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STUDIO KAMADA

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News and updates, August 2008

Aug 31, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(5·10¹⁸⁸+7)/3 = 1(6)₁₈₇9_<189> = 13 · 4508291 · C181
C181 = P64 · P117
P64 = 5572625206496682509937965003069828168574001110247054129799055991_<64>
P117 = 510309462344547784599419974697282044175752543112956276456061023653909400195521795522887826526858682926321882006053773_<117>

Number: n N=2843763372974996625732569796517753737019307941859303339740161586843622231311269130700041437613612967865832199567532978796803603143744008652684689790546533156981329027011082583804043 ( 181 digits) SNFS difficulty: 190 digits. Divisors found: Sun Aug 31 21:55:16 2008 prp64 factor: 5572625206496682509937965003069828168574001110247054129799055991 Sun Aug 31 21:55:16 2008 prp117 factor: 510309462344547784599419974697282044175752543112956276456061023653909400195521795522887826526858682926321882006053773 Sun Aug 31 21:55:16 2008 elapsed time 05:08:39 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 214.52 hours. Scaled time: 179.76 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_6_187_9 n: 2843763372974996625732569796517753737019307941859303339740161586843622231311269130700041437613612967865832199567532978796803603143744008652684689790546533156981329027011082583804043 type: snfs skew: 2.69 deg: 5 c5: 1 c0: 140 m: 100000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 8900001) Primes: RFBsize:602489, AFBsize:603790, largePrimes:10824329 encountered Relations: rels:10821915, finalFF:1236646 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 214.11 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,190,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000 total time: 214.52 hours. --------- CPU info (if available) ----------

Aug 31, 2008 (2nd)

By Wataru Sakai / GGNFS
(2·10¹⁹⁹-17)/3 = (6)₁₉₈1_<199> = C199
C199 = P61 · P138
P61 = 7746198155672718412194373416422042294291282224078057676781559_<61>
P138 = 860637248452586240793411305547124642667894480293199002512800099070390305673067846165291277474909445333699703778303587085959036214662816579_<138>

Number: 66661_199 N=6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 ( 199 digits) SNFS difficulty: 200 digits. Divisors found: r1=7746198155672718412194373416422042294291282224078057676781559 (pp61) r2=860637248452586240793411305547124642667894480293199002512800099070390305673067846165291277474909445333699703778303587085959036214662816579 (pp138) Version: GGNFS-0.77.1-20060722-nocona Total time: 6373.94 hours. Scaled time: 11944.77 units (timescale=1.874). Factorization parameters were as follows: n: 6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 m: 10000000000000000000000000000000000000000 c5: 1 c0: -85 skew: 2.43 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 107400001) Primes: RFBsize:501962, AFBsize:502501, largePrimes:10315349 encountered Relations: rels:12144748, finalFF:1129224 Max relations in full relation-set: 32 Initial matrix: 1004527 x 1129224 with sparse part having weight 218619771. Pruned matrix : 945193 x 950279 with weight 202057474. Total sieving time: 6350.64 hours. Total relation processing time: 1.31 hours. Matrix solve time: 21.57 hours. Time per square root: 0.43 hours. Prototype def-par.txt line would be: snfs,200,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 6373.94 hours. --------- CPU info (if available) ----------

Aug 31, 2008

By Sinkiti Sibata / GMP-ECM
(8·10¹⁷⁰-11)/3 = 2(6)₁₆₉3_<171> = 733 · 433336074385189_<15> · 4848705026009567_<16> · C138
C138 = P41 · P97
P41 = 21444720061961923459119388271642272065257_<41>
P97 = 8074093367579318645109991039242689165888372857971148977391463264840925662722940362463996964183521_<97>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 173146672021881921378896373090978957549911838084851329459712681790545591628898153652066417156764183279951056853213653990375319291436029897 Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1148971329 Step 1 took 48953ms Step 2 took 16973ms ********** Factor found in step 2: 21444720061961923459119388271642272065257 Found probable prime factor of 41 digits: 21444720061961923459119388271642272065257 Probable prime cofactor 8074093367579318645109991039242689165888372857971148977391463264840925662722940362463996964183521 has 97 digits

Aug 30, 2008 (2nd)

By Tyler Cadigan / GGNFS, Msieve
(25·10¹⁹⁵-1)/3 = 8(3)_195<196> = 13 · 191 · 641 · 2521 · 70360703591_<11> · C176
C176 = P45 · P131
P45 = 347475803459299610733739361332835589747500711_<45>
P131 = 84948637535002693046809344987987788506145903659602270746463195239782274901028606636613753795353452586876315488810371234015435431391_<131>

Number: 83333_195 N=29517596080247877525790851053981747064359792547947739805692098981033869953189081994166555707582584397071309454538456953939153374792078239873193031003841009649977944238364219001 ( 176 digits) SNFS difficulty: 196 digits. Divisors found: r1=347475803459299610733739361332835589747500711 r2=84948637535002693046809344987987788506145903659602270746463195239782274901028606636613753795353452586876315488810371234015435431391 Version: Total time: 436.75 hours. Scaled time: 1128.56 units (timescale=2.584). Factorization parameters were as follows: n: 29517596080247877525790851053981747064359792547947739805692098981033869953189081994166555707582584397071309454538456953939153374792078239873193031003841009649977944238364219001 m: 1000000000000000000000000000000000000000 c5: 25 c0: -1 skew: 0.53 Y0: 1000000000000000000000000000000000000000 Y1: -1 type: snfs lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 rlim: 20000000 alim: 20000000 qintsize: 1000000Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved algebraic special-q in [10000000, 16000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2686515 x 2686763 Total sieving time: 436.75 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,196,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,58,58,2.6,2.6,100000 total time: 436.75 hours. --------- CPU info (if available) ----------

Factorizations of 833...33 have been completed up to n=200.

Aug 30, 2008

By Jo Yeong Uk / GGNFS
8·10¹⁷⁴-9 = 7(9)₁₇₃1_<175> = 41 · 173743074481_<12> · 19106912458400837994080317241_<29> · 451656251742733916273683704772193_<33> · C102
C102 = P45 · P57
P45 = 592251998082554341409369753785202370375115807_<45>
P57 = 219732123875349514938455918437129730022904144914165154681_<57>

Number: 79991_174 N=130136789408099093943642895529280422128901086592792253560350069883955602104627506623059801699443142567 ( 102 digits) Divisors found: r1=592251998082554341409369753785202370375115807 (pp45) r2=219732123875349514938455918437129730022904144914165154681 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.00 hours. Scaled time: 9.56 units (timescale=2.392). Factorization parameters were as follows: name: 79991_174 n: 130136789408099093943642895529280422128901086592792253560350069883955602104627506623059801699443142567 skew: 10873.83 # norm 5.58e+13 c5: 8280 c4: -265261398 c3: -736553682108 c2: 6989101037039633 c1: -128237153725381623216 c0: 63440594100681936495345 # alpha -5.23 Y1: 31466063483 Y0: -27496482160245593002 # Murphy_E 2.83e-09 # M 12646438619583911536750972380335684031448376564007326365424264391297480438938008412765721828969481049 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [750000, 1350001) Primes: RFBsize:114155, AFBsize:113556, largePrimes:4385038 encountered Relations: rels:4331759, finalFF:321559 Max relations in full relation-set: 28 Initial matrix: 227790 x 321559 with sparse part having weight 27654118. Pruned matrix : 180096 x 181298 with weight 12977876. Polynomial selection time: 0.31 hours. Total sieving time: 3.46 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.12 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,49,49,2.6,2.6,50000 total time: 4.00 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2460k kernel code, 339200k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347) Calibrating delay using timer specific routine.. 5344.51 BogoMIPS (lpj=2672259) Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672350)

Aug 29, 2008

By Serge Batalov / GMP-ECM 6.2.1, pol51+Msieve 1.37
(14·10¹⁷¹+31)/9 = 1(5)₁₇₀9_<172> = 53 · 496681 · 410603139824071_<15> · 2475177024694321515444421_<25> · C125
C125 = P34 · P92
P34 = 5813483701575740349680035428752387_<34>
P92 = 10001545600677817037581209402111644839880337297632163971294502938355625025052962872656161339_<92>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=783124874 Step 1 took 11510ms Step 2 took 6852ms ********** Factor found in step 2: 5813483701575740349680035428752387 Found probable prime factor of 34 digits: 5813483701575740349680035428752387 Probable prime cofactor 10001545600677817037581209402111644839880337297632163971294502938355625025052962872656161339 has 92 digits

8·10¹⁷⁴-9 = 7(9)₁₇₃1_<175> = 41 · 173743074481_<12> · 19106912458400837994080317241_<29> · C134
C134 = P33 · C102
P33 = 451656251742733916273683704772193_<33>
C102 = [130136789408099093943642895529280422128901086592792253560350069883955602104627506623059801699443142567_<102>]

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=1366989160 Step 1 took 10130ms Step 2 took 6967ms ********** Factor found in step 2: 451656251742733916273683704772193 Found probable prime factor of 33 digits: 451656251742733916273683704772193 Composite cofactor 130136789408099093943642895529280422128901086592792253560350069883955602104627506623059801699443142567 has 102 digits

(4·10¹⁷⁶+11)/3 = 1(3)₁₇₅7_<177> = 654817399 · 2654433511_<10> · 651698912539_<12> · 137745684013733_<15> · C132
C132 = P34 · P34 · P66
P34 = 1089318090564868475456017418176427_<34>
P34 = 1231627716604690046697182424513253_<34>
P66 = 636923845516948278854619576438453364025839828712022887610324552089_<66>

#ECM, then gnfs/Msieve # Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=3838364986 Step 1 took 11629ms Step 2 took 7041ms ********** Factor found in step 2: 1089318090564868475456017418176427 Found probable prime factor of 34 digits: 1089318090564868475456017418176427 Composite cofactor 784453061505117357864038664345811078914332428946244066627988881633785366535204327880785191069335517 has 99 digits Number: 13337_176 N=784453061505117357864038664345811078914332428946244066627988881633785366535204327880785191069335517 ( 99 digits) Divisors found: r1=1231627716604690046697182424513253 r2=636923845516948278854619576438453364025839828712022887610324552089 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: name: 13337_176 n: 784453061505117357864038664345811078914332428946244066627988881633785366535204327880785191069335517 skew: 2513.29 # norm 1.16e+13 c5: 20580 c4: 508307051 c3: 557345214445 c2: -470168275690464 c1: -2589049590718293107 c0: -52486279407165116565 # alpha -4.66 Y1: 5234753843 Y0: -8245613164455536492 # Murphy_E 3.94e-09 # M 675691405801972959220472988772094584688379672974200505104477011633136745725111786358588561469188675 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 165902 x 166133 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 2.50 hours.

Aug 28, 2008 (3rd)

By Sinkiti Sibata / GGNFS
(8·10¹⁵⁵-11)/3 = 2(6)₁₅₄3_<156> = 23 · 383 · 7853 · 140143 · 89728591 · 1561361513_<10> · C126
C126 = P46 · P80
P46 = 8627089357765378991076246682719777963998610241_<46>
P80 = 22758126142966332417669133587283570000761657492867169951767849493683399601751411_<80>

Number: 26663_155 N=196336387850666898435886985994390947515578847455806385406582232661469625771635883806609574286096836768770851495960073560800051 ( 126 digits) SNFS difficulty: 155 digits. Divisors found: r1=8627089357765378991076246682719777963998610241 (pp46) r2=22758126142966332417669133587283570000761657492867169951767849493683399601751411 (pp80) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 38.18 hours. Scaled time: 18.02 units (timescale=0.472). Factorization parameters were as follows: name: 26663_155 n: 196336387850666898435886985994390947515578847455806385406582232661469625771635883806609574286096836768770851495960073560800051 m: 10000000000000000000000000000000 c5: 8 c0: -11 skew: 1.07 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:216082, largePrimes:5574642 encountered Relations: rels:5553841, finalFF:573445 Max relations in full relation-set: 28 Initial matrix: 432963 x 573445 with sparse part having weight 42953283. Pruned matrix : 333445 x 335673 with weight 26446379. Total sieving time: 34.16 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.70 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 38.18 hours. --------- CPU info (if available) ----------

Aug 28, 2008 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, ***Msieve-1.37***
(19·10¹⁷⁶+17)/9 = 2(1)₁₇₅3_<177> = 3² · 167 · 1543 · 53611 · 2401409 · 974819639393790407634579313_<27> · C132
C132 = P31 · P102
P31 = 4956648204881915050768672150327_<31>
P102 = 146336874948973085318917842213648178095098263874900615495508640162228819919842162403788352528350133653_<102>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2131237211 Step 1 took 16750ms Step 2 took 6958ms ********** Factor found in step 2: 4956648204881915050768672150327 Found probable prime factor of 31 digits: 4956648204881915050768672150327 Probable prime cofactor 146336874948973085318917842213648178095098263874900615495508640162228819919842162403788352528350133653 has 102 digits

(8·10¹⁶³-11)/3 = 2(6)₁₆₂3_<164> = 814320350738108743_<18> · 2763870653886852635716885631_<28> · C119
C119 = P42 · P77
P42 = 301147670230833087243353381876753817878047_<42>
P77 = 39343792552349727779693072074780867921299727848712907400115696799639680859713_<77>

Number: 26663_163 N=11848291465185322644709783710930277954304746404731360294607998144533448422134791685213367257651306885901437134349420511 ( 119 digits) SNFS difficulty: 163 digits. Divisors found: r1=301147670230833087243353381876753817878047 r2=39343792552349727779693072074780867921299727848712907400115696799639680859713 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 11848291465185322644709783710930277954304746404731360294607998144533448422134791685213367257651306885901437134349420511 Y1: 1 Y0: -200000000000000000000000000000000 c5: 250 c0: -11 skew: 0.54 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2250000, 2850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 741400 x 741648 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 2.10 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.5,2.5,100000 total time: 14.00 hours.

Aug 28, 2008

Msieve 1.37 has been released.
HOW TO for Japanese users

Aug 27, 2008 (3rd)

By Wataru Sakai / GGNFS
6·10¹⁸⁷+1 = 6(0)₁₈₆1_<188> = 4547 · C185
C185 = P67 · P118
P67 = 6536834037833420095985946925674276836560136508795702561667702266167_<67>
P118 = 2018639826103785865286631933082975605890545795355024440916114945745465813061205948102752034943266139296166842862791149_<118>

Number: 60001_187 N=13195513525401363536397624807565427754563448427534638223004178579283043765119859247855729052122278425335385968770617989883439630525621288761820980866505388168022872223444029030129755883 ( 185 digits) SNFS difficulty: 187 digits. Divisors found: r1=6536834037833420095985946925674276836560136508795702561667702266167 (pp67) r2=2018639826103785865286631933082975605890545795355024440916114945745465813061205948102752034943266139296166842862791149 (pp118) Version: GGNFS-0.77.1-20060722-nocona Total time: 777.86 hours. Scaled time: 1561.95 units (timescale=2.008). Factorization parameters were as follows: n: 13195513525401363536397624807565427754563448427534638223004178579283043765119859247855729052122278425335385968770617989883439630525621288761820980866505388168022872223444029030129755883 m: 10000000000000000000000000000000000000 c5: 600 c0: 1 skew: 0.28 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 15700001) Primes: RFBsize:501962, AFBsize:501791, largePrimes:6891187 encountered Relations: rels:7436758, finalFF:1180022 Max relations in full relation-set: 32 Initial matrix: 1003819 x 1180022 with sparse part having weight 115293725. Pruned matrix : 865389 x 870472 with weight 93704423. Total sieving time: 768.45 hours. Total relation processing time: 0.14 hours. Matrix solve time: 9.03 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 777.86 hours. --------- CPU info (if available) ----------

Aug 27, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(8·10¹⁶²-11)/3 = 2(6)₁₆₁3_<163> = 359 · 4507487 · 27059729 · 6315921853_<10> · 103496669775133_<15> · C122
C122 = P40 · P83
P40 = 4696433042047289514966970256674200476261_<40>
P83 = 19837415944333569454521178385670584763249729870811764701051961027139351921162624331_<83>

Number: 26663_162 N=93165095709803910034220755200074213920442816991906500418090991135299650476503556714014354208663641612641625384792826506391 ( 122 digits) SNFS difficulty: 162 digits. Divisors found: r1=4696433042047289514966970256674200476261 (pp40) r2=19837415944333569454521178385670584763249729870811764701051961027139351921162624331 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 53.91 hours. Scaled time: 54.39 units (timescale=1.009). Factorization parameters were as follows: name: 26663_162 n: 93165095709803910034220755200074213920442816991906500418090991135299650476503556714014354208663641612641625384792826506391 m: 200000000000000000000000000000000 c5: 25 c0: -11 skew: 0.85 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4350001) Primes: RFBsize:315948, AFBsize:315742, largePrimes:5978765 encountered Relations: rels:6297572, finalFF:922018 Max relations in full relation-set: 28 Initial matrix: 631754 x 922018 with sparse part having weight 52727144. Pruned matrix : 405565 x 408787 with weight 39479532. Total sieving time: 52.40 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.34 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 53.91 hours. --------- CPU info (if available) ----------

Aug 27, 2008

By Serge Batalov / Msieve 1.36, GMP-ECM 6.2.1
(8·10¹⁵⁷-11)/3 = 2(6)₁₅₆3_<158> = 11069 · C154
C154 = P40 · P115
P40 = 1105327928036418569669147130317306733637_<40>
P115 = 2179561869275003655805053554544359944708001505318774837743094477875371215017299055737728009643796884495907468594071_<115>

Number: 26663_157 N=2409130604992923178847833288162134489716023729936459180293311651157888397024723702833739874122925889119763905200710693528472912337760110820007829674466227 ( 154 digits) SNFS difficulty: 157 digits. Divisors found: r1=1105327928036418569669147130317306733637 r2=2179561869275003655805053554544359944708001505318774837743094477875371215017299055737728009643796884495907468594071 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.313). Factorization parameters were as follows: n: 2409130604992923178847833288162134489716023729936459180293311651157888397024723702833739874122925889119763905200710693528472912337760110820007829674466227 Y1: 1 Y0: -20000000000000000000000000000000 c5: 25 c0: -11 skew: 0.85 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1500000, 2300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 496232 x 496474 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,52,52,2.5,2.5,100000 total time: 15.20 hours.

(8·10¹⁶⁴-11)/3 = 2(6)₁₆₃3_<165> = 179 · 77450201 · 386822927 · C146
C146 = P35 · P112
P35 = 10865659052292619388679044078475137_<35>
P112 = 4576409430557803066039585822705526398937317357435248022811589980525323757752016816620470019755082138495042370603_<112>

Using B1=25000000, B2=96190324246, polynomial Dickson(12), sigma=2919656688 Step 1 took 173974ms Step 2 took 45112ms ********** Factor found in step 2: 10865659052292619388679044078475137 Found probable prime factor of 35 digits: 10865659052292619388679044078475137 Probable prime cofactor 4576409430557803066039585822705526398937317357435248022811589980525323757752016816620470019755082138495042370603 has 112 digits

Aug 26, 2008 (3rd)

By Hugo Platzer / Msieve-1.36 optimized 64-bit linux lattice siever from Greg Childers
6·10¹⁸⁰-7 = 5(9)₁₇₉3_<181> = 17 · 5791 · C176
C176 = P61 · P116
P61 = 4830487850130825355136992625082278853531328717363811995759451_<61>
P116 = 12617048427077972576764760920138324767170820384685368004188695290274577720048489648872812603297601032348850349016469_<116>

