Factor found in step 2: 1241191640392313005099385818109 Found probable prime factor of 31 digits: 1241191640392313005099385818109 Composite cofactor has 153 digits
(49·10¹⁶⁹-31)/9 = 5(4)₁₆₈1_<170> = 3 · 1087 · 675074612021_<12> · 2254401221812081_<16> · 910389927427035326570473463_<27> · C113
C113 = P35 · P78
P35 = 29391527720593538801969447888738177_<35>
P78 = 409987089110436215559923537098846799981853399910166677561191189758960834735231_<78>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3128579257 Step 1 took 5816ms Step 2 took 6796ms ********** Factor found in step 2: 29391527720593538801969447888738177 Found probable prime factor of 35 digits: 29391527720593538801969447888738177 Probable prime cofactor has 78 digits
(49·10¹⁶⁵-31)/9 = 5(4)₁₆₄1_<166> = 2657 · 3415503671_<10> · 97183337723738729_<17> · 17795071470385183553_<20> · C117
C117 = P31 · P86
P31 = 3634817774191577551868236530631_<31>
P86 = 95440579885143177494526759532437749091043702738081194606442117590125371568906001930449_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1236416677 Step 1 took 7152ms Step 2 took 4841ms ********** Factor found in step 2: 3634817774191577551868236530631 Found probable prime factor of 31 digits: 3634817774191577551868236530631 Probable prime cofactor 95440579885143177494526759532437749091043702738081194606442117590125371568906001930449 has 86 digits
Mar 21, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Mar 21, 2009
(49·10¹²⁷-31)/9 = 5(4)₁₂₆1_<128> = 3 · C128
C128 = P42 · P86
P42 = 212686756056207820346328747855854527191863_<42>
P86 = 85328059370805598805282609306653258989436996598344573461264897015482912785725445799269_<86>

Number: 54441_127 N=18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147 ( 128 digits) SNFS difficulty: 129 digits. Divisors found: r1=212686756056207820346328747855854527191863 r2=85328059370805598805282609306653258989436996598344573461264897015482912785725445799269 Version: Total time: 3.09 hours. Scaled time: 3.10 units (timescale=1.003). Factorization parameters were as follows: n: 18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147 m: 20000000000000000000000000 deg: 5 c5: 1225 c0: -248 skew: 0.73 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 135042 x 135285 Total sieving time: 3.09 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,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 3.09 hours. --------- CPU info (if available) ----------
(49·10¹²⁰-31)/9 = 5(4)₁₁₉1_<121> = 257 · 35597 · C114
C114 = P54 · P61
P54 = 536245068924591737124655246514569309654380430554957439_<54>
P61 = 1109797486936534216431504198518455998801702013987553663743811_<61>

Number: 54441_120 N=595123429874620488877865745522476530609183767447333792987237966698374600102864048509798178949024411125062504660029 ( 114 digits) SNFS difficulty: 121 digits. Divisors found: r1=536245068924591737124655246514569309654380430554957439 r2=1109797486936534216431504198518455998801702013987553663743811 Version: Total time: 2.27 hours. Scaled time: 1.79 units (timescale=0.789). Factorization parameters were as follows: n: 595123429874620488877865745522476530609183767447333792987237966698374600102864048509798178949024411125062504660029 m: 1000000000000000000000000 deg: 5 c5: 49 c0: -31 skew: 0.91 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, 625001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 80161 x 80380 Total sieving time: 2.27 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,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 2.27 hours. --------- CPU info (if available) ----------
Mar 21, 2009: By Ignacio Santos / GGNFS, Msieve / Mar 21, 2009
(47·10¹⁶²+61)/9 = 5(2)₁₆₁9_<163> = 3 · 329083 · C157
C157 = P42 · P115
P42 = 971829109621331280713052310611805906814693_<42>
P115 = 5443005115212690963075124445015554464452373759718062686515066448009637291266093021375952448364071566322188969133697_<115>

Number: 52229_162 N=5289670814781501143300446211869773706757081771895663831740748506427681590178589415863902847429799596882065438630195849499186347337117811435840626044921010021 ( 157 digits) SNFS difficulty: 164 digits. Divisors found: r1=971829109621331280713052310611805906814693 (pp42) r2=5443005115212690963075124445015554464452373759718062686515066448009637291266093021375952448364071566322188969133697 (pp115) Version: Msieve-1.39 Total time: 53.98 hours. Scaled time: 138.18 units (timescale=2.560). Factorization parameters were as follows: n: 5289670814781501143300446211869773706757081771895663831740748506427681590178589415863902847429799596882065438630195849499186347337117811435840626044921010021 m: 200000000000000000000000000000000 deg: 5 c5: 1175 c0: 488 skew: 0.84 type: snfs lss: 1 rlim: 3900000 alim: 3900000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor 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, 4850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 809812 x 810060 Total sieving time: 53.98 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: 53.98 hours. --------- CPU info (if available) ----------
(49·10¹¹⁴-31)/9 = 5(4)₁₁₃1_<115> = 23 · 43 · 109 · 4813 · C107
C107 = P53 · P54
P53 = 22217334636516340591183544712573576415815305878084841_<53>
P54 = 472305456504688210183240694188825900424928109872524477_<54>

Number: 54441_114 N=10493368377817271347115806055703917115117200333973420452515559643189386533008085084441860317566670655153157 ( 107 digits) SNFS difficulty: 116 digits. Divisors found: r1=22217334636516340591183544712573576415815305878084841 (pp53) r2=472305456504688210183240694188825900424928109872524477 (pp54) Version: Msieve-1.39 Total time: 0.96 hours. Scaled time: 2.48 units (timescale=2.571). Factorization parameters were as follows: n: 10493368377817271347115806055703917115117200333973420452515559643189386533008085084441860317566670655153157 m: 100000000000000000000000 deg: 5 c5: 49 c0: -310 skew: 1.45 type: snfs lss: 1 rlim: 620000 alim: 620000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 620000/620000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [310000, 510001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 75195 x 75435 Total sieving time: 0.96 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,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000 total time: 0.96 hours. --------- CPU info (if available) ----------
(49·10¹¹⁷-31)/9 = 5(4)₁₁₆1_<118> = C118
C118 = P39 · P80
P39 = 154246452441159111248982572678667916573_<39>
P80 = 35297048057045941607042149181609332851433750679475844777668550528971140848239917_<80>

Number: 54441_117 N=5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 ( 118 digits) SNFS difficulty: 119 digits. Divisors found: r1=154246452441159111248982572678667916573 (pp39) r2=35297048057045941607042149181609332851433750679475844777668550528971140848239917 (pp80) Version: Msieve-1.39 Total time: 1.25 hours. Scaled time: 3.21 units (timescale=2.571). Factorization parameters were as follows: n: 5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 m: 200000000000000000000000 deg: 5 c5: 1225 c0: -248 skew: 0.73 type: snfs lss: 1 rlim: 690000 alim: 690000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 690000/690000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [345000, 595001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 74942 x 75178 Total sieving time: 1.25 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,119,5,0,0,0,0,0,0,0,0,690000,690000,25,25,45,45,2.2,2.2,50000 total time: 1.25 hours. --------- CPU info (if available) ----------
(49·10¹²⁵-31)/9 = 5(4)₁₂₄1_<126> = 4804924649857833704429_<22> · C105
C105 = P40 · P66
P40 = 1025115644707967819539554614441428582207_<40>
P66 = 110533552316652305766096265640112667609906689555884231601589422947_<66>

Number: 54441_125 N=113309673744946918369078305215256276714041773591243698665463621421495132893957196327768571317221481704029 ( 105 digits) SNFS difficulty: 126 digits. Divisors found: r1=1025115644707967819539554614441428582207 (pp40) r2=110533552316652305766096265640112667609906689555884231601589422947 (pp66) Version: Msieve-1.39 Total time: 1.87 hours. Scaled time: 4.82 units (timescale=2.571). Factorization parameters were as follows: n: 113309673744946918369078305215256276714041773591243698665463621421495132893957196327768571317221481704029 m: 10000000000000000000000000 deg: 5 c5: 49 c0: -31 skew: 0.91 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor 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 : 112522 x 112770 Total sieving time: 1.87 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: 1.87 hours. --------- CPU info (if available) ----------
(49·10¹³⁰-31)/9 = 5(4)₁₂₉1_<131> = 3³ · C130
C130 = P43 · P87
P43 = 3485194438046429071043711780795569694241101_<43>
P87 = 578579170027623963886718225384340201589963557785325638183886905382835163611758103197383_<87>

Number: 54441_130 N=2016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683 ( 130 digits) SNFS difficulty: 131 digits. Divisors found: r1=3485194438046429071043711780795569694241101 (pp43) r2=578579170027623963886718225384340201589963557785325638183886905382835163611758103197383 (pp87) Version: Msieve-1.39 Total time: 2.36 hours. Scaled time: 6.06 units (timescale=2.571). Factorization parameters were as follows: n: 2016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683 m: 100000000000000000000000000 deg: 5 c5: 49 c0: -31 skew: 0.91 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 146156 x 146404 Total sieving time: 2.36 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,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 2.36 hours. --------- CPU info (if available) ----------
(49·10¹²⁴-31)/9 = 5(4)₁₂₃1_<125> = 3 · 149 · C123
C123 = P46 · P77
P46 = 3678469373978815613162658522544463360181425083_<46>
P77 = 33111503622293235320810964516155255520009807603765550297505951353818595518341_<77>

Number: 54441_124 N=121799652000994282873477504349987571464081531195625155356698980860054685558041262739249316430524484215759383544618443947303 ( 123 digits) SNFS difficulty: 126 digits. Divisors found: r1=3678469373978815613162658522544463360181425083 (pp46) r2=33111503622293235320810964516155255520009807603765550297505951353818595518341 (pp77) Version: Msieve-1.39 Total time: 1.91 hours. Scaled time: 4.88 units (timescale=2.560). Factorization parameters were as follows: n: 121799652000994282873477504349987571464081531195625155356698980860054685558041262739249316430524484215759383544618443947303 m: 10000000000000000000000000 deg: 5 c5: 49 c0: -310 skew: 1.45 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor 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, 800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 135026 x 135274 Total sieving time: 1.91 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: 1.91 hours. --------- CPU info (if available) ----------
(49·10¹³²-31)/9 = 5(4)₁₃₁1_<133> = 937 · 4933 · 135039659411715644318569_<24> · C103
C103 = P48 · P55
P48 = 917343383904947349456475388877809429569624434029_<48>
P55 = 9508447156545723192298461689453019352567992309220057321_<55>

Number: 54441_132 N=8722511090267028359167642705465348623623120554971794762786759770704907991910292127174579618889562976309 ( 103 digits) SNFS difficulty: 134 digits. Divisors found: r1=917343383904947349456475388877809429569624434029 (pp48) r2=9508447156545723192298461689453019352567992309220057321 (pp55) Version: Msieve-1.39 Total time: 3.04 hours. Scaled time: 7.78 units (timescale=2.560). Factorization parameters were as follows: n: 8722511090267028359167642705465348623623120554971794762786759770704907991910292127174579618889562976309 m: 200000000000000000000000000 deg: 5 c5: 1225 c0: -248 skew: 0.73 type: snfs lss: 1 rlim: 1230000 alim: 1230000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1230000/1230000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [615000, 1140001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 190721 x 190969 Total sieving time: 3.04 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,134,5,0,0,0,0,0,0,0,0,1230000,1230000,26,26,47,47,2.3,2.3,75000 total time: 3.04 hours. --------- CPU info (if available) ----------
(49·10¹³⁹-31)/9 = 5(4)₁₃₈1_<140> = 3² · 29 · 141301 · 452326029838012123503316567_<27> · C106
C106 = P45 · P61
P45 = 750377221650197702999288202630635030091562231_<45>
P61 = 4349472657235673314417701685009106480893148418132764187177953_<61>

Number: 54441_139 N=3263745208180007214729459399101391881242230962552165253868053894917788151729797936352756748668504970693143 ( 106 digits) SNFS difficulty: 141 digits. Divisors found: r1=750377221650197702999288202630635030091562231 (pp45) r2=4349472657235673314417701685009106480893148418132764187177953 (pp61) Version: Msieve-1.39 Total time: 6.53 hours. Scaled time: 16.72 units (timescale=2.560). Factorization parameters were as follows: n: 3263745208180007214729459399101391881242230962552165253868053894917788151729797936352756748668504970693143 m: 10000000000000000000000000000 deg: 5 c5: 49 c0: -310 skew: 1.45 type: snfs lss: 1 rlim: 1610000 alim: 1610000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1610000/1610000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [805000, 1905001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 254680 x 254928 Total sieving time: 6.53 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,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000 total time: 6.53 hours. --------- CPU info (if available) ----------
(49·10¹⁵⁷-31)/9 = 5(4)₁₅₆1_<158> = 3³ · 6122309 · C150
C150 = P31 · P120
P31 = 1923220060004563723065726411371_<31>
P120 = 171255915216534977122827386763108934627093798220839334994149913976056197515328298881509804914207268712955084143436490397_<120>

Number: 54441_157 N=329362811538880876264678501528828568657641134853390701452092814222508899613385664136922998389952914608381833065998613488766123807721493968445713104287 ( 150 digits) SNFS difficulty: 159 digits. Divisors found: r1=1923220060004563723065726411371 (pp31) r2=171255915216534977122827386763108934627093798220839334994149913976056197515328298881509804914207268712955084143436490397 (pp120) Version: Msieve-1.39 Total time: 24.52 hours. Scaled time: 62.77 units (timescale=2.560). Factorization parameters were as follows: n: 329362811538880876264678501528828568657641134853390701452092814222508899613385664136922998389952914608381833065998613488766123807721493968445713104287 m: 20000000000000000000000000000000 deg: 5 c5: 1225 c0: -248 skew: 0.73 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1600000, 2900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 608559 x 608807 Total sieving time: 24.52 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,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000 total time: 24.52 hours. --------- CPU info (if available) ----------
(47·10¹⁷⁴+43)/9 = 5(2)₁₇₃7_<175> = 23² · C172
C172 = P47 · P126
P47 = 20155372881344237249701760518000538181423547561_<47>
P126 = 489788788056215750930608840816878998358650966697873970244482403849329672929816622034720262339309577873049188174812546664400683_<126>

Number: 52227_174 N=9871875656374711195127074144087376601554295316110060911573198907792480571308548624238605335013652593992858643142197017433312329342575089266960722537282083595883217811384163 ( 172 digits) SNFS difficulty: 176 digits. Divisors found: r1=20155372881344237249701760518000538181423547561 (pp47) r2=489788788056215750930608840816878998358650966697873970244482403849329672929816622034720262339309577873049188174812546664400683 (pp126) Version: Msieve-1.39 Total time: 101.80 hours. Scaled time: 177.03 units (timescale=1.739). Factorization parameters were as follows: n: 9871875656374711195127074144087376601554295316110060911573198907792480571308548624238605335013652593992858643142197017433312329342575089266960722537282083595883217811384163 m: 100000000000000000000000000000000000 deg: 5 c5: 47 c0: 430 skew: 1.56 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3100000, 8400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1363720 x 1363968 Total sieving time: 101.80 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,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000 total time: 101.80 hours. --------- CPU info (if available) ----------
Mar 20, 2009 (8th): By Wataru Sakai / GMP-ECM / Mar 20, 2009
(23·10¹⁹¹-41)/9 = 2(5)₁₉₀1_<192> = 536749 · 1049437 · 2222514223_<10> · 164646728337905536231_<21> · 640556862356338194459757_<24> · C127
C127 = P44 · P84
P44 = 18183469352047122005819738271467857341848407_<44>
P84 = 106445086486657196807532944997246788012201790725070046199662462071658155594075770621_<84>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3307947160 Step 1 took 151244ms Step 2 took 48221ms ********** Factor found in step 2: 18183469352047122005819738271467857341848407 Found probable prime factor of 44 digits: 18183469352047122005819738271467857341848407 Probable prime cofactor 106445086486657196807532944997246788012201790725070046199662462071658155594075770621 has 84 digits
Mar 20, 2009 (7th): By Erik Branger / GGNFS, Msieve / Mar 20, 2009
(47·10¹⁵²+61)/9 = 5(2)₁₅₁9_<153> = 67 · 5963899 · 50127534151990733094529_<23> · C122
C122 = P58 · P65
P58 = 1142881122706237152034929100702236331731481069594600653461_<58>
P65 = 22812499110881731749464498894319372578237508831024251483110858577_<65>

Number: 52229_152 N=26071974595579550393999475913790933972486860700120637626726518445387274546574219539309075431750905426207893727988956584997 ( 122 digits) SNFS difficulty: 154 digits. Divisors found: r1=1142881122706237152034929100702236331731481069594600653461 r2=22812499110881731749464498894319372578237508831024251483110858577 Version: Total time: 35.93 hours. Scaled time: 36.25 units (timescale=1.009). Factorization parameters were as follows: n: 26071974595579550393999475913790933972486860700120637626726518445387274546574219539309075431750905426207893727988956584997 m: 2000000000000000000000000000000 deg: 5 c5: 1175 c0: 488 skew: 0.84 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor 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, 2700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 508553 x 508801 Total sieving time: 35.93 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 35.93 hours. --------- CPU info (if available) ----------
(16·10¹⁴⁷+17)/3 = 5(3)₁₄₆9_<148> = 19² · 844735909 · C137
C137 = P31 · P49 · P58
P31 = 1027482580059048117497952822277_<31>
P49 = 9409699702063826388217071571541161674436721450537_<49>
P58 = 1808924074299550618481698414759567874414711834398853215939_<58>

Number: 53339_147 N=17489225199528876930103479638040835832191914225321633209217253619853852876614293076683294006157083460741282726660636470553825466010806311 ( 137 digits) SNFS difficulty: 148 digits. Divisors found: r1=1027482580059048117497952822277 r2=9409699702063826388217071571541161674436721450537 r3=1808924074299550618481698414759567874414711834398853215939 Version: Total time: 9.11 hours. Scaled time: 9.07 units (timescale=0.995). Factorization parameters were as follows: n: 17489225199528876930103479638040835832191914225321633209217253619853852876614293076683294006157083460741282726660636470553825466010806311 m: 200000000000000000000000000000 deg: 5 c5: 50 c0: 17 skew: 0.81 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 299724 x 299972 Total sieving time: 9.11 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,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 9.11 hours. --------- CPU info (if available) ----------
(16·10¹⁴¹+17)/3 = 5(3)₁₄₀9_<142> = 627491 · C136
C136 = P53 · P83
P53 = 98531454093262507723164589411652625162805522024873067_<53>
P83 = 86261366709419004879256051310572074798571199905749754449998290361726951365465220987_<83>

Number: 53339_141 N=8499457893951201424934115920918918890204534142056751942790148915814463208768465736294756950033280689816002673079507647652848141779457129 ( 136 digits) SNFS difficulty: 142 digits. Divisors found: r1=98531454093262507723164589411652625162805522024873067 r2=86261366709419004879256051310572074798571199905749754449998290361726951365465220987 Version: Total time: 7.22 hours. Scaled time: 5.69 units (timescale=0.789). Factorization parameters were as follows: n: 8499457893951201424934115920918918890204534142056751942790148915814463208768465736294756950033280689816002673079507647652848141779457129 m: 20000000000000000000000000000 deg: 5 c5: 5 c0: 17 skew: 1.28 type: snfs lss: 1 rlim: 1700000 alim: 1700000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1700000/1700000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [850000, 1450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 218106 x 218354 Total sieving time: 7.22 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,142,5,0,0,0,0,0,0,0,0,1700000,1700000,26,26,48,48,2.3,2.3,100000 total time: 7.22 hours. --------- CPU info (if available) ----------
Mar 20, 2009 (6th): By Robert Backstrom / Msieve / Mar 20, 2009
(16·10¹²⁶+17)/3 = 5(3)₁₂₅9_<127> = 11² · 937 · 1537258295437_<13> · 9025370693297974973_<19> · C91
C91 = P41 · P50
P41 = 77645603363146301434635923149259748641629_<41>
P50 = 43666160215801579806770536601220923608024965501583_<50>