Tue Aug 26 11:38:06 2008 Tue Aug 26 11:38:06 2008 Tue Aug 26 11:38:06 2008 Msieve v. 1.36 Tue Aug 26 11:38:06 2008 random seeds: d67440d2 74216d9f Tue Aug 26 11:38:06 2008 factoring 60946499131512387375948479892734161528538198218330675388787875709772771135738011315733338750799922801101100084309323798592135870062063851615590114477840868690767621156561398519 (176 digits) Tue Aug 26 11:38:08 2008 no P-1/P+1/ECM available, skipping Tue Aug 26 11:38:08 2008 commencing number field sieve (176-digit input) Tue Aug 26 11:38:08 2008 R0: -1000000000000000000000000000000000000 Tue Aug 26 11:38:08 2008 R1: 1 Tue Aug 26 11:38:08 2008 A0: -7 Tue Aug 26 11:38:08 2008 A1: 0 Tue Aug 26 11:38:08 2008 A2: 0 Tue Aug 26 11:38:08 2008 A3: 0 Tue Aug 26 11:38:08 2008 A4: 0 Tue Aug 26 11:38:08 2008 A5: 6 Tue Aug 26 11:38:08 2008 size score = 2.794913e-12, Murphy alpha = 1.791017, combined = 1.538481e-12 Tue Aug 26 11:38:08 2008 generating factor base Tue Aug 26 11:38:11 2008 factor base complete: Tue Aug 26 11:38:11 2008 539777 rational roots (max prime = 7999993) Tue Aug 26 11:38:11 2008 539975 algebraic roots (max prime = 7999993) Tue Aug 26 11:38:12 2008 a range: [-60000000, 60000000] Tue Aug 26 11:38:12 2008 b range: [1, 4294967295] Tue Aug 26 11:38:12 2008 number of hash buckets: 123 Tue Aug 26 11:38:12 2008 sieve block size: 65536 Tue Aug 26 11:38:12 2008 Tue Aug 26 11:38:12 2008 maximum RFB prime: 7999993 Tue Aug 26 11:38:12 2008 RFB entries: 539777 Tue Aug 26 11:38:12 2008 medium RFB entries: 6542 Tue Aug 26 11:38:12 2008 resieved RFB entries: 6374 Tue Aug 26 11:38:12 2008 small RFB prime powers: 28 Tue Aug 26 11:38:12 2008 projective RFB roots: 0 Tue Aug 26 11:38:12 2008 RFB trial factoring cutoff: 60 or 89 bits Tue Aug 26 11:38:12 2008 single large prime RFB range: 23 - 27 bits Tue Aug 26 11:38:12 2008 double large prime RFB range: 46 - 52 bits Tue Aug 26 11:38:12 2008 triple large prime RFB range: 72 - 79 bits Tue Aug 26 11:38:12 2008 Tue Aug 26 11:38:12 2008 maximum AFB prime: 7999993 Tue Aug 26 11:38:12 2008 AFB entries: 539975 Tue Aug 26 11:38:12 2008 medium AFB entries: 6517 Tue Aug 26 11:38:12 2008 resieved AFB entries: 6364 Tue Aug 26 11:38:12 2008 small AFB prime powers: 6 Tue Aug 26 11:38:12 2008 projective AFB roots: 2 Tue Aug 26 11:38:12 2008 AFB trial factoring cutoff: 60 or 89 bits Tue Aug 26 11:38:12 2008 single large prime AFB range: 23 - 27 bits Tue Aug 26 11:38:12 2008 double large prime AFB range: 46 - 52 bits Tue Aug 26 11:38:12 2008 triple large prime AFB range: 72 - 79 bits Tue Aug 26 11:38:12 2008 Tue Aug 26 11:38:12 2008 multiplying 1523913 primes from 7999993 to 33554432 Tue Aug 26 11:38:16 2008 multiply complete, product has 36865603 bits Tue Aug 26 11:38:44 2008 completed b = 3, found 172 relations Tue Aug 26 11:38:44 2008 elapsed time 00:00:38 Tue Aug 26 11:43:18 2008 Tue Aug 26 11:43:18 2008 Tue Aug 26 11:43:18 2008 Msieve v. 1.36 Tue Aug 26 11:43:18 2008 random seeds: 0d302a09 c30c0b1f Tue Aug 26 11:43:18 2008 factoring 60946499131512387375948479892734161528538198218330675388787875709772771135738011315733338750799922801101100084309323798592135870062063851615590114477840868690767621156561398519 (176 digits) Tue Aug 26 11:43:20 2008 no P-1/P+1/ECM available, skipping Tue Aug 26 11:43:20 2008 commencing number field sieve (176-digit input) Tue Aug 26 11:43:20 2008 R0: -1000000000000000000000000000000000000 Tue Aug 26 11:43:20 2008 R1: 1 Tue Aug 26 11:43:20 2008 A0: -7 Tue Aug 26 11:43:20 2008 A1: 0 Tue Aug 26 11:43:20 2008 A2: 0 Tue Aug 26 11:43:20 2008 A3: 0 Tue Aug 26 11:43:20 2008 A4: 0 Tue Aug 26 11:43:20 2008 A5: 6 Tue Aug 26 11:43:20 2008 size score = 2.794913e-12, Murphy alpha = 1.791017, combined = 1.538481e-12 Tue Aug 26 11:43:46 2008 restarting with 11607220 relations Tue Aug 26 11:43:48 2008 added 27651 free relations Tue Aug 26 11:43:48 2008 Tue Aug 26 11:43:48 2008 commencing relation filtering Tue Aug 26 11:43:48 2008 commencing duplicate removal, pass 1 Tue Aug 26 11:44:34 2008 error -9 reading relation 6604032 Tue Aug 26 11:44:41 2008 error -11 reading relation 7631047 Tue Aug 26 11:44:48 2008 error -9 reading relation 8631315 Tue Aug 26 11:44:55 2008 error -5 reading relation 9591341 Tue Aug 26 11:44:58 2008 error -11 reading relation 10123854 Tue Aug 26 11:45:02 2008 error -9 reading relation 10634976 Tue Aug 26 11:45:05 2008 error -15 reading relation 11125754 Tue Aug 26 11:45:09 2008 error -11 reading relation 11607220 Tue Aug 26 11:45:09 2008 found 1494552 hash collisions in 11634863 relations Tue Aug 26 11:45:09 2008 commencing duplicate removal, pass 2 Tue Aug 26 11:45:18 2008 found 1523897 duplicates and 10110966 unique relations Tue Aug 26 11:45:18 2008 memory use: 65.3 MB Tue Aug 26 11:45:20 2008 ignoring smallest 592937 rational and 593231 algebraic ideals Tue Aug 26 11:45:20 2008 filtering rational ideals above 8847360 Tue Aug 26 11:45:20 2008 filtering algebraic ideals above 8847360 Tue Aug 26 11:45:20 2008 need 1779252 more relations than ideals Tue Aug 26 11:45:20 2008 commencing singleton removal, pass 1 Tue Aug 26 11:46:32 2008 relations with 0 large ideals: 97035 Tue Aug 26 11:46:32 2008 relations with 1 large ideals: 975911 Tue Aug 26 11:46:32 2008 relations with 2 large ideals: 3729723 Tue Aug 26 11:46:32 2008 relations with 3 large ideals: 4605398 Tue Aug 26 11:46:32 2008 relations with 4 large ideals: 676207 Tue Aug 26 11:46:32 2008 relations with 5 large ideals: 26692 Tue Aug 26 11:46:32 2008 relations with 6 large ideals: 0 Tue Aug 26 11:46:32 2008 relations with 7+ large ideals: 0 Tue Aug 26 11:46:32 2008 10110966 relations and about 7977776 large ideals Tue Aug 26 11:46:32 2008 commencing singleton removal, pass 2 Tue Aug 26 11:47:43 2008 found 3829552 singletons Tue Aug 26 11:47:43 2008 current dataset: 6281414 relations and about 3704726 large ideals Tue Aug 26 11:47:43 2008 commencing singleton removal, pass 3 Tue Aug 26 11:48:29 2008 found 415704 singletons Tue Aug 26 11:48:29 2008 current dataset: 5865710 relations and about 3281204 large ideals Tue Aug 26 11:48:29 2008 commencing singleton removal, final pass Tue Aug 26 11:49:15 2008 memory use: 97.1 MB Tue Aug 26 11:49:15 2008 commencing in-memory singleton removal Tue Aug 26 11:49:15 2008 begin with 5865710 relations and 3465322 unique ideals Tue Aug 26 11:49:18 2008 reduce to 5552191 relations and 3148643 ideals in 7 passes Tue Aug 26 11:49:18 2008 max relations containing the same ideal: 27 Tue Aug 26 11:49:20 2008 removing 981791 relations and 669643 ideals in 312148 cliques Tue Aug 26 11:49:21 2008 commencing in-memory singleton removal Tue Aug 26 11:49:21 2008 begin with 4570400 relations and 3148643 unique ideals Tue Aug 26 11:49:23 2008 reduce to 4538232 relations and 2445242 ideals in 5 passes Tue Aug 26 11:49:23 2008 max relations containing the same ideal: 23 Tue Aug 26 11:49:24 2008 removing 695031 relations and 382883 ideals in 312148 cliques Tue Aug 26 11:49:25 2008 commencing in-memory singleton removal Tue Aug 26 11:49:25 2008 begin with 3843201 relations and 2445242 unique ideals Tue Aug 26 11:49:26 2008 reduce to 3788806 relations and 2003161 ideals in 5 passes Tue Aug 26 11:49:26 2008 max relations containing the same ideal: 21 Tue Aug 26 11:49:28 2008 filtering rational ideals above 720000 Tue Aug 26 11:49:28 2008 filtering algebraic ideals above 720000 Tue Aug 26 11:49:28 2008 need 116061 more relations than ideals Tue Aug 26 11:49:28 2008 commencing singleton removal, final pass Tue Aug 26 11:50:21 2008 keeping 3928915 ideals with weight <= 20, new excess is 405849 Tue Aug 26 11:50:25 2008 memory use: 173.7 MB Tue Aug 26 11:50:25 2008 commencing in-memory singleton removal Tue Aug 26 11:50:26 2008 begin with 5552191 relations and 3928915 unique ideals Tue Aug 26 11:50:29 2008 reduce to 5551567 relations and 3928291 ideals in 4 passes Tue Aug 26 11:50:29 2008 max relations containing the same ideal: 20 Tue Aug 26 11:50:32 2008 removing 1158851 relations and 758851 ideals in 400000 cliques Tue Aug 26 11:50:33 2008 commencing in-memory singleton removal Tue Aug 26 11:50:33 2008 begin with 4392716 relations and 3928291 unique ideals Tue Aug 26 11:50:37 2008 reduce to 4330937 relations and 3103156 ideals in 6 passes Tue Aug 26 11:50:37 2008 max relations containing the same ideal: 20 Tue Aug 26 11:50:39 2008 removing 880038 relations and 480038 ideals in 400000 cliques Tue Aug 26 11:50:40 2008 commencing in-memory singleton removal Tue Aug 26 11:50:40 2008 begin with 3450899 relations and 3103156 unique ideals Tue Aug 26 11:50:42 2008 reduce to 3381301 relations and 2546450 ideals in 5 passes Tue Aug 26 11:50:42 2008 max relations containing the same ideal: 20 Tue Aug 26 11:50:44 2008 removing 775867 relations and 411801 ideals in 364066 cliques Tue Aug 26 11:50:45 2008 commencing in-memory singleton removal Tue Aug 26 11:50:45 2008 begin with 2605434 relations and 2546450 unique ideals Tue Aug 26 11:50:47 2008 reduce to 2540585 relations and 2063741 ideals in 6 passes Tue Aug 26 11:50:47 2008 max relations containing the same ideal: 19 Tue Aug 26 11:50:48 2008 relations with 0 large ideals: 7566 Tue Aug 26 11:50:48 2008 relations with 1 large ideals: 73927 Tue Aug 26 11:50:48 2008 relations with 2 large ideals: 377040 Tue Aug 26 11:50:48 2008 relations with 3 large ideals: 723326 Tue Aug 26 11:50:48 2008 relations with 4 large ideals: 726199 Tue Aug 26 11:50:48 2008 relations with 5 large ideals: 427856 Tue Aug 26 11:50:48 2008 relations with 6 large ideals: 164504 Tue Aug 26 11:50:48 2008 relations with 7+ large ideals: 40167 Tue Aug 26 11:50:48 2008 commencing 2-way merge Tue Aug 26 11:50:50 2008 reduce to 2074143 relation sets and 1597299 unique ideals Tue Aug 26 11:50:50 2008 commencing full merge Tue Aug 26 11:51:16 2008 memory use: 159.8 MB Tue Aug 26 11:51:16 2008 found 1023946 cycles, need 953499 Tue Aug 26 11:51:16 2008 weight of 953499 cycles is about 67027131 (70.30/cycle) Tue Aug 26 11:51:16 2008 distribution of cycle lengths: Tue Aug 26 11:51:16 2008 1 relations: 27101 Tue Aug 26 11:51:16 2008 2 relations: 92836 Tue Aug 26 11:51:16 2008 3 relations: 126795 Tue Aug 26 11:51:16 2008 4 relations: 136910 Tue Aug 26 11:51:16 2008 5 relations: 133726 Tue Aug 26 11:51:16 2008 6 relations: 116981 Tue Aug 26 11:51:16 2008 7 relations: 97766 Tue Aug 26 11:51:16 2008 8 relations: 76828 Tue Aug 26 11:51:16 2008 9 relations: 58371 Tue Aug 26 11:51:16 2008 10+ relations: 86185 Tue Aug 26 11:51:16 2008 heaviest cycle: 15 relations Tue Aug 26 11:51:16 2008 commencing cycle optimization Tue Aug 26 11:51:17 2008 start with 5257576 relations Tue Aug 26 11:51:28 2008 pruned 115780 relations Tue Aug 26 11:51:28 2008 memory use: 158.4 MB Tue Aug 26 11:51:28 2008 distribution of cycle lengths: Tue Aug 26 11:51:28 2008 1 relations: 27101 Tue Aug 26 11:51:28 2008 2 relations: 94079 Tue Aug 26 11:51:28 2008 3 relations: 130300 Tue Aug 26 11:51:28 2008 4 relations: 140494 Tue Aug 26 11:51:28 2008 5 relations: 138881 Tue Aug 26 11:51:28 2008 6 relations: 120218 Tue Aug 26 11:51:28 2008 7 relations: 100012 Tue Aug 26 11:51:28 2008 8 relations: 76349 Tue Aug 26 11:51:28 2008 9 relations: 56039 Tue Aug 26 11:51:28 2008 10+ relations: 70026 Tue Aug 26 11:51:28 2008 heaviest cycle: 15 relations Tue Aug 26 11:51:29 2008 Tue Aug 26 11:51:29 2008 commencing linear algebra Tue Aug 26 11:51:30 2008 read 953499 cycles Tue Aug 26 11:51:31 2008 cycles contain 2367107 unique relations Tue Aug 26 11:51:56 2008 read 2367107 relations Tue Aug 26 11:52:00 2008 using 32 quadratic characters above 134213508 Tue Aug 26 11:52:21 2008 building initial matrix Tue Aug 26 11:52:40 2008 Tue Aug 26 11:52:40 2008 Tue Aug 26 11:52:40 2008 Msieve v. 1.36 Tue Aug 26 11:52:40 2008 random seeds: 091c43c1 ad0d2b3e Tue Aug 26 11:52:40 2008 factoring 60946499131512387375948479892734161528538198218330675388787875709772771135738011315733338750799922801101100084309323798592135870062063851615590114477840868690767621156561398519 (176 digits) Tue Aug 26 11:52:42 2008 no P-1/P+1/ECM available, skipping Tue Aug 26 11:52:42 2008 commencing number field sieve (176-digit input) Tue Aug 26 11:52:42 2008 R0: -1000000000000000000000000000000000000 Tue Aug 26 11:52:42 2008 R1: 1 Tue Aug 26 11:52:42 2008 A0: -7 Tue Aug 26 11:52:42 2008 A1: 0 Tue Aug 26 11:52:42 2008 A2: 0 Tue Aug 26 11:52:42 2008 A3: 0 Tue Aug 26 11:52:42 2008 A4: 0 Tue Aug 26 11:52:42 2008 A5: 6 Tue Aug 26 11:52:42 2008 size score = 2.794913e-12, Murphy alpha = 1.791017, combined = 1.538481e-12 Tue Aug 26 11:52:42 2008 Tue Aug 26 11:52:42 2008 commencing linear algebra Tue Aug 26 11:52:42 2008 read 953499 cycles Tue Aug 26 11:52:44 2008 cycles contain 2367107 unique relations Tue Aug 26 11:53:13 2008 read 2367107 relations Tue Aug 26 11:53:17 2008 using 32 quadratic characters above 134213508 Tue Aug 26 11:53:38 2008 building initial matrix Tue Aug 26 11:54:12 2008 memory use: 311.7 MB Tue Aug 26 11:54:14 2008 read 953499 cycles Tue Aug 26 11:54:16 2008 matrix is 953311 x 953499 (283.2 MB) with weight 89798014 (94.18/col) Tue Aug 26 11:54:16 2008 sparse part has weight 63743099 (66.85/col) Tue Aug 26 11:54:24 2008 filtering completed in 2 passes Tue Aug 26 11:54:24 2008 matrix is 952824 x 953012 (283.1 MB) with weight 89772381 (94.20/col) Tue Aug 26 11:54:24 2008 sparse part has weight 63730580 (66.87/col) Tue Aug 26 11:54:34 2008 read 953012 cycles Tue Aug 26 11:54:34 2008 matrix is 952824 x 953012 (283.1 MB) with weight 89772381 (94.20/col) Tue Aug 26 11:54:34 2008 sparse part has weight 63730580 (66.87/col) Tue Aug 26 11:54:35 2008 saving the first 48 matrix rows for later Tue Aug 26 11:54:35 2008 matrix is 952776 x 953012 (270.1 MB) with weight 68365485 (71.74/col) Tue Aug 26 11:54:35 2008 sparse part has weight 61268317 (64.29/col) Tue Aug 26 11:54:35 2008 matrix includes 64 packed rows Tue Aug 26 11:54:35 2008 using block size 65536 for processor cache size 4096 kB Tue Aug 26 11:54:40 2008 commencing Lanczos iteration (4 threads) Tue Aug 26 11:54:40 2008 memory use: 279.2 MB Tue Aug 26 13:05:42 2008 lanczos halted after 15067 iterations (dim = 952776) Tue Aug 26 13:05:44 2008 recovered 49 nontrivial dependencies Tue Aug 26 13:05:44 2008 elapsed time 01:13:04 Tue Aug 26 13:16:40 2008 Tue Aug 26 13:16:40 2008 Tue Aug 26 13:16:40 2008 Msieve v. 1.36 Tue Aug 26 13:16:40 2008 random seeds: d1ae08a7 def52c6a Tue Aug 26 13:16:40 2008 factoring 60946499131512387375948479892734161528538198218330675388787875709772771135738011315733338750799922801101100084309323798592135870062063851615590114477840868690767621156561398519 (176 digits) Tue Aug 26 13:16:42 2008 no P-1/P+1/ECM available, skipping Tue Aug 26 13:16:42 2008 commencing number field sieve (176-digit input) Tue Aug 26 13:16:42 2008 R0: -1000000000000000000000000000000000000 Tue Aug 26 13:16:42 2008 R1: 1 Tue Aug 26 13:16:42 2008 A0: -7 Tue Aug 26 13:16:42 2008 A1: 0 Tue Aug 26 13:16:42 2008 A2: 0 Tue Aug 26 13:16:42 2008 A3: 0 Tue Aug 26 13:16:42 2008 A4: 0 Tue Aug 26 13:16:42 2008 A5: 6 Tue Aug 26 13:16:42 2008 size score = 2.794913e-12, Murphy alpha = 1.791017, combined = 1.538481e-12 Tue Aug 26 13:16:42 2008 Tue Aug 26 13:16:42 2008 commencing square root phase Tue Aug 26 13:16:42 2008 reading relations for dependency 1 Tue Aug 26 13:16:42 2008 read 476023 cycles Tue Aug 26 13:16:43 2008 cycles contain 1540727 unique relations Tue Aug 26 13:17:11 2008 read 1540727 relations Tue Aug 26 13:17:20 2008 multiplying 2569832 relations Tue Aug 26 13:20:01 2008 multiply complete, coefficients have about 64.69 million bits Tue Aug 26 13:20:03 2008 initial square root is modulo 1936936291 Tue Aug 26 13:25:03 2008 reading relations for dependency 2 Tue Aug 26 13:25:03 2008 read 476612 cycles Tue Aug 26 13:25:04 2008 cycles contain 1542603 unique relations Tue Aug 26 13:25:25 2008 read 1542603 relations Tue Aug 26 13:25:34 2008 multiplying 2570336 relations Tue Aug 26 13:28:16 2008 multiply complete, coefficients have about 64.70 million bits Tue Aug 26 13:28:17 2008 initial square root is modulo 1946412371 Tue Aug 26 13:33:19 2008 reading relations for dependency 3 Tue Aug 26 13:33:19 2008 read 476357 cycles Tue Aug 26 13:33:20 2008 cycles contain 1541319 unique relations Tue Aug 26 13:33:33 2008 read 1541319 relations Tue Aug 26 13:33:41 2008 multiplying 2568952 relations Tue Aug 26 13:36:23 2008 multiply complete, coefficients have about 64.67 million bits Tue Aug 26 13:36:24 2008 initial square root is modulo 1924029001 Tue Aug 26 13:41:25 2008 prp61 factor: 4830487850130825355136992625082278853531328717363811995759451 Tue Aug 26 13:41:25 2008 prp116 factor: 12617048427077972576764760920138324767170820384685368004188695290274577720048489648872812603297601032348850349016469 Tue Aug 26 13:41:25 2008 elapsed time 00:24:45

Aug 26, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve
(8·10¹⁴⁸-11)/3 = 2(6)₁₄₇3_<149> = 7 · 13 · C147
C147 = P36 · P36 · P75
P36 = 631170595247677325494007511276201721_<36>
P36 = 737524339058375728078988025299221609_<36>
P75 = 629512306969773167184550234503027158972717529174606520898597164110023596037_<75>

Number: 26663_148 N=293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293 ( 147 digits) SNFS difficulty: 148 digits. Divisors found: r1=631170595247677325494007511276201721 (pp36) r2=737524339058375728078988025299221609 (pp36) r3=629512306969773167184550234503027158972717529174606520898597164110023596037 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.94 hours. Scaled time: 21.21 units (timescale=1.013). Factorization parameters were as follows: name: 26663_148 n: 293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293040293 m: 200000000000000000000000000000 c5: 250 c0: -11 skew: 0.54 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3650001) Primes: RFBsize:114155, AFBsize:114243, largePrimes:3091916 encountered Relations: rels:3208626, finalFF:346994 Max relations in full relation-set: 28 Initial matrix: 228464 x 346994 with sparse part having weight 42238202. Pruned matrix : 199407 x 200613 with weight 24522224. Total sieving time: 20.55 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.28 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 20.94 hours. --------- CPU info (if available) ----------

(8·10¹⁴¹-11)/3 = 2(6)₁₄₀3_<142> = 5483 · C138
C138 = P65 · P74
P65 = 42566066342315420407961503276609805239725144032539524413928807061_<65>
P74 = 11425809234867554634313801966008971003354585779235506262097186026891882401_<74>

Number: 26663_141 N=486351753906012523557663079822481609824305428901452975864794212414128518450969663809350112468843090765396072709587208948872271870630433461 ( 138 digits) SNFS difficulty: 142 digits. Divisors found: r1=42566066342315420407961503276609805239725144032539524413928807061 (pp65) r2=11425809234867554634313801966008971003354585779235506262097186026891882401 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 14.88 hours. Scaled time: 15.04 units (timescale=1.011). Factorization parameters were as follows: name: 26663_141 n: 486351753906012523557663079822481609824305428901452975864794212414128518450969663809350112468843090765396072709587208948872271870630433461 m: 20000000000000000000000000000 c5: 5 c0: -22 skew: 1.34 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2350001) Primes: RFBsize:100021, AFBsize:100104, largePrimes:3163162 encountered Relations: rels:3417143, finalFF:483950 Max relations in full relation-set: 28 Initial matrix: 200190 x 483950 with sparse part having weight 54374487. Pruned matrix : 151850 x 152914 with weight 22718147. Total sieving time: 14.49 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.29 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 14.88 hours. --------- CPU info (if available) ----------

(8·10¹¹⁰-11)/3 = 2(6)₁₀₉3_<111> = 422270161 · C102
C102 = P50 · P53
P50 = 16332279646114817898481597976376858514229176394471_<50>
P53 = 38666203384806306112733511010467776636962683473769073_<53>

Mon Aug 25 15:02:36 2008 Msieve v. 1.36 Mon Aug 25 15:02:36 2008 random seeds: fad24d48 84aab7b6 Mon Aug 25 15:02:36 2008 factoring 631507246534207911192348413807687128209531875179469919179694694711489848004360096537028735655007995383 (102 digits) Mon Aug 25 15:02:37 2008 no P-1/P+1/ECM available, skipping Mon Aug 25 15:02:38 2008 commencing quadratic sieve (102-digit input) Mon Aug 25 15:02:38 2008 using multiplier of 3 Mon Aug 25 15:02:38 2008 using 32kb Intel Core sieve core Mon Aug 25 15:02:38 2008 sieve interval: 36 blocks of size 32768 Mon Aug 25 15:02:38 2008 processing polynomials in batches of 6 Mon Aug 25 15:02:38 2008 using a sieve bound of 3264419 (117500 primes) Mon Aug 25 15:02:38 2008 using large prime bound of 489662850 (28 bits) Mon Aug 25 15:02:38 2008 using double large prime bound of 4383437839720350 (44-52 bits) Mon Aug 25 15:02:38 2008 using trial factoring cutoff of 52 bits Mon Aug 25 15:02:38 2008 polynomial 'A' values have 13 factors Tue Aug 26 11:57:29 2008 117764 relations (27401 full + 90363 combined from 1765490 partial), need 117596 Tue Aug 26 11:57:34 2008 begin with 1792891 relations Tue Aug 26 11:57:36 2008 reduce to 313570 relations in 12 passes Tue Aug 26 11:57:36 2008 attempting to read 313570 relations Tue Aug 26 11:57:44 2008 recovered 313570 relations Tue Aug 26 11:57:44 2008 recovered 305981 polynomials Tue Aug 26 11:57:44 2008 attempting to build 117764 cycles Tue Aug 26 11:57:44 2008 found 117764 cycles in 6 passes Tue Aug 26 11:57:44 2008 distribution of cycle lengths: Tue Aug 26 11:57:44 2008 length 1 : 27401 Tue Aug 26 11:57:44 2008 length 2 : 19789 Tue Aug 26 11:57:44 2008 length 3 : 19479 Tue Aug 26 11:57:44 2008 length 4 : 16071 Tue Aug 26 11:57:44 2008 length 5 : 12409 Tue Aug 26 11:57:44 2008 length 6 : 8719 Tue Aug 26 11:57:44 2008 length 7 : 5710 Tue Aug 26 11:57:44 2008 length 9+: 8186 Tue Aug 26 11:57:44 2008 largest cycle: 24 relations Tue Aug 26 11:57:45 2008 matrix is 117500 x 117764 (34.8 MB) with weight 8659607 (73.53/col) Tue Aug 26 11:57:45 2008 sparse part has weight 8659607 (73.53/col) Tue Aug 26 11:57:46 2008 filtering completed in 3 passes Tue Aug 26 11:57:46 2008 matrix is 113226 x 113290 (33.6 MB) with weight 8365111 (73.84/col) Tue Aug 26 11:57:46 2008 sparse part has weight 8365111 (73.84/col) Tue Aug 26 11:57:47 2008 saving the first 48 matrix rows for later Tue Aug 26 11:57:47 2008 matrix is 113178 x 113290 (23.7 MB) with weight 6978451 (61.60/col) Tue Aug 26 11:57:47 2008 sparse part has weight 5540716 (48.91/col) Tue Aug 26 11:57:47 2008 matrix includes 64 packed rows Tue Aug 26 11:57:47 2008 using block size 45316 for processor cache size 2048 kB Tue Aug 26 11:57:48 2008 commencing Lanczos iteration Tue Aug 26 11:57:48 2008 memory use: 21.2 MB Tue Aug 26 11:59:27 2008 lanczos halted after 1792 iterations (dim = 113178) Tue Aug 26 11:59:27 2008 recovered 18 nontrivial dependencies Tue Aug 26 11:59:29 2008 prp50 factor: 16332279646114817898481597976376858514229176394471 Tue Aug 26 11:59:29 2008 prp53 factor: 38666203384806306112733511010467776636962683473769073 Tue Aug 26 11:59:29 2008 elapsed time 20:56:53

(8·10¹⁵³-11)/3 = 2(6)₁₅₂3_<154> = 19 · 403653373 · C144
C144 = P67 · P77
P67 = 9584647896404527490150217237474587315829821200029362091271254431753_<67>
P77 = 36276917910572708977019726585543332934889029681264749296841149667688620319833_<77>

Number: 26663_153 N=347701484939610441804361875586216038235238225528174779157242115236783754412850842678285896895876743219937012988495149260111487140603869530857249 ( 144 digits) SNFS difficulty: 153 digits. Divisors found: r1=9584647896404527490150217237474587315829821200029362091271254431753 (pp67) r2=36276917910572708977019726585543332934889029681264749296841149667688620319833 (pp77) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.00 hours. Scaled time: 24.07 units (timescale=1.003). Factorization parameters were as follows: name: 26663_153 n: 347701484939610441804361875586216038235238225528174779157242115236783754412850842678285896895876743219937012988495149260111487140603869530857249 m: 2000000000000000000000000000000 c5: 250 c0: -11 skew: 0.54 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176244, largePrimes:5838800 encountered Relations: rels:5925527, finalFF:616857 Max relations in full relation-set: 28 Initial matrix: 352612 x 616857 with sparse part having weight 59940685. Pruned matrix : 264646 x 266473 with weight 31491438. Total sieving time: 23.08 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.76 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 24.00 hours. --------- CPU info (if available) ----------

Aug 26, 2008

By Serge Batalov / GMP-ECM 6.2.1, pol51, Msieve 1.36
(8·10¹⁹⁷-11)/3 = 2(6)₁₉₆3_<198> = 111733 · 5397377 · 30795825067283_<14> · 255721698337823_<15> · 1123975172813840253229_<22> · C137
C137 = P30 · P107
P30 = 584631897521184211264327771703_<30>
P107 = 85448780591496185069139272511079480379794034535247604377701836586510272565252157696362447303206979984172421_<107>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4075465090 Step 1 took 7029ms Step 2 took 5423ms ********** Factor found in step 2: 584631897521184211264327771703 Found probable prime factor of 30 digits: 584631897521184211264327771703 Probable prime cofactor 85448780591496185069139272511079480379794034535247604377701836586510272565252157696362447303206979984172421 has 107 digits

(8·10¹⁷⁸-11)/3 = 2(6)₁₇₇3_<179> = 7² · 13 · 68889803 · C168
C168 = P32 · C137
P32 = 24902290071539505232947157370809_<32>
C137 = [24402542030292362032996350257126313176584682115300957283898560700731379335812856761997377266656064229543530545017001142017298689072691137_<137>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2294159883 Step 1 took 8351ms Step 2 took 6372ms ********** Factor found in step 2: 24902290071539505232947157370809 Found probable prime factor of 32 digits: 24902290071539505232947157370809 Composite cofactor 24402542030292362032996350257126313176584682115300957283898560700731379335812856761997377266656064229543530545017001142017298689072691137 has 137 digits

(8·10¹⁹⁴-11)/3 = 2(6)₁₉₃3_<195> = 173 · 1489 · C190
C190 = P32 · C158
P32 = 13268292354555506055377112473833_<32>
C158 = [78021249133662649201010056260756443212459081834801215517983657063217652246078341944261089148602713232013125543543274882835988069853193682190413043480015720763_<158>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2757967481 Step 1 took 9391ms Step 2 took 7236ms ********** Factor found in step 2: 13268292354555506055377112473833 Found probable prime factor of 32 digits: 13268292354555506055377112473833 Composite cofactor 78021249133662649201010056260756443212459081834801215517983657063217652246078341944261089148602713232013125543543274882835988069853193682190413043480015720763 has 158 digits

(8·10¹⁸⁰-11)/3 = 2(6)₁₇₉3_<181> = 3397753236583_<13> · 392394707280681851533_<21> · 205355556215967421129829_<24> · C124
C124 = P28 · P41 · P56
P28 = 3400747871425819708132739489_<28>
P41 = 38816920840993351478857495860128753476187_<41>
P56 = 73782230785092535333770078843852428216528975329015286611_<56>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1157696711 Step 1 took 5689ms Step 2 took 3166ms ********** Factor found in step 2: 3400747871425819708132739489 Found probable prime factor of 28 digits: 3400747871425819708132739489 Composite cofactor 2863999011856839684189632857032227275314528666558642362791977590502022197508465810654828368432257 has 97 digits Number: 26663_180 N=2863999011856839684189632857032227275314528666558642362791977590502022197508465810654828368432257 ( 97 digits) Divisors found: r1=38816920840993351478857495860128753476187 r2=73782230785092535333770078843852428216528975329015286611 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.953). Factorization parameters were as follows: name: 26663_180 n: 2863999011856839684189632857032227275314528666558642362791977590502022197508465810654828368432257 skew: 4520.93 # norm 1.38e+13 c5: 32880 c4: 2367442 c3: -1766456187165 c2: 3692732179295755 c1: 21831126546193430705 c0: 6433261978193336300543 # alpha -5.40 Y1: 10108298959 Y0: -2443476604716635280 # Murphy_E 4.95e-09 # M 1500633408794892675967970158936107201052746886196142694054793555285370286000876464460094243978359 type: gnfs rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1020001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 123265 x 123498 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 1.70 hours.

(8·10¹⁵⁸-11)/3 = 2(6)₁₅₇3_<159> = 29 · 89 · C156
C156 = P41 · P115
P41 = 85645030255583612491797176677799392292263_<41>
P115 = 1206364533295746858405918018055464413960376241979912931904257349702717955872012065492560876276627423631920046146621_<115>

Number: 26663_158 N=103319126953377243962288518662017305953764690688363683326875887898747255585690300916957251711223040165310603125403590339661629859227689526023505101381893323 ( 156 digits) SNFS difficulty: 158 digits. Divisors found: r1=85645030255583612491797176677799392292263 r2=1206364533295746858405918018055464413960376241979912931904257349702717955872012065492560876276627423631920046146621 Version: Total time: 22.37 hours. Scaled time: 76.54 units (timescale=3.422). Factorization parameters were as follows: n: 103319126953377243962288518662017305953764690688363683326875887898747255585690300916957251711223040165310603125403590339661629859227689526023505101381893323 Y1: 1 Y0: -20000000000000000000000000000000 c5: 250 c0: -11 skew: 0.54 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 490121 x 490369 Total sieving time: 22.37 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.70 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 22.37 hours.

Aug 25, 2008 (5th)

By Jo Yeong Uk / GMP-ECM
(8·10²⁰¹-11)/3 = 2(6)₂₀₀3_<202> = C202
C202 = P30 · C172
P30 = 451812655504187553833642493151_<30>
C172 = [5902151332372209503609296911272406487211881024719526726349392490909514083822506333934172090530872360967046140330267742066517371414348495611729173874621014004093969936550713_<172>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 (202 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2863822186 Step 1 took 7248ms ********** Factor found in step 1: 451812655504187553833642493151 Found probable prime factor of 30 digits: 451812655504187553833642493151 Composite cofactor 5902151332372209503609296911272406487211881024719526726349392490909514083822506333934172090530872360967046140330267742066517371414348495611729173874621014004093969936550713 has 172 digits

Aug 25, 2008 (4th)

By Sinkiti Sibata / Msieve, GGNFS
(8·10¹¹⁵-11)/3 = 2(6)₁₁₄3_<116> = 27327373 · 744960989 · 159825498529_<12> · C88
C88 = P38 · P51
P38 = 36394744129187324330831066302113920077_<38>
P51 = 225191803222073042077948412162190617679629996439163_<51>

Msieve v. 1.36 Mon Aug 25 09:12:26 2008 random seeds: 022eeabf 0fc3ee48 factoring 8195798058257650035222798926893206468073882016281189047624546008259499 372911085174775551 (88 digits) no P-1/P+1/ECM available, skipping commencing quadratic sieve (88-digit input) using multiplier of 15 using 32kb Intel Core sieve core sieve interval: 28 blocks of size 32768 processing polynomials in batches of 8 using a sieve bound of 1533799 (58333 primes) using large prime bound of 122703920 (26 bits) using double large prime bound of 363032185823760 (42-49 bits) using trial factoring cutoff of 49 bits polynomial 'A' values have 11 factors sieving in progress (press Ctrl-C to pause) 58733 relations (16463 full + 42270 combined from 612585 partial), need 58429 58733 relations (16463 full + 42270 combined from 612585 partial), need 58429 sieving complete, commencing postprocessing begin with 629048 relations reduce to 140284 relations in 10 passes attempting to read 140284 relations recovered 140284 relations recovered 117682 polynomials attempting to build 58733 cycles found 58733 cycles in 5 passes distribution of cycle lengths: length 1 : 16463 length 2 : 11455 length 3 : 10354 length 4 : 7733 length 5 : 5344 length 6 : 3310 length 7 : 1921 length 9+: 2153 largest cycle: 18 relations matrix is 58333 x 58733 (14.2 MB) with weight 3477966 (59.22/col) sparse part has weight 3477966 (59.22/col) filtering completed in 3 passes matrix is 53756 x 53820 (13.0 MB) with weight 3201859 (59.49/col) sparse part has weight 3201859 (59.49/col) saving the first 48 matrix rows for later matrix is 53708 x 53820 (9.4 MB) with weight 2620040 (48.68/col) sparse part has weight 2132255 (39.62/col) matrix includes 64 packed rows using block size 21528 for processor cache size 4096 kB commencing Lanczos iteration memory use: 8.6 MB lanczos halted after 851 iterations (dim = 53706) recovered 17 nontrivial dependencies prp38 factor: 36394744129187324330831066302113920077 prp51 factor: 225191803222073042077948412162190617679629996439163 elapsed time 00:54:52

(8·10¹³⁸-11)/3 = 2(6)₁₃₇3_<139> = 8419 · 185873959 · 1807965893376375389_<19> · C108
C108 = P31 · P78
P31 = 4022953384627041789849995127289_<31>
P78 = 234290370863190928348570573401696087817693212086985056963495641872571535390143_<78>

Number: 26663_138 N=942539240449598799728657907393877165710658736278448078722000554709399106887259501615297280227529767560912327 ( 108 digits) SNFS difficulty: 138 digits. Divisors found: r1=4022953384627041789849995127289 (pp31) r2=234290370863190928348570573401696087817693212086985056963495641872571535390143 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.64 hours. Scaled time: 9.25 units (timescale=0.869). Factorization parameters were as follows: name: 26663_138 n: 942539240449598799728657907393877165710658736278448078722000554709399106887259501615297280227529767560912327 m: 2000000000000000000000000000 c5: 250 c0: -11 skew: 0.54 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1675001) Primes: RFBsize:78498, AFBsize:64024, largePrimes:1644943 encountered Relations: rels:1676321, finalFF:186319 Max relations in full relation-set: 28 Initial matrix: 142588 x 186319 with sparse part having weight 19451277. Pruned matrix : 131689 x 132465 with weight 12236740. Total sieving time: 10.38 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.16 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 10.64 hours. --------- CPU info (if available) ----------

(8·10¹²⁶-11)/3 = 2(6)₁₂₅3_<127> = 349 · C124
C124 = P34 · P91
P34 = 1077539553478360533230464619964479_<34>
P91 = 7091042436804680319855247362684038701737502682164360896283654857951232009654026676364876653_<91>

Number: 26663_126 N=7640878701050620821394460362941738299904489016236867239732569245463228271251193887297039159503342884431709646609360076408787 ( 124 digits) SNFS difficulty: 127 digits. Divisors found: r1=1077539553478360533230464619964479 (pp34) r2=7091042436804680319855247362684038701737502682164360896283654857951232009654026676364876653 (pp91) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.46 hours. Scaled time: 2.70 units (timescale=0.780). Factorization parameters were as follows: name: 26663_126 n: 7640878701050620821394460362941738299904489016236867239732569245463228271251193887297039159503342884431709646609360076408787 m: 20000000000000000000000000 c5: 5 c0: -22 skew: 1.34 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:49098, AFBsize:63744, largePrimes:2346493 encountered Relations: rels:2596068, finalFF:320129 Max relations in full relation-set: 28 Initial matrix: 112907 x 320129 with sparse part having weight 33834564. Pruned matrix : 89415 x 90043 with weight 8750419. Total sieving time: 3.31 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.46 hours. --------- CPU info (if available) ----------

(8·10¹³⁶-11)/3 = 2(6)₁₃₅3_<137> = 7² · 13 · 2477 · 958183397433934124845303_<24> · C107
C107 = P43 · P65
P43 = 1571318684431170472268584011635077965756373_<43>
P65 = 11225104096442483874271543011120612457408910397229839548437445173_<65>

Number: 26663_136 N=17638215801424946277538705205049357412849843641681158464695470568727377018710107384739025942038188662837529 ( 107 digits) SNFS difficulty: 137 digits. Divisors found: r1=1571318684431170472268584011635077965756373 (pp43) r2=11225104096442483874271543011120612457408910397229839548437445173 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.52 hours. Scaled time: 6.91 units (timescale=0.657). Factorization parameters were as follows: name: 26663_136 n: 17638215801424946277538705205049357412849843641681158464695470568727377018710107384739025942038188662837529 m: 2000000000000000000000000000 c5: 5 c0: -22 skew: 1.34 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1675001) Primes: RFBsize:78498, AFBsize:63744, largePrimes:1792261 encountered Relations: rels:1939159, finalFF:299448 Max relations in full relation-set: 28 Initial matrix: 142307 x 299448 with sparse part having weight 29445787. Pruned matrix : 112486 x 113261 with weight 11386504. Total sieving time: 10.31 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 10.52 hours. --------- CPU info (if available) ----------

(8·10¹⁰⁸-11)/3 = 2(6)₁₀₇3_<109> = 173 · 1396985297_<10> · C98
C98 = P46 · P52
P46 = 9478218721635962950063775331955797995694998263_<46>
P52 = 1164136932415231088051595778237945031400502778838821_<52>

Msieve v. 1.36 Mon Aug 25 10:36:30 2008 random seeds: 38e93f28 18cf46c6 factoring 1103394446736590300212881872621524333132390980448938746594859925015513 3200443654428583548751967923 (98 digits) no P-1/P+1/ECM available, skipping commencing quadratic sieve (98-digit input) using multiplier of 3 using 32kb Intel Core sieve core sieve interval: 36 blocks of size 32768 processing polynomials in batches of 6 using a sieve bound of 2439067 (89109 primes) using large prime bound of 365860050 (28 bits) using double large prime bound of 2593981779484650 (43-52 bits) using trial factoring cutoff of 52 bits polynomial 'A' values have 13 factors sieving in progress (press Ctrl-C to pause) 89224 relations (20824 full + 68400 combined from 1362659 partial), need 89205 89224 relations (20824 full + 68400 combined from 1362659 partial), need 89205 sieving complete, commencing postprocessing begin with 1383483 relations reduce to 237176 relations in 10 passes attempting to read 237176 relations recovered 237176 relations recovered 226560 polynomials attempting to build 89224 cycles found 89224 cycles in 6 passes distribution of cycle lengths: length 1 : 20824 length 2 : 15190 length 3 : 14918 length 4 : 12146 length 5 : 9457 length 6 : 6438 length 7 : 4306 length 9+: 5945 largest cycle: 21 relations matrix is 89109 x 89224 (24.4 MB) with weight 6042868 (67.73/col) sparse part has weight 6042868 (67.73/col) filtering completed in 3 passes matrix is 85635 x 85699 (23.6 MB) with weight 5842727 (68.18/col) sparse part has weight 5842727 (68.18/col) saving the first 48 matrix rows for later matrix is 85587 x 85699 (14.7 MB) with weight 4635880 (54.09/col) sparse part has weight 3342133 (39.00/col) matrix includes 64 packed rows using block size 34279 for processor cache size 4096 kB commencing Lanczos iteration memory use: 14.2 MB linear algebra completed 80326 out of 85699 dimensions (93.7%) lanczos halted after 1355 iterations (dim = 85586) recovered 17 nontrivial dependencies prp46 factor: 9478218721635962950063775331955797995694998263 prp52 factor: 1164136932415231088051595778237945031400502778838821 elapsed time 06:57:03

(8·10¹⁴³-11)/3 = 2(6)₁₄₂3_<144> = 17 · 7146336199_<10> · C133
C133 = P35 · P45 · P53
P35 = 74131706740520134432488133381283627_<35>
P45 = 473918783322639150993506355219846282948081391_<45>
P53 = 62478190973515905091229270530795437441876297718914173_<53>

Number: 26663_143 N=2195009312883842615956312494274824259880177803431059411666199434226845762617106919694017756641960595544954965800031013549434101030161 ( 133 digits) SNFS difficulty: 143 digits. Divisors found: r1=74131706740520134432488133381283627 (pp35) r2=473918783322639150993506355219846282948081391 (pp45) r3=62478190973515905091229270530795437441876297718914173 (pp53) Version: GGNFS-0.77.1-20050930-nocona Total time: 12.89 hours. Scaled time: 12.93 units (timescale=1.003). Factorization parameters were as follows: name: 26663_143 n: 2195009312883842615956312494274824259880177803431059411666199434226845762617106919694017756641960595544954965800031013549434101030161 m: 20000000000000000000000000000 c5: 250 c0: -11 skew: 0.54 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2350001) Primes: RFBsize:100021, AFBsize:100179, largePrimes:2890914 encountered Relations: rels:2943556, finalFF:305165 Max relations in full relation-set: 28 Initial matrix: 200266 x 305165 with sparse part having weight 33397507. Pruned matrix : 173998 x 175063 with weight 17976771. Total sieving time: 12.62 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.18 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 12.89 hours. --------- CPU info (if available) ----------

Aug 25, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(8·10¹⁰³-11)/3 = 2(6)₁₀₂3_<104> = 42640406154121325305813_<23> · C81
C81 = P29 · P53
P29 = 32310722809845102049503136009_<29>
P53 = 19355336495052044162304280966510001150870536267517939_<53>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 625384912382905433497831556663133629465431712905651150435013281886485743164365451 (81 digits) Using B1=716000, B2=696728352, polynomial Dickson(3), sigma=3553693662 Step 1 took 3813ms Step 2 took 2156ms ********** Factor found in step 2: 32310722809845102049503136009 Found probable prime factor of 29 digits: 32310722809845102049503136009 Probable prime cofactor 19355336495052044162304280966510001150870536267517939 has 53 digits

(8·10¹¹⁴-11)/3 = 2(6)₁₁₃3_<115> = 89 · C113
C113 = P34 · P80
P34 = 2259115997850597640784499152946323_<34>
P80 = 13262951900206461666213310460070950876252932275320620693018204736411989385181029_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 29962546816479400749063670411985018726591760299625468164794007490636704119850187265917602996254681647940074906367 (113 digits) Using B1=1054000, B2=1045563762, polynomial Dickson(6), sigma=3402612825 Step 1 took 8203ms Step 2 took 4407ms ********** Factor found in step 2: 2259115997850597640784499152946323 Found probable prime factor of 34 digits: 2259115997850597640784499152946323 Probable prime cofactor 13262951900206461666213310460070950876252932275320620693018204736411989385181029 has 80 digits

(8·10¹²⁸-11)/3 = 2(6)₁₂₇3_<129> = C129
C129 = P36 · P93
P36 = 497804025886962506207714390938400623_<36>
P93 = 535686038680649951068585178875042757472954243229661921056248994248736475025875054178317329481_<93>

Number: n N=266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 129 digits) SNFS difficulty: 128 digits. Divisors found: r1=497804025886962506207714390938400623 (pp36) r2=535686038680649951068585178875042757472954243229661921056248994248736475025875054178317329481 (pp93) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.27 hours. Scaled time: 2.96 units (timescale=0.905). Factorization parameters were as follows: name: KA_2_6_127_3 n: 266666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 type: snfs skew: 0.54 deg: 5 c5: 250 c0: -11 m: 20000000000000000000000000 rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 360001) Primes: RFBsize:56543, AFBsize:56529, largePrimes:5287037 encountered Relations: rels:4505640, finalFF:143302 Max relations in full relation-set: 48 Initial matrix: 113138 x 143302 with sparse part having weight 17608215. Pruned matrix : 105459 x 106088 with weight 9691679. Total sieving time: 2.98 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.12 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,700000,700000,28,28,50,50,2.5,2.5,50000 total time: 3.27 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(17·10¹⁹²+1)/9 = 1(8)₁₉₁9_<193> = 23 · C191
C191 = P94 · P98
P94 = 1948662034201098323710903730958276574627075333548724371561250262056978094886490485343891106957_<94>
P98 = 42144611237527240110223119654035423284203139603203167827807897848137401763143004307433958811849899_<98>

Number: n N=82125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647343 ( 191 digits) SNFS difficulty: 193 digits. Divisors found: Mon Aug 25 19:56:31 2008 prp94 factor: 1948662034201098323710903730958276574627075333548724371561250262056978094886490485343891106957 Mon Aug 25 19:56:31 2008 prp98 factor: 42144611237527240110223119654035423284203139603203167827807897848137401763143004307433958811849899 Mon Aug 25 19:56:31 2008 elapsed time 07:59:02 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 177.74 hours. Scaled time: 364.55 units (timescale=2.051). Factorization parameters were as follows: name: KA_1_8_191_9 n: 82125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647343 type: snfs skew: 0.23 deg: 5 c5: 1700 c0: 1 m: 100000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 13700001) Primes: RFBsize:633578, AFBsize:634678, largePrimes:11237680 encountered Relations: rels:11302726, finalFF:1311085 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 177.34 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,193,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000 total time: 177.74 hours. --------- CPU info (if available) ----------

(8·10¹³⁹-11)/3 = 2(6)₁₃₈3_<140> = C140
C140 = P33 · P107
P33 = 959282682025957797850608113019113_<33>
P107 = 27798549026599729182324561097530178917531373289574911508549281342744062452451420379597840926261692683566351_<107>

Number: n N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 140 digits) SNFS difficulty: 140 digits. Divisors found: Mon Aug 25 20:32:13 2008 prp33 factor: 959282682025957797850608113019113 Mon Aug 25 20:32:13 2008 prp107 factor: 27798549026599729182324561097530178917531373289574911508549281342744062452451420379597840926261692683566351 Mon Aug 25 20:32:13 2008 elapsed time 00:17:59 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.66 hours. Scaled time: 10.35 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_6_138_3 n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 type: snfs skew: 1.69 deg: 5 c5: 4 c0: -55 m: 10000000000000000000000000000 rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 560001) Primes: RFBsize:92938, AFBsize:92975, largePrimes:7002152 encountered Relations: rels:6006723, finalFF:211320 Max relations in full relation-set: 28 Initial matrix: 185977 x 211320 with sparse part having weight 22376445. Pruned matrix : Total sieving time: 4.96 hours. Total relation processing time: 0.69 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,50,50,2.5,2.5,100000 total time: 5.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(8·10¹²³-11)/3 = 2(6)₁₂₂3_<124> = 193 · 3323 · C118
C118 = P45 · P73
P45 = 642613838830751806249659095006571736039311649_<45>
P73 = 6470398189326729013605156656933550973595555578999795769319970345586959333_<73>

Number: n N=4157967419206794950356467744307872539587747925304194297659532114321235207381223762575902395872801539695335332276170117 ( 118 digits) SNFS difficulty: 123 digits. Divisors found: r1=642613838830751806249659095006571736039311649 (pp45) r2=6470398189326729013605156656933550973595555578999795769319970345586959333 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.50 hours. Scaled time: 2.74 units (timescale=1.827). Factorization parameters were as follows: name: KA_2_6_122_3 n: 4157967419206794950356467744307872539587747925304194297659532114321235207381223762575902395872801539695335332276170117 type: snfs skew: 0.54 deg: 5 c5: 250 c0: -11 m: 2000000000000000000000000 rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 260001) Primes: RFBsize:56543, AFBsize:56529, largePrimes:4753006 encountered Relations: rels:3997616, finalFF:139366 Max relations in full relation-set: 48 Initial matrix: 113138 x 139366 with sparse part having weight 13526645. Pruned matrix : 104170 x 104799 with weight 7166986. Total sieving time: 1.29 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.05 hours. Total square root time: 0.09 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,123,5,0,0,0,0,0,0,0,0,700000,700000,28,28,50,50,2.5,2.5,50000 total time: 1.50 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Aug 25, 2008 (2nd)

By Serge Batalov / Msieve
(8·10¹³²-11)/3 = 2(6)₁₃₁3_<133> = 15536946350327_<14> · 57716815808783_<14> · 97764490225841183_<17> · C89
C89 = P31 · P59
P31 = 2878173973878396344472623824273_<31>
P59 = 10568236438025805805146214006943933895776577890265004772977_<59>

Sun Aug 24 12:23:27 2008 Msieve v. 1.36 Sun Aug 24 12:23:27 2008 random seeds: 91c7b3f0 39fd5771 Sun Aug 24 12:23:27 2008 factoring 30417223065719202025408393332329506476088430781684930885264026157024451489312987907070721 (89 digits) Sun Aug 24 12:23:27 2008 searching for 15-digit factors Sun Aug 24 12:23:28 2008 commencing quadratic sieve (89-digit input) Sun Aug 24 12:23:28 2008 using multiplier of 1 Sun Aug 24 12:23:28 2008 using 32kb Intel Core sieve core Sun Aug 24 12:23:28 2008 sieve interval: 30 blocks of size 32768 Sun Aug 24 12:23:28 2008 processing polynomials in batches of 7 Sun Aug 24 12:23:28 2008 using a sieve bound of 1546697 (58666 primes) Sun Aug 24 12:23:28 2008 using large prime bound of 123735760 (26 bits) Sun Aug 24 12:23:28 2008 using double large prime bound of 368545723802400 (42-49 bits) Sun Aug 24 12:23:28 2008 using trial factoring cutoff of 49 bits Sun Aug 24 12:23:28 2008 polynomial 'A' values have 11 factors Sun Aug 24 12:49:33 2008 59095 relations (17383 full + 41712 combined from 602353 partial), need 58762 Sun Aug 24 12:49:34 2008 begin with 619735 relations Sun Aug 24 12:49:34 2008 reduce to 137172 relations in 9 passes Sun Aug 24 12:49:34 2008 attempting to read 137172 relations Sun Aug 24 12:49:35 2008 recovered 137172 relations Sun Aug 24 12:49:35 2008 recovered 103123 polynomials Sun Aug 24 12:49:35 2008 attempting to build 59095 cycles Sun Aug 24 12:49:35 2008 found 59095 cycles in 5 passes Sun Aug 24 12:49:35 2008 distribution of cycle lengths: Sun Aug 24 12:49:35 2008 length 1 : 17383 Sun Aug 24 12:49:35 2008 length 2 : 12291 Sun Aug 24 12:49:35 2008 length 3 : 10403 Sun Aug 24 12:49:35 2008 length 4 : 7514 Sun Aug 24 12:49:35 2008 length 5 : 5032 Sun Aug 24 12:49:35 2008 length 6 : 2924 Sun Aug 24 12:49:35 2008 length 7 : 1676 Sun Aug 24 12:49:35 2008 length 9+: 1872 Sun Aug 24 12:49:35 2008 largest cycle: 16 relations Sun Aug 24 12:49:36 2008 matrix is 58666 x 59095 (13.6 MB) with weight 3325898 (56.28/col) Sun Aug 24 12:49:36 2008 sparse part has weight 3325898 (56.28/col) Sun Aug 24 12:49:36 2008 filtering completed in 4 passes Sun Aug 24 12:49:36 2008 matrix is 53129 x 53193 (12.3 MB) with weight 3012466 (56.63/col) Sun Aug 24 12:49:36 2008 sparse part has weight 3012466 (56.63/col) Sun Aug 24 12:49:36 2008 saving the first 48 matrix rows for later Sun Aug 24 12:49:36 2008 matrix is 53081 x 53193 (8.4 MB) with weight 2389276 (44.92/col) Sun Aug 24 12:49:36 2008 sparse part has weight 1875750 (35.26/col) Sun Aug 24 12:49:36 2008 matrix includes 64 packed rows Sun Aug 24 12:49:36 2008 using block size 21277 for processor cache size 4096 kB Sun Aug 24 12:49:37 2008 commencing Lanczos iteration Sun Aug 24 12:49:37 2008 memory use: 7.9 MB Sun Aug 24 12:49:50 2008 lanczos halted after 841 iterations (dim = 53079) Sun Aug 24 12:49:50 2008 recovered 16 nontrivial dependencies Sun Aug 24 12:49:50 2008 prp31 factor: 2878173973878396344472623824273 Sun Aug 24 12:49:50 2008 prp59 factor: 10568236438025805805146214006943933895776577890265004772977 Sun Aug 24 12:49:50 2008 elapsed time 00:26:23

(8·10¹¹³-11)/3 = 2(6)₁₁₂3_<114> = 2341 · 30810511543917882721369333_<26> · C85
C85 = P28 · P57
P28 = 6149421791025899547499894967_<28>
P57 = 601220980001406340971556885053700885153827701171358855913_<57>

Sun Aug 24 12:53:43 2008 Msieve v. 1.36 Sun Aug 24 12:53:43 2008 random seeds: 7f72a470 3623d00f Sun Aug 24 12:53:43 2008 factoring 3697161395642594715145547845696911974342125553234116133620464452526327268032786889871 (85 digits) Sun Aug 24 12:53:43 2008 searching for 15-digit factors Sun Aug 24 12:53:44 2008 commencing quadratic sieve (85-digit input) Sun Aug 24 12:53:44 2008 using multiplier of 47 Sun Aug 24 12:53:44 2008 using 32kb Intel Core sieve core Sun Aug 24 12:53:44 2008 sieve interval: 12 blocks of size 32768 Sun Aug 24 12:53:44 2008 processing polynomials in batches of 17 Sun Aug 24 12:53:44 2008 using a sieve bound of 1422583 (54412 primes) Sun Aug 24 12:53:44 2008 using large prime bound of 116651806 (26 bits) Sun Aug 24 12:53:44 2008 using double large prime bound of 331439743440844 (41-49 bits) Sun Aug 24 12:53:44 2008 using trial factoring cutoff of 49 bits Sun Aug 24 12:53:44 2008 polynomial 'A' values have 11 factors Sun Aug 24 13:17:41 2008 54639 relations (16031 full + 38608 combined from 572576 partial), need 54508 Sun Aug 24 13:17:42 2008 begin with 588606 relations Sun Aug 24 13:17:43 2008 reduce to 127985 relations in 11 passes Sun Aug 24 13:17:43 2008 attempting to read 127985 relations Sun Aug 24 13:17:44 2008 recovered 127985 relations Sun Aug 24 13:17:44 2008 recovered 109198 polynomials Sun Aug 24 13:17:44 2008 attempting to build 54639 cycles Sun Aug 24 13:17:44 2008 found 54639 cycles in 6 passes Sun Aug 24 13:17:44 2008 distribution of cycle lengths: Sun Aug 24 13:17:44 2008 length 1 : 16031 Sun Aug 24 13:17:44 2008 length 2 : 11091 Sun Aug 24 13:17:44 2008 length 3 : 9819 Sun Aug 24 13:17:44 2008 length 4 : 6949 Sun Aug 24 13:17:44 2008 length 5 : 4532 Sun Aug 24 13:17:44 2008 length 6 : 2756 Sun Aug 24 13:17:44 2008 length 7 : 1649 Sun Aug 24 13:17:44 2008 length 9+: 1812 Sun Aug 24 13:17:44 2008 largest cycle: 19 relations Sun Aug 24 13:17:44 2008 matrix is 54412 x 54639 (12.2 MB) with weight 2973852 (54.43/col) Sun Aug 24 13:17:44 2008 sparse part has weight 2973852 (54.43/col) Sun Aug 24 13:17:44 2008 filtering completed in 3 passes Sun Aug 24 13:17:44 2008 matrix is 49179 x 49239 (11.1 MB) with weight 2708823 (55.01/col) Sun Aug 24 13:17:44 2008 sparse part has weight 2708823 (55.01/col) Sun Aug 24 13:17:44 2008 saving the first 48 matrix rows for later Sun Aug 24 13:17:45 2008 matrix is 49131 x 49239 (7.1 MB) with weight 2122297 (43.10/col) Sun Aug 24 13:17:45 2008 sparse part has weight 1554725 (31.58/col) Sun Aug 24 13:17:45 2008 matrix includes 64 packed rows Sun Aug 24 13:17:45 2008 using block size 19695 for processor cache size 4096 kB Sun Aug 24 13:17:45 2008 commencing Lanczos iteration Sun Aug 24 13:17:45 2008 memory use: 7.0 MB Sun Aug 24 13:17:55 2008 lanczos halted after 779 iterations (dim = 49130) Sun Aug 24 13:17:55 2008 recovered 17 nontrivial dependencies Sun Aug 24 13:17:57 2008 prp28 factor: 6149421791025899547499894967 Sun Aug 24 13:17:57 2008 prp57 factor: 601220980001406340971556885053700885153827701171358855913 Sun Aug 24 13:17:57 2008 elapsed time 00:24:14

(8·10¹³⁵-11)/3 = 2(6)₁₃₄3_<136> = 19 · 1399 · 28360288684575581731_<20> · 6005110147387091815727_<22> · C90
C90 = P39 · P51
P39 = 760367035665068717323133747416114223399_<39>
P51 = 774715974656339115136575138199572212734645113395921_<51>

Sun Aug 24 13:20:02 2008 Msieve v. 1.36 Sun Aug 24 13:20:02 2008 random seeds: fbaa4548 d5ff5a09 Sun Aug 24 13:20:02 2008 factoring 589068489131815076485354105182151500327586386083290131231332775086317716668600958529355479 (90 digits) Sun Aug 24 13:20:03 2008 searching for 15-digit factors Sun Aug 24 13:20:04 2008 commencing quadratic sieve (90-digit input) Sun Aug 24 13:20:04 2008 using multiplier of 31 Sun Aug 24 13:20:04 2008 using 32kb Intel Core sieve core Sun Aug 24 13:20:04 2008 sieve interval: 36 blocks of size 32768 Sun Aug 24 13:20:04 2008 processing polynomials in batches of 6 Sun Aug 24 13:20:04 2008 using a sieve bound of 1615223 (61176 primes) Sun Aug 24 13:20:04 2008 using large prime bound of 135678732 (27 bits) Sun Aug 24 13:20:04 2008 using double large prime bound of 435031874203416 (42-49 bits) Sun Aug 24 13:20:04 2008 using trial factoring cutoff of 49 bits Sun Aug 24 13:20:04 2008 polynomial 'A' values have 12 factors Sun Aug 24 14:23:42 2008 61374 relations (16026 full + 45348 combined from 666990 partial), need 61272 Sun Aug 24 14:23:44 2008 begin with 683015 relations Sun Aug 24 14:23:44 2008 reduce to 150768 relations in 11 passes Sun Aug 24 14:23:44 2008 attempting to read 150768 relations Sun Aug 24 14:23:45 2008 recovered 150768 relations Sun Aug 24 14:23:45 2008 recovered 132163 polynomials Sun Aug 24 14:23:46 2008 attempting to build 61374 cycles Sun Aug 24 14:23:46 2008 found 61374 cycles in 5 passes Sun Aug 24 14:23:46 2008 distribution of cycle lengths: Sun Aug 24 14:23:46 2008 length 1 : 16026 Sun Aug 24 14:23:46 2008 length 2 : 11796 Sun Aug 24 14:23:46 2008 length 3 : 10722 Sun Aug 24 14:23:46 2008 length 4 : 8278 Sun Aug 24 14:23:46 2008 length 5 : 5853 Sun Aug 24 14:23:46 2008 length 6 : 3771 Sun Aug 24 14:23:46 2008 length 7 : 2257 Sun Aug 24 14:23:46 2008 length 9+: 2671 Sun Aug 24 14:23:46 2008 largest cycle: 20 relations Sun Aug 24 14:23:46 2008 matrix is 61176 x 61374 (15.1 MB) with weight 3710603 (60.46/col) Sun Aug 24 14:23:46 2008 sparse part has weight 3710603 (60.46/col) Sun Aug 24 14:23:46 2008 filtering completed in 4 passes Sun Aug 24 14:23:46 2008 matrix is 57514 x 57578 (14.3 MB) with weight 3511473 (60.99/col) Sun Aug 24 14:23:46 2008 sparse part has weight 3511473 (60.99/col) Sun Aug 24 14:23:46 2008 saving the first 48 matrix rows for later Sun Aug 24 14:23:46 2008 matrix is 57466 x 57578 (9.1 MB) with weight 2779570 (48.27/col) Sun Aug 24 14:23:46 2008 sparse part has weight 2038144 (35.40/col) Sun Aug 24 14:23:46 2008 matrix includes 64 packed rows Sun Aug 24 14:23:46 2008 using block size 23031 for processor cache size 4096 kB Sun Aug 24 14:23:47 2008 commencing Lanczos iteration Sun Aug 24 14:23:47 2008 memory use: 8.8 MB Sun Aug 24 14:24:02 2008 lanczos halted after 911 iterations (dim = 57464) Sun Aug 24 14:24:02 2008 recovered 16 nontrivial dependencies Sun Aug 24 14:24:03 2008 prp39 factor: 760367035665068717323133747416114223399 Sun Aug 24 14:24:03 2008 prp51 factor: 774715974656339115136575138199572212734645113395921 Sun Aug 24 14:24:03 2008 elapsed time 01:04:01

(8·10¹⁰²-11)/3 = 2(6)₁₀₁3_<103> = 29 · 70516981 · C94
C94 = P45 · P49
P45 = 919296806573087122167025368337737943218105509_<45>
P49 = 1418473648139463334070630967104623852741892124443_<49>

Number: 26663_102 N=1303998294942685466447248806768902972446460444933734162001625398992691667717090268173731856487 ( 94 digits) SNFS difficulty: 102 digits. Divisors found: r1=919296806573087122167025368337737943218105509 (pp45) r2=1418473648139463334070630967104623852741892124443 (pp49) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 0.29 hours. Scaled time: 0.99 units (timescale=3.423). Factorization parameters were as follows: n: 1303998294942685466447248806768902972446460444933734162001625398992691667717090268173731856487 Y1: 1 Y0: -200000000000000000000 c5: 25 c0: -11 skew: 0.85 type: snfs Factor base limits: 300000/350000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [175000, 235001) Relations: rels:882623, finalFF:80529 Initial matrix: 55859 x 80529 with sparse part having weight 2078125. Pruned matrix : 44104 x 44447 with weight 826916. Total sieving time: 0.27 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.00 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,300000,350000,25,25,43,43,2.1,2.1,10000 total time: 0.29 hours.

Aug 25, 2008

Factorizations of 266...663 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 24, 2008

By Robert Backstrom / GGNFS, Msieve
(28·10¹⁹²+17)/9 = 3(1)₁₉₁3_<193> = 521 · C190
C190 = P73 · P118
P73 = 1458937323972688141163556335746502776674397881172224762818763944697215069_<73>
P118 = 4092994524178830122862088646214472282038812569865140154265414739307172089165984897534485615008489229532328512174074037_<118>

Number: n N=5971422478140328428236297718063552996374493495414800597142247814032842823629771806355299637449349541480059714224781403284282362977180635529963744934954148005971422478140328428236297718063553 ( 190 digits) SNFS difficulty: 193 digits. Divisors found: Sun Aug 24 01:06:20 2008 prp73 factor: 1458937323972688141163556335746502776674397881172224762818763944697215069 Sun Aug 24 01:06:20 2008 prp118 factor: 4092994524178830122862088646214472282038812569865140154265414739307172089165984897534485615008489229532328512174074037 Sun Aug 24 01:06:20 2008 elapsed time 13:52:38 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 205.33 hours. Scaled time: 269.80 units (timescale=1.314). Factorization parameters were as follows: name: KA_3_1_191_3 n: 5971422478140328428236297718063552996374493495414800597142247814032842823629771806355299637449349541480059714224781403284282362977180635529963744934954148005971422478140328428236297718063553 type: snfs skew: 0.66 deg: 5 c5: 175 c0: 34 m: 200000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 19100001) Primes: RFBsize:633578, AFBsize:634408, largePrimes:11259898 encountered Relations: rels:11316728, finalFF:1301584 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 204.60 hours. Total relation processing time: 0.73 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,193,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000 total time: 205.33 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Aug 23, 2008

By Serge Batalov / Msieve
(5·10¹⁶⁶+1)/3 = 1(6)₁₆₅7_<167> = 7 · 2412311810963_<13> · 21681484588402783327_<20> · C134
C134 = P60 · P75
P60 = 120290653074033155377693119077932432451849157820371719000141_<60>
P75 = 378439419381373063595334977207576433701637494219631261758036807264278082741_<75>

Number: 16667_166 N=45522724906343286192598532980210324781874447309646171866952716995837515000348028814367639145587478869903469660672480559082664988666481 ( 134 digits) SNFS difficulty: 166 digits. Divisors found: r1=120290653074033155377693119077932432451849157820371719000141 r2=378439419381373063595334977207576433701637494219631261758036807264278082741 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.719). Factorization parameters were as follows: n: 45522724906343286192598532980210324781874447309646171866952716995837515000348028814367639145587478869903469660672480559082664988666481 Y1: 1 Y0: -1000000000000000000000000000000000 c5: 50 c0: 1 skew: 0.46 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 4000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 714390 x 714638 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 1.90 hours. Time per square root: 0.60 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000 total time: 24.00 hours.