Fri Mar 20 03:19:19 2009 Fri Mar 20 03:19:19 2009 Fri Mar 20 03:19:19 2009 Msieve v. 1.39 Fri Mar 20 03:19:19 2009 random seeds: 01ab27d4 f393454b Fri Mar 20 03:19:19 2009 factoring 3390485356507728372669909109598783194410042535424399523149281361272522288277422770899198707 (91 digits) Fri Mar 20 03:19:20 2009 searching for 15-digit factors Fri Mar 20 03:19:22 2009 commencing quadratic sieve (91-digit input) Fri Mar 20 03:19:22 2009 using multiplier of 43 Fri Mar 20 03:19:22 2009 using 64kb Opteron sieve core Fri Mar 20 03:19:22 2009 sieve interval: 18 blocks of size 65536 Fri Mar 20 03:19:22 2009 processing polynomials in batches of 6 Fri Mar 20 03:19:22 2009 using a sieve bound of 1683637 (63529 primes) Fri Mar 20 03:19:22 2009 using large prime bound of 154894604 (27 bits) Fri Mar 20 03:19:22 2009 using double large prime bound of 552160384714396 (42-49 bits) Fri Mar 20 03:19:22 2009 using trial factoring cutoff of 49 bits Fri Mar 20 03:19:22 2009 polynomial 'A' values have 12 factors Fri Mar 20 04:18:10 2009 64199 relations (17518 full + 46681 combined from 716708 partial), need 63625 Fri Mar 20 04:18:11 2009 begin with 734226 relations Fri Mar 20 04:18:11 2009 reduce to 155637 relations in 9 passes Fri Mar 20 04:18:11 2009 attempting to read 155637 relations Fri Mar 20 04:18:12 2009 recovered 155637 relations Fri Mar 20 04:18:12 2009 recovered 132969 polynomials Fri Mar 20 04:18:13 2009 attempting to build 64199 cycles Fri Mar 20 04:18:13 2009 found 64199 cycles in 6 passes Fri Mar 20 04:18:13 2009 distribution of cycle lengths: Fri Mar 20 04:18:13 2009 length 1 : 17518 Fri Mar 20 04:18:13 2009 length 2 : 12567 Fri Mar 20 04:18:13 2009 length 3 : 11363 Fri Mar 20 04:18:13 2009 length 4 : 8435 Fri Mar 20 04:18:13 2009 length 5 : 5794 Fri Mar 20 04:18:13 2009 length 6 : 3759 Fri Mar 20 04:18:13 2009 length 7 : 2181 Fri Mar 20 04:18:13 2009 length 9+: 2582 Fri Mar 20 04:18:13 2009 largest cycle: 18 relations Fri Mar 20 04:18:13 2009 matrix is 63529 x 64199 (15.4 MB) with weight 3775271 (58.81/col) Fri Mar 20 04:18:13 2009 sparse part has weight 3775271 (58.81/col) Fri Mar 20 04:18:14 2009 filtering completed in 3 passes Fri Mar 20 04:18:14 2009 matrix is 58990 x 59053 (14.2 MB) with weight 3474411 (58.84/col) Fri Mar 20 04:18:14 2009 sparse part has weight 3474411 (58.84/col) Fri Mar 20 04:18:14 2009 saving the first 48 matrix rows for later Fri Mar 20 04:18:14 2009 matrix is 58942 x 59053 (8.3 MB) with weight 2643233 (44.76/col) Fri Mar 20 04:18:14 2009 sparse part has weight 1831762 (31.02/col) Fri Mar 20 04:18:14 2009 matrix includes 64 packed rows Fri Mar 20 04:18:14 2009 using block size 23621 for processor cache size 1024 kB Fri Mar 20 04:18:15 2009 commencing Lanczos iteration Fri Mar 20 04:18:15 2009 memory use: 8.5 MB Fri Mar 20 04:18:33 2009 lanczos halted after 934 iterations (dim = 58938) Fri Mar 20 04:18:33 2009 recovered 16 nontrivial dependencies Fri Mar 20 04:18:34 2009 prp41 factor: 77645603363146301434635923149259748641629 Fri Mar 20 04:18:34 2009 prp50 factor: 43666160215801579806770536601220923608024965501583 Fri Mar 20 04:18:34 2009 elapsed time 00:59:15
(16·10¹³⁷+17)/3 = 5(3)₁₃₆9_<138> = 2087 · 7759 · 28201 · 792993427 · 20925773837827387826419_<23> · C95
C95 = P34 · P61
P34 = 7354562144409310904345832577230403_<34>
P61 = 9569694675376026666594225015995206118078921791743315366068497_<61>

Fri Mar 20 04:35:22 2009 Fri Mar 20 04:35:22 2009 Fri Mar 20 04:35:22 2009 Msieve v. 1.39 Fri Mar 20 04:35:22 2009 random seeds: bb7c5658 294ba63c Fri Mar 20 04:35:22 2009 factoring 70380914193075875069160056899381282352396507812412050756086369583463941326145489766315048914291 (95 digits) Fri Mar 20 04:35:22 2009 searching for 15-digit factors Fri Mar 20 04:35:23 2009 commencing quadratic sieve (95-digit input) Fri Mar 20 04:35:23 2009 using multiplier of 1 Fri Mar 20 04:35:23 2009 using 64kb Opteron sieve core Fri Mar 20 04:35:23 2009 sieve interval: 18 blocks of size 65536 Fri Mar 20 04:35:23 2009 processing polynomials in batches of 6 Fri Mar 20 04:35:23 2009 using a sieve bound of 2196599 (80820 primes) Fri Mar 20 04:35:23 2009 using large prime bound of 329489850 (28 bits) Fri Mar 20 04:35:23 2009 using double large prime bound of 2148402323041500 (43-51 bits) Fri Mar 20 04:35:23 2009 using trial factoring cutoff of 51 bits Fri Mar 20 04:35:23 2009 polynomial 'A' values have 12 factors Fri Mar 20 07:49:29 2009 81047 relations (19018 full + 62029 combined from 1236147 partial), need 80916 Fri Mar 20 07:49:31 2009 begin with 1255165 relations Fri Mar 20 07:49:32 2009 reduce to 215317 relations in 11 passes Fri Mar 20 07:49:32 2009 attempting to read 215317 relations Fri Mar 20 07:49:35 2009 recovered 215317 relations Fri Mar 20 07:49:35 2009 recovered 201777 polynomials Fri Mar 20 07:49:35 2009 attempting to build 81047 cycles Fri Mar 20 07:49:35 2009 found 81047 cycles in 7 passes Fri Mar 20 07:49:36 2009 distribution of cycle lengths: Fri Mar 20 07:49:36 2009 length 1 : 19018 Fri Mar 20 07:49:36 2009 length 2 : 13676 Fri Mar 20 07:49:36 2009 length 3 : 13585 Fri Mar 20 07:49:36 2009 length 4 : 11033 Fri Mar 20 07:49:36 2009 length 5 : 8460 Fri Mar 20 07:49:36 2009 length 6 : 5900 Fri Mar 20 07:49:36 2009 length 7 : 3881 Fri Mar 20 07:49:36 2009 length 9+: 5494 Fri Mar 20 07:49:36 2009 largest cycle: 23 relations Fri Mar 20 07:49:36 2009 matrix is 80820 x 81047 (22.0 MB) with weight 5430538 (67.00/col) Fri Mar 20 07:49:36 2009 sparse part has weight 5430538 (67.00/col) Fri Mar 20 07:49:38 2009 filtering completed in 3 passes Fri Mar 20 07:49:38 2009 matrix is 77513 x 77577 (21.1 MB) with weight 5218749 (67.27/col) Fri Mar 20 07:49:38 2009 sparse part has weight 5218749 (67.27/col) Fri Mar 20 07:49:38 2009 saving the first 48 matrix rows for later Fri Mar 20 07:49:38 2009 matrix is 77465 x 77577 (13.7 MB) with weight 4138441 (53.35/col) Fri Mar 20 07:49:38 2009 sparse part has weight 3127760 (40.32/col) Fri Mar 20 07:49:38 2009 matrix includes 64 packed rows Fri Mar 20 07:49:38 2009 using block size 31030 for processor cache size 1024 kB Fri Mar 20 07:49:38 2009 commencing Lanczos iteration Fri Mar 20 07:49:38 2009 memory use: 13.0 MB Fri Mar 20 07:50:22 2009 lanczos halted after 1226 iterations (dim = 77462) Fri Mar 20 07:50:22 2009 recovered 15 nontrivial dependencies Fri Mar 20 07:50:23 2009 prp34 factor: 7354562144409310904345832577230403 Fri Mar 20 07:50:23 2009 prp61 factor: 9569694675376026666594225015995206118078921791743315366068497 Fri Mar 20 07:50:23 2009 elapsed time 03:15:01
Mar 20, 2009 (5th): By Sinkiti Sibata / GGNFS, Msieve / Mar 20, 2009
(47·10¹⁵⁵+61)/9 = 5(2)₁₅₄9_<156> = 43 · 35909329 · 58770731 · 20170670960464360204959468810331_<32> · C108
C108 = P40 · P69
P40 = 1362060369851719248423367258847794687379_<40>
P69 = 209460342073774190375828058205240979575586001449705679614534145203053_<69>