Aug 22, 2008 (2nd)

By Serge Batalov / Msieve
4·10¹⁶⁶+1 = 4(0)₁₆₅1_<167> = 13 · 41 · 4517 · 152421337841_<12> · 941160476969540120952877_<24> · C126
C126 = P51 · P75
P51 = 338717486802811900673981008844119653096357974239957_<51>
P75 = 341928753479598700237304527485927308118819144008567869244980664981674968409_<75>

Number: 40001_166 N=115817248044227896509289122964484316966630639321189981212930837312203257669785275747098638613513868711415814586413023760518413 ( 126 digits) SNFS difficulty: 166 digits. Divisors found: r1=338717486802811900673981008844119653096357974239957 r2=341928753479598700237304527485927308118819144008567869244980664981674968409 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.694). Factorization parameters were as follows: n: 115817248044227896509289122964484316966630639321189981212930837312203257669785275747098638613513868711415814586413023760518413 Y1: 1 Y0: -1000000000000000000000000000000000 c5: 40 c0: 1 skew: 0.48 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 3900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 741740 x 741988 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 2.20 hours. Time per square root: 0.40 hours. * 2 Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000 total time: 23.50 hours.

(7·10¹⁷¹-1)/3 = 2(3)_171<172> = 1138853 · C166
C166 = P56 · P110
P56 = 52466933536616764762455731674465527913345675902479976653_<56>
P110 = 39050215312850715281346300573082614025282121181643881618463088046577029592640409813713876589831290571574330037_<110>

Number: 23333_171 N=2048845051409912722127731439732198390251712322251715834557518251550756184804652868573321871508731445878733544481450488634910153754113422305893151559800372245876626161 ( 166 digits) SNFS difficulty: 171 digits. Divisors found: r1=52466933536616764762455731674465527913345675902479976653 r2=39050215312850715281346300573082614025282121181643881618463088046577029592640409813713876589831290571574330037 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.726). Factorization parameters were as follows: n: 2048845051409912722127731439732198390251712322251715834557518251550756184804652868573321871508731445878733544481450488634910153754113422305893151559800372245876626161 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 70 c0: -1 skew: 0.43 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3000000, 5700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1012135 x 1012383 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 4.20 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000 total time: 44.50 hours.

Aug 22, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(5·10¹⁹⁸-23)/9 = (5)₁₉₇3_<198> = 79 · 1787 · 92166227 · 62964716122813547478189355909_<29> · 119356565544646731891786102577789_<33> · C124
C124 = P42 · P83
P42 = 396488530126012349110486416962263561871273_<42>
P83 = 14329460853556106742975766217842853536031643858403149301167495308116549583366771591_<83>
(22·10¹⁷⁴+23)/9 = 2(4)₁₇₃7_<175> = 947 · C172
C172 = P44 · P45 · P85
P44 = 13793496764933613173998444708639348503342167_<44>
P45 = 110540140507371818048930699460533646011671649_<45>
P85 = 1692917532546119710378264581159890068911580941102272929764210993817970269701152940547_<85>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 2581250733309867417575970902264460870585474598146192655168367945559075442919159920215886424967734365833626657280300363721694239117681567523172591810395400680511556963510501 (172 digits) Using B1=4606000, B2=8562235510, polynomial Dickson(6), sigma=970024370 Step 1 took 65031ms Step 2 took 21375ms ********** Factor found in step 2: 13793496764933613173998444708639348503342167 Found probable prime factor of 44 digits: 13793496764933613173998444708639348503342167 Composite cofactor 187135341915041275536807385055191549657231130756477371436302859011515528532617086139748716813756071039729965347118336379382452003 has 129 digits Number: n N=187135341915041275536807385055191549657231130756477371436302859011515528532617086139748716813756071039729965347118336379382452003 ( 129 digits) SNFS difficulty: 176 digits. Divisors found: Fri Aug 22 16:47:46 2008 prp45 factor: 110540140507371818048930699460533646011671649 Fri Aug 22 16:47:46 2008 prp85 factor: 1692917532546119710378264581159890068911580941102272929764210993817970269701152940547 Fri Aug 22 16:47:46 2008 elapsed time 02:52:14 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 48.99 hours. Scaled time: 41.06 units (timescale=0.838). Factorization parameters were as follows: name: KA_2_4_173_7 n: 187135341915041275536807385055191549657231130756477371436302859011515528532617086139748716813756071039729965347118336379382452003 type: snfs skew: 1.60 deg: 5 c5: 11 c0: 115 m: 100000000000000000000000000000000000 rlim: 7400000 alim: 7400000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 5300001) Primes: RFBsize:501962, AFBsize:502147, largePrimes:10305780 encountered Relations: rels:10097030, finalFF:1048955 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 48.70 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,50,50,2.5,2.5,100000 total time: 48.99 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

Aug 21, 2008

By Serge Batalov / Msieve
9·10¹⁷⁷-1 = 8(9)_177<178> = 89 · 757 · C174
C174 = P76 · P98
P76 = 2795376519729848150784923706882701877318922481507609115407740172075186231071_<76>
P98 = 47787719999108578060151819968036562451065721814882830579492456551763376466710619837746260674550853_<98>

Number: 89999_177 N=133584670416932599112404078785270063675359565404538910245944220978730351921392842830213883900078666528134415863921749068617992370831045077404895136033722707909696762798153563 ( 174 digits) SNFS difficulty: 177 digits. Divisors found: r1=2795376519729848150784923706882701877318922481507609115407740172075186231071 r2=47787719999108578060151819968036562451065721814882830579492456551763376466710619837746260674550853 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.651). Factorization parameters were as follows: n: 133584670416932599112404078785270063675359565404538910245944220978730351921392842830213883900078666528134415863921749068617992370831045077404895136033722707909696762798153563 Y1: 1 Y0: -100000000000000000000000000000000000 c5: 900 c0: -1 skew: 0.26 type: snfs Factor base limits: 11400000/11400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [5700000, 9700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1301455 x 1301703 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 7.00 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,177,5,0,0,0,0,0,0,0,0,11400000,11400000,27,27,52,52,2.6,2.6,100000 total time: 76.00 hours.

Aug 20, 2008 (2nd)

By matsui / GGNFS
10¹⁹¹+9 = 1(0)₁₉₀9_<192> = 7 · 13 · 103 · C188
C188 = P39 · P149
P39 = 558512525126795884293354955450279221529_<39>
P149 = 19102423361688353491586596941283273631279087307124210159959098992316128275614458548628339728160988510023049614103059197070847250912364210612167195877_<149>

N=10668942707777659233969913581564067000960204843699989331057292222340766030086418435932999039795156300010668942707777659233969913581564067000960204843699989331057292222340766030086418435933 ( 188 digits) SNFS difficulty: 191 digits. Divisors found: r1=558512525126795884293354955450279221529 (pp39) r2=19102423361688353491586596941283273631279087307124210159959098992316128275614458548628339728160988510023049614103059197070847250912364210612167195877 (pp149) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 477.36 hours. Scaled time: 915.57 units (timescale=1.918). Factorization parameters were as follows: n: 10668942707777659233969913581564067000960204843699989331057292222340766030086418435932999039795156300010668942707777659233969913581564067000960204843699989331057292222340766030086418435933 m: 100000000000000000000000000000000000000 c5: 10 c0: 9 skew: 0.98 type: snfs rlim: 10000000 alim: 10000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [5000000, 14500001) Primes: RFBsize:664579, AFBsize:664685, largePrimes:11579378 encountered Relations: rels:11937015, finalFF:1530165 Max relations in full relation-set: 28 Initial matrix: 1329331 x 1530165 with sparse part having weight 146036484. Pruned matrix : 1164732 x 1171442 with weight 119352904. Total sieving time: 456.55 hours. Total relation processing time: 0.53 hours. Matrix solve time: 19.77 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000 total time: 477.36 hours.

Aug 20, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(5·10¹⁷⁴-23)/9 = (5)₁₇₃3_<174> = 17 · 29 · C172
C172 = P63 · P109
P63 = 359886655710553109256565370413038399176555884657330308072113227_<63>
P109 = 3131229009864065205534482597030840703301171760518459388457299185286436731474229584526926422614873427573448623_<109>

Number: n N=1126887536623844940274960558936218165427090376380437232364210051836826684696867252648185711066035609646157313500112688753662384494027496055893621816542709037638043723236421 ( 172 digits) SNFS difficulty: 175 digits. Divisors found: Wed Aug 20 12:24:15 2008 prp63 factor: 359886655710553109256565370413038399176555884657330308072113227 Wed Aug 20 12:24:15 2008 prp109 factor: 3131229009864065205534482597030840703301171760518459388457299185286436731474229584526926422614873427573448623 Wed Aug 20 12:24:15 2008 elapsed time 02:54:01 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 43.83 hours. Scaled time: 36.90 units (timescale=0.842). Factorization parameters were as follows: name: KA_5_173_3 n: 1126887536623844940274960558936218165427090376380437232364210051836826684696867252648185711066035609646157313500112688753662384494027496055893621816542709037638043723236421 type: snfs skew: 2.15 deg: 5 c5: 1 c0: -46 m: 100000000000000000000000000000000000 rlim: 7400000 alim: 7400000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 4700001) Primes: RFBsize:501962, AFBsize:502151, largePrimes:10263667 encountered Relations: rels:10063226, finalFF:1058780 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 43.56 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,50,50,2.5,2.5,100000 total time: 43.83 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

(67·10¹⁷⁰+23)/9 = 7(4)₁₆₉7_<171> = 3 · 2340797939300562583_<19> · 702139207668471108691_<21> · C132
C132 = P42 · P90
P42 = 391473357601478428260308573141911055833729_<42>
P90 = 385675167227586804576204636749049134730109858952723259341925218373142706418135301504058177_<90>

Aug 19, 2008 (2nd)

By Wataru Sakai / GGNFS
(5·10¹⁸⁹+1)/3 = 1(6)₁₈₈7_<190> = 89 · C188
C188 = P69 · P120
P69 = 155220716217629705641047956974028903638974953850976713020609050449043_<69>
P120 = 120644925604155219989104828180435891279930064771908342549722918494534590742040930991869791304135720103379793852604543921_<120>

Number: 16667_189 N=18726591760299625468164794007490636704119850187265917602996254681647940074906367041198501872659176029962546816479400749063670411985018726591760299625468164794007490636704119850187265917603 ( 188 digits) SNFS difficulty: 190 digits. Divisors found: r1=155220716217629705641047956974028903638974953850976713020609050449043 (pp69) r2=120644925604155219989104828180435891279930064771908342549722918494534590742040930991869791304135720103379793852604543921 (pp120) Version: GGNFS-0.77.1-20060722-nocona Total time: 878.82 hours. Scaled time: 1761.16 units (timescale=2.004). Factorization parameters were as follows: n: 18726591760299625468164794007490636704119850187265917602996254681647940074906367041198501872659176029962546816479400749063670411985018726591760299625468164794007490636704119850187265917603 m: 100000000000000000000000000000000000000 c5: 1 c0: 2 skew: 1.15 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 15700001) Primes: RFBsize:501962, AFBsize:501936, largePrimes:6977777 encountered Relations: rels:7567375, finalFF:1214697 Max relations in full relation-set: 32 Initial matrix: 1003962 x 1214697 with sparse part having weight 117983597. Pruned matrix : 840086 x 845169 with weight 98678495. Total sieving time: 869.86 hours. Total relation processing time: 0.12 hours. Matrix solve time: 8.60 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 878.82 hours. --------- CPU info (if available) ----------

10¹⁸⁸+7 = 1(0)₁₈₇7_<189> = 919 · C186
C186 = P48 · P138
P48 = 546994870962230793373065729931284587933779712219_<48>
P138 = 198930436022901655488560388986742823483843042807587457103337590796061445066460085353325337124807905412409771088506395458055122523822016387_<138>

Number: 10007_188 N=108813928182807399347116430903155603917301414581066376496191512513601741022850924918389553862894450489662676822633297062023939064200217627856365614798694232861806311207834602829162132753 ( 186 digits) SNFS difficulty: 188 digits. Divisors found: r1=546994870962230793373065729931284587933779712219 (pp48) r2=198930436022901655488560388986742823483843042807587457103337590796061445066460085353325337124807905412409771088506395458055122523822016387 (pp138) Version: GGNFS-0.77.1-20060722-nocona Total time: 842.87 hours. Scaled time: 1690.80 units (timescale=2.006). Factorization parameters were as follows: n: 108813928182807399347116430903155603917301414581066376496191512513601741022850924918389553862894450489662676822633297062023939064200217627856365614798694232861806311207834602829162132753 m: 10000000000000000000000000000000000000 c5: 1000 c0: 7 skew: 0.37 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 15000001) Primes: RFBsize:501962, AFBsize:501101, largePrimes:6954314 encountered Relations: rels:7527639, finalFF:1210235 Max relations in full relation-set: 32 Initial matrix: 1003129 x 1210235 with sparse part having weight 117655184. Pruned matrix : 840397 x 845476 with weight 97173257. Total sieving time: 833.71 hours. Total relation processing time: 0.14 hours. Matrix solve time: 8.78 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,188,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 842.87 hours. --------- CPU info (if available) ----------

Aug 19, 2008

By Serge Batalov / Msieve
(23·10¹⁷¹+31)/9 = 2(5)₁₇₀9_<172> = 3 · 347 · C169
C169 = P46 · P123
P46 = 2507406786358400630053956114754671784954141033_<46>
P123 = 979061110287926914452686823674334926754673406716505690256590865236353645010621985257918365427531665179753798361452391361503_<123>

Number: 25559_171 N=2454904472195538477959227238766143665279111964990927526950581705624933290639342512541359803607642224356921763261820898708506777671042800725797843953463550005336748852599 ( 169 digits) SNFS difficulty: 172 digits. Divisors found: r1=2507406786358400630053956114754671784954141033 r2=979061110287926914452686823674334926754673406716505690256590865236353645010621985257918365427531665179753798361452391361503 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.721). Factorization parameters were as follows: n: 2454904472195538477959227238766143665279111964990927526950581705624933290639342512541359803607642224356921763261820898708506777671042800725797843953463550005336748852599 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 230 c0: 31 skew: 0.67 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [4500000, 10000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1302887 x 1303135 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 7.15 hours. Time per square root: 2.70 hours. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,9000000,9000000,27,27,52,52,2.6,2.6,100000 total time: 84.00 hours.

Aug 18, 2008 (2nd)

By Sinkiti Sibata / GMP-ECM
(22·10¹⁷⁹-13)/9 = 2(4)₁₇₈3_<180> = 3 · 167 · 630373842617_<12> · 2216727877196124340330489_<25> · C141
C141 = P47 · P95
P47 = 24726223009098487467636225633358624031335131751_<47>
P95 = 14121281057022318743169320232071258885317897178039011226565812763366085713013565900617484617961_<95>

factor24443_179 GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 349165944590091867944970739224950115657298071576715071521804379303095232821001110672336976242671808298508474956698907944114498422023835979711 Run 1472 out of 2350: Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1048915276 Step 1 took 49375ms Step 2 took 17269ms ********** Factor found in step 2: 24726223009098487467636225633358624031335131751 Found probable prime factor of 47 digits: 24726223009098487467636225633358624031335131751 Probable prime cofactor 14121281057022318743169320232071258885317897178039011226565812763366085713013565900617484617961 has 95 digits

Aug 18, 2008

By Robert Backstrom / GGNFS, Msieve
9·10¹⁹²+1 = 9(0)₁₉₁1_<193> = 1109 · C190
C190 = P62 · P129
P62 = 14734116298400713270539985713991888026642775154005017603856013_<62>
P129 = 550791043881235942395862556041076669468450897765276463896412425335034457457595786628772946981138862497150863003489314800842696753_<129>

Number: n N=8115419296663660955816050495942290351668169522091974752028854824165915238954012623985572587917042380522993688007213706041478809738503155996393146979260595130748422001803426510369702434625789 ( 190 digits) SNFS difficulty: 192 digits. Divisors found: Mon Aug 18 06:37:29 2008 prp62 factor: 14734116298400713270539985713991888026642775154005017603856013 Mon Aug 18 06:37:30 2008 prp129 factor: 550791043881235942395862556041076669468450897765276463896412425335034457457595786628772946981138862497150863003489314800842696753 Mon Aug 18 06:37:30 2008 elapsed time 06:34:54 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 151.51 hours. Scaled time: 309.84 units (timescale=2.045). Factorization parameters were as follows: name: KA_9_0_191_1 n: 8115419296663660955816050495942290351668169522091974752028854824165915238954012623985572587917042380522993688007213706041478809738503155996393146979260595130748422001803426510369702434625789 type: snfs skew: 0.26 deg: 5 c5: 900 c0: 1 m: 100000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 12100001) Primes: RFBsize:633578, AFBsize:632398, largePrimes:11067961 encountered Relations: rels:11117802, finalFF:1296478 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 151.11 hours. Total relation processing time: 0.40 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,192,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000 total time: 151.51 hours. --------- CPU info (if available) ----------

(23·10¹⁶⁶+31)/9 = 2(5)₁₆₅9_<167> = 17² · 107 · C162
C162 = P56 · P107
P56 = 18196127155026565765210313040636762315634917977595426793_<56>
P107 = 45417658774727419799492427840630036712482623752503343649034406587180499821842694832789683367090599801389581_<107>

Number: n N=826425494148548185996040343936731738691445058873833572278095771935308849579780601997075172381578616419996622434936958107413755313376954226807087137585472158443733 ( 162 digits) SNFS difficulty: 167 digits. Divisors found: Mon Aug 18 12:45:53 2008 prp56 factor: 18196127155026565765210313040636762315634917977595426793 Mon Aug 18 12:45:57 2008 prp107 factor: 45417658774727419799492427840630036712482623752503343649034406587180499821842694832789683367090599801389581 Mon Aug 18 12:45:57 2008 elapsed time 01:29:48 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 49.69 hours. Scaled time: 41.59 units (timescale=0.837). Factorization parameters were as follows: name: KA_2_5_165_9 n: 826425494148548185996040343936731738691445058873833572278095771935308849579780601997075172381578616419996622434936958107413755313376954226807087137585472158443733 type: snfs deg: 5 c5: 230 c0: 31 skew: 0.28 m: 1000000000000000000000000000000000 rlim: 6000000 alim: 6000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 5700001) Primes: RFBsize:412849, AFBsize:413297, largePrimes:5940623 encountered Relations: rels:6154327, finalFF:881975 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 49.48 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,167,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.5,2.5,100000 total time: 49.69 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

Aug 16, 2008 (5th)

By Jo Yeong Uk / GGNFS
(23·10¹⁷⁰+31)/9 = 2(5)₁₆₉9_<171> = 7 · 37 · 26671840033_<11> · 161421299558369246533_<21> · 297906976876056499602031_<24> · C114
C114 = P50 · P65
P50 = 36980604693757519861771088341660957144857651838787_<50>
P65 = 20802573382540544081050343846624872121634029784960968772855844397_<65>

Number: 25559_170 N=769291742872614091219688752614724603405832009110180438834256123590702076321274183344961360080414224048366601226439 ( 114 digits) Divisors found: r1=36980604693757519861771088341660957144857651838787 (pp50) r2=20802573382540544081050343846624872121634029784960968772855844397 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 19.66 hours. Scaled time: 46.86 units (timescale=2.383). Factorization parameters were as follows: name: 25559_170 n: 769291742872614091219688752614724603405832009110180438834256123590702076321274183344961360080414224048366601226439 skew: 46401.47 # norm 1.16e+16 c5: 59280 c4: -555799160 c3: -633544502641438 c2: 2986793278184410387 c1: 397242036976346980316280 c0: -1036910798119627579106192689 # alpha -6.47 Y1: 467621825129 Y0: -6647167652001661320280 # Murphy_E 5.90e-10 # M 68984389221729131535103752351912674335008154275451042128487769092207973153624902851094592364583691152142341444552 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 70000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2870001) Primes: RFBsize:250150, AFBsize:249788, largePrimes:7423751 encountered Relations: rels:7272702, finalFF:578183 Max relations in full relation-set: 28 Initial matrix: 500021 x 578183 with sparse part having weight 47872572. Pruned matrix : 436944 x 439508 with weight 31525107. Polynomial selection time: 1.19 hours. Total sieving time: 17.17 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.05 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000 total time: 19.66 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2459k kernel code, 339200k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.73 BogoMIPS (lpj=2672366) Calibrating delay using timer specific routine.. 5343.99 BogoMIPS (lpj=2671997) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Aug 16, 2008 (4th)

By Serge Batalov / Msieve
(23·10¹⁶⁵+31)/9 = 2(5)₁₆₄9_<166> = 3 · C165
C165 = P57 · P109
P57 = 352723018532378683493559904773387908384026434468579905407_<57>
P109 = 2415073037751447362227275468798835152491591313608019272430734224422879445896978821428462796498802433657712179_<109>

Number: 25559_165 N=851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853 ( 165 digits) SNFS difficulty: 166 digits. Divisors found: r1=352723018532378683493559904773387908384026434468579905407 r2=2415073037751447362227275468798835152491591313608019272430734224422879445896978821428462796498802433657712179 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.740). Factorization parameters were as follows: n: 851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853 Y1: 1 Y0: -1000000000000000000000000000000000 c5: 23 c0: 31 skew: 1.06 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 4600001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 874652 x 874900 Total sieving time: 0.00 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.00 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000 total time: 32.00 hours.

Aug 16, 2008 (3rd)

By Sinkiti Sibata / GGNFS, GMP-ECM
(22·10¹⁶⁵-31)/9 = 2(4)₁₆₄1_<166> = 1697 · 111127 · 3102605993391224233_<19> · C139
C139 = P43 · P96
P43 = 9181028417573967427804067865162623442511111_<43>
P96 = 455051740794629015966935014142950094789983481286596107420482412029657149588773814025318977528753_<96>

Number: 24441_165 N=4177842963701992033746833730712078164567800348143405756245054797703306366232238457460680059458300800412620841713791420956286274751524474583 ( 139 digits) SNFS difficulty: 166 digits. Divisors found: r1=9181028417573967427804067865162623442511111 (pp43) r2=455051740794629015966935014142950094789983481286596107420482412029657149588773814025318977528753 (pp96) Version: GGNFS-0.77.1-20050930-nocona Total time: 92.09 hours. Scaled time: 92.92 units (timescale=1.009). Factorization parameters were as follows: name: 24441_165 n: 4177842963701992033746833730712078164567800348143405756245054797703306366232238457460680059458300800412620841713791420956286274751524474583 m: 1000000000000000000000000000000000 c5: 22 c0: -31 skew: 1.07 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5800001) Primes: RFBsize:348513, AFBsize:349063, largePrimes:6054324 encountered Relations: rels:6306720, finalFF:875688 Max relations in full relation-set: 28 Initial matrix: 697642 x 875688 with sparse part having weight 62365519. Pruned matrix : 559325 x 562877 with weight 44759532. Total sieving time: 89.22 hours. Total relation processing time: 0.12 hours. Matrix solve time: 2.66 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 92.09 hours. --------- CPU info (if available) ----------

(23·10¹⁶⁴+31)/9 = 2(5)₁₆₃9_<165> = 7³ · 37 · 53 · 724604863 · 2644339927_<10> · 149558255498137_<15> · 31384734606290870461_<20> · C107
C107 = P44 · P64
P44 = 20314652098684047620712717838258567099838687_<44>
P64 = 2079490044692460090839907111629368942340721746105913902433258787_<64>

Number: 25559_164 N=42244116800604268366529850193804123484513381418170860149158312723787899125249545685537409884760891425292669 ( 107 digits) Divisors found: r1=20314652098684047620712717838258567099838687 (pp44) r2=2079490044692460090839907111629368942340721746105913902433258787 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 18.02 hours. Scaled time: 13.97 units (timescale=0.775). Factorization parameters were as follows: name: 25559_164 n: 42244116800604268366529850193804123484513381418170860149158312723787899125249545685537409884760891425292669 skew: 16965.36 # norm 7.81e+14 c5: 37380 c4: -2072117878 c3: 459849219343 c2: 650402933349225612 c1: 3693541153055369233838 c0: -99725642052992786755340 # alpha -6.01 Y1: 244617478073 Y0: -257412696036039939867 # Murphy_E 1.59e-09 # M 14173624692086331959785602197541481713292728257386366262229978088003544278931180429090516706414989995363285 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2600001) Primes: RFBsize:183072, AFBsize:182751, largePrimes:4603461 encountered Relations: rels:4871820, finalFF:586406 Max relations in full relation-set: 28 Initial matrix: 365902 x 586406 with sparse part having weight 48127292. Pruned matrix : 228725 x 230618 with weight 25556880. Total sieving time: 17.12 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.56 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 18.02 hours. --------- CPU info (if available) ----------

(22·10¹⁷⁵-13)/9 = 2(4)₁₇₄3_<176> = 499 · 665179 · C167
C167 = P39 · C129
P39 = 108255761415671706622622739225515636293_<39>
C129 = [680283718429769696056120418073040544541397423248695726710441763806401518016805452458069590962210373264962514288556879937951373631_<129>]

Aug 16, 2008 (2nd)

Factorizations of 244...443 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 16, 2008

By Tyler Cadigan / GGNFS, Msieve
10¹⁹¹-9 = (9)₁₉₀1_<191> = 25890181282711_<14> · 19215578593700683_<17> · C162
C162 = P55 · P108
P55 = 1107810740439824418721011542356263180679141608975450841_<55>
P108 = 181445361934394941929618652274442590996558678743985524419560737457231701804057845993063138605270872862639227_<108>

Number: 99991_191 N=201007120753913992913726676871999752197866484593647274473058062430107124951627993332234694165639979396161961186666496539291615060870044793869267715322527456739907 ( 162 digits) SNFS difficulty: 191 digits. Divisors found: r1=1107810740439824418721011542356263180679141608975450841 r2=181445361934394941929618652274442590996558678743985524419560737457231701804057845993063138605270872862639227 Version: Total time: 363.74 hours. Scaled time: 939.54 units (timescale=2.583). Factorization parameters were as follows: n: 201007120753913992913726676871999752197866484593647274473058062430107124951627993332234694165639979396161961186666496539291615060870044793869267715322527456739907 m: 100000000000000000000000000000000000000 Y0: -100000000000000000000000000000000000000 Y1: 1 c5: 10 c0: -9 skew: 0.98 type: snfs lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 rlim: 20000000 alim: 20000000 qintsize: 1000000Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved algebraic special-q in [10000000, 15000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2351993 x 2352241 Total sieving time: 363.74 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,191,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,58,58,2.6,2.6,100000 total time: 363.74 hours. --------- CPU info (if available) ----------

Aug 15, 2008 (3rd)

By Jo Yeong Uk / GGNFS
(5·10¹⁷²+31)/9 = (5)₁₇₁9_<172> = 3³ · 19 · 367 · 43714416961213_<14> · 1653798301727248021218700562722037_<34> · C120
C120 = P44 · P76
P44 = 72241579725298286703752721169908212029424891_<44>
P76 = 5650014980209093403988213136282838275204663201213283605113623503379000966699_<76>

Number: 55559_172 N=408166007641904842658786198853065554777699197980622797915618429703920585969239307313834166622909064779063867322012704809 ( 120 digits) Divisors found: r1=72241579725298286703752721169908212029424891 (pp44) r2=5650014980209093403988213136282838275204663201213283605113623503379000966699 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 42.61 hours. Scaled time: 99.58 units (timescale=2.337). Factorization parameters were as follows: name: 55559_172 n: 408166007641904842658786198853065554777699197980622797915618429703920585969239307313834166622909064779063867322012704809 skew: 54464.11 # norm 3.98e+16 c5: 40560 c4: 6211959848 c3: 1146515758710458 c2: -11049075575316808459 c1: -1084310473612104839818758 c0: 92932460856167809044240576 # alpha -6.32 Y1: 5874725186849 Y0: -100126030045029031070743 # Murphy_E 2.99e-10 # M 258527015088446783614594124384726963336972174365477566922540598905648026740976070805859456854511819187120769710896024535 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 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, 4650001) Primes: RFBsize:315948, AFBsize:316780, largePrimes:7744450 encountered Relations: rels:7832498, finalFF:721672 Max relations in full relation-set: 28 Initial matrix: 632807 x 721672 with sparse part having weight 65602018. Pruned matrix : 562992 x 566220 with weight 47467813. Polynomial selection time: 2.63 hours. Total sieving time: 37.39 hours. Total relation processing time: 0.15 hours. Matrix solve time: 2.29 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 42.61 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2459k kernel code, 339200k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.73 BogoMIPS (lpj=2672366) Calibrating delay using timer specific routine.. 5343.99 BogoMIPS (lpj=2671997) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Aug 15, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(23·10¹⁴⁹+31)/9 = 2(5)₁₄₈9_<150> = 37 · 191 · 15679 · 37011751151_<11> · C131
C131 = P34 · P98
P34 = 3361584197264652895273596117265271_<34>
P98 = 18537375539177608834436534677836482023113574981058078117740700688664556806167695348972239081086803_<98>

Number: 25559_149 N=62314948671259774341306738441476012012330414940443595705313775103277218363502467421308755586346875644340628426542897274022928318613 ( 131 digits) SNFS difficulty: 151 digits. Divisors found: r1=3361584197264652895273596117265271 (pp34) r2=18537375539177608834436534677836482023113574981058078117740700688664556806167695348972239081086803 (pp98) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.35 hours. Scaled time: 24.57 units (timescale=1.009). Factorization parameters were as follows: name: 25559_149 n: 62314948671259774341306738441476012012330414940443595705313775103277218363502467421308755586346875644340628426542897274022928318613 m: 1000000000000000000000000000000 c5: 23 c0: 310 skew: 1.68 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176064, largePrimes:5968072 encountered Relations: rels:6262049, finalFF:824133 Max relations in full relation-set: 28 Initial matrix: 352431 x 824133 with sparse part having weight 71719533. Pruned matrix : 215298 x 217124 with weight 31813327. Total sieving time: 23.81 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.40 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 24.35 hours. --------- CPU info (if available) ----------

(23·10¹⁴²+31)/9 = 2(5)₁₄₁9_<143> = 48904153 · C135
C135 = P30 · P106
P30 = 444194718344280895043997630773_<30>
P106 = 1176430281451362767142572801287387880687088852707840173878701242816842277224993751011294270542540793205411_<106>