Number: 52227_155 N=285297630994272504091552978449388295403830314074853375107757128116579477814437793906499110695817310611368087 ( 108 digits) Divisors found: r1=1362060369851719248423367258847794687379 (pp40) r2=209460342073774190375828058205240979575586001449705679614534145203053 (pp69) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 20.73 hours. Scaled time: 9.78 units (timescale=0.472). Factorization parameters were as follows: name: 52227_155 n: 285297630994272504091552978449388295403830314074853375107757128116579477814437793906499110695817310611368087 skew: 12217.28 # norm 5.15e+14 c5: 24480 c4: 2762001072 c3: -4673288308058 c2: -155456926716493285 c1: 560007686009585776790 c0: -3036206145102312397412120 # alpha -6.01 Y1: 239892078833 Y0: -410479642376546949693 # Murphy_E 1.42e-09 # M 253874833941645235923460218686059303773393118734419260658942706884390200216848854565959869477840516971217388 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:182725, largePrimes:4485821 encountered Relations: rels:4584016, finalFF:461794 Max relations in full relation-set: 28 Initial matrix: 365882 x 461794 with sparse part having weight 37155706. Pruned matrix : 295333 x 297226 with weight 21432233. Total sieving time: 17.67 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.50 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: 20.73 hours. --------- CPU info (if available) ----------
(16·10¹¹⁹+17)/3 = 5(3)₁₁₈9_<120> = 31 · 7079 · 7507 · 32909 · C106
C106 = P37 · P70
P37 = 4977605857740139864313943677940325771_<37>
P70 = 1976348440568735697281734967191062750712135499265960643476367149133007_<70>

Number: 53339_119 N=9837483574710529484514161171773761501488325082032517410013632145633355081949361660424442639434305788823397 ( 106 digits) SNFS difficulty: 120 digits. Divisors found: r1=4977605857740139864313943677940325771 (pp37) r2=1976348440568735697281734967191062750712135499265960643476367149133007 (pp70) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.22 hours. Scaled time: 1.05 units (timescale=0.471). Factorization parameters were as follows: name: 53339_119 n: 9837483574710529484514161171773761501488325082032517410013632145633355081949361660424442639434305788823397 m: 1000000000000000000000000 deg: 5 c5: 8 c0: 85 skew: 1.60 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: RFBsize:58029, AFBsize:58122, largePrimes:1442756 encountered Relations: rels:1515012, finalFF:240263 Max relations in full relation-set: 28 Initial matrix: 116216 x 240263 with sparse part having weight 10375872. Pruned matrix : 73227 x 73872 with weight 2689877. Total sieving time: 2.11 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 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: 2.22 hours. --------- CPU info (if available) ----------
(16·10¹³⁴+17)/3 = 5(3)₁₃₃9_<135> = 7 · 11 · 31 · 4163857 · 129955037024232517_<18> · C108
C108 = P34 · P37 · P38
P34 = 7099268159581713691554413997525083_<34>
P37 = 4760738577651298269591554866833674069_<37>
P38 = 12217137744962110664685060042692824819_<38>

Number: 53339_134 N=412911886952778951482599343105106825878811600735884610546214381342461568817914643805148222356406506358511413 ( 108 digits) SNFS difficulty: 135 digits. Divisors found: r1=7099268159581713691554413997525083 r2=4760738577651298269591554866833674069 r3=12217137744962110664685060042692824819 Version: Total time: 2.82 hours. Scaled time: 7.21 units (timescale=2.554). Factorization parameters were as follows: name: 53339_134 n: 412911886952778951482599343105106825878811600735884610546214381342461568817914643805148222356406506358511413 m: 1000000000000000000000000000 deg: 5 c5: 8 c0: 85 skew: 1.60 type: snfs lss: 1 rlim: 1290000 alim: 1290000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 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: 47/47 Sieved rational special-q in [645000, 1020001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 153532 x 153780 Total sieving time: 2.82 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,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000 total time: 2.82 hours. --------- CPU info (if available) ----------
(16·10¹³⁵+17)/3 = 5(3)₁₃₄9_<136> = 53 · 109 · 39983 · C128
C128 = P42 · P87
P42 = 133371437502545860492092625754017350087647_<42>
P87 = 173124348209509979320647923853723089400683536821989636733066792235614750308712167807707_<87>

Number: 53339_135 N=23089843187393647550915965204085430843911558956321943721240490915291817671174492422795930841723074756716789564305237088292095429 ( 128 digits) SNFS difficulty: 136 digits. Divisors found: r1=133371437502545860492092625754017350087647 r2=173124348209509979320647923853723089400683536821989636733066792235614750308712167807707 Version: Total time: 2.81 hours. Scaled time: 7.21 units (timescale=2.564). Factorization parameters were as follows: name: 53339_135 n: 23089843187393647550915965204085430843911558956321943721240490915291817671174492422795930841723074756716789564305237088292095429 m: 1000000000000000000000000000 deg: 5 c5: 16 c0: 17 skew: 1.01 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, 1025001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 165863 x 166111 Total sieving time: 2.81 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 2.81 hours. --------- CPU info (if available) ----------
(16·10¹³⁰+17)/3 = 5(3)₁₂₉9_<131> = 11 · 13 · 499 · 32102129 · C119
C119 = P42 · P77
P42 = 275816506470850227753681936494105767780247_<42>
P77 = 84412751354152141283549803205638828396580374356093958903094653958614394263729_<77>

Number: 53339_130 N=23282430180094775401664521018455232150876520275482514920064567080964332978328610680296163882721213301511223106234761063 ( 119 digits) SNFS difficulty: 131 digits. Divisors found: r1=275816506470850227753681936494105767780247 (pp42) r2=84412751354152141283549803205638828396580374356093958903094653958614394263729 (pp77) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.44 hours. Scaled time: 1.62 units (timescale=0.471). Factorization parameters were as follows: name: 53339_130 n: 23282430180094775401664521018455232150876520275482514920064567080964332978328610680296163882721213301511223106234761063 m: 100000000000000000000000000 deg: 5 c5: 16 c0: 17 skew: 1.01 type: snfs lss: 1 rlim: 1080000 alim: 1080000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor 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, 790001) Primes: RFBsize:84270, AFBsize:83658, largePrimes:2549375 encountered Relations: rels:2425796, finalFF:198554 Max relations in full relation-set: 28 Initial matrix: 167992 x 198554 with sparse part having weight 12368837. Pruned matrix : 152731 x 153634 with weight 7390128. Total sieving time: 3.02 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.30 hours. Time per square root: 0.04 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: 3.44 hours. --------- CPU info (if available) ----------
(16·10¹³¹+17)/3 = 5(3)₁₃₀9_<132> = 61 · 113 · 1171 · 1184923 · 754627619 · 7329756391_<10> · C101
C101 = P46 · P55
P46 = 1715422178096007542208514188552440247371207737_<46>
P55 = 5876925256617012992829424695030398752503942555565595747_<55>

Number: 53339_131 N=10081407924213394489644691046726487228205642771742243655608201909603448312917038974804331061300694539 ( 101 digits) SNFS difficulty: 132 digits. Divisors found: r1=1715422178096007542208514188552440247371207737 (pp46) r2=5876925256617012992829424695030398752503942555565595747 (pp55) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.88 hours. Scaled time: 1.83 units (timescale=0.471). Factorization parameters were as follows: name: 53339_131 n: 10081407924213394489644691046726487228205642771742243655608201909603448312917038974804331061300694539 m: 200000000000000000000000000 deg: 5 c5: 5 c0: 17 skew: 1.28 type: snfs rlim: 1120000 alim: 1120000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1120000/1120000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [560000, 860001) Primes: RFBsize:87166, AFBsize:87008, largePrimes:2732090 encountered Relations: rels:2654691, finalFF:241993 Max relations in full relation-set: 28 Initial matrix: 174239 x 241993 with sparse part having weight 16453366. Pruned matrix : 145300 x 146235 with weight 7280426. Total sieving time: 3.47 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.28 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1120000,1120000,26,26,47,47,2.3,2.3,50000 total time: 3.88 hours. --------- CPU info (if available) ----------
(16·10¹³⁸+17)/3 = 5(3)₁₃₇9_<139> = 11 · 9187 · 15215909 · C127
C127 = P39 · P88
P39 = 454899394030094871696840828218919010961_<39>
P88 = 7624635131405306021976110358540209676561181550632754418412763175674346292489709058390223_<88>

Number: 53339_138 N=3468441900976846493796351077859498146675611652658964776630576869620175883842676469694774931859655655146040671758074217952234303 ( 127 digits) SNFS difficulty: 140 digits. Divisors found: r1=454899394030094871696840828218919010961 r2=7624635131405306021976110358540209676561181550632754418412763175674346292489709058390223 Version: Total time: 4.22 hours. Scaled time: 10.83 units (timescale=2.564). Factorization parameters were as follows: name: 53339_138 n: 3468441900976846493796351077859498146675611652658964776630576869620175883842676469694774931859655655146040671758074217952234303 m: 4000000000000000000000000000 deg: 5 c5: 125 c0: 136 skew: 1.02 type: snfs rlim: 1510000 alim: 1510000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1510000/1510000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [755000, 1355001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 207358 x 207606 Total sieving time: 4.22 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,140,5,0,0,0,0,0,0,0,0,1510000,1510000,26,26,48,48,2.3,2.3,75000 total time: 4.22 hours. --------- CPU info (if available) ----------
(16·10¹²⁷+17)/3 = 5(3)₁₂₆9_<128> = 5246909 · 4320900800743087688077_<22> · C100
C100 = P31 · P69
P31 = 9558968044013240910768539170267_<31>
P69 = 246099023374013580364688187219244824856754420286164173821931207411369_<69>

Fri Mar 20 02:52:59 2009 Msieve v. 1.39 Fri Mar 20 02:52:59 2009 random seeds: 487af480 a062588b Fri Mar 20 02:52:59 2009 factoring 2352452700095063449936800197036820541946192934736737492782356811379725987285009842257277012202565523 (100 digits) Fri Mar 20 02:53:00 2009 searching for 15-digit factors Fri Mar 20 02:53:02 2009 commencing quadratic sieve (100-digit input) Fri Mar 20 02:53:02 2009 using multiplier of 7 Fri Mar 20 02:53:02 2009 using 32kb Intel Core sieve core Fri Mar 20 02:53:02 2009 sieve interval: 36 blocks of size 32768 Fri Mar 20 02:53:02 2009 processing polynomials in batches of 6 Fri Mar 20 02:53:02 2009 using a sieve bound of 2712223 (98824 primes) Fri Mar 20 02:53:02 2009 using large prime bound of 406833450 (28 bits) Fri Mar 20 02:53:02 2009 using double large prime bound of 3140146831659150 (43-52 bits) Fri Mar 20 02:53:02 2009 using trial factoring cutoff of 52 bits Fri Mar 20 02:53:02 2009 polynomial 'A' values have 13 factors Fri Mar 20 15:36:05 2009 99080 relations (22548 full + 76532 combined from 1498989 partial), need 98920 Fri Mar 20 15:36:07 2009 begin with 1521537 relations Fri Mar 20 15:36:08 2009 reduce to 264208 relations in 11 passes Fri Mar 20 15:36:08 2009 attempting to read 264208 relations Fri Mar 20 15:36:13 2009 recovered 264208 relations Fri Mar 20 15:36:13 2009 recovered 256016 polynomials Fri Mar 20 15:36:14 2009 attempting to build 99080 cycles Fri Mar 20 15:36:14 2009 found 99080 cycles in 6 passes Fri Mar 20 15:36:14 2009 distribution of cycle lengths: Fri Mar 20 15:36:14 2009 length 1 : 22548 Fri Mar 20 15:36:14 2009 length 2 : 16737 Fri Mar 20 15:36:14 2009 length 3 : 16641 Fri Mar 20 15:36:14 2009 length 4 : 13788 Fri Mar 20 15:36:14 2009 length 5 : 10419 Fri Mar 20 15:36:14 2009 length 6 : 7348 Fri Mar 20 15:36:14 2009 length 7 : 4725 Fri Mar 20 15:36:14 2009 length 9+: 6874 Fri Mar 20 15:36:14 2009 largest cycle: 21 relations Fri Mar 20 15:36:14 2009 matrix is 98824 x 99080 (26.9 MB) with weight 6658301 (67.20/col) Fri Mar 20 15:36:14 2009 sparse part has weight 6658301 (67.20/col) Fri Mar 20 15:36:16 2009 filtering completed in 3 passes Fri Mar 20 15:36:16 2009 matrix is 95296 x 95360 (26.0 MB) with weight 6432846 (67.46/col) Fri Mar 20 15:36:16 2009 sparse part has weight 6432846 (67.46/col) Fri Mar 20 15:36:16 2009 saving the first 48 matrix rows for later Fri Mar 20 15:36:16 2009 matrix is 95248 x 95360 (15.2 MB) with weight 4959974 (52.01/col) Fri Mar 20 15:36:16 2009 sparse part has weight 3417728 (35.84/col) Fri Mar 20 15:36:16 2009 matrix includes 64 packed rows Fri Mar 20 15:36:16 2009 using block size 38144 for processor cache size 1024 kB Fri Mar 20 15:36:17 2009 commencing Lanczos iteration Fri Mar 20 15:36:17 2009 memory use: 15.4 MB Fri Mar 20 15:37:20 2009 lanczos halted after 1508 iterations (dim = 95246) Fri Mar 20 15:37:20 2009 recovered 17 nontrivial dependencies Fri Mar 20 15:37:21 2009 prp31 factor: 9558968044013240910768539170267 Fri Mar 20 15:37:21 2009 prp69 factor: 246099023374013580364688187219244824856754420286164173821931207411369 Fri Mar 20 15:37:21 2009 elapsed time 12:44:22
(16·10¹⁴⁵+17)/3 = 5(3)₁₄₄9_<146> = 29 · 751 · 750670353889_<12> · C130
C130 = P37 · P94
P37 = 1017920604757100124175506379483305391_<37>
P94 = 3204775581603897617400152633317975172533435467301482055633599256186949556972877362944784052759_<94>

Number: 53339_145 N=3262207098137026742245065842599988326637156703447034000654332100641563831391951069640537622805004889844622538445754817690253123769 ( 130 digits) SNFS difficulty: 146 digits. Divisors found: r1=1017920604757100124175506379483305391 (pp37) r2=3204775581603897617400152633317975172533435467301482055633599256186949556972877362944784052759 (pp94) Version: GGNFS-0.77.1-20060513-nocona Total time: 17.11 hours. Scaled time: 44.07 units (timescale=2.575). Factorization parameters were as follows: name: 53339_145 n: 3262207098137026742245065842599988326637156703447034000654332100641563831391951069640537622805004889844622538445754817690253123769 m: 100000000000000000000000000000 deg: 5 c5: 16 c0: 17 skew: 1.01 type: snfs 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 algebraic special-q in [955000, 2255001) Primes: RFBsize:142718, AFBsize:142015, largePrimes:4682805 encountered Relations: rels:5729679, finalFF:1220613 Max relations in full relation-set: 28 Initial matrix: 284797 x 1220613 with sparse part having weight 121044188. Pruned matrix : 178108 x 179595 with weight 38970759. Total sieving time: 16.63 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.33 hours. Time per square root: 0.06 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: 17.11 hours. --------- CPU info (if available) ----------
Mar 20, 2009 (4th): By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.39 / Mar 20, 2009
(16·10¹³⁶+17)/3 = 5(3)₁₃₅9_<137> = 11 · 13 · 347897551 · 2941447767611012578678018619_<28> · C99
C99 = P30 · P69
P30 = 771382818250946354031587328347_<30>
P69 = 472476504763422496979618639544003838355917850725179339642495333077011_<69>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1151270288 Step 1 took 5788ms Step 2 took 6180ms ********** Factor found in step 2: 771382818250946354031587328347 Found probable prime factor of 30 digits: 771382818250946354031587328347 Probable prime cofactor has 69 digits
(16·10¹⁵⁹+17)/3 = 5(3)₁₅₈9_<160> = 4201 · 11369 · 20060626646968543458887062589_<29> · C124
C124 = P30 · C95
P30 = 181460042160288350794014941791_<30>
C95 = [30675968082864569337146521319456691256436797450754597199363823113423792359722327736654385550169_<95>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1862731850 Step 1 took 6880ms Step 2 took 7373ms ********** Factor found in step 2: 181460042160288350794014941791 Found probable prime factor of 30 digits: 181460042160288350794014941791 Composite cofactor has 95 digits
(10²¹¹+53)/9 = (1)₂₁₀7_<211> = 7 · 181 · C207
C207 = P60 · P148
P60 = 775679158324538211798792416886447302960143319020119609397291_<60>
P148 = 1130573373691367761073599909764570902857706940533980710309137548448013445674329861601139507177146771800294938047935087576614132552921906658313292861_<148>

SNFS difficulty: 211 digits. Divisors found: r1=775679158324538211798792416886447302960143319020119609397291 (pp60) r2=1130573373691367761073599909764570902857706940533980710309137548448013445674329861601139507177146771800294938047935087576614132552921906658313292861 (pp148) Version: Msieve-1.39 Total time: 700 hours. Factorization parameters were as follows: n: 876962202929053757783039550995352100324476015083749890379724633868280277120056125580987459440498114531263702534420766464965359992984302376567569937735683592037183197404191879330000876962202929053757783039551 m: 100000000000000000000000000000000000 c6: 10 c0: 53 skew: 1.32 type: snfs lss: 0 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 special-q in [12000000, 12000000) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3105940 x 3106188 Total sieving time: 638.24 hours. Total relation processing time: 13.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.70 hours. Prototype def-par.txt line would be: snfs,211,6,0,0,0,0,0,0,0,0,24000000,24000000,29,29,57,57,2.6,2.6,100000 total time: 700 hours. --------- CPU info (if available) ---------- CPU0: AMD Phenom(tm) II X4 940 Processor stepping 02 CPU1: AMD Phenom(tm) II X4 940 Processor stepping 02 CPU2: AMD Phenom(tm) II X4 940 Processor stepping 02 CPU3: AMD Phenom(tm) II X4 940 Processor stepping 02 Memory: 3529040k/4980736k available (2699k kernel code, 139436k reserved, 3164k data, 788k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 6012.71 BogoMIPS (lpj=12025428) Calibrating delay using timer specific routine.. 6012.89 BogoMIPS (lpj=12025792) Calibrating delay using timer specific routine.. 6012.90 BogoMIPS (lpj=12025816) Calibrating delay using timer specific routine.. 6012.92 BogoMIPS (lpj=12025858) Total of 4 processors activated (24051.44 BogoMIPS).
(16·10¹⁷⁸+17)/3 = 5(3)₁₇₇9_<179> = 11 · 13² · 347 · 32983 · 12815736715308752903_<20> · C150
C150 = P31 · P119
P31 = 8027904486080268433980556857271_<31>
P119 = 24364299818203828966518485563165406695156284904992604114161373746380016498564692263558254965206297584342752781795141517_<119>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1159831445 Step 1 took 8153ms Step 2 took 8392ms ********** Factor found in step 2: 8027904486080268433980556857271 Found probable prime factor of 31 digits: 8027904486080268433980556857271 Probable prime cofactor has 119 digits
(16·10¹⁹⁸+17)/3 = 5(3)₁₉₇9_<199> = 11 · 785468738335223_<15> · C183
C183 = P29 · C155
P29 = 10809721554503831623054520711_<29>
C155 = [57103487227479446124405422629494541923845415148310131046666472629860297816874516504637895482742596878953891789085625659624914076124765874321722241320269233_<155>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2135270727 Step 1 took 11285ms Step 2 took 10733ms ********** Factor found in step 2: 10809721554503831623054520711 Found probable prime factor of 29 digits: 10809721554503831623054520711 Composite cofactor has 155 digits
(16·10²⁰¹+17)/3 = 5(3)₂₀₀9_<202> = 19 · 29 · 313 · 1901 · 94360271 · C186
C186 = P31 · C155
P31 = 2501174201872189797561830194829_<31>
C155 = [68926710845622768023245400986497791282629481535689213308309687739001187639469203420891227576987844761091134389590016352081985710450401698271387066361347267_<155>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1396396328 Step 1 took 11309ms Step 2 took 10765ms ********** Factor found in step 2: 2501174201872189797561830194829 Found probable prime factor of 31 digits: 2501174201872189797561830194829 Composite cofactor has 155 digits
(16·10¹⁷⁹+17)/3 = 5(3)₁₇₈9_<180> = 31 · C179
C179 = P28 · C151
P28 = 4352766929105745465096103339_<28>
C151 = [3952497653901114378182237986523852819615423623387147757833038683132838563176883622310981910798946192505014288043510847790520570489159500579928667953871_<151>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1608146848 Step 1 took 11397ms Step 2 took 10308ms ********** Factor found in step 2: 4352766929105745465096103339 Found probable prime factor of 28 digits: 4352766929105745465096103339 Composite cofactor has 151 digits
(10²¹⁴+17)/9 = (1)₂₁₃3_<214> = 3⁴ · 7 · C211
C211 = P31 · C180
P31 = 2400620043423893687330474477519_<31>
C180 = [816302269336336417450842188577028118534151673845025146540677993240102379833555401451594875762033128334475072601234838476484961787092961779341206131926579524992582962870838310352081_<180>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4255587043 Step 1 took 13105ms Step 2 took 11832ms ********** Factor found in step 2: 2400620043423893687330474477519 Found probable prime factor of 31 digits: 2400620043423893687330474477519 Composite cofactor has 180 digits
Mar 20, 2009 (3rd): By Ignacio Santos / GGNFS, Msieve / Mar 20, 2009
(16·10¹⁰²+17)/3 = 5(3)₁₀₁9_<103> = 11 · C102
C102 = P37 · P66
P37 = 2216835011184651104357370439054681171_<37>
P66 = 218712029719066643999777936156525071087223952004261785269174040619_<66>