Number: 25559_142 N=522564117520971185321532008857316382834716625304921558616004566228875399509639918629314683265356943316359155746047898131587220323712703 ( 135 digits) SNFS difficulty: 143 digits. Divisors found: r1=444194718344280895043997630773 (pp30) r2=1176430281451362767142572801287387880687088852707840173878701242816842277224993751011294270542540793205411 (pp106) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.94 hours. Scaled time: 16.94 units (timescale=1.000). Factorization parameters were as follows: name: 25559_142 n: 522564117520971185321532008857316382834716625304921558616004566228875399509639918629314683265356943316359155746047898131587220323712703 m: 10000000000000000000000000000 c5: 2300 c0: 31 skew: 0.42 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 3150001) Primes: RFBsize:100021, AFBsize:100199, largePrimes:3033286 encountered Relations: rels:3111625, finalFF:248898 Max relations in full relation-set: 28 Initial matrix: 200287 x 248898 with sparse part having weight 31797235. Pruned matrix : 188622 x 189687 with weight 23055159. Total sieving time: 16.58 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.25 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 16.94 hours. --------- CPU info (if available) ----------

(23·10¹⁴⁷+31)/9 = 2(5)₁₄₆9_<148> = 3 · 607 · 613 · 11814950847142514192592437550491_<32> · C111
C111 = P44 · P67
P44 = 75103645093403353316146749218224397401074883_<44>
P67 = 2580013458340758255133834372880389552639163595586137327515941451111_<67>

Number: 25559_147 N=193768415111428505634206429615235537385350691524879778259506099811343404692477670800012264250391853206194545013 ( 111 digits) SNFS difficulty: 148 digits. Divisors found: r1=75103645093403353316146749218224397401074883 (pp44) r2=2580013458340758255133834372880389552639163595586137327515941451111 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 37.50 hours. Scaled time: 37.92 units (timescale=1.011). Factorization parameters were as follows: name: 25559_147 n: 193768415111428505634206429615235537385350691524879778259506099811343404692477670800012264250391853206194545013 m: 100000000000000000000000000000 c5: 2300 c0: 31 skew: 0.42 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 6050001) Primes: RFBsize:114155, AFBsize:114273, largePrimes:3381300 encountered Relations: rels:3629815, finalFF:298783 Max relations in full relation-set: 28 Initial matrix: 228495 x 298783 with sparse part having weight 41916253. Pruned matrix : 212196 x 213402 with weight 29855920. Total sieving time: 36.99 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.37 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 37.50 hours. --------- CPU info (if available) ----------

(23·10¹⁵⁶+31)/9 = 2(5)₁₅₅9_<157> = 3 · 103 · 30103 · 356309378983_<12> · 1282946082595495938311_<22> · C117
C117 = P37 · P81
P37 = 2246093478334450292669536908800692657_<37>
P81 = 267579958753199187375886538609657583415035345954915647058260946016914480850748237_<81>

Number: 25559_156 N=601009600288561901917388771431808879676434281891754853211007016430854322163937732912532470157987210701592422321595709 ( 117 digits) SNFS difficulty: 157 digits. Divisors found: r1=2246093478334450292669536908800692657 (pp37) r2=267579958753199187375886538609657583415035345954915647058260946016914480850748237 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 60.72 hours. Scaled time: 46.39 units (timescale=0.764). Factorization parameters were as follows: name: 25559_156 n: 601009600288561901917388771431808879676434281891754853211007016430854322163937732912532470157987210701592422321595709 m: 10000000000000000000000000000000 c5: 230 c0: 31 skew: 0.67 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3600001) Primes: RFBsize:216816, AFBsize:217007, largePrimes:5989157 encountered Relations: rels:6100315, finalFF:603185 Max relations in full relation-set: 28 Initial matrix: 433890 x 603185 with sparse part having weight 65102898. Pruned matrix : 365549 x 367782 with weight 42219288. Total sieving time: 58.23 hours. Total relation processing time: 0.23 hours. Matrix solve time: 2.14 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 60.72 hours. --------- CPU info (if available) ----------

Aug 15, 2008

By Serge Batalov / Msieve
(23·10¹⁵⁴+31)/9 = 2(5)₁₅₃9_<155> = C155
C155 = P68 · P88
P68 = 24004480982001907880256277793174862134905775836273857482990834610803_<68>
P88 = 1064616042926177540280830726352520704884408223688229599012984589433059561384926047461053_<88>

Number: 25559_154 N=25555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559 ( 155 digits) SNFS difficulty: 156 digits. Divisors found: r1=24004480982001907880256277793174862134905775836273857482990834610803 r2=1064616042926177540280830726352520704884408223688229599012984589433059561384926047461053 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 25555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559 Y1: 1 Y0: -10000000000000000000000000000000 c5: 23 c0: 310 skew: 1.68 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1500000, 2200001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 536384 x 536632 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,52,52,2.5,2.5,100000 total time: 12.00 hours.

(23·10¹⁵⁹+31)/9 = 2(5)₁₅₈9_<160> = 3² · 151 · 173 · C155
C155 = P68 · P87
P68 = 89402830646845862862212588779611774210792761685868432636233023487881_<68>
P87 = 121581779965533991572064099812148849337116961553860068777860822932046094064865597027077_<87>

Number: 25559_159 N=10869755284000712677868185785857314140181090123031451873213283975192382853575416961449703988207733311026705098340566446577752068443540836961704906938353837 ( 155 digits) SNFS difficulty: 161 digits. Divisors found: r1=89402830646845862862212588779611774210792761685868432636233023487881 r2=121581779965533991572064099812148849337116961553860068777860822932046094064865597027077 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.725). Factorization parameters were as follows: n: 10869755284000712677868185785857314140181090123031451873213283975192382853575416961449703988207733311026705098340566446577752068443540836961704906938353837 Y1: 1 Y0: -100000000000000000000000000000000 c5: 23 c0: 310 skew: 1.68 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2000000, 3100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 612972 x 613220 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.5,2.5,100000 total time: 17.20 hours.

(23·10¹⁵⁷+31)/9 = 2(5)₁₅₆9_<158> = C158
C158 = P50 · P108
P50 = 49305565416638237546855293608378285511055783935823_<50>
P108 = 518309755493277331341705329873406123057615376398129738348359754423513248803380888816255348102631292457305833_<108>

Number: 25559_157 N=25555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559 ( 158 digits) SNFS difficulty: 158 digits. Divisors found: r1=49305565416638237546855293608378285511055783935823 r2=518309755493277331341705329873406123057615376398129738348359754423513248803380888816255348102631292457305833 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.707). Factorization parameters were as follows: n: 25555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559 Y1: 1 Y0: -10000000000000000000000000000000 c5: 2300 c0: 31 skew: 0.42 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2000000, 5300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 775626 x 775874 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.5,2.5,100000 total time: 23.00 hours.

(23·10¹⁶³+31)/9 = 2(5)₁₆₂9_<164> = 11197 · 600135654958518913015121_<24> · 15917843362328931372400174231396061_<35> · C102
C102 = P46 · P56
P46 = 4777261969155687481306587205398516207932071267_<46>
P56 = 50011621397949403287827699425161427247300887932441419861_<56>

N=238918616920236482284688193493767802557297554431710259935973434002654087902904166343115871840121233887 ( 102 digits) Divisors found: r1=4777261969155687481306587205398516207932071267 r2=50011621397949403287827699425161427247300887932441419861 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.718). Factorization parameters were as follows: name: 25559_163 n: 238918616920236482284688193493767802557297554431710259935973434002654087902904166343115871840121233887 skew: 26690.28 # norm 3.49e+14 c5: 11340 c4: 172695024 c3: -21952003729623 c2: -183405417277364978 c1: 2326716827805210224682 c0: 34516205836374053444042628 # alpha -7.10 Y1: 46579288979 Y0: -29155820963474000399 # Murphy_E 2.89e-09 # M 60712994758916835332065667762407420644104045750246852901951305449959008087828470303990127529380791560 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1750001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 215230 x 215478 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 4.50 hours.

Aug 14, 2008 (5th)

By Sinkiti Sibata / GGNFS
(23·10¹³⁶+31)/9 = 2(5)₁₃₅9_<137> = 227 · 397 · 727 · 773 · C126
C126 = P37 · P42 · P48
P37 = 4294379808444677906913969409355254559_<37>
P42 = 377963583243089172487553781282255778332803_<42>
P48 = 310888493269623289140455555332340572349264972183_<48>

Number: 25559_136 N=504609076331431584228366233423443440822540269199705375616028388572415036563660999834170097655998553802901539210099104791238491 ( 126 digits) SNFS difficulty: 137 digits. Divisors found: r1=4294379808444677906913969409355254559 (pp37) r2=377963583243089172487553781282255778332803 (pp42) r3=310888493269623289140455555332340572349264972183 (pp48) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.32 hours. Scaled time: 11.19 units (timescale=0.988). Factorization parameters were as follows: name: 25559_136 n: 504609076331431584228366233423443440822540269199705375616028388572415036563660999834170097655998553802901539210099104791238491 m: 1000000000000000000000000000 c5: 230 c0: 31 skew: 0.67 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 2275001) Primes: RFBsize:78498, AFBsize:63729, largePrimes:1760780 encountered Relations: rels:1843501, finalFF:205262 Max relations in full relation-set: 28 Initial matrix: 142294 x 205262 with sparse part having weight 24445222. Pruned matrix : 129188 x 129963 with weight 14345545. Total sieving time: 11.15 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 11.32 hours. --------- CPU info (if available) ----------

(23·10¹⁴¹+31)/9 = 2(5)₁₄₀9_<142> = 3² · 29 · 10607 · 372078052816479538519637_<24> · C112
C112 = P35 · P77
P35 = 76194565446367493174455763880460463_<35>
P77 = 32560735029065341214128814187400511581285961062243794359923482842555071079407_<77>

Number: 25559_141 N=2480951056153949701228703243919926546283721927193703106236404703317962887038008437037078659456775758113596985441 ( 112 digits) SNFS difficulty: 142 digits. Divisors found: r1=76194565446367493174455763880460463 (pp35) r2=32560735029065341214128814187400511581285961062243794359923482842555071079407 (pp77) Version: GGNFS-0.77.1-20050930-nocona Total time: 14.76 hours. Scaled time: 14.76 units (timescale=1.000). Factorization parameters were as follows: name: 25559_141 n: 2480951056153949701228703243919926546283721927193703106236404703317962887038008437037078659456775758113596985441 m: 10000000000000000000000000000 c5: 230 c0: 31 skew: 0.67 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2750001) Primes: RFBsize:100021, AFBsize:99799, largePrimes:3038180 encountered Relations: rels:3144558, finalFF:307864 Max relations in full relation-set: 28 Initial matrix: 199887 x 307864 with sparse part having weight 38526056. Pruned matrix : 175685 x 176748 with weight 21820711. Total sieving time: 14.44 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.21 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 14.76 hours. --------- CPU info (if available) ----------

(23·10¹³⁷+31)/9 = 2(5)₁₃₆9_<138> = 37 · 308555744497093_<15> · C122
C122 = P42 · P80
P42 = 305762271390977651319812135780994171599831_<42>
P80 = 73209268986643556707742394636801129517180084446760232905412721334096208230335929_<80>

Number: 25559_137 N=22384632372229190609714858716588723245099169836977091812409926831894009881923370879370091085934184452345263599880489627999 ( 122 digits) SNFS difficulty: 138 digits. Divisors found: r1=305762271390977651319812135780994171599831 (pp42) r2=73209268986643556707742394636801129517180084446760232905412721334096208230335929 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.38 hours. Scaled time: 13.37 units (timescale=0.769). Factorization parameters were as follows: name: 25559_137 n: 22384632372229190609714858716588723245099169836977091812409926831894009881923370879370091085934184452345263599880489627999 m: 1000000000000000000000000000 c5: 2300 c0: 31 skew: 0.42 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 2725001) Primes: RFBsize:78498, AFBsize:64019, largePrimes:1757390 encountered Relations: rels:1826972, finalFF:174401 Max relations in full relation-set: 28 Initial matrix: 142584 x 174401 with sparse part having weight 21121949. Pruned matrix : 135557 x 136333 with weight 15350591. Total sieving time: 17.08 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.16 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 17.38 hours. --------- CPU info (if available) ----------

(23·10¹³⁸+31)/9 = 2(5)₁₃₇9_<139> = 3 · 53 · 389 · 1433539 · C128
C128 = P64 · P65
P64 = 1279333927545199012128258534852861478951245004473500538855514499_<64>
P65 = 22529168901137974895314002117395908892469523921646148358021532669_<65>

Number: 25559_138 N=28822330134622000820620584010253028421676120212058138406067842081365878773742408071645154741613441781555667878148540074531667831 ( 128 digits) SNFS difficulty: 139 digits. Divisors found: r1=1279333927545199012128258534852861478951245004473500538855514499 (pp64) r2=22529168901137974895314002117395908892469523921646148358021532669 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 14.19 hours. Scaled time: 14.19 units (timescale=1.000). Factorization parameters were as follows: name: 25559_138 n: 28822330134622000820620584010253028421676120212058138406067842081365878773742408071645154741613441781555667878148540074531667831 m: 1000000000000000000000000000 c5: 23000 c0: 31 skew: 0.27 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 2875001) Primes: RFBsize:78498, AFBsize:63914, largePrimes:1802628 encountered Relations: rels:1904248, finalFF:193118 Max relations in full relation-set: 28 Initial matrix: 142479 x 193118 with sparse part having weight 24230890. Pruned matrix : 132213 x 132989 with weight 15653467. Total sieving time: 14.00 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.11 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 14.19 hours. --------- CPU info (if available) ----------

Aug 14, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve
(23·10¹⁰²+31)/9 = 2(5)₁₀₁9_<103> = 3 · 17 · 336761 · 14684161 · C89
C89 = P38 · P51
P38 = 36174622317116628604747601318347875179_<38>
P51 = 280117484022614210615310757466475649891967034175151_<51>

Number: n N=10133144188939020667332924829099166344145459417174872384023152068186407293124797771477029 ( 89 digits) SNFS difficulty: 103 digits. Divisors found: r1=36174622317116628604747601318347875179 (pp38) r2=280117484022614210615310757466475649891967034175151 (pp51) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.75 hours. Scaled time: 1.09 units (timescale=1.449). Factorization parameters were as follows: name: KA_2_5_101_9 n: 10133144188939020667332924829099166344145459417174872384023152068186407293124797771477029 type: snfs skew: 0.42 deg: 5 c5: 2300 c0: 31 m: 100000000000000000000 rlim: 300000 alim: 300000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 300000/300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:25997, AFBsize:25925, largePrimes:3193322 encountered Relations: rels:2812979, finalFF:136783 Max relations in full relation-set: 28 Initial matrix: 51989 x 136783 with sparse part having weight 12094637. Pruned matrix : 40477 x 40800 with weight 2131424. Total sieving time: 0.67 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.01 hours. Total square root time: 0.02 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,103,5,0,0,0,0,0,0,0,0,300000,300000,28,28,50,50,2.5,2.5,20000 total time: 0.75 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(23·10¹²⁷+31)/9 = 2(5)₁₂₆9_<128> = 47 · 67 · 19474127 · C117
C117 = P50 · P68
P50 = 37482453682442295251317733556828300327910374081709_<50>
P68 = 11117999624135567706071487447289819238425678281178420561049303069537_<68>

Number: n N=416729905953072264269507026565861748886593163661877469648194994869817747460538910312526637595843864694003181346798733 ( 117 digits) SNFS difficulty: 128 digits. Divisors found: Thu Aug 14 14:30:21 2008 prp50 factor: 37482453682442295251317733556828300327910374081709 Thu Aug 14 14:30:21 2008 prp68 factor: 11117999624135567706071487447289819238425678281178420561049303069537 Thu Aug 14 14:30:21 2008 elapsed time 00:25:45 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.18 hours. Scaled time: 4.59 units (timescale=1.444). Factorization parameters were as follows: name: KA_2_5_126_9 n: 416729905953072264269507026565861748886593163661877469648194994869817747460538910312526637595843864694003181346798733 type: snfs skew: 0.42 deg: 5 c5: 2300 c0: 31 m: 10000000000000000000000000 rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 460001) Primes: RFBsize:56543, AFBsize:56539, largePrimes:5776983 encountered Relations: rels:4980603, finalFF:104656 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 3.05 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,700000,700000,28,28,50,50,2.5,2.5,50000 total time: 3.18 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

7·10¹⁹¹+9 = 7(0)₁₉₀9_<192> = 97 · C190
C190 = P57 · P65 · P69
P57 = 234464897294589778294207283924185372179122521034823214261_<57>
P65 = 37245591958990518315896750106678790768293832822047005717210831897_<65>
P69 = 826368192949751598558367932833322291039122696920944478534061838111341_<69>

Number: n N=7216494845360824742268041237113402061855670103092783505154639175257731958762886597938144329896907216494845360824742268041237113402061855670103092783505154639175257731958762886597938144329897 ( 190 digits) SNFS difficulty: 191 digits. Divisors found: Thu Aug 14 17:44:30 2008 prp57 factor: 234464897294589778294207283924185372179122521034823214261 Thu Aug 14 17:44:30 2008 prp65 factor: 37245591958990518315896750106678790768293832822047005717210831897 Thu Aug 14 17:44:30 2008 prp69 factor: 826368192949751598558367932833322291039122696920944478534061838111341 Thu Aug 14 17:44:30 2008 elapsed time 12:59:34 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 167.63 hours. Scaled time: 218.25 units (timescale=1.302). Factorization parameters were as follows: name: KA_7_0_190_9 n: 7216494845360824742268041237113402061855670103092783505154639175257731958762886597938144329896907216494845360824742268041237113402061855670103092783505154639175257731958762886597938144329897 type: snfs skew: 0.66 deg: 5 c5: 70 c0: 9 m: 100000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 14600001) Primes: RFBsize:633578, AFBsize:635068, largePrimes:11104373 encountered Relations: rels:11157968, finalFF:1297829 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 166.97 hours. Total relation processing time: 0.66 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000 total time: 167.63 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(23·10¹³⁰+31)/9 = 2(5)₁₂₉9_<131> = 233 · 6949 · 15443 · 12049469 · 67386721 · C106
C106 = P44 · P62
P44 = 14880480537836991036560178301181133024307979_<44>
P62 = 84589456232401803618572893875810928263984685426113509528121359_<62>

Number: n N=1258731757172469004163889939303851535943090531086634050129863780310728667440482666587361506345620904023461 ( 106 digits) SNFS difficulty: 131 digits. Divisors found: r1=14880480537836991036560178301181133024307979 (pp44) r2=84589456232401803618572893875810928263984685426113509528121359 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.43 hours. Scaled time: 4.98 units (timescale=1.450). Factorization parameters were as follows: name: KA_2_5_129_9 n: 1258731757172469004163889939303851535943090531086634050129863780310728667440482666587361506345620904023461 type: snfs skew: 1.06 deg: 5 c5: 23 c0: 31 m: 100000000000000000000000000 rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 480001) Primes: RFBsize:63951, AFBsize:63869, largePrimes:6329489 encountered Relations: rels:5532637, finalFF:154928 Max relations in full relation-set: 28 Initial matrix: 127885 x 154928 with sparse part having weight 14763138. Pruned matrix : 119834 x 120537 with weight 9726166. Total sieving time: 2.95 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.27 hours. Total square root time: 0.08 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,28,28,50,50,2.5,2.5,50000 total time: 3.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Aug 14, 2008 (3rd)

By Serge Batalov / Msieve, GMP-ECM, pol51
(23·10¹⁰⁸+31)/9 = 2(5)₁₀₇9_<109> = 3 · C108
C108 = P32 · P76
P32 = 87457626883402500347090286707579_<32>
P76 = 9740166549311141470879840695000672432811606088405464382425229128401576277207_<76>

Number: 25559_108 N=851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853 ( 108 digits) SNFS difficulty: 109 digits. Divisors found: r1=87457626883402500347090286707579 r2=9740166549311141470879840695000672432811606088405464382425229128401576277207 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=1.875). Factorization parameters were as follows: n: 851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853 Y1: 1 Y0: -1000000000000000000000 c5: 23000 c0: 31 skew: 0.27 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 73371 x 73604 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,109,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.90 hours.

(23·10¹³²+31)/9 = 2(5)₁₃₁9_<133> = 3² · 415729 · 11552413 · 38085356615361651136669097_<26> · C94
C94 = P43 · P51
P43 = 1655570577258704683443960244245536278805161_<43>
P51 = 937678728208859008823339976946357714452296342866939_<51>

Wed Aug 13 10:45:30 2008 Msieve v. 1.36 Wed Aug 13 10:45:30 2008 random seeds: 9f5c825b c4951560 Wed Aug 13 10:45:30 2008 factoring 1552393313343948764302713161569033385259291635053878410148001293956160874279801427032129472179 (94 digits) Wed Aug 13 10:45:31 2008 no P-1/P+1/ECM available, skipping Wed Aug 13 10:45:31 2008 commencing quadratic sieve (94-digit input) Wed Aug 13 10:45:31 2008 using multiplier of 1 Wed Aug 13 10:45:31 2008 using 64kb Opteron sieve core Wed Aug 13 10:45:31 2008 sieve interval: 18 blocks of size 65536 Wed Aug 13 10:45:31 2008 processing polynomials in batches of 6 Wed Aug 13 10:45:31 2008 using a sieve bound of 1984859 (74118 primes) Wed Aug 13 10:45:31 2008 using large prime bound of 256046811 (27 bits) Wed Aug 13 10:45:31 2008 using double large prime bound of 1364503925389509 (42-51 bits) Wed Aug 13 10:45:31 2008 using trial factoring cutoff of 51 bits Wed Aug 13 10:45:31 2008 polynomial 'A' values have 12 factors Wed Aug 13 14:12:07 2008 74570 relations (18435 full + 56135 combined from 1036730 partial), need 74214 Wed Aug 13 14:12:07 2008 begin with 1055165 relations Wed Aug 13 14:12:08 2008 reduce to 193738 relations in 11 passes Wed Aug 13 14:12:08 2008 attempting to read 193738 relations Wed Aug 13 14:12:10 2008 recovered 193738 relations Wed Aug 13 14:12:10 2008 recovered 177248 polynomials Wed Aug 13 14:12:10 2008 attempting to build 74570 cycles Wed Aug 13 14:12:10 2008 found 74570 cycles in 5 passes Wed Aug 13 14:12:10 2008 distribution of cycle lengths: Wed Aug 13 14:12:10 2008 length 1 : 18435 Wed Aug 13 14:12:10 2008 length 2 : 13018 Wed Aug 13 14:12:10 2008 length 3 : 12408 Wed Aug 13 14:12:10 2008 length 4 : 10058 Wed Aug 13 14:12:10 2008 length 5 : 7624 Wed Aug 13 14:12:10 2008 length 6 : 5079 Wed Aug 13 14:12:10 2008 length 7 : 3422 Wed Aug 13 14:12:10 2008 length 9+: 4526 Wed Aug 13 14:12:10 2008 largest cycle: 21 relations Wed Aug 13 14:12:11 2008 matrix is 74118 x 74570 (20.0 MB) with weight 4654747 (62.42/col) Wed Aug 13 14:12:11 2008 sparse part has weight 4654747 (62.42/col) Wed Aug 13 14:12:12 2008 filtering completed in 3 passes Wed Aug 13 14:12:12 2008 matrix is 70647 x 70711 (19.0 MB) with weight 4418943 (62.49/col) Wed Aug 13 14:12:12 2008 sparse part has weight 4418943 (62.49/col) Wed Aug 13 14:12:13 2008 saving the first 48 matrix rows for later Wed Aug 13 14:12:13 2008 matrix is 70599 x 70711 (11.6 MB) with weight 3378476 (47.78/col) Wed Aug 13 14:12:13 2008 sparse part has weight 2338269 (33.07/col) Wed Aug 13 14:12:13 2008 matrix includes 64 packed rows Wed Aug 13 14:12:13 2008 using block size 28284 for processor cache size 1024 kB Wed Aug 13 14:12:13 2008 commencing Lanczos iteration Wed Aug 13 14:12:13 2008 memory use: 10.7 MB Wed Aug 13 14:12:53 2008 lanczos halted after 1118 iterations (dim = 70597) Wed Aug 13 14:12:54 2008 recovered 16 nontrivial dependencies Wed Aug 13 14:12:54 2008 prp43 factor: 1655570577258704683443960244245536278805161 Wed Aug 13 14:12:54 2008 prp51 factor: 937678728208859008823339976946357714452296342866939 Wed Aug 13 14:12:54 2008 elapsed time 03:27:24

(23·10¹¹⁶+31)/9 = 2(5)₁₁₅9_<117> = 7 · 37 · 173 · 6650044967_<10> · C102
C102 = P44 · P59
P44 = 54931236506670937151390207759795749240532083_<44>
P59 = 15613328680502956072470938717289086244068747139245028532717_<59>

Number: 25559_116 N=857659450405096353317645695092954648720447466263198250149873858089122806724718795563981780401853659511 ( 102 digits) SNFS difficulty: 117 digits. Divisors found: r1=54931236506670937151390207759795749240532083 r2=15613328680502956072470938717289086244068747139245028532717 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: n: 857659450405096353317645695092954648720447466263198250149873858089122806724718795563981780401853659511 Y1: 1 Y0: -100000000000000000000000 c5: 230 c0: 31 skew: 0.67 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 450001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 107451 x 107666 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.00 hours.

(23·10¹²³+31)/9 = 2(5)₁₂₂9_<124> = 3³ · 89 · 426530711 · 346377283131541_<15> · C97
C97 = P33 · P65
P33 = 714725418909421255436482397289613_<33>
P65 = 10071464350712919091136784607863782767507181435730410139468751531_<65>
(23·10¹⁵¹+31)/9 = 2(5)₁₅₀9_<152> = 53 · 3631 · 6833 · C143
C143 = P35 · P108
P35 = 28491347801258535159984087380636957_<35>
P108 = 682116873892988320832073056144143663626338689069642201544762686263040341183467097296639486409774086795960473_<108>
(23·10¹⁶³+31)/9 = 2(5)₁₆₂9_<164> = 11197 · 600135654958518913015121_<24> · C136
C136 = P35 · C102
P35 = 15917843362328931372400174231396061_<35>
C102 = [238918616920236482284688193493767802557297554431710259935973434002654087902904166343115871840121233887_<102>]
(23·10¹⁵³+31)/9 = 2(5)₁₅₂9_<154> = 3 · 14207 · 542856502895113009_<18> · C132
C132 = P30 · P33 · P69
P30 = 148492579562995654158351194371_<30>
P33 = 751293507943332722148018478605683_<33>
P69 = 990061696833602124338231060672328983775827259228387769290559186187867_<69>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3707587740 Step 1 took 5072ms Step 2 took 4844ms ********** Factor found in step 2: 148492579562995654158351194371 Found probable prime factor of 30 digits: 148492579562995654158351194371 Composite cofactor 743826925294445331005247766856880519633040968045235123810908647040711559143705680259634454974251848161 has 102 digits Number: 25559_153 N=743826925294445331005247766856880519633040968045235123810908647040711559143705680259634454974251848161 ( 102 digits) Divisors found: r1=751293507943332722148018478605683 r2=990061696833602124338231060672328983775827259228387769290559186187867 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.948). Factorization parameters were as follows: name: 25559_153 n: 743826925294445331005247766856880519633040968045235123810908647040711559143705680259634454974251848161 skew: 7667.78 # norm 1.63e+14 c5: 79380 c4: -1220023119 c3: -11990119136399 c2: 43162577465978701 c1: -50323790623128607716 c0: 595649923520302040373 # alpha -5.39 Y1: 40114117769 Y0: -24794440917443004098 # Murphy_E 2.51e-09 # M 108954050070074233826012025933116688514356381169118919916758488143137004054206742903805050301638526229 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1950001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 269347 x 269595 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.10 hours.