Number: 53339_102 N=484848484848484848484848484848484848484848484848484848484848484848484848484848484848484848484848484849 ( 102 digits) SNFS difficulty: 103 digits. Divisors found: r1=2216835011184651104357370439054681171 (pp37) r2=218712029719066643999777936156525071087223952004261785269174040619 (pp66) Version: Msieve-1.39 Total time: 0.22 hours. Scaled time: 0.26 units (timescale=1.161). Factorization parameters were as follows: n: 484848484848484848484848484848484848484848484848484848484848484848484848484848484848484848484848484849 m: 40000000000000000000000000 deg: 4 c4: 25 c0: 68 skew: 1.28 type: snfs lss: 1 rlim: 380000 alim: 380000 lpbr: 25 lpba: 25 mfbr: 43 mfba: 43 rlambda: 2.2 alambda: 2.2 Factor base limits: 380000/380000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [190000, 230001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 37393 x 37641 Total sieving time: 0.22 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,103,4,0,0,0,0,0,0,0,0,380000,380000,25,25,43,43,2.2,2.2,10000 total time: 0.22 hours. --------- CPU info (if available) ----------
(16·10¹¹⁰+17)/3 = 5(3)₁₀₉9_<111> = 7 · 11 · C109
C109 = P51 · P59
P51 = 135086690288448751461631065121489142470928690167339_<51>
P59 = 51273792492932242100515971807088862039055864903322893309013_<59>

Number: 53339_110 N=6926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926407 ( 109 digits) SNFS difficulty: 111 digits. Divisors found: r1=135086690288448751461631065121489142470928690167339 (pp51) r2=51273792492932242100515971807088862039055864903322893309013 (pp59) Version: Msieve-1.39 Total time: 0.60 hours. Scaled time: 0.69 units (timescale=1.141). Factorization parameters were as follows: n: 6926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926407 m: 10000000000000000000000 deg: 5 c5: 16 c0: 17 skew: 1.01 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [250000, 350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 41203 x 41434 Total sieving time: 0.60 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,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000 total time: 0.60 hours. --------- CPU info (if available) ----------
(16·10¹¹²+17)/3 = 5(3)₁₁₁9_<113> = 11 · 13 · 991 · 5851 · C104
C104 = P44 · P61
P44 = 10052627114734674217024858005477241449308291_<44>
P61 = 6398517534744581605598630845005091076336770653616769994460283_<61>

Number: 53339_112 N=64321910863878643972984750803785593219329524248465718103326515801739318258957238451545530070232222106353 ( 104 digits) SNFS difficulty: 113 digits. Divisors found: r1=10052627114734674217024858005477241449308291 (pp44) r2=6398517534744581605598630845005091076336770653616769994460283 (pp61) Version: Msieve-1.39 Total time: 0.55 hours. Scaled time: 0.64 units (timescale=1.153). Factorization parameters were as follows: n: 64321910863878643972984750803785593219329524248465718103326515801739318258957238451545530070232222106353 m: 20000000000000000000000 deg: 5 c5: 50 c0: 17 skew: 0.81 type: snfs lss: 1 rlim: 540000 alim: 540000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 540000/540000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [270000, 370001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 53786 x 54015 Total sieving time: 0.55 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,113,5,0,0,0,0,0,0,0,0,540000,540000,25,25,45,45,2.2,2.2,50000 total time: 0.55 hours. --------- CPU info (if available) ----------
(16·10¹¹⁸+17)/3 = 5(3)₁₁₇9_<119> = 11 · 13 · 283 · 364415983 · C106
C106 = P40 · P67
P40 = 2517482123877466831458022023288845848163_<40>
P67 = 1436522534239865706135598288861372125341339035520699265067882825739_<67>

Number: 53339_118 N=3616419800496018185554643018778838665393873550895999781300841991930045462239647250842316622568282582267457 ( 106 digits) SNFS difficulty: 120 digits. Divisors found: r1=2517482123877466831458022023288845848163 (pp40) r2=1436522534239865706135598288861372125341339035520699265067882825739 (pp67) Version: Msieve-1.39 Total time: 0.85 hours. Scaled time: 1.01 units (timescale=1.188). Factorization parameters were as follows: n: 3616419800496018185554643018778838665393873550895999781300841991930045462239647250842316622568282582267457 m: 400000000000000000000000 deg: 5 c5: 125 c0: 136 skew: 1.02 type: snfs lss: 1 rlim: 700000 alim: 700000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [350000, 500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 68036 x 68272 Total sieving time: 0.85 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,120,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.2,2.2,50000 total time: 0.85 hours. --------- CPU info (if available) ----------
(47·10¹⁷⁴+7)/9 = 5(2)₁₇₃3_<175> = 3 · C175
C175 = P75 · P100
P75 = 620557364544933209347505543283287271715542928474811138177123479741287954493_<75>
P100 = 2805124618925858366785530971753399005552313623794237404028517151752362815052615083829211038292546537_<100>

Number: 52223_174 N=1740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741 ( 175 digits) SNFS difficulty: 176 digits. Divisors found: r1=620557364544933209347505543283287271715542928474811138177123479741287954493 (pp75) r2=2805124618925858366785530971753399005552313623794237404028517151752362815052615083829211038292546537 (pp100) Version: Msieve-1.39 Total time: 102.99 hours. Scaled time: 179.10 units (timescale=1.739). Factorization parameters were as follows: n: 1740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741 m: 100000000000000000000000000000000000 deg: 5 c5: 47 c0: 70 skew: 1.08 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3100000, 8500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1410995 x 1411243 Total sieving time: 102.99 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: snfs,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000 total time: 102.99 hours. --------- CPU info (if available) ----------
(16·10¹²⁴+17)/3 = 5(3)₁₂₃9_<125> = 11 · 13 · C123
C123 = P37 · P86
P37 = 4344103805341820701058553135691460443_<37>
P86 = 85854387849055129411080779368254210843202081626934091049880827926685804285234450918511_<86>

Number: 53339_124 N=372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960373 ( 123 digits) SNFS difficulty: 125 digits. Divisors found: r1=4344103805341820701058553135691460443 r2=85854387849055129411080779368254210843202081626934091049880827926685804285234450918511 Version: Total time: 2.03 hours. Scaled time: 5.16 units (timescale=2.544). Factorization parameters were as follows: n: 372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960373 m: 10000000000000000000000000 deg: 5 c5: 8 c0: 85 skew: 1.60 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, 640001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 95005 x 95253 Total sieving time: 2.03 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,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000 total time: 2.03 hours. --------- CPU info (if available) ----------
(47·10¹⁶⁵+61)/9 = 5(2)₁₆₄9_<166> = 3² · 7 · 5591 · 57457 · C156
C156 = P77 · P79
P77 = 72533535683897919367050843049102695262622230330026538812469651505101456980937_<77>
P79 = 3557488562285399128352167251090547646264542317070408776923597887660186679045557_<79>

Number: 52229_165 N=258037223577586703584366939521687141457565042608347763233440879201328184257788165302728714631007910945833069136088685122225466935446774836043071413903546909 ( 156 digits) SNFS difficulty: 166 digits. Divisors found: r1=72533535683897919367050843049102695262622230330026538812469651505101456980937 (pp77) r2=3557488562285399128352167251090547646264542317070408776923597887660186679045557 (pp79) Version: Msieve-1.39 Total time: 43.32 hours. Scaled time: 110.89 units (timescale=2.560). Factorization parameters were as follows: n: 258037223577586703584366939521687141457565042608347763233440879201328184257788165302728714631007910945833069136088685122225466935446774836043071413903546909 m: 1000000000000000000000000000000000 deg: 5 c5: 47 c0: 61 skew: 1.05 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, 4300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 743624 x 743872 Total sieving time: 43.32 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: 43.32 hours. --------- CPU info (if available) ----------
(16·10¹⁶⁶+17)/3 = 5(3)₁₆₅9_<167> = 11 · 13 · C165
C165 = P32 · P134
P32 = 18446113805573149007822003131717_<32>
P134 = 20218913148399309160757726082320481802184037361213630414348530230821676575403409534317023506556541934147864836343737525024390817510769_<134>

Number: 53339_166 N=372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960373 ( 165 digits) SNFS difficulty: 167 digits. Divisors found: r1=18446113805573149007822003131717 (pp32) r2=20218913148399309160757726082320481802184037361213630414348530230821676575403409534317023506556541934147864836343737525024390817510769 (pp134) Version: Msieve-1.39 Total time: 26.55 hours. Scaled time: 46.17 units (timescale=1.739). Factorization parameters were as follows: n: 372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960373 m: 2000000000000000000000000000000000 deg: 5 c5: 5 c0: 17 skew: 1.28 type: snfs lss: 1 rlim: 4300000 alim: 4300000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4300000/4300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2150000, 3550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 705711 x 705959 Total sieving time: 26.55 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,167,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,51,51,2.4,2.4,100000 total time: 26.55 hours. --------- CPU info (if available) ----------
Mar 20, 2009 (2nd): By Tyler Cadigan / GGNFS, msieve / Mar 20, 2009
(10¹⁸⁵+53)/9 = (1)₁₈₄7_<185> = 8527 · 29587001068429855351442206649_<29> · C152
C152 = P67 · P85
P67 = 5477538869759508716233535573334454107332303923923355918060914957961_<67>
P85 = 8040347369121449262829305304011094341740754632560203590976683381742939344017026888739_<85>

Number: 11117_185 N=44041315240731342627152033825315210424898830618066156602341326236451254516042808567074969782491829929498528258973637320140692358628653317197742809301179 ( 152 digits) SNFS difficulty: 185 digits. Divisors found: r1=5477538869759508716233535573334454107332303923923355918060914957961 (pp67) r2=8040347369121449262829305304011094341740754632560203590976683381742939344017026888739 (pp85) Version: Msieve-1.39 Total time: 250.09 hours. Scaled time: 641.24 units (timescale=2.564). Factorization parameters were as follows: n: 44041315240731342627152033825315210424898830618066156602341326236451254516042808567074969782491829929498528258973637320140692358628653317197742809301179 m: 10000000000000000000000000000000000000 deg: 5 c5: 1 c0: 53 skew: 2.21 type: snfs lss: 1 rlim: 8500000 alim: 8500000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4250000, 8250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1207241 x 1207489 Total sieving time: 250.09 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,185,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,54,54,2.5,2.5,100000 total time: 250.09 hours. --------- CPU info (if available) ----------
Mar 20, 2009: Factorizations of 544...441 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.
Mar 19, 2009 (4th): By Robert Backstrom / GGNFS, Msieve / Mar 19, 2009
(47·10¹⁵⁵+43)/9 = 5(2)₁₅₄7_<156> = 53 · 1123 · 6854419180999669_<16> · 9562893297694897418761_<22> · C114
C114 = P43 · P71
P43 = 1397470491947633752572738006663140974036393_<43>
P71 = 95784912349718487411932418288029995627417379622853984198602872452343209_<71>

Number: n N=133856588582522074245145041981306385740123220548779419003259092949533192359296116928474190874485652535703692405137 ( 114 digits) Divisors found: Thu Mar 19 20:53:29 2009 prp43 factor: 1397470491947633752572738006663140974036393 Thu Mar 19 20:53:29 2009 prp71 factor: 95784912349718487411932418288029995627417379622853984198602872452343209 Thu Mar 19 20:53:29 2009 elapsed time 01:42:06 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.11 hours. Scaled time: 34.84 units (timescale=1.823). Factorization parameters were as follows: n: 133856588582522074245145041981306385740123220548779419003259092949533192359296116928474190874485652535703692405137 skew: 80691.62 Y0: -8289403519030582587562 Y1: 509751010163 c0: -2041210546406800131753532935 c1: 1083180025265749843277181 c2: 3650027098564077305 c3: -235277594845393 c4: -353315578 c5: 3420 type: gnfs name: KA_5_2_154_7 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1750000, 2602283) Primes: RFBsize:250150, AFBsize:248462, largePrimes:16642854 encountered Relations: rels:14546049, finalFF:509469 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 905433 hash collisions in 15107156 relations Msieve: matrix is 598018 x 598266 (167.6 MB) Total sieving time: 18.64 hours. Total relation processing time: 0.47 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000 total time: 19.11 hours. --------- CPU info (if available) ----------
Mar 19, 2009 (3rd): By Ignacio Santos / GGNFS, Msieve / Mar 19, 2009
(47·10¹⁴⁸+43)/9 = 5(2)₁₄₇7_<149> = 3³ · 7 · 29 · 67 · 1223 · 21705793 · 2017078085045614618421_<22> · C112
C112 = P55 · P57
P55 = 3980941556193166603838231490318104342696694098555483207_<55>
P57 = 667129456521162682500034200289208198670786991776880206997_<57>

Number: 52227_148 N=2655803376825658847637458230916276479422795676367628311147056956567958355588426064464073349447932249543517399379 ( 112 digits) SNFS difficulty: 151 digits. Divisors found: r1=3980941556193166603838231490318104342696694098555483207 (pp55) r2=667129456521162682500034200289208198670786991776880206997 (pp57) Version: Msieve-1.39 Total time: 17.37 hours. Scaled time: 44.66 units (timescale=2.571). Factorization parameters were as follows: n: 2655803376825658847637458230916276479422795676367628311147056956567958355588426064464073349447932249543517399379 m: 500000000000000000000000000000 deg: 5 c5: 376 c0: 1075 skew: 1.23 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 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: 49/49 Sieved rational special-q in [1150000, 2150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 431941 x 432189 Total sieving time: 17.37 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,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 17.37 hours. --------- CPU info (if available) ----------
Mar 19, 2009 (2nd): By Erik Branger / GGNFS, Msieve, GMP-ECM / Mar 19, 2009
(47·10¹⁵³+43)/9 = 5(2)₁₅₂7_<154> = 2002540933830131711_<19> · C136
C136 = P36 · P101
P36 = 257352985880137140848352215811551723_<36>
P101 = 10133156143982625350749263738927449627185877360057069960197245768769800614330181000523922313277930759_<101>

Number: 52227_153 N=2607797990043585498486776563577293170179160358822379016514029370980619932719161276506780892488605173914090155178598786073131670341147757 ( 136 digits) SNFS difficulty: 156 digits. Divisors found: r1=257352985880137140848352215811551723 r2=10133156143982625350749263738927449627185877360057069960197245768769800614330181000523922313277930759 Version: Total time: 37.46 hours. Scaled time: 36.11 units (timescale=0.964). Factorization parameters were as follows: n: 2607797990043585498486776563577293170179160358822379016514029370980619932719161276506780892488605173914090155178598786073131670341147757 m: 5000000000000000000000000000000 deg: 5 c5: 376 c0: 1075 skew: 1.23 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor 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, 2900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 570944 x 571192 Total sieving time: 37.46 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,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 37.46 hours. --------- CPU info (if available) ----------
(10²²⁵-7)/3 = (3)₂₂₄1_<225> = 137737 · 134156123 · 67743226688030353193_<20> · 199494502930691408785361_<24> · 122625043098363429270779593379_<30> · C140
C140 = P42 · P98
P42 = 860214666824601272460880156994772578011619_<42>
P98 = 12654203042712555984328454204858279619330389192948935697292522058994841156413713475656590209377697_<98>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 10885331054317837011064517548146007631894457980921054037615043412068918053334979676466099035906851721409340820885267078426597342035625461443 (140 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1082531224 Step 1 took 42901ms Step 2 took 15132ms ********** Factor found in step 2: 860214666824601272460880156994772578011619 Found probable prime factor of 42 digits: 860214666824601272460880156994772578011619 Probable prime cofactor 12654203042712555984328454204858279619330389192948935697292522058994841156413713475656590209377697 has 98 digits
(47·10¹⁵²+43)/9 = 5(2)₁₅₁7_<153> = 23 · 31 · 5977957 · C144
C144 = P42 · P103
P42 = 102954757437537587020286226041931725738471_<42>
P103 = 1190053845694343160057405598164702056965447494076340682927117292004770107354365772690735150938069056457_<103>

Number: 52227_152 N=122521705021069884387637246526784156891699758592426768050055408604573625933007212113030244983476855679600447806602593063561942636751192515857247 ( 144 digits) SNFS difficulty: 154 digits. Divisors found: r1=102954757437537587020286226041931725738471 r2=1190053845694343160057405598164702056965447494076340682927117292004770107354365772690735150938069056457 Version: Total time: 33.77 hours. Scaled time: 26.44 units (timescale=0.783). Factorization parameters were as follows: n: 122521705021069884387637246526784156891699758592426768050055408604573625933007212113030244983476855679600447806602593063561942636751192515857247 m: 2000000000000000000000000000000 deg: 5 c5: 1175 c0: 344 skew: 0.78 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor 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, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 499587 x 499835 Total sieving time: 33.77 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,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 33.77 hours. --------- CPU info (if available) ----------
Mar 19, 2009: Factorizations of 533...339 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.
Mar 18, 2009 (4th): By Sinkiti Sibata / GGNFS / Mar 18, 2009
(47·10¹⁴³+43)/9 = 5(2)₁₄₂7_<144> = 1256797 · C138
C138 = P37 · P101
P37 = 4843817090846848103800130938749666541_<37>
P101 = 85783246430773379911102166695200551942332371371885262915582905035373010589522772606960016182845664651_<101>