Aug 14, 2008 (2nd)

Factorizations of 255...559 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 14, 2008

By Jo Yeong Uk / GGNFS, GMP-ECM
(67·10¹⁸⁶+23)/9 = 7(4)₁₈₅7_<187> = 19 · 195493 · 9573671 · 15879889 · 867874901 · 21647287940191_<14> · 89421769771573038016990490819_<29> · C115
C115 = P37 · P79
P37 = 1746382501984432932253147027099413497_<37>
P79 = 4493432943695280633611271672078629570872945669670928390073563152978895513171103_<79>

Number: 74447_186 N=7847252666709839743467752504350917467823681102493087715558574118900695078873620596188423137154878036922729908577191 ( 115 digits) Divisors found: r1=1746382501984432932253147027099413497 (pp37) r2=4493432943695280633611271672078629570872945669670928390073563152978895513171103 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 22.87 hours. Scaled time: 54.46 units (timescale=2.381). Factorization parameters were as follows: name: 74447_186 n: 7847252666709839743467752504350917467823681102493087715558574118900695078873620596188423137154878036922729908577191 skew: 51581.35 # norm 1.74e+16 c5: 44400 c4: 11244086600 c3: -438029123632375 c2: -16066004853798946614 c1: 595416047125765423448296 c0: 2879863880296498472471170048 # alpha -6.95 Y1: 2243360191787 Y0: -11206307361932270455113 # Murphy_E 5.39e-10 # M 2501025341128000393248592538385081061341254539000833808236602444299295780685350436595419391261914916678877912287855 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 70000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3080001) Primes: RFBsize:250150, AFBsize:250380, largePrimes:7570818 encountered Relations: rels:7503217, finalFF:612787 Max relations in full relation-set: 28 Initial matrix: 500610 x 612787 with sparse part having weight 54051584. Pruned matrix : 411617 x 414184 with weight 34251677. Polynomial selection time: 1.33 hours. Total sieving time: 20.21 hours. Total relation processing time: 0.13 hours. Matrix solve time: 1.07 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000 total time: 22.87 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2459k kernel code, 339200k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.73 BogoMIPS (lpj=2672366) Calibrating delay using timer specific routine.. 5343.99 BogoMIPS (lpj=2671997) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(55·10¹⁸⁴-1)/9 = 6(1)_184<185> = 113113526204811467_<18> · 902962100831388890356903_<24> · 30298080812156225043145231_<26> · C119
C119 = P33 · P86
P33 = 299222870320790868968071687171273_<33>
P86 = 65997306601865480874354633900283209180626121298931610636261094645539057137062347684197_<86>

Aug 13, 2008 (3rd)

By Sinkiti Sibata / GGNFS
6·10¹⁶⁵+1 = 6(0)₁₆₄1_<166> = 108649 · 1383530154323_<13> · 10418259026881_<14> · C136
C136 = P59 · P78
P59 = 12198214958645406697515956553865609339286480946779228031841_<59>
P78 = 314083740589948806536874133179020940182628645393194584520163117078481245780803_<78>

Number: 60001_165 N=3831260982731617026109963484953683259170695517683951964059413219775587940296031765586309929215323885262414918355104547162842906990548323 ( 136 digits) SNFS difficulty: 165 digits. Divisors found: r1=12198214958645406697515956553865609339286480946779228031841 (pp59) r2=314083740589948806536874133179020940182628645393194584520163117078481245780803 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 73.33 hours. Scaled time: 73.92 units (timescale=1.008). Factorization parameters were as follows: name: 60001_165 n: 3831260982731617026109963484953683259170695517683951964059413219775587940296031765586309929215323885262414918355104547162842906990548323 m: 1000000000000000000000000000000000 c5: 6 c0: 1 skew: 0.7 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5000001) Primes: RFBsize:348513, AFBsize:348726, largePrimes:6213178 encountered Relations: rels:6700823, finalFF:1088127 Max relations in full relation-set: 28 Initial matrix: 697305 x 1088127 with sparse part having weight 65822247. Pruned matrix : 402300 x 405850 with weight 63363491. Total sieving time: 71.21 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.94 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 73.33 hours. --------- CPU info (if available) ----------

Aug 13, 2008 (2nd)

By Serge Batalov / pol51, Franke/Childers-64bit-assembly-sievers, Msieve
(19·10¹⁷⁶+53)/9 = 2(1)₁₇₅7_<177> = 7 · 288499 · 2637468153113_<13> · 246110466160057_<15> · 7544750677235511008287_<22> · C122
C122 = P45 · P77
P45 = 664699855687740871426245760733544298057358189_<45>
P77 = 32113005584426118305653746784676287558964283770905370659367037921112708262563_<77>

Number: 21117_176 N=21345510177667657540730006301434663701471756955685409885592596413899469145549610473198894598984475625669925326599950178407 ( 122 digits) Divisors found: r1=664699855687740871426245760733544298057358189 r2=32113005584426118305653746784676287558964283770905370659367037921112708262563 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.719). Factorization parameters were as follows: name: 21117_176 n: 21345510177667657540730006301434663701471756955685409885592596413899469145549610473198894598984475625669925326599950178407 skew: 170756.40 # norm 7.43e+16 c5: 3960 c4: -2169820698 c3: 1300114549842949 c2: 51004422752112391841 c1: -13720078057851879793267805 c0: -306179776140910730398882578519 # alpha -6.28 Y1: 9129774563993 Y0: -351822415252155645580046 # Murphy_E 2.29e-10 # M 19568358484057287237196273449831904887169580518105982422756745467726799115462603151064661311112921045638463225213236455353 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 9100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 815845 x 816093 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 3.00 hours. Time per square root: 0.35 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000 total time: 51 hours.

(64·10²³²+53)/9 = 7(1)₂₃₁7_<233> = 29 · 31 · 25544394638150569_<17> · 21891861055037187204902189298063661_<35> · 1156244055915277149927645527883080159_<37> · C144
C144 = P70 · P74
P70 = 5629056896456130761115640768115712949562588093167473845957065096607951_<70>
P74 = 21732731937076769089333819026656467057955775638915262225760919560406955043_<74>

Number: 71117_232 N=122334784589234392683295194652612149338189319179115868523072772347572950426690801931827228533310815015647306731512386262336087369965447853346893 ( 144 digits) Divisors found: r1=5629056896456130761115640768115712949562588093167473845957065096607951 r2=21732731937076769089333819026656467057955775638915262225760919560406955043 Version: Total time: 22 CPU-days. Scaled time: ? units (timescale=2.739). Factorization parameters were as follows: name: 71117_232 n: 122334784589234392683295194652612149338189319179115868523072772347572950426690801931827228533310815015647306731512386262336087369965447853346893 skew: 690006.04 # norm 1.16e+20 c5: 366240 c4: -200755493198 c3: -1264280431194248789 c2: 30690227552865176460280 c1: 116115356677156443273022507812 c0: 1643772806174680731101452821850125 # alpha -6.86 Y1: 12549580773819617 Y0: -3197105916158047746993222154 # Murphy_E 1.41e-11 # M 5734946885270096719071646003056964635381291967622973864385956607094834583149950289638574241818695561052754902888430269917445698295408593930669 type: gnfs rlim: 20000000 alim: 20000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [10000000, 11400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 24,475,000 relations (22,067,313 unique) vs. 19,071,047 large primes Max relations in full relation-set: Initial matrix: Pruned matrix : 2595393 x 2595641 Total sieving time: 20 CPU-days. (with 8cpus * a 2.5-day weekend) Total relation processing time: 0.50 hours. Top memory use in filtering: 1.5 Gb Matrix solve time: 37.35 hours. Time per square root: 1.90 hours. Prototype def-par.txt line would be: gnfs,144,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,20000000,20000000,28,28,56,56,2.6,2.6,100000 #use this line, sieve algebraic (or better yet, always do test runs) total time: 22 CPU-days. # Note: my estimate of a general case GNFS:SNFS break-even ratio is 72:100 # this is GNFS-144 ~= complexity of SNFS-200 # GNFS is absolutely better for this particular number

Note: C144 is the largest composite number factored by GNFS so far in our tables.

Aug 13, 2008

By Robert Backstrom / GMP-ECM
7·10¹⁷¹+1 = 7(0)₁₇₀1_<172> = 191 · 11351 · 200087 · 199743193690849_<15> · 503783621180657_<15> · C132
C132 = P42 · P90
P42 = 640757244242093195737825269513973688101421_<42>
P90 = 250266153200200437607062854749076319929624557778915248618363969037755267406743304872865851_<90>

Aug 12, 2008 (3rd)

By Sinkiti Sibata / GGNFS
(23·10¹⁶⁵-41)/9 = 2(5)₁₆₄1_<166> = 29 · 71 · 132745428289_<12> · 1240062004353599171_<19> · C133
C133 = P66 · P68
P66 = 620307761470091015755690541703303810222293530677225354864980633273_<66>
P68 = 12155107128456035886009851568901921324819251306725762561321071641847_<68>

Number: 25551_165 N=7539907293281709664021555033543314880138720337710856966983086890475334408273968539560151442899749274783057664654530833081819907375231 ( 133 digits) SNFS difficulty: 166 digits. Divisors found: r1=620307761470091015755690541703303810222293530677225354864980633273 (pp66) r2=12155107128456035886009851568901921324819251306725762561321071641847 (pp68) Version: GGNFS-0.77.1-20050930-nocona Total time: 101.57 hours. Scaled time: 102.39 units (timescale=1.008). Factorization parameters were as follows: name: 25551_165 n: 7539907293281709664021555033543314880138720337710856966983086890475334408273968539560151442899749274783057664654530833081819907375231 m: 1000000000000000000000000000000000 c5: 23 c0: -41 skew: 1.12 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 6200001) Primes: RFBsize:348513, AFBsize:348762, largePrimes:6205595 encountered Relations: rels:6582900, finalFF:985608 Max relations in full relation-set: 28 Initial matrix: 697340 x 985608 with sparse part having weight 70810848. Pruned matrix : 477437 x 480987 with weight 57774851. Total sieving time: 98.88 hours. Total relation processing time: 0.11 hours. Matrix solve time: 2.49 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 101.57 hours. --------- CPU info (if available) ----------

Aug 12, 2008 (2nd)

By Jo Yeong Uk / GGNFS
(4·10¹⁹³-31)/9 = (4)₁₉₂1_<193> = C193
C193 = P57 · P136
P57 = 646181061524363199600970571839514279881175613475434692033_<57>
P136 = 6878017182923696594530988282380362877712659016819970541769693419701317790915722248377653237079002311402940729245426422513461529454956377_<136>

Number: 44441_193 N=4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 ( 193 digits) SNFS difficulty: 195 digits. Divisors found: r1=646181061524363199600970571839514279881175613475434692033 (pp57) r2=6878017182923696594530988282380362877712659016819970541769693419701317790915722248377653237079002311402940729245426422513461529454956377 (pp136) Version: GGNFS-0.77.1-20050930-nocona Total time: 633.40 hours. Scaled time: 1503.05 units (timescale=2.373). Factorization parameters were as follows: n: 4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 m: 1000000000000000000000000000000000000000 c5: 1 c0: -775 skew: 3.78 type: snfs Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 52/52 Sieved algebraic special-q in [10000000, 20400001) Primes: RFBsize:1270607, AFBsize:1272451, largePrimes:21030425 encountered Relations: rels:21534447, finalFF:2888534 Max relations in full relation-set: 28 Initial matrix: 2543122 x 2888533 with sparse part having weight 170079893. Pruned matrix : 2224800 x 2237579 with weight 124339102. Total sieving time: 591.27 hours. Total relation processing time: 0.69 hours. Matrix solve time: 41.22 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,52,52,2.6,2.6,100000 total time: 633.40 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047092k/8912896k available (2459k kernel code, 339200k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.73 BogoMIPS (lpj=2672366) Calibrating delay using timer specific routine.. 5343.99 BogoMIPS (lpj=2671997) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Aug 12, 2008

By Serge Batalov / Msieve
(85·10¹⁸⁵+41)/9 = 9(4)₁₈₄9_<186> = 11 · 97 · 859 · 994769 · 725406797 · 1283920045522639113163_<22> · 49703136401507545869061_<23> · C122
C122 = P55 · P67
P55 = 5945312755539665917551963829023944543338834374958932437_<55>
P67 = 3763730250037354798169122734936464412007531853274549949355322112591_<67>

Number: 94449_185 N=22376553463957581646819827364810402074663641841688814278996265692919457557189900085368580368180018925514654615380876014267 ( 122 digits) Divisors found: r1=5945312755539665917551963829023944543338834374958932437 r2=3763730250037354798169122734936464412007531853274549949355322112591 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.719). Factorization parameters were as follows: name: 94449_185 n: 22376553463957581646819827364810402074663641841688814278996265692919457557189900085368580368180018925514654615380876014267 skew: 395089.16 # norm 8.53e+16 c5: 1920 c4: -2122639568 c3: -1001519971436916 c2: 252010646313405784356 c1: 17053914602620055702421409 c0: -5102205586876697697049786391166 # alpha -6.67 Y1: 14417436812383 Y0: -410489229162219968921845 # Murphy_E 2.43e-10 # M 13327227797342778556781154439976826870101708204128832160162315240816752369766045276700781494476592724195508665899854601153 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5800001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 693877 x 694113 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 1.80 hours. Time per square root: 1.80 hours / 6deps. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000 total time: 41.00 hours.

(8·10¹⁷⁸-53)/9 = (8)₁₇₇3_<178> = 3 · 7 · 580033 · 4121233246377533370895087_<25> · 11414389645507504885866557_<26> · C122
C122 = P61 · P61
P61 = 2084319019311817485408263671504067644597211773621536836338031_<61>
P61 = 7442715191706727951117023466133424089625836289964455009349139_<61>

# Nice split, again, P61.P61 :-) ...guys, don't shy away from gnfs-122 # Number: 88883_178 N=15512992829395332874459989302553000844308438535363267904145402644391992053787434208266071942229443864121635964649502805309 ( 122 digits) Divisors found: r1=2084319019311817485408263671504067644597211773621536836338031 r2=7442715191706727951117023466133424089625836289964455009349139 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.740). Factorization parameters were as follows: name: 88883_178 n: 15512992829395332874459989302553000844308438535363267904145402644391992053787434208266071942229443864121635964649502805309 skew: 98981.13 # norm 3.36e+16 c5: 1320 c4: -10396789456 c3: -66076991548644 c2: 78186712031832272171 c1: 200139365179873413081944 c0: -88020638544471412575938322460 # alpha -5.65 Y1: 1247076274951 Y0: -411174721634384235437837 # Murphy_E 2.21e-10 # M 12429707818737800271460182262993084301376975976751266457817355689134402992212562892000794069795686993932653381134042300059 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 727897 x 728145 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 2.50 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000 total time: 43.00 hours.

(23·10¹⁶⁹+13)/9 = 2(5)₁₆₈7_<170> = 3 · 83 · 311 · 28517 · 199813 · C155
C155 = P64 · P91
P64 = 7124994157222814707790131826005124154401833141434559408862786761_<64>
P91 = 8128557869000804133044033360884580345414021448333631032282453920166787798539408237113453723_<91>

Number: 25557_169 N=57915927323278263122576779147506228774571092503906587992363346778093393164170615259694974150158339232963013238210915096456461157537716585458112711190561203 ( 155 digits) SNFS difficulty: 171 digits. Divisors found: r1=7124994157222814707790131826005124154401833141434559408862786761 r2=8128557869000804133044033360884580345414021448333631032282453920166787798539408237113453723 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.649). Factorization parameters were as follows: n: 57915927323278263122576779147506228774571092503906587992363346778093393164170615259694974150158339232963013238210915096456461157537716585458112711190561203 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 23 c0: 130 skew: 1.41 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3000000, 11500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1186790 x 1187021 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 5.75 hours. Time per square root: 0.6 hours. * 2 Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000 total time: 81 hours.

Aug 11, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(55·10¹⁹⁰-1)/9 = 6(1)_190<191> = 19 · C190
C190 = P70 · P120
P70 = 4021755757979865444475768755543444537089434622309462148175034259090497_<70>
P120 = 799743809062497136193595600318187981540855191647234243172296174585420358670139789796095969053096762864603044328884198077_<120>

Number: n N=3216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269 ( 190 digits) SNFS difficulty: 191 digits. Divisors found: Mon Aug 11 14:32:35 2008 prp70 factor: 4021755757979865444475768755543444537089434622309462148175034259090497 Mon Aug 11 14:32:35 2008 prp120 factor: 799743809062497136193595600318187981540855191647234243172296174585420358670139789796095969053096762864603044328884198077 Mon Aug 11 14:32:36 2008 elapsed time 05:04:45 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 112.32 hours. Scaled time: 230.37 units (timescale=2.051). Factorization parameters were as follows: name: KA_6_1_190 n: 3216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269 type: snfs skew: 0.45 deg: 5 c5: 55 c0: -1 m: 100000000000000000000000000000000000000 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 10100001) Primes: RFBsize:633578, AFBsize:632819, largePrimes:10786354 encountered Relations: rels:10836389, finalFF:1293401 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 111.99 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,50,50,2.5,2.5,100000 total time: 112.32 hours. --------- CPU info (if available) ----------

5·10¹⁹²+9 = 5(0)₁₉₁9_<193> = 7 · C192
C192 = P33 · P160
P33 = 185946012230334004175737692114361_<33>
P160 = 3841360756911088155477151257427655759049773811262830812715564417935995018641284052166995975037217217287976245074877594743197862509898796882391887621294514456167_<160>

Aug 11, 2008

By Serge Batalov / Msieve
(8·10¹⁷⁰+1)/9 = (8)₁₆₉9_<170> = 17 · 5099 · 31249 · C161
C161 = P47 · P114
P47 = 40186975583101099592439039411422087973769840987_<47>
P114 = 816567512176293048559848164336180107760931586096734124270214265473016206624606162885231652725468625601857209063441_<114>

N=32815378673782298576607235073579556585939084838902199304862538597260220415657115437029661430649398611754093077143742580179076977702588819453143262953557765056267 ( 161 digits) SNFS difficulty: 170 digits. Divisors found: r1=40186975583101099592439039411422087973769840987 r2=816567512176293048559848164336180107760931586096734124270214265473016206624606162885231652725468625601857209063441 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.384). Factorization parameters were as follows: n: 32815378673782298576607235073579556585939084838902199304862538597260220415657115437029661430649398611754093077143742580179076977702588819453143262953557765056267 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 8 c0: 1 skew: 0.66 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3000000, 7700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1009103 x 1009351 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 4.00 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000 total time: 41 hours.

(14·10¹⁷⁶-41)/9 = 1(5)₁₇₅1_<177> = 2259105661271087_<16> · 80720351480358203_<17> · 6253487942641704767889353221_<28> · C117
C117 = P46 · P72
P46 = 1019051608417910918330923759093085376287866529_<46>
P72 = 133858958754694373843982955055938024720353027482661337116522058059690599_<72>

Number: 15551_176 N=136409187220118099594259543876309212197184154651522471682143115643170104578299575205818479783053844257159831548060871 ( 117 digits) Divisors found: r1=1019051608417910918330923759093085376287866529 r2=133858958754694373843982955055938024720353027482661337116522058059690599 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: name: 15551_176 n: 136409187220118099594259543876309212197184154651522471682143115643170104578299575205818479783053844257159831548060871 skew: 49132.51 # norm 2.08e+16 c5: 6660 c4: 447743516 c3: -609459037292731 c2: -187213174297973853 c1: 85240638334503841045441 c0: 142345279227926981946484747 # alpha -5.80 Y1: 173069743693 Y0: -28991710782521877328584 # Murphy_E 4.58e-10 # M 111726850663256429068149510231893237790161040770684032330899062146596737783001767146726624576283412255547250616765441 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 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, 5550001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 624752 x 624980 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 1.9 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000 total time: 31 hours.

(55·10¹⁷⁰-1)/9 = 6(1)_170<171> = 13 · 4669558519_<10> · C161
C161 = P39 · P122
P39 = 153955579103572816331228445297936006451_<39>
P122 = 65389132198097929317384532477022329243907106763690774891859053196341390466253053476569510421739623931334520824845665359863_<122>

Number: 61111_170 N=10067021714638245985971023443671936676077995417139563755622043422676508607003185306595149781655096762809625375423750419979908286273807163855998898770530004476213 ( 161 digits) SNFS difficulty: 171 digits. Divisors found: r1=153955579103572816331228445297936006451 r2=65389132198097929317384532477022329243907106763690774891859053196341390466253053476569510421739623931334520824845665359863 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.728). Factorization parameters were as follows: n: 10067021714638245985971023443671936676077995417139563755622043422676508607003185306595149781655096762809625375423750419979908286273807163855998898770530004476213 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 55 c0: -1 skew: 0.45 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3000000, 8300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1037714 x 1037962 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 4.00 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000 total time: 46.00 hours.

(2·10¹⁷⁰-11)/9 = (2)₁₆₉1_<170> = 3 · 7 · 521 · 19415939 · C159
C159 = P69 · P90
P69 = 210932730451696181940250897337150581037995111538975826259659355381171_<69>
P90 = 495938809108537651024325469852249119314303434921038892150321898130866669026706293313313849_<90>

Number: 22221_170 N=104609727142226379588669649515486510594483116351492265894829942358267978639698604872885143129569104911079270956508881509938720071447460557768825472436548137179 ( 159 digits) SNFS difficulty: 170 digits. Divisors found: r1=210932730451696181940250897337150581037995111538975826259659355381171 r2=495938809108537651024325469852249119314303434921038892150321898130866669026706293313313849 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: n: 104609727142226379588669649515486510594483116351492265894829942358267978639698604872885143129569104911079270956508881509938720071447460557768825472436548137179 Y1: 1 Y0: -10000000000000000000000000000000000 c5: 2 c0: -11 skew: 1.41 type: snfsFactor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3000000, 7300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 973133 x 973381 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 5.00 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.6,2.6,100000 total time: 47.00 hours.

Aug 10, 2008

By Serge Batalov / GMP-ECM, Msieve
(5·10¹⁸⁵-23)/9 = (5)₁₈₄3_<185> = 79 · 76231583 · 1164328700579194207_<19> · 44029950759275554233180522078377_<32> · C126
C126 = P55 · P71
P55 = 4447157373848506897595629163234478692497222248038378089_<55>
P71 = 40463101119128220174838353390558913450445769536584152739988540703367199_<71>

Number: 55553_185 N=179945778510708836080589448871146949371246104317066383335530794551793683889740159757425063640639714889836321930337300962902711 ( 126 digits) Divisors found: r1=4447157373848506897595629163234478692497222248038378089 r2=40463101119128220174838353390558913450445769536584152739988540703367199 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.737). Factorization parameters were as follows: name: 55553_185 n: 179945778510708836080589448871146949371246104317066383335530794551793683889740159757425063640639714889836321930337300962902711 skew: 78436.96 # norm 4.47e+17 c5: 141120 c4: 210798550396 c3: -2311548511262600 c2: -1331340454492406883599 c1: -12898272503990683384020858 c0: 342428524648698367377122484465 # alpha -6.86 Y1: 28117900703519 Y0: -1049801391123476444878468 # Murphy_E 1.33e-10 # M 159496249529484995713156133406394224529425016161226558234898604187480904861637765732940295828492291561597036179686238567469420 type: gnfs rlim: 8000000 alim: 8000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [4000000, 7800001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 994198 x 994446 Poly selection time: 4.00 hours Total sieving time: 60.00 hours. Total relation processing time: 0.50 hours. Matrix solve time: 4.00 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,27,27,52,52,2.5,2.5,100000 total time: 69 hours.

(37·10¹⁷⁹-1)/9 = 4(1)_179<180> = 3 · 1097 · 13591 · 75541 · 45882114659_<11> · 7184177864869_<13> · C144
C144 = P31 · P36 · P78
P31 = 1722998328122894393200632853951_<31>
P36 = 692868277288158536240177021151239891_<36>
P78 = 309201188459405009925071126374392611866926465706986114595332287804513277197981_<78>

#ECM, then gnfs-114 # Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=3638089732 Step 1 took 70571ms Step 2 took 43411ms ********** Factor found in step 2: 1722998328122894393200632853951 Found probable prime factor of 31 digits: 1722998328122894393200632853951 Composite cofactor 214235694783319195542137193905151660133632944476526636783089769017222260753479030798583580704509521146076431860071 has 114 digits Number: 41111_179 N=214235694783319195542137193905151660133632944476526636783089769017222260753479030798583580704509521146076431860071 ( 114 digits) Divisors found: r1=692868277288158536240177021151239891 r2=309201188459405009925071126374392611866926465706986114595332287804513277197981 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.650). Factorization parameters were as follows: name: 41111_179 n: 214235694783319195542137193905151660133632944476526636783089769017222260753479030798583580704509521146076431860071 skew: 51889.37 # norm 2.73e+15 c5: 22320 c4: -30532338 c3: -142817595591249 c2: 809069780721612917 c1: 203983597776382398282865 c0: -2359341539772994802155635507 # alpha -5.57 Y1: 1833293458381 Y0: -6258057702735141305522 # Murphy_E 6.49e-10 # M 162728657052454355033301763797280575233678834117861705307163381743582580557743703942799163215917912548867785628741 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3950001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 492737 x 492977 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.90 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 16.00 hours.

Aug 9, 2008

By Serge Batalov / GMP-ECM, pol51, Msieve
(67·10¹⁸⁶+23)/9 = 7(4)₁₈₅7_<187> = 19 · 195493 · 9573671 · 15879889 · 867874901 · 21647287940191_<14> · C144
C144 = P29 · C115
P29 = 89421769771573038016990490819_<29>
C115 = [7847252666709839743467752504350917467823681102493087715558574118900695078873620596188423137154878036922729908577191_<115>]
(46·10¹⁹³-1)/9 = 5(1)_193<194> = 3³ · 17 · 2721767 · 3878672933_<10> · 18833673139_<11> · 253531733109664214357_<21> · C145
C145 = P30 · P116
P30 = 219941831910466951808401970081_<30>
P116 = 10043690953294073007230012497539826164684415783776924661750095830636397234524639892390514224691823099504978786649353_<116>
(10¹⁸⁰+71)/9 = (1)₁₇₉9_<180> = 10627 · 7936631 · 699357776561_<12> · 9775791858109_<13> · C144
C144 = P34 · P34 · P77
P34 = 1226535304270133824209889298575081_<34>
P34 = 9646827652244259591998878269506813_<34>
P77 = 16285259880623894915342400241019541187822058715291361864722782960855927435971_<77>

#ECM, then gnfs/Msieve # Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=3029909724 Step 1 took 70033ms Step 2 took 4611ms ********** Factor found in step 2: 9646827652244259591998878269506813 Found probable prime factor of 34 digits: 9646827652244259591998878269506813 Composite cofactor 19974446182799232189458363156421231710407036132090260102835765147805964274317792564316416219690880744163638651 has 110 digits Number: 11119_180 N=19974446182799232189458363156421231710407036132090260102835765147805964274317792564316416219690880744163638651 ( 110 digits) Divisors found: r1=1226535304270133824209889298575081 r2=16285259880623894915342400241019541187822058715291361864722782960855927435971 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.718). Factorization parameters were as follows: name: 11119_180 n: 19974446182799232189458363156421231710407036132090260102835765147805964274317792564316416219690880744163638651 skew: 33063.44 # norm 4.01e+15 c5: 22800 c4: 3094334570 c3: -43841089883993 c2: 652837658814255144 c1: -1748227893997554020746 c0: -332389422893059106735269160 # alpha -6.55 Y1: 199871801533 Y0: -973880254752302195949 # Murphy_E 1.01e-09 # M 3541451005798240763734180262500322055167427459870109414796898368049994906448361437203335532088229954682971890 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 3000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 400903 x 401151 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 10.1 hours.

(82·10¹⁹⁰-1)/9 = 9(1)_190<191> = 3677 · 27737 · 428987020794740431_<18> · 139985185084079890573_<21> · C146
C146 = P32 · P40 · P75
P32 = 44235066145162170816345276923453_<32>
P40 = 1525202975164716560489995462930009247117_<40>
P75 = 220494455529149193117835135530917883959908968067515100876835257557187880353_<75>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3120628407 Step 1 took 4820ms Step 2 took 3349ms ********** Factor found in step 2: 44235066145162170816345276923453 Found probable prime factor of 32 digits: 44235066145162170816345276923453 Composite cofactor 336298799580382636884047391898935435196982232927500031943041760199290494110321251616554876960770043264810606192301 has 114 digits Number: 91111_190 N=336298799580382636884047391898935435196982232927500031943041760199290494110321251616554876960770043264810606192301 ( 114 digits) Divisors found: r1=1525202975164716560489995462930009247117 r2=220494455529149193117835135530917883959908968067515100876835257557187880353 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.739). Factorization parameters were as follows: name: 91111_190 n: 336298799580382636884047391898935435196982232927500031943041760199290494110321251616554876960770043264810606192301 skew: 32758.65 # norm 6.57e+15 c5: 50880 c4: -4540729432 c3: -272586044989870 c2: 3297416222680395891 c1: 23148281183123748940654 c0: -388365960665666774880376595 # alpha -6.25 Y1: 1469988935897 Y0: -5808147070876337435082 # Murphy_E 6.48e-10 # M 229552349424334768180847434863489988993809348628602001900164640068452475773800216940633862159662059995974114158504 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3950001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 504464 x 504706 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 15.5 hours.

(16·10¹⁷⁶+11)/9 = 1(7)₁₇₅9_<177> = 4061677 · 1714060249079230343915479_<25> · C146
C146 = P30 · P39 · P78
P30 = 496354928791903362317826467779_<30>
P39 = 387669240746989213840155332047740229877_<39>
P78 = 132706539281050231573399714574367502225844538391956406948964649195004351055911_<78>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=4163435521 Step 1 took 4756ms Step 2 took 3461ms ********** Factor found in step 2: 496354928791903362317826467779 Found probable prime factor of 30 digits: 496354928791903362317826467779 Composite cofactor 51446243325245243124883276436320816900607858949251075683543295198629791680567051300669622750582627486876398819652947 has 116 digits Number: 17779_176 N=51446243325245243124883276436320816900607858949251075683543295198629791680567051300669622750582627486876398819652947 ( 116 digits) Divisors found: r1=387669240746989213840155332047740229877 r2=132706539281050231573399714574367502225844538391956406948964649195004351055911 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.725). Factorization parameters were as follows: name: 17779_176 n: 51446243325245243124883276436320816900607858949251075683543295198629791680567051300669622750582627486876398819652947 skew: 49622.16 # norm 1.82e+16 c5: 35640 c4: 4885507446 c3: 532420277871665 c2: -13094255266500546523 c1: -567963476960577454726385 c0: 9529471883982232144532871901 # alpha -6.81 Y1: 446283389723 Y0: -17056223681646455534652 # Murphy_E 4.89e-10 # M 44535924776312533812638796895673595643407947395099259882857573980766606301104420581431481670434365857616130626039851 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 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, 5150001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 602954 x 603191 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000 total time: 22.5 hours.

(11·10¹⁷³+61)/9 = 1(2)₁₇₂9_<174> = 3 · 167 · 9393214717_<10> · 3991464716169220319_<19> · C142
C142 = P36 · P39 · P69
P36 = 370213993053058810577180008052464963_<36>
P39 = 135581314979100013821605633469943622819_<39>
P69 = 129632302176827106237494463843268187181151032935432367315492954199859_<69>

#ECM, then gnfs/Msieve # Using B1=2000000, B2=11413147210, polynomial Dickson(12), sigma=774383078 Step 1 took 13440ms Step 2 took 13985ms ********** Factor found in step 2: 370213993053058810577180008052464963 Found probable prime factor of 36 digits: 370213993053058810577180008052464963 Composite cofactor 17575717992902268267555073239638187779950682665186919490503984459819118518231525646978446649297579838982521 has 107 digits Number: 12229_173 N=17575717992902268267555073239638187779950682665186919490503984459819118518231525646978446649297579838982521 ( 107 digits) Divisors found: r1=135581314979100013821605633469943622819 r2=129632302176827106237494463843268187181151032935432367315492954199859 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.719). Factorization parameters were as follows: name: 12229_173 n: 17575717992902268267555073239638187779950682665186919490503984459819118518231525646978446649297579838982521 skew: 12412.40 # norm 3.95e+14 c5: 23880 c4: -801144701 c3: -28651090013206 c2: 233589483730740904 c1: 1012470718482202241190 c0: 858705876167084202647853 # alpha -5.24 Y1: 60738216517 Y0: -236252547292224089980 # Murphy_E 1.52e-09 # M 17395019518137050286633518025364420683886479604045755806861763608633749627030105245197574996886503717697083 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: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 298764 x 299012 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 8.50 hours.