Number: 52227_143 N=415518355169706979108179142870505119141931610452779742649148766445354518050426777134431592550127206081986368699338256076536005593761142191 ( 138 digits) SNFS difficulty: 146 digits. Divisors found: r1=4843817090846848103800130938749666541 (pp37) r2=85783246430773379911102166695200551942332371371885262915582905035373010589522772606960016182845664651 (pp101) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 30.82 hours. Scaled time: 14.52 units (timescale=0.471). Factorization parameters were as follows: name: 52227_143 n: 415518355169706979108179142870505119141931610452779742649148766445354518050426777134431592550127206081986368699338256076536005593761142191 m: 50000000000000000000000000000 deg: 5 c5: 376 c0: 1075 skew: 1.23 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, 3450001) Primes: RFBsize:142029, AFBsize:141497, largePrimes:4391493 encountered Relations: rels:4701517, finalFF:334993 Max relations in full relation-set: 28 Initial matrix: 283593 x 334993 with sparse part having weight 40541816. Pruned matrix : 267398 x 268879 with weight 31033526. Total sieving time: 27.63 hours. Total relation processing time: 0.33 hours. Matrix solve time: 2.77 hours. Time per square root: 0.10 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: 30.82 hours. --------- CPU info (if available) ----------
Mar 18, 2009 (3rd): By Ignacio Santos / GGNFS, Msieve / Mar 18, 2009
(46·10¹⁶⁷+71)/9 = 5(1)₁₆₆9_<168> = 3² · 7 · 19 · 1117 · 4679 · 27883 · C154
C154 = P54 · P101
P54 = 107947980468983175179209407936978627331988033676681083_<54>
P101 = 27143192890863234580560273644490456064319074781755462331364854263414746355660087083256912160513206201_<101>

Number: 51119_167 N=2930052856048747415696412580021740877656459525605510537337184012695666922105062747081510430361540113889889941395993487864740777776024112205338840894995683 ( 154 digits) SNFS difficulty: 169 digits. Divisors found: r1=107947980468983175179209407936978627331988033676681083 (pp54) r2=27143192890863234580560273644490456064319074781755462331364854263414746355660087083256912160513206201 (pp101) Version: Msieve-1.39 Total time: 62.79 hours. Scaled time: 161.43 units (timescale=2.571). Factorization parameters were as follows: n: 2930052856048747415696412580021740877656459525605510537337184012695666922105062747081510430361540113889889941395993487864740777776024112205338840894995683 m: 2000000000000000000000000000000000 deg: 5 c5: 575 c0: 284 skew: 0.87 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [2300000, 5500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 916037 x 916285 Total sieving time: 62.79 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000 total time: 62.79 hours. --------- CPU info (if available) ----------
(47·10¹⁶¹+61)/9 = 5(2)₁₆₀9_<162> = 140853961 · C154
C154 = P63 · P92
P63 = 219943733041963750242646478617524491832623759499803899627166611_<63>
P92 = 16856782845527874382183048874522274027542137890355911903085056358760184087391042615656550399_<92>

Number: 52229_161 N=3707543746123136872396667795676844488755429619918336710617759781865291116820081632082907645190199672284844174330477097638895807993800204328099954691527789 ( 154 digits) SNFS difficulty: 162 digits. Divisors found: r1=219943733041963750242646478617524491832623759499803899627166611 (pp63) r2=16856782845527874382183048874522274027542137890355911903085056358760184087391042615656550399 (pp92) Version: Msieve-1.39 Total time: 36.14 hours. Scaled time: 92.92 units (timescale=2.571). Factorization parameters were as follows: n: 3707543746123136872396667795676844488755429619918336710617759781865291116820081632082907645190199672284844174330477097638895807993800204328099954691527789 m: 100000000000000000000000000000000 deg: 5 c5: 470 c0: 61 skew: 0.66 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, 3700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 669486 x 669734 Total sieving time: 36.14 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000 total time: 36.14 hours. --------- CPU info (if available) ----------
(47·10¹⁴⁹+61)/9 = 5(2)₁₄₈9_<150> = 4076210434301839_<16> · 211174768175632908845141_<24> · C111
C111 = P54 · P58
P54 = 219213132009021623869566675173488915702299783936522029_<54>
P58 = 2767516118398801454302828847039547607150038471761799341899_<58>

Number: 52229_149 N=606675876199651581317035127957145483690901889131660586888217858313407073692363357548983792092630032283116193071 ( 111 digits) SNFS difficulty: 151 digits. Divisors found: r1=219213132009021623869566675173488915702299783936522029 (pp54) r2=2767516118398801454302828847039547607150038471761799341899 (pp58) Version: Msieve-1.39 Total time: 16.20 hours. Scaled time: 41.65 units (timescale=2.571). Factorization parameters were as follows: n: 606675876199651581317035127957145483690901889131660586888217858313407073692363357548983792092630032283116193071 m: 1000000000000000000000000000000 deg: 5 c5: 47 c0: 610 skew: 1.67 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 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: 49/49 Sieved rational special-q in [1200000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 436101 x 436349 Total sieving time: 16.20 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: 16.20 hours. --------- CPU info (if available) ----------
Mar 18, 2009 (2nd): By Max Dettweiler / GGNFS, msieve v1.40beta2 / Mar 18, 2009
(47·10¹⁵¹+61)/9 = 5(2)₁₅₀9_<152> = 73 · 691 · 5003 · 84389 · 6105956179_<10> · C129
C129 = P47 · P83
P47 = 13551298952508005615508715858630155784976003377_<47>
P83 = 29634901503428958238102266429923613340973044009914909611452496602972186130738987123_<83>

Number: 52229_151 N=401591409701094762557236606442942058249930610119999828677048360538804414672459347923455562310561948894319531364533784369607514371 ( 129 digits) SNFS difficulty: 152 digits. Divisors found: r1=13551298952508005615508715858630155784976003377 (pp47) r2=29634901503428958238102266429923613340973044009914909611452496602972186130738987123 (pp83) Version: Msieve-1.40 Total time: 21.55 hours. Scaled time: 35.41 units (timescale=1.643). Factorization parameters were as follows: n: 401591409701094762557236606442942058249930610119999828677048360538804414672459347923455562310561948894319531364533784369607514371 m: 1000000000000000000000000000000 deg: 5 c5: 470 c0: 61 skew: 0.66 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, 2150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 433946 x 434194 Total sieving time: 21.55 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,152,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000 total time: 21.55 hours. --------- CPU info (if available) ---------- [ 0.366872] CPU0: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.456430] CPU1: Intel(R) Core(TM)2 Duo CPU E4500 @ 2.20GHz stepping 0d [ 0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem) [ 0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.13 BogoMIPS (lpj=8800268) [ 0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821) [ 0.460050] Total of 2 processors activated (8800.54 BogoMIPS).
Mar 18, 2009: By Robert Backstrom / GGNFS, Msieve / Mar 18, 2009
(47·10¹⁴⁷+43)/9 = 5(2)₁₄₆7_<148> = 419 · 1230122762141569_<16> · 384189113824853757332970331_<27> · C104
C104 = P48 · P57
P48 = 185767993337027714455265134749591365614059015697_<48>
P57 = 141963574575550541691236928123164412858691879492806034451_<57>

Number: n N=26372288375851510075141295091256465723888801319948296741264515789328641332678379950721528722522931777347 ( 104 digits) Divisors found: Wed Mar 18 02:57:01 2009 prp48 factor: 185767993337027714455265134749591365614059015697 Wed Mar 18 02:57:01 2009 prp57 factor: 141963574575550541691236928123164412858691879492806034451 Wed Mar 18 02:57:01 2009 elapsed time 00:31:08 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.77 hours. Scaled time: 12.35 units (timescale=1.823). Factorization parameters were as follows: n: 26372288375851510075141295091256465723888801319948296741264515789328641332678379950721528722522931777347 skew: 29710.99 Y0: -144401432342722261807 Y1: 36431541157 c0: -15122488454704756317858600 c1: -13242623711720306931140 c2: -210177813641840938 c3: 18447924067323 c4: 157240256 c5: 420 type: gnfs name: KA_5_2_146_7 rlim: 2300000 alim: 2300000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1150000, 10000000 ) Primes: RFBsize:169511, AFBsize:169780, largePrimes:14660589 encountered Relations: rels:12861753, finalFF:536940 Max relations in full relation-set: 28 Initial matrix: 339372 x 536940 with sparse part having weight 62352556. Pruned matrix : 237664 x 239424 with weight 22900522. Msieve: found 823997 hash collisions in 13420417 relations Msieve: matrix is 276291 x 276539 (76.0 MB) Total sieving time: 6.44 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,28,28,56,56,2.6,2.6,100000 total time: 6.77 hours. --------- CPU info (if available) ----------
Mar 17, 2009 (10th): By Luigi Morelli / GGNFS 0.77.1 Msieve 1.39 / Mar 17, 2009
(4·10¹⁷⁴+41)/9 = (4)₁₇₃9_<174> = 401 · 1531 · 2333 · 11103172231868232665208082632227_<32> · C134
C134 = P41 · P93
P41 = 38399983418304274738274024976546740584967_<41>
P93 = 727788294601551888099993904173706931765025315072705833126180244134209183779214775385936665507_<93>

Tue Mar 17 12:36:41 2009 Msieve v. 1.39 Tue Mar 17 12:36:41 2009 random seeds: 9f714800 598b1444 Tue Mar 17 12:36:41 2009 factoring 27947058444735539012965143631675640717984624676970856746909322865014587987121750699821648616857592608427104241739512228516510591633269 (134 digits) Tue Mar 17 12:36:43 2009 searching for 15-digit factors Tue Mar 17 12:36:44 2009 commencing number field sieve (134-digit input) Tue Mar 17 12:36:44 2009 R0: -100000000000000000000000000000000000 Tue Mar 17 12:36:44 2009 R1: 1 Tue Mar 17 12:36:44 2009 A0: 205 Tue Mar 17 12:36:44