(16·10¹⁹⁵+11)/9 = 1(7)₁₉₄9_<196> = 3² · 740087 · 230743222131950995499_<21> · 162777255677946980081591009_<27> · C142
C142 = P32 · P44 · P67
P32 = 73424827831293500485868707674581_<32>
P44 = 20303773842269115123939467873342342848136567_<44>
P67 = 4766612074547657425113602299458810889222950655299003162801405514909_<67>

#ECM, then Msieve-1.36/gnfs # Using B1=2000000, B2=11413147210, polynomial Dickson(12), sigma=3622984911 Step 1 took 13465ms Step 2 took 14018ms ********** Factor found in step 2: 73424827831293500485868707674581 Found probable prime factor of 32 digits: 73424827831293500485868707674581 Composite cofactor 96780213555444848209611889152187386372688573948470598229105258151036484021479960765765687805868153067786577403 has 110 digits Number: 17779_195 N=96780213555444848209611889152187386372688573948470598229105258151036484021479960765765687805868153067786577403 ( 110 digits) Divisors found: r1=20303773842269115123939467873342342848136567 r2=4766612074547657425113602299458810889222950655299003162801405514909 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.734). Factorization parameters were as follows: name: 17779_195 n: 96780213555444848209611889152187386372688573948470598229105258151036484021479960765765687805868153067786577403 skew: 39343.05 # norm 4.40e+15 c5: 29700 c4: -2720680614 c3: -229660812986110 c2: 3755159898497477197 c1: 103107695126468227504850 c0: -1036926091866752413602699423 # alpha -6.52 Y1: 416125022923 Y0: -1266510048212425943194 # Murphy_E 9.33e-10 # M 38482898344273848443470793235030589679953893757120088997777761815782974719049996096666657288907626213621790808 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 3100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 401501 x 401746 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 12.00 hours.

Aug 8, 2008 (5th)

By Wataru Sakai / GGNFS
(67·10¹⁸⁹+23)/9 = 7(4)₁₈₈7_<190> = 11 · C189
C189 = P41 · P41 · P109
P41 = 12302291030660287515731443085247910553801_<41>
P41 = 33535040497930633918581716583415099870073_<41>
P109 = 1640418944811902951085590868766787391959788474209885459585076912235664555929048919674251980667635272532335549_<109>

Number: 74447_189 N=676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767677 ( 189 digits) SNFS difficulty: 191 digits. Divisors found: r1=12302291030660287515731443085247910553801 (pp41) r2=33535040497930633918581716583415099870073 (pp41) r3=1640418944811902951085590868766787391959788474209885459585076912235664555929048919674251980667635272532335549 (pp109) Version: GGNFS-0.77.1-20060722-nocona Total time: 1521.52 hours. Scaled time: 2985.23 units (timescale=1.962). Factorization parameters were as follows: n: 676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767676767677 m: 100000000000000000000000000000000000000 c5: 67 c0: 230 skew: 1.28 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 3700000) Primes: RFBsize:501962, AFBsize:501696, largePrimes:7422129 encountered Relations: rels:8069778, finalFF:1154154 Max relations in full relation-set: 32 Initial matrix: 1003723 x 1154154 with sparse part having weight 155775130. Pruned matrix : 901456 x 906538 with weight 137484835. Total sieving time: 1508.35 hours. Total relation processing time: 0.18 hours. Matrix solve time: 12.67 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1521.52 hours. --------- CPU info (if available) ----------

Aug 8, 2008 (4th)

By Serge Batalov / GMP-ECM
(17·10¹⁷³-53)/9 = 1(8)₁₇₂3_<174> = 3 · 33538283375647_<14> · 344480854549100429_<18> · C142
C142 = P31 · P112
P31 = 5082667344375497681419535599351_<31>
P112 = 1072229004522264389297731966081077378110519279231987469943729528228287736187297292244073007381734462645151035597_<112>

Aug 8, 2008 (3rd)

By Sinkiti Sibata / GMP-ECM, GGNFS
(5·10¹⁷²+31)/9 = (5)₁₇₁9_<172> = 3³ · 19 · 367 · 43714416961213_<14> · C153
C153 = P34 · C120
P34 = 1653798301727248021218700562722037_<34>
C120 = [408166007641904842658786198853065554777699197980622797915618429703920585969239307313834166622909064779063867322012704809_<120>]
(23·10¹⁶¹+13)/9 = 2(5)₁₆₀7_<162> = 599 · 15607 · C155
C155 = P41 · P115
P41 = 19719319340366401075426222484741876988119_<41>
P115 = 1386267857558319169729300035985642690747006048187548119187725566550353932206640751237137083635630032062262815957971_<115>

Number: 25557_161 N=27336258574478058415373902314022608060438138183527249026196300935932878408072268795481368753089962901963488575826924496077169639918601179402671135170346549 ( 155 digits) SNFS difficulty: 162 digits. Divisors found: r1=19719319340366401075426222484741876988119 (pp41) r2=1386267857558319169729300035985642690747006048187548119187725566550353932206640751237137083635630032062262815957971 (pp115) Version: GGNFS-0.77.1-20050930-nocona Total time: 80.39 hours. Scaled time: 81.11 units (timescale=1.009). Factorization parameters were as follows: name: 25557_161 n: 27336258574478058415373902314022608060438138183527249026196300935932878408072268795481368753089962901963488575826924496077169639918601179402671135170346549 m: 100000000000000000000000000000000 c5: 230 c0: 13 skew: 0.56 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4750001) Primes: RFBsize:315948, AFBsize:315406, largePrimes:5864181 encountered Relations: rels:5997416, finalFF:758540 Max relations in full relation-set: 28 Initial matrix: 631421 x 758540 with sparse part having weight 49501404. Pruned matrix : 535315 x 538536 with weight 34463912. Total sieving time: 78.17 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.97 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 80.39 hours. --------- CPU info (if available) ----------

(23·10¹⁶⁸+13)/9 = 2(5)₁₆₇7_<169> = 19 · 324341 · 532000939 · 216482375323_<12> · 425109585038514342899997341_<27> · C115
C115 = P57 · P59
P57 = 752167598816115129543711951071928819636012261007143013921_<57>
P59 = 11261063627173626179935047244183866914533647947005762221199_<59>

Number: 25557_168 N=8470207188566678333602446992785470861350447681497005619521829651930901627167738151021929008822533350752240338311279 ( 115 digits) Divisors found: r1=752167598816115129543711951071928819636012261007143013921 (pp57) r2=11261063627173626179935047244183866914533647947005762221199 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 68.17 hours. Scaled time: 32.18 units (timescale=0.472). Factorization parameters were as follows: name: 25557_168 n: 8470207188566678333602446992785470861350447681497005619521829651930901627167738151021929008822533350752240338311279 skew: 27936.96 # norm 2.58e+16 c5: 124740 c4: 8884344672 c3: -720747713544096 c2: 14872117333479277883 c1: 141746735268279867872576 c0: 287065501993506415599337280 # alpha -6.37 Y1: 2338220458913 Y0: -9254993027360638988041 # Murphy_E 4.89e-10 # M 2062918138089881151250020832567888086452521627216082223859635173810679776500422403196605929108393081923762769012169 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3150001) Primes: RFBsize:250150, AFBsize:250255, largePrimes:7732143 encountered Relations: rels:7764575, finalFF:677928 Max relations in full relation-set: 28 Initial matrix: 500489 x 677928 with sparse part having weight 63776725. Pruned matrix : 367416 x 369982 with weight 38952604. Polynomial selection time: 2.60 hours. Total sieving time: 58.12 hours. Total relation processing time: 0.68 hours. Matrix solve time: 6.40 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 68.17 hours. --------- CPU info (if available) ----------

Aug 8, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(23·10¹⁵⁵+13)/9 = 2(5)₁₅₄7_<156> = 27733 · 298395011 · C143
C143 = P64 · P80
P64 = 1536858237752765680135546884026991837272131624810560183412405141_<64>
P80 = 20093847776981569795021169228096774173833895240522025864774809260371178027213679_<80>

Number: 25557_155 N=30881395484204223525048363706070578871079743618026477135015191321940299122219049311869646894913492403479134345321756517220076016992416125123739 ( 143 digits) SNFS difficulty: 156 digits. Divisors found: r1=1536858237752765680135546884026991837272131624810560183412405141 (pp64) r2=20093847776981569795021169228096774173833895240522025864774809260371178027213679 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 36.57 hours. Scaled time: 28.09 units (timescale=0.768). Factorization parameters were as follows: name: 25557_155 n: 30881395484204223525048363706070578871079743618026477135015191321940299122219049311869646894913492403479134345321756517220076016992416125123739 m: 10000000000000000000000000000000 c5: 23 c0: 13 skew: 0.89 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2600001) Primes: RFBsize:216816, AFBsize:215956, largePrimes:5538932 encountered Relations: rels:5466993, finalFF:530339 Max relations in full relation-set: 28 Initial matrix: 432837 x 530339 with sparse part having weight 40290796. Pruned matrix : 366783 x 369011 with weight 26137725. Total sieving time: 34.89 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.44 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 36.57 hours. --------- CPU info (if available) ----------

Aug 8, 2008

By Serge Batalov / GMP-ECM, pol51, Msieve
8·10¹⁷³-9 = 7(9)₁₇₂1_<174> = 762946411 · 25759368564863328438503015111_<29> · C137
C137 = P41 · P97
P41 = 23660900021573994987453189462396384397709_<41>
P97 = 1720400179231385795985452436310629205021018478432220686288060649998543845046452046194341069059519_<97>
(22·10¹⁷⁶-13)/9 = 2(4)₁₇₅3_<177> = 3 · 47 · 11795329101796117_<17> · 9398668257774823337_<19> · C140
C140 = P37 · P103
P37 = 3402062619689460830934510402880048421_<37>
P103 = 4596659900995630289638965548262792933809828494069495661471865826071626866018519050235823880497506667447_<103>
(46·10¹⁷⁴-1)/9 = 5(1)_174<175> = 35159 · 58943237 · 1746625507597_<13> · 248922781670497343680620477691_<30> · C121
C121 = P61 · P61
P61 = 1067893823990919847935504982633835567161445887859246435573567_<61>
P61 = 5311929554816100268964112016368816505627228318873420984890013_<61>

# Nice split = P61 . P61 # Number: 51111_174 N=5672576765062949804877898588549304541456787458112679112216952341251445580533290906546230462728475408918734991394065086371 ( 121 digits) Divisors found: r1=1067893823990919847935504982633835567161445887859246435573567 r2=5311929554816100268964112016368816505627228318873420984890013 Version: Msieve 1.36 Total time: 42.5 hours. Scaled time: 0.00 units (timescale=2.731). Factorization parameters were as follows: name: 51111_174 n: 5672576765062949804877898588549304541456787458112679112216952341251445580533290906546230462728475408918734991394065086371 skew: 102014.76 # norm 3.35e+16 c5: 19140 c4: -9372030763 c3: -731870746623170 c2: 92837430175095225840 c1: 5337914859676003650431006 c0: 58938389159516231169474581275 # alpha -6.11 Y1: 216595974521 Y0: -196955329213367588586144 # Murphy_E 2.63e-10 # M 5469059722226539692538946386706739042829288291660310148684440958350372775671721201637447869734866081337144509489415174153 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 7900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 749432 x 749653 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 2.10 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000 total time: 42.5 hours.

7·10¹⁷¹-9 = 6(9)₁₇₀1_<172> = 1951 · 32173 · 42839 · 191392620057115592363_<21> · C140
C140 = P30 · P44 · P67
P30 = 121675574481606991533348359183_<30>
P44 = 37422933325867189106477419970456951426047763_<44>
P67 = 2987056712446451498387325795625445621950302093418101807281997373189_<67>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3791932801 Step 1 took 4752ms Step 2 took 4028ms ********** Factor found in step 2: 121675574481606991533348359183 Found probable prime factor of 30 digits: 121675574481606991533348359183 Composite cofactor 111784424190467595098459056149911917007502961485656473196420609707893662179624033360420585864758177758049626207 has 111 digits Number: 69991_171 N=111784424190467595098459056149911917007502961485656473196420609707893662179624033360420585864758177758049626207 ( 111 digits) Divisors found: r1=37422933325867189106477419970456951426047763 r2=2987056712446451498387325795625445621950302093418101807281997373189 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.731). Factorization parameters were as follows: name: 69991_171 n: 111784424190467595098459056149911917007502961485656473196420609707893662179624033360420585864758177758049626207 skew: 16193.65 # norm 1.24e+15 c5: 11520 c4: 3427171552 c3: -6558936108298 c2: -63252626562105279 c1: 1972660268393096151002 c0: -13877734259057275740107961 # alpha -5.84 Y1: 104053675033 Y0: -1575375388115067456790 # Murphy_E 9.89e-10 # M 37041568271832547269366268052856747176849485994032370674464185504456218729408930988297991607542039622190059088 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 3100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 416881 x 417129 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.60 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 12.00 hours.

(7·10¹⁷³+11)/9 = (7)₁₇₂9_<173> = 13 · 41 · 97 · 1187 · 4283 · 20123 · 2542985731006770567379_<22> · C136
C136 = P33 · P44 · P61
P33 = 148374117022910019762569059285381_<33>
P44 = 12742154383891239743677658168449128630353237_<44>
P61 = 3058582034683493208292511149822611160088020815388316641196351_<61>

#ECM, then gnfs/Msieve # Using B1=6000000, B2=46838457130, polynomial Dickson(12), sigma=3016012969 Step 1 took 41693ms Step 2 took 28838ms ********** Factor found in step 2: 148374117022910019762569059285381 Found probable prime factor of 33 digits: 148374117022910019762569059285381 Composite cofactor 38972924481733260870403559566764442799445187208849829731616034785643738108037675326777009491015405438187 has 104 digits Number: 77779_173 N=38972924481733260870403559566764442799445187208849829731616034785643738108037675326777009491015405438187 ( 104 digits) Divisors found: r1=12742154383891239743677658168449128630353237 r2=3058582034683493208292511149822611160088020815388316641196351 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: name: 77779_173 n: 38972924481733260870403559566764442799445187208849829731616034785643738108037675326777009491015405438187 skew: 9933.83 # norm 1.97e+14 c5: 34860 c4: 901297777 c3: -21180099304087 c2: -78583700990596635 c1: 703469453536820960998 c0: -394872940644774252554872 # alpha -5.56 Y1: 92456260217 Y0: -64518446932467432327 # Murphy_E 2.08e-09 # M 30218089768888548155266849306367562088407850169320702880711957874078613122326425973957506041161891019394 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1950001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 246221 x 246469 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.00 hours.

(22·10²⁰¹+41)/9 = 2(4)₂₀₀9_<202> = 3797 · 3739573 · 9224921 · 103799099 · 1624797562127_<13> · 1003362284833326692245409_<25> · C141
C141 = P36 · P41 · P64
P36 = 330339604811711267297717657513076361_<36>
P41 = 98925041246554540448114569641042954062293_<41>
P64 = 3374717342088131963785890619806166620582933081953540929990793009_<64>

#ECM, then gnfs/Msieve # Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3739902623 Step 1 took 19269ms Step 2 took 16557ms ********** Factor found in step 2: 330339604811711267297717657513076361 Found probable prime factor of 36 digits: 330339604811711267297717657513076361 Composite cofactor 333844052261531363551751769986354954315086292507097564052612942432609377571688862191585189443825054909637 has 105 digits Number: 24449_201 N=333844052261531363551751769986354954315086292507097564052612942432609377571688862191585189443825054909637 ( 105 digits) Divisors found: r1=98925041246554540448114569641042954062293 r2=3374717342088131963785890619806166620582933081953540929990793009 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.640). Factorization parameters were as follows: name: 24449_201 n: 333844052261531363551751769986354954315086292507097564052612942432609377571688862191585189443825054909637 skew: 13311.19 # norm 3.73e+14 c5: 12600 c4: 1440916962 c3: -12014813041711 c2: -50543851810534588 c1: 1101519325379670022132 c0: 88313820922993320076000 # alpha -6.41 Y1: 81213642653 Y0: -121514465581815833139 # Murphy_E 2.04e-09 # M 101610898617811713987352624168799700761878918485444785286881499599136886363679267953692098842357271862008 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, 2000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 305904 x 306152 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 5.00 hours.

(14·10¹⁷⁶-41)/9 = 1(5)₁₇₅1_<177> = 2259105661271087_<16> · 80720351480358203_<17> · C144
C144 = P28 · C117
P28 = 6253487942641704767889353221_<28>
C117 = [136409187220118099594259543876309212197184154651522471682143115643170104578299575205818479783053844257159831548060871_<117>]
(55·10¹⁸⁴-1)/9 = 6(1)_184<185> = 113113526204811467_<18> · 902962100831388890356903_<24> · C144
C144 = P26 · C119
P26 = 30298080812156225043145231_<26>
C119 = [19747903514851469875519184933191367723255404512820964004527952705940791479122740524381113999412093592853212505254472781_<119>]
2·10¹⁷⁹-1 = 1(9)_179<180> = 149 · 19645014971_<11> · 838639710091_<12> · 13513905648601_<14> · C142
C142 = P34 · P108
P34 = 7736164186569272400196540924681661_<34>
P108 = 779308440001156560248963164065011218680470960978737478778245389819252290693403741828408530381050760178412831_<108>
(7·10¹⁸⁴-61)/9 = (7)₁₈₃1_<184> = 17 · 19 · 12973 · 154681 · 1214431 · 8563859219_<10> · 125889320445307_<15> · C142
C142 = P33 · P110
P33 = 129094206503327431146389777618501_<33>
P110 = 70996610207680637642204608399521543078046698423883298589248821326163661299941720117124087158672108046378173023_<110>
(7·10¹⁷⁵-43)/9 = (7)₁₇₄3_<175> = 3 · 382871 · 4421693 · 17287094566914421_<17> · C146
C146 = P37 · P110
P37 = 1684109493826672636928080591712280253_<37>
P110 = 52601833872567659626851043826581619661581030085497192629117169385792946029809296953983334314216888134146219869_<110>
(88·10¹⁹²-7)/9 = 9(7)_192<193> = 3 · 23 · 7288271 · 64712835717378481819_<20> · 464852779560926987089_<21> · C144
C144 = P32 · P113
P32 = 18366535073149532144552799837541_<32>
P113 = 35191150359072223380378605356328279445463560817952105212736869086800146064986873859220813359328377257541095219333_<113>

Aug 7, 2008 (6th)

By Sinkiti Sibata / GGNFS
(23·10¹⁵⁶+13)/9 = 2(5)₁₅₅7_<157> = 17657 · 44971 · C148
C148 = P54 · P94
P54 = 781907070859593547152702692114831874677192073746363363_<54>
P94 = 4116050781119597221247693666790093823786502395231349904415402687602576392453281676423041883437_<94>

Number: 25557_156 N=3218369209774566274049173141039366428490259800717741754764314923643946321825760512611705672009243932137381206086696326505234361349905745712893318631 ( 148 digits) SNFS difficulty: 157 digits. Divisors found: r1=781907070859593547152702692114831874677192073746363363 (pp54) r2=4116050781119597221247693666790093823786502395231349904415402687602576392453281676423041883437 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 40.68 hours. Scaled time: 40.56 units (timescale=0.997). Factorization parameters were as follows: name: 25557_156 n: 3218369209774566274049173141039366428490259800717741754764314923643946321825760512611705672009243932137381206086696326505234361349905745712893318631 m: 10000000000000000000000000000000 c5: 230 c0: 13 skew: 0.56 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3200001) Primes: RFBsize:216816, AFBsize:216366, largePrimes:6056710 encountered Relations: rels:6288634, finalFF:749664 Max relations in full relation-set: 28 Initial matrix: 433249 x 749664 with sparse part having weight 72754471. Pruned matrix : 315959 x 318189 with weight 42689934. Total sieving time: 39.53 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.98 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 40.68 hours. --------- CPU info (if available) ----------

Aug 7, 2008 (5th)

By Serge Batalov / GMP-ECM
3·10¹⁷⁴-7 = 2(9)₁₇₃3_<175> = 17 · 13707838783_<11> · 37843367550258766630487_<23> · C141
C141 = P34 · P108
P34 = 2335652610416605452519508897978433_<34>
P108 = 145648266590335890831386445560195486299154390924262334577765318323875048848015754190501837612604655871004353_<108>

Aug 7, 2008 (4th)

By Serge Batalov / GMP-ECM, pol51, Msieve
7·10¹⁷³+1 = 7(0)₁₇₂1_<174> = 62473 · 1835807801_<10> · 3510906612731053298436347_<25> · C136
C136 = P33 · P34 · P70
P33 = 992595949608553727415223604789713_<33>
P34 = 1626878119033344343859043164870647_<34>
P70 = 1076543722683910823425060595208148712881299436943475382391159481127061_<70>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3918156657 Step 1 took 4876ms Step 2 took 3917ms ********** Factor found in step 2: 1626878119033344343859043164870647 Found probable prime factor of 34 digits: 1626878119033344343859043164870647 Composite cofactor 1068572938712563985973724191660647332399339731320429804051791387573023191775826284252964977667138723493 has 103 digits Number: 70001_173 N=1068572938712563985973724191660647332399339731320429804051791387573023191775826284252964977667138723493 ( 103 digits) Divisors found: r1=992595949608553727415223604789713 r2=1076543722683910823425060595208148712881299436943475382391159481127061 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.735). Factorization parameters were as follows: name: 70001_173 n: 1068572938712563985973724191660647332399339731320429804051791387573023191775826284252964977667138723493 skew: 15552.49 # norm 5.16e+13 c5: 2940 c4: 129072552 c3: 676512448813 c2: -10144897000555416 c1: -183754969317295252134 c0: 1149836521829367843055935 # alpha -4.98 Y1: 2140818119 Y0: -51533686343477739386 # Murphy_E 2.69e-09 # M 737117335365418159696785999293603511904503343401603691135378419973771783304690523634342544985619791933 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 273072 x 273320 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 4.00 hours.

Aug 7, 2008 (3rd)

By Serge Batalov / GMP-ECM, pol51, Msieve
5·10¹⁸⁸-7 = 4(9)₁₈₇3_<189> = 1013 · 5167 · 304746299542785906368113_<24> · 305640055064400234524887_<24> · C136
C136 = P31 · P52 · P54
P31 = 1125757121291323820335846959911_<31>
P52 = 7781904029500380045551718378173661286980891261937589_<52>
P54 = 117069244032165610046166201324768623892290569937890367_<54>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1218311065 Step 1 took 6562ms Step 2 took 5173ms ********** Factor found in step 2: 1125757121291323820335846959911 Found probable prime factor of 31 digits: 1125757121291323820335846959911 Composite cofactor 911021621864472880075023900946638173443125657307892780789019050463547543440983821891566758943879478305163 has 105 digits # Number: 49993_188 N=911021621864472880075023900946638173443125657307892780789019050463547543440983821891566758943879478305163 ( 105 digits) Divisors found: r1=7781904029500380045551718378173661286980891261937589 r2=117069244032165610046166201324768623892290569937890367 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.734). Factorization parameters were as follows: name: 49993_188 n: 911021621864472880075023900946638173443125657307892780789019050463547543440983821891566758943879478305163 skew: 25126.52 # norm 1.03e+14 c5: 3000 c4: -184008800 c3: -4855436126528 c2: 67822196941694137 c1: 1629442699164998766054 c0: -1737491899063811738070735 # alpha -5.76 Y1: 37648389859 Y0: -197916726587171231828 # Murphy_E 2.09e-09 # M 765710024518842781312326828781050795290290399363406343051939875665884698804336614622533704295513648569450 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, 2000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 254568 x 254816 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 5.1 hours.

(8·10¹⁷⁴-71)/9 = (8)₁₇₃1_<174> = 7 · 53 · 12101 · 1939607078801257064760060301_<28> · C141
C141 = P33 · P41 · P67
P33 = 850114323448304243508033259581857_<33>
P41 = 78519989734889223718360727461925074539577_<41>
P67 = 1529258766563958643337276955202978587578375066092351071414778732099_<67>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2137109807 Step 1 took 6074ms Step 2 took 5382ms ********** Factor found in step 2: 850114323448304243508033259581857 Found probable prime factor of 33 digits: 850114323448304243508033259581857 Composite cofactor 120077382652591388295983297045168552769870447621305691159671304298960005415149680145939340552228814255782123 has 108 digits Number: 88881_174 N=120077382652591388295983297045168552769870447621305691159671304298960005415149680145939340552228814255782123 ( 108 digits) Divisors found: r1=78519989734889223718360727461925074539577 r2=1529258766563958643337276955202978587578375066092351071414778732099 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.737). Factorization parameters were as follows: name: 88881_174 n: 120077382652591388295983297045168552769870447621305691159671304298960005415149680145939340552228814255782123 skew: 15539.87 # norm 5.21e+14 c5: 10620 c4: 2345195624 c3: -9769755854673 c2: -757793244395768101 c1: -346626392993315128485 c0: 663410832095626035419180 # alpha -5.61 Y1: 214905875723 Y0: -407997250730317195257 # Murphy_E 1.32e-09 # M 45879032032193932672059950995837741871759094187743379265860171579020205688976944665220708460720323858425038 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1600000, 2900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 335656 x 335899 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,26,26,49,49,2.6,2.6,100000 total time: 8.5 hours.

(8·10¹⁷⁷-71)/9 = (8)₁₇₆1_<177> = 2521 · 12347 · 508009 · 2364600556759857195209813_<25> · C140
C140 = P39 · P42 · P60
P39 = 652164356657968751849283918254856440873_<39>
P42 = 286392555317369108538464512499833719018257_<42>
P60 = 127281476955854375844191574769583701186317121525016829505199_<60>

#ECM, then gnfs/Msieve # Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2437338572 Step 1 took 6152ms Step 2 took 5294ms ********** Factor found in step 2: 652164356657968751849283918254856440873 Found probable prime factor of 39 digits: 652164356657968751849283918254856440873 Composite cofactor 36452467429955965780886924086595385555832450018859545691294583204020859281578886114742778261357418143 has 101 digits Number: 88881_177 N=36452467429955965780886924086595385555832450018859545691294583204020859281578886114742778261357418143 ( 101 digits) Divisors found: r1=286392555317369108538464512499833719018257 r2=127281476955854375844191574769583701186317121525016829505199 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.313). Factorization parameters were as follows: name: 88881_177 n: 36452467429955965780886924086595385555832450018859545691294583204020859281578886114742778261357418143 skew: 12368.22 # norm 1.12e+14 c5: 15120 c4: 150264694 c3: -11598943337685 c2: -17156313923209009 c1: 524819569682653239745 c0: 949953813586943591715135 # alpha -5.76 Y1: 139498271 Y0: -18898834485199271362 # Murphy_E 3.00e-09 # M 26093282328691552134264344581641201739610238309972482507984177247986435870294398991833476024748170828 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 196349 x 196597 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 5.2 hours.

(29·10¹⁸⁵+7)/9 = 3(2)₁₈₄3_<186> = 11 · 59 · 685249 · 171202729 · 734289631 · 411680179561846754678303_<24> · C137
C137 = P36 · P42 · P59
P36 = 998491758420129256214012778643327061_<36>
P42 = 191014929503817134873863510492700758731779_<42>
P59 = 73402786568103797704687105151174128789470935649299173949761_<59>

#ECM, then gnfs/Msieve # Using B1=2000000, B2=8559543730, polynomial Dickson(6), sigma=2737868976 Step 1 took 9609ms Step 2 took 7188ms ********** Factor found in step 2: 998491758420129256214012778643327061 Found probable prime factor of 36 digits: 998491758420129256214012778643327061 Composite cofactor 14021028101690082203690938282107943503058227685215117433407131744368757397621888113439598832620154819 has 101 digits Number: 32223_185 N=14021028101690082203690938282107943503058227685215117433407131744368757397621888113439598832620154819 ( 101 digits) Divisors found: r1=191014929503817134873863510492700758731779 r2=73402786568103797704687105151174128789470935649299173949761 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.738). Factorization parameters were as follows: name: 32223_185 n: 14021028101690082203690938282107943503058227685215117433407131744368757397621888113439598832620154819 skew: 5770.54 # norm 1.14e+14 c5: 48600 c4: 1184294521 c3: -12491219393246 c2: -27607875436124762 c1: 101137989921524038740 c0: 155838742740402087911160 # alpha -5.97 Y1: 29392050083 Y0: -12360148402989801913 # Murphy_E 3.32e-09 # M 10280378046388752780938709639775952386580967738344090357039117454518361154218840421540055381266736973 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 201675 x 201913 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 3.4 hours.

(2·10¹⁸³+7)/9 = (2)₁₈₂3_<183> = 17 · 361822305232022329_<18> · 152872903897698185022599_<24> · C141
C141 = P41 · P42 · P59
P41 = 56504766697054018996849756720133510657753_<41>
P42 = 129327126139044059461605326059944584322779_<42>
P59 = 32339849927200696698255186332877160637861959050438843478747_<59>

#ECM, then gnfs/Msieve # Using B1=2000000, B2=8559543730, polynomial Dickson(6), sigma=1270233868 Step 1 took 9533ms Step 2 took 7464ms ********** Factor found in step 2: 129327126139044059461605326059944584322779 Found probable prime factor of 42 digits: 129327126139044059461605326059944584322779 Composite cofactor 1827355675154214767482106570239375220163114678088840958328885624433969277661546681725988126646275491 has 100 digits Number: 22223_183 N=1827355675154214767482106570239375220163114678088840958328885624433969277661546681725988126646275491 ( 100 digits) Divisors found: r1=56504766697054018996849756720133510657753 r2=32339849927200696698255186332877160637861959050438843478747 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: name: 22223_183 n: 1827355675154214767482106570239375220163114678088840958328885624433969277661546681725988126646275491 skew: 3575.19 # norm 2.82e+13 c5: 102900 c4: -1062787720 c3: -2272158754673 c2: 10216394129434064 c1: 16004713462425507864 c0: 8663053915124755834480 # alpha -5.13 Y1: 3656686517 Y0: -7077534675564246313 # Murphy_E 3.52e-09 # M 940969014475266382158432414369008942926809560248257615283982847759757507643575631266244431986526342 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 178248 x 178496 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 3.9 hours.

4·10¹⁸²+7 = 4(0)₁₈₁7_<183> = 11 · 37 · 5902703 · 37760843933_<11> · 1674936332852367533987873251_<28> · C136
C136 = P37 · P41 · P59
P37 = 2330176577666875374606105976962270839_<37>
P41 = 47627606812357868080621344383726803782953_<41>
P59 = 23720676061967159486831460421686709294636997657176676784247_<59>

#ECM, then gnfs/Msieve # Using B1=2000000, B2=8559543730, polynomial Dickson(6), sigma=55071172 Step 1 took 10844ms Step 2 took 7141ms ********** Factor found in step 2: 2330176577666875374606105976962270839 Found probable prime factor of 37 digits: 2330176577666875374606105976962270839 Composite cofactor 1129759032802681292108641345913746599729470090263548664373455174466738092066408583230872690597541391 has 100 digits Number: 40007_182 N=1129759032802681292108641345913746599729470090263548664373455174466738092066408583230872690597541391 ( 100 digits) Divisors found: r1=47627606812357868080621344383726803782953 r2=23720676061967159486831460421686709294636997657176676784247 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.313). Factorization parameters were as follows: name: 40007_182 n: 1129759032802681292108641345913746599729470090263548664373455174466738092066408583230872690597541391 skew: 5286.20 # norm 4.88e+13 c5: 58800 c4: -906758215 c3: -6836595460751 c2: 23281841126672733 c1: 66931458270165345836 c0: -88859584402032996519968 # alpha -5.55 Y1: 15480297767 Y0: -7189928693554233609 # Murphy_E 3.55e-09 # M 947782540688762278453606516086462947233300208592534816796037426704101353095513118854962769689206778 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 180923 x 181171 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 4.3 hours.

(19·10¹⁹³-1)/9 = 2(1)_193<194> = 3 · 7 · 23 · 613 · 2833 · 416490302317_<12> · 33136289468939_<14> · 6387850378064999378621_<22> · C138
C138 = P34 · P36 · P69
P34 = 3585254944930175016436306851443401_<34>
P36 = 105774509586365818991279929828972043_<36>
P69 = 752822071840582304755740077449928254967150719264138691792961720686657_<69>

#ECM, then gnfs/Msieve # Using B1=2000000, B2=8559543730, polynomial Dickson(6), sigma=1729672148 Step 1 took 9573ms Step 2 took 7300ms ********** Factor found in step 2: 3585254944930175016436306851443401 Found probable prime factor of 34 digits: 3585254944930175016436306851443401 Composite cofactor 79629385454729450269141990896146731249794383524320855682484215788054337303524638643371992825766416130251 has 104 digits Number: 21111_193 N=79629385454729450269141990896146731249794383524320855682484215788054337303524638643371992825766416130251 ( 104 digits) Divisors found: r1=105774509586365818991279929828972043 r2=752822071840582304755740077449928254967150719264138691792961720686657 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.737). Factorization parameters were as follows: name: 21111_193 n: 79629385454729450269141990896146731249794383524320855682484215788054337303524638643371992825766416130251 skew: 11440.70 # norm 3.65e+14 c5: 49560 c4: 954446464 c3: -11673185859318 c2: 99159039807627574 c1: 85142343816020421663 c0: -3137015993006215705337408 # alpha -5.99 Y1: 67495019713 Y0: -69372410581475242965 # Murphy_E 1.98e-09 # M 71658718969377613232222706448506061496258100849620301512030428716481435024437065551927822137618899207361 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1950001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 281490 x 281734 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 4.9 hours.

Aug 7, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(23·10¹⁵⁸+13)/9 = 2(5)₁₅₇7_<159> = 179 · 857 · 5853319 · 10428049068221_<14> · 396542762668729543_<18> · C116
C116 = P38 · P79
P38 = 28481733151018451194381169971516170137_<38>
P79 = 2416516546246403734291325726758822978398144770574446242022023119207272957248691_<79>

Number: 25557_158 N=68826579425210809470015553353770765456077504207060256500230860436840512081806665744753698910449007201997412976540667 ( 116 digits) SNFS difficulty: 159 digits. Divisors found: r1=28481733151018451194381169971516170137 (pp38) r2=2416516546246403734291325726758822978398144770574446242022023119207272957248691 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 58.23 hours. Scaled time: 58.75 units (timescale=1.009). Factorization parameters were as follows: name: 25557_158 n: 68826579425210809470015553353770765456077504207060256500230860436840512081806665744753698910449007201997412976540667 m: 10000000000000000000000000000000 c5: 23000 c0: 13 skew: 0.22 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 4100001) Primes: RFBsize:283146, AFBsize:282137, largePrimes:5923659 encountered Relations: rels:6064985, finalFF:735082 Max relations in full relation-set: 28 Initial matrix: 565350 x 735082 with sparse part having weight 58078754. Pruned matrix : 446248 x 449138 with weight 41455549. Total sieving time: 56.27 hours. Total relation processing time: 0.11 hours. Matrix solve time: 1.76 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 58.23 hours. --------- CPU info (if available) ----------

(23·10¹⁴⁹+13)/9 = 2(5)₁₄₈7_<150> = 64772479953469503305191_<23> · C127
C127 = P45 · P82
P45 = 566133521560795325889304563432237670928480249_<45>
P82 = 6969087711214779205512251281730735486566945920175972509570822329865906521478641323_<82>

Number: 25557_149 N=3945434168016085953016073180664300665240976809696498373238898533666905590653549512885830295321311057834646752892450153760729427 ( 127 digits) SNFS difficulty: 151 digits. Divisors found: r1=566133521560795325889304563432237670928480249 (pp45) r2=6969087711214779205512251281730735486566945920175972509570822329865906521478641323 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 30.98 hours. Scaled time: 24.11 units (timescale=0.778). Factorization parameters were as follows: name: 25557_149 n: 3945434168016085953016073180664300665240976809696498373238898533666905590653549512885830295321311057834646752892450153760729427 m: 1000000000000000000000000000000 c5: 23 c0: 130 skew: 1.41 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176533, largePrimes:5965007 encountered Relations: rels:6142480, finalFF:692622 Max relations in full relation-set: 28 Initial matrix: 352900 x 692622 with sparse part having weight 67465135. Pruned matrix : 251696 x 253524 with weight 35454550. Total sieving time: 29.81 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.93 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 30.98 hours. --------- CPU info (if available) ----------

Aug 7, 2008

By Robert Backstrom / GGNFS, Msieve
(19·10¹⁸⁷-1)/9 = 2(1)_187<188> = 3² · 7 · C186
C186 = P48 · P59 · P80
P48 = 329022937768969847915045880276123722387918253629_<48>
P59 = 94329378756867316059517725551482756560238888705578834764291_<59>
P80 = 10796858061879096975942872469334528421951068133497198680481477155854888637343823_<80>

Number: n N=335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097 ( 186 digits) SNFS difficulty: 188 digits. Divisors found: Thu Aug 07 03:14:08 2008 prp48 factor: 329022937768969847915045880276123722387918253629 Thu Aug 07 03:14:08 2008 prp59 factor: 94329378756867316059517725551482756560238888705578834764291 Thu Aug 07 03:14:08 2008 prp80 factor: 10796858061879096975942872469334528421951068133497198680481477155854888637343823 Thu Aug 07 03:14:08 2008 elapsed time 10:51:17 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 128.02 hours. Scaled time: 167.58 units (timescale=1.309). Factorization parameters were as follows: name: KA_2_1_187 n: 335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097001763668430335097 type: snfs skew: 0.22 deg: 5 c5: 1900 c0: -1 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 10350001) Primes: RFBsize:602489, AFBsize:602920, largePrimes:11018733 encountered Relations: rels:11102338, finalFF:1302917 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 127.32 hours. Total relation processing time: 0.71 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000 total time: 128.02 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Aug 6, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(16·10¹⁸⁷-7)/9 = 1(7)_187<188> = 23 · C186
C186 = P61 · P125
P61 = 8413570336737408496831483163541109031813882697182810158716967_<61>
P125 = 91869067348061522362678558846592350747618316691107208817401001795528904555531717670493313920079035651924077479602838554208497_<125>

Number: n N=772946859903381642512077294685990338164251207729468599033816425120772946859903381642512077294685990338164251207729468599033816425120772946859903381642512077294685990338164251207729468599 ( 186 digits) SNFS difficulty: 188 digits. Divisors found: Wed Aug 06 14:01:52 2008 prp61 factor: 8413570336737408496831483163541109031813882697182810158716967 Wed Aug 06 14:01:52 2008 prp125 factor: 91869067348061522362678558846592350747618316691107208817401001795528904555531717670493313920079035651924077479602838554208497 Wed Aug 06 14:01:52 2008 elapsed time 04:55:33 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 104.83 hours. Scaled time: 215.00 units (timescale=2.051). Factorization parameters were as follows: name: KA_1_7_187 n: 772946859903381642512077294685990338164251207729468599033816425120772946859903381642512077294685990338164251207729468599033816425120772946859903381642512077294685990338164251207729468599 type: snfs skew: 0.67 deg: 5 c5: 50 c0: -7 m: 20000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 7700001) Primes: RFBsize:602489, AFBsize:603650, largePrimes:10820302 encountered Relations: rels:10822304, finalFF:1234763 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 104.47 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000 total time: 104.83 hours. --------- CPU info (if available) ----------

Aug 6, 2008 (2nd)

By Sinkiti Sibata / GGNFS, GMP-ECM
(23·10¹⁴⁴+13)/9 = 2(5)₁₄₃7_<145> = 457 · 17183 · 4178794657_<10> · 343786229129288649902671981_<27> · C102
C102 = P40 · P62
P40 = 4114335642866747764693039576228582994911_<40>
P62 = 55059328596536920501386029149429591370549677520488608295796081_<62>

Number: 25557_144 N=226532558117044239774320977876345460092466644275246353722984829588615428664800021207013083965916743791 ( 102 digits) Divisors found: r1=4114335642866747764693039576228582994911 (pp40) r2=55059328596536920501386029149429591370549677520488608295796081 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.89 hours. Scaled time: 7.61 units (timescale=0.769). Factorization parameters were as follows: name: 25557_144 n: 226532558117044239774320977876345460092466644275246353722984829588615428664800021207013083965916743791 skew: 7988.34 # norm 3.60e+14 c5: 71400 c4: -774575110 c3: 15524586669067 c2: -87782106422671083 c1: -780942194720821060323 c0: -750391296517424150053023 # alpha -6.72 Y1: 23670384947 Y0: -19965840648434549932 # Murphy_E 2.77e-09 # M 83675160995847320103734812275915734706169745801809051083627009931664545162604386774762890030652613951 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1650001) Primes: RFBsize:169511, AFBsize:169027, largePrimes:4335727 encountered Relations: rels:4400992, finalFF:476262 Max relations in full relation-set: 28 Initial matrix: 338623 x 476262 with sparse part having weight 33631253. Pruned matrix : 223554 x 225311 with weight 14342686. Total sieving time: 9.27 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.34 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 9.89 hours. --------- CPU info (if available) ----------

(23·10¹⁶⁴+13)/9 = 2(5)₁₆₃7_<165> = 173 · 2459 · 69821287 · C151
C151 = P35 · P116
P35 = 97996674633214703904333152367330721_<35>
P116 = 87797369882483358127297218980473387849967031598734392845350193043538916210511016929393258070159166263052725101579213_<116>
(23·10¹⁴⁶+13)/9 = 2(5)₁₄₅7_<147> = 15881 · 92333 · 217691 · 522492712207777_<15> · C118
C118 = P41 · P77
P41 = 30395386576514997938657854711907051494819_<41>
P77 = 50410633075491711788515806989680923366586844061809091392422973274639746710273_<77>

Number: 25557_146 N=1532250679896423743216230013144060122627556389523592324124708922006937367233119275394131176657352314823367662353575587 ( 118 digits) SNFS difficulty: 147 digits. Divisors found: r1=30395386576514997938657854711907051494819 (pp41) r2=50410633075491711788515806989680923366586844061809091392422973274639746710273 (pp77) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.21 hours. Scaled time: 18.60 units (timescale=0.768). Factorization parameters were as follows: name: 25557_146 n: 1532250679896423743216230013144060122627556389523592324124708922006937367233119275394131176657352314823367662353575587 m: 100000000000000000000000000000 c5: 230 c0: 13 skew: 0.56 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3450001) Primes: RFBsize:114155, AFBsize:113437, largePrimes:2959727 encountered Relations: rels:2981079, finalFF:268285 Max relations in full relation-set: 28 Initial matrix: 227659 x 268285 with sparse part having weight 31407304. Pruned matrix : 216257 x 217459 with weight 23868475. Total sieving time: 23.52 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.49 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 24.21 hours. --------- CPU info (if available) ----------

Aug 6, 2008

By Serge Batalov / GMP-ECM, pol51, Msieve
(23·10¹⁴²+13)/9 = 2(5)₁₄₁7_<143> = 3 · 7 · 489601939 · 1872029835859049_<16> · C118
C118 = P55 · P63
P55 = 6625098495942842425461341162814530427168462082503703937_<55>
P63 = 200409265926613305929760532852100392767304804014811227076778131_<63>

Number: 25557_142 N=1327731126263414951933406087090320904441165906586586461502979533450403825686008579656045087639294576190702887860201747 ( 118 digits) SNFS difficulty: 143 digits. Divisors found: r1=6625098495942842425461341162814530427168462082503703937 r2=200409265926613305929760532852100392767304804014811227076778131 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.316). Factorization parameters were as follows: n: 1327731126263414951933406087090320904441165906586586461502979533450403825686008579656045087639294576190702887860201747 Y1: 1 Y0: -10000000000000000000000000000 c5: 2300 c0: 13 skew: 0.36 type: snfsFactor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved rational special-q in [650000, 2550001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 232957 x 233174 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 8.8 hours.

(23·10¹⁴³+13)/9 = 2(5)₁₄₂7_<144> = 17 · 61744519 · 101301403166701741_<18> · C118
C118 = P53 · P65
P53 = 65859675644733747744876500166006837201688502506803137_<53>
P65 = 36492443555669713830870958080651283618116301983410638260983585327_<65>

Number: 25557_143 N=2403380496060161658259467596978281135018814158374470115183024859384918654165882944235953366808378500030515903230770799 ( 118 digits) SNFS difficulty: 144 digits. Divisors found: r1=65859675644733747744876500166006837201688502506803137 r2=36492443555669713830870958080651283618116301983410638260983585327 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: n: 2403380496060161658259467596978281135018814158374470115183024859384918654165882944235953366808378500030515903230770799 Y1: 1 Y0: -10000000000000000000000000000 c5: 23000 c0: 13 skew: 0.22 type: snfsFactor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved rational special-q in [650000, 2750001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 239842 x 240061 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 9.50 hours.

(23·10¹⁶¹-41)/9 = 2(5)₁₆₀1_<162> = 34239449 · 2926008353_<10> · C145
C145 = P37 · P108
P37 = 3265797762225884596670732499419492287_<37>
P108 = 781076750339822130193637764085753788800316293642129828413036710971415513493721659905790281056519495473703209_<108>

Number: 25551_161 N=2550838703386457058983851982174471636580809444581382140772962847792680968368041877385417491833370434666366908243887386972936845573239198502648983 ( 145 digits) SNFS difficulty: 162 digits. Divisors found: r1=3265797762225884596670732499419492287 r2=781076750339822130193637764085753788800316293642129828413036710971415513493721659905790281056519495473703209 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.735). Factorization parameters were as follows: n: 2550838703386457058983851982174471636580809444581382140772962847792680968368041877385417491833370434666366908243887386972936845573239198502648983 Y1: 1 Y0: -100000000000000000000000000000000 c5: 230 c0: -41 skew: 0.71 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2250000, 5850001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 847882 x 848130 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.5,2.5,100000 total time: 31.00 hours.

(89·10¹⁸³+1)/9 = 9(8)₁₈₂9_<184> = 11 · 31 · 230939 · 6528699292836557_<16> · 45042607302532677661259_<23> · C138
C138 = P30 · P48 · P61
P30 = 855468002423990818667567862479_<30>
P48 = 275723309612424883809954589539130241126436024793_<48>
P61 = 1810374387839617565875816723065884562933961409570318045244551_<61>

# by ECM - Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3594520275 Step 1 took 4753ms Step 2 took 2516ms ********** Factor found in step 2: 855468002423990818667567862479 Found probable prime factor of 30 digits: 855468002423990818667567862479 Composite cofactor 499162417852707040683001124722295789588462930665489693937531449950777948895806297476020644412226345984152943 has 108 digits # # then gnfs-108 # Number: 98889_183 N=499162417852707040683001124722295789588462930665489693937531449950777948895806297476020644412226345984152943 ( 108 digits) Divisors found: r1=275723309612424883809954589539130241126436024793 r2=1810374387839617565875816723065884562933961409570318045244551 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.731). Factorization parameters were as follows: name: 98889_183 n: 499162417852707040683001124722295789588462930665489693937531449950777948895806297476020644412226345984152943 skew: 6367.74 # norm 1.99e+14 c5: 98280 c4: -3932189772 c3: -14195911115856 c2: 168247492708970018 c1: 394303928144318474569 c0: 11250118535848240977980 # alpha -4.82 Y1: 146536788547 Y0: -347661669355558617337 # Murphy_E 1.26e-09 # M 234099490853764417282034601725069136841311422359331376023196173334057189716504940742691805709108107303510010 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1600000, 2900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 363455 x 363690 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,26,26,49,49,2.6,2.6,100000 total time: 9.00 hours.

(23·10¹⁷⁸+13)/9 = 2(5)₁₇₇7_<179> = 3 · 7 · 3089 · 30965694031_<11> · 105798861707767097_<18> · C147
C147 = P34 · P113
P34 = 9190189260448802869426553982826697_<34>
P113 = 13084642307823470911065057058071680416067637028123994347405023218259557598814694113241703703772546244245296570607_<113>
(23·10¹⁹⁷+13)/9 = 2(5)₁₉₆7_<198> = 53714423800700912989_<20> · 1014976496456936546473_<22> · C157
C157 = P34 · P124
P34 = 2580874998888541245310406445060083_<34>
P124 = 1816232526436507979241205514927769365658211492022209623151229839650671428819401905149150226796372100647466485902499391480507_<124>
(23·10¹⁹⁶+13)/9 = 2(5)₁₉₅7_<197> = 3 · 7 · 4871 · 961159 · 131819032819_<12> · 1698569523257_<13> · C163
C163 = P35 · C128
P35 = 53004070707953670657090858563081161_<35>
C128 = [21901910122835344256061530624500431703779582143146602139059801748063458973892397511598243950760773344980568496721822880202328731_<128>]
(23·10¹⁷⁰+13)/9 = 2(5)₁₆₉7_<171> = 131 · C169
C169 = P37 · P133
P37 = 1044017213865280636808570384948699591_<37>
P133 = 1868557090526470524991054799255390917927347831803388988191607353986471639712766833299263075001398831704077334177755758059926799038417_<133>
(23·10¹⁸⁶+13)/9 = 2(5)₁₈₅7_<187> = 19 · 98830288759_<11> · 13923449887211_<14> · 7114090681306556579_<19> · 88088266222011349289720093_<26> · C117
C117 = P44 · P73
P44 = 27296107544757600811971553165015267535987419_<44>
P73 = 5714215643994044486498201355639702225760874868392820299955666521320942079_<73>
(23·10¹⁵⁷+13)/9 = 2(5)₁₅₆7_<158> = 3 · C157
C157 = P60 · P98
P60 = 126011477037647694969872702702861906404388540860818011857969_<60>
P98 = 67601132204596663156815669683198816877432469167676276619995009811867251792268967419820117585110951_<98>

Number: 25557_157 N=8518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519 ( 157 digits) SNFS difficulty: 158 digits. Divisors found: r1=126011477037647694969872702702861906404388540860818011857969 r2=67601132204596663156815669683198816877432469167676276619995009811867251792268967419820117585110951 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.735). Factorization parameters were as follows: n: 8518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519 Y1: 1 Y0: -10000000000000000000000000000000 c5: 2300 c0: 13 skew: 0.36 type: snfsFactor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2000000, 3300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 759044 x 759292 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 2.10 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,52,52,2.5,2.5,100000 total time: 20 hours.

2·10¹⁷⁵-7 = 1(9)₁₇₄3_<176> = 13 · 17 · 19 · 263 · 1061 · 2381 · 13441 · 4860859 · 226155589725368669_<18> · C135
C135 = P32 · P36 · P68
P32 = 39446498300985945769793398333109_<32>
P36 = 938415519872263667316969095279317859_<36>
P68 = 13106840786581520901091016381324397299535250533490063320445846306169_<68>
(5·10¹⁸³-17)/3 = 1(6)₁₈₂1_<184> = 11³ · 12379 · 1256764309_<10> · 125559628324721_<15> · 10322887976088217_<17> · C137
C137 = P31 · P107
P31 = 4829132631888808394893101232471_<31>
P107 = 12859110351779873791714693881189925990159509826139111805995342132170989852683935783801451769837720188516543_<107>
5·10¹⁷⁹+9 = 5(0)₁₇₈9_<180> = 19 · 24379 · 343338641215057_<15> · 14527279412530452112203563_<26> · C135
C135 = P35 · P37 · P65
P35 = 12944269695080218973540346309891121_<35>
P37 = 1416113441407550287859867356704288481_<37>
P65 = 11806412269556885461858705275762974929092425790557887195787409499_<65>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3581677858 Step 1 took 3904ms Step 2 took 3752ms ********** Factor found in step 2: 12944269695080218973540346309891121 Found probable prime factor of 35 digits: 12944269695080218973540346309891121 Composite cofactor 16719219109718527335685783927057161772888685825706508837251201359866567487929188872684878878975681019 has 101 digits # # then gnfs-101 # Number: 50009_179 N=16719219109718527335685783927057161772888685825706508837251201359866567487929188872684878878975681019 ( 101 digits) Divisors found: r1=1416113441407550287859867356704288481 r2=11806412269556885461858705275762974929092425790557887195787409499 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.736). Factorization parameters were as follows: name: 50009_179 n: 16719219109718527335685783927057161772888685825706508837251201359866567487929188872684878878975681019 skew: 6884.51 # norm 1.80e+14 c5: 59040 c4: 1540165672 c3: 1429662248062 c2: -5353850835984479 c1: -182843902268221600200 c0: 165393405335782266813485 # alpha -6.13 Y1: 32528906267 Y0: -12314249336339487954 # Murphy_E 3.05e-09 # M 2698677695487388832340123883243887723436621037793473171541586333935792498476842577280377936006176964 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 220160 x 220404 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 3.10 hours.

7·10¹⁷⁵-3 = 6(9)₁₇₄7_<176> = 23 · 29 · 1945849999_<10> · 2698778453724854253232121_<25> · C140
C140 = P29 · P111
P29 = 35295282339376795682867577001_<29>
P111 = 566211848432648253496266298077169810224298129799525026373713085611725821142446735214380281508918974507036807529_<111>
(2·10¹⁹⁶+43)/9 = (2)₁₉₅7_<196> = 17 · 110603 · 230233 · 3753551 · 6394253894512031_<16> · 27649217431563171213901_<23> · C139
C139 = P32 · P107
P32 = 81138414297630889430251145739989_<32>
P107 = 95337229664362344632451111019572229885524724831347194268019251865868739229410557616425622800014970494708241_<107>
(82·10¹⁸³+71)/9 = 9(1)₁₈₂9_<184> = 11 · 23 · 163 · 197 · 3274339280356427_<16> · 3335041541237212183843_<22> · C141
C141 = P38 · P103
P38 = 41480030672124309263512074376549364243_<38>
P103 = 2475899410245908517561043105208184696388776127548286273247484238023102962064108404636745176885425655191_<103>
(4·10¹⁷⁹+23)/9 = (4)₁₇₈7_<179> = 13 · 1129 · 1068209353_<10> · 4580453449268690402279557_<25> · C141
C141 = P37 · P105
P37 = 4350096229342528260116893990630301077_<37>
P105 = 142271029265416575875338086225461356162340830827056279182201282910066824179702907590984231521837085273683_<105>
(4·10¹⁷⁷+11)/3 = 1(3)₁₇₆7_<178> = 7 · 17 · 2441851757_<10> · 344843269369_<12> · 17322469213591_<14> · C141
C141 = P31 · P111
P31 = 1310834231603013835472766122929_<31>
P111 = 585993979754822263932541066661484381757424330937782473588984197513512092586728761605870328163008363244704467429_<111>
7·10¹⁷⁶+1 = 7(0)₁₇₅1_<177> = 71 · 8573471 · 805581827 · 284095648103_<12> · 8413635332369_<13> · C135
C135 = P34 · P37 · P65
P34 = 1772201439222433182847040694601969_<34>
P37 = 5991250959750702185019813412247610703_<37>
P65 = 56246368184668911475605266297942702738852214410521358324628735307_<65>

Aug 5, 2008 (6th)

By Sinkiti Sibata / GGNFS
(23·10¹³¹+13)/9 = 2(5)₁₃₀7_<132> = 61 · 419 · 1365289 · 9462091313_<10> · C111
C111 = P50 · P62
P50 = 29649551865195893964260815165749888504612732839393_<50>
P62 = 26104273375312135035055511375576115903150531981672897300414523_<62>

Number: 25557_131 N=773980007344569427881399921940724281760206790024553518841461247679190814482147572814023669633379467193683704539 ( 111 digits) SNFS difficulty: 132 digits. Divisors found: r1=29649551865195893964260815165749888504612732839393 (pp50) r2=26104273375312135035055511375576115903150531981672897300414523 (pp62) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 6.72 hours. Scaled time: 3.17 units (timescale=0.472). Factorization parameters were as follows: name: 25557_131 n: 773980007344569427881399921940724281760206790024553518841461247679190814482147572814023669633379467193683704539 m: 100000000000000000000000000 c5: 230 c0: 13 skew: 0.56 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1100001) Primes: RFBsize:63951, AFBsize:63408, largePrimes:1478490 encountered Relations: rels:1453525, finalFF:144533 Max relations in full relation-set: 28 Initial matrix: 127426 x 144533 with sparse part having weight 11750424. Pruned matrix : 123058 x 123759 with weight 8687465. Total sieving time: 6.39 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.21 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.72 hours. --------- CPU info (if available) ----------

Aug 5, 2008 (5th)

By Sinkiti Sibata / GGNFS
(23·10¹²⁷+13)/9 = 2(5)₁₂₆7_<128> = 3² · 17 · 89 · 550127 · 15161969 · C111
C111 = P35 · P77
P35 = 13962671799159788912176788641978303_<35>
P77 = 16114498505559821766333917333370677084205143841791033427451207993209327515189_<77>

Number: 25557_127 N=225001453841182686270734845345767763482321035145545368687777587106504220899885180817018327157682834904240944267 ( 111 digits) SNFS difficulty: 128 digits. Divisors found: r1=13962671799159788912176788641978303 (pp35) r2=16114498505559821766333917333370677084205143841791033427451207993209327515189 (pp77) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.50 hours. Scaled time: 3.52 units (timescale=0.782). Factorization parameters were as follows: name: 25557_127 n: 225001453841182686270734845345767763482321035145545368687777587106504220899885180817018327157682834904240944267 m: 10000000000000000000000000 c5: 2300 c0: 13 skew: 0.36 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:64288, largePrimes:1480412 encountered Relations: rels:1464229, finalFF:157594 Max relations in full relation-set: 28 Initial matrix: 128306 x 157594 with sparse part having weight 11631696. Pruned matrix : 119660 x 120365 with weight 7163626. Total sieving time: 4.35 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.50 hours. --------- CPU info (if available) ----------

(23·10¹¹⁹+13)/9 = 2(5)₁₁₈7_<120> = 280032133 · 16397289482959744157_<20> · C92
C92 = P44 · P48
P44 = 96993982263781813971167216661363091550858813_<44>
P48 = 573800079124972352177927819974219178800933411769_<48>

Number: 25557_119 N=55655154697604169806028078164116264032438483353137260828203497020024427432838560478111570197 ( 92 digits) SNFS difficulty: 121 digits. Divisors found: r1=96993982263781813971167216661363091550858813 (pp44) r2=573800079124972352177927819974219178800933411769 (pp48) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.02 hours. Scaled time: 1.43 units (timescale=0.472). Factorization parameters were as follows: name: 25557_119 n: 55655154697604169806028078164116264032438483353137260828203497020024427432838560478111570197 m: 1000000000000000000000000 c5: 23 c0: 130 skew: 1.41 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63533, largePrimes:2228706 encountered Relations: rels:2377123, finalFF:258771 Max relations in full relation-set: 28 Initial matrix: 112696 x 258771 with sparse part having weight 25229340. Pruned matrix : 86971 x 87598 with weight 6306762. Total sieving time: 2.82 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.09 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.02 hours. --------- CPU info (if available) ----------

(23·10¹²⁸+13)/9 = 2(5)₁₂₇7_<129> = 83 · 920849 · 1030201 · 24436253 · C108
C108 = P34 · P74
P34 = 7593900515955794514613493406731977_<34>
P74 = 17490302870130540569518879363200396131415419419892069960190397320321006691_<74>

Number: 25557_128 N=132819619989707425690297221931201401167919173092980715094496396268807687443328293733002387041546989060658107 ( 108 digits) SNFS difficulty: 129 digits. Divisors found: r1=7593900515955794514613493406731977 (pp34) r2=17490302870130540569518879363200396131415419419892069960190397320321006691 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.15 hours. Scaled time: 4.00 units (timescale=0.778). Factorization parameters were as follows: name: 25557_128 n: 132819619989707425690297221931201401167919173092980715094496396268807687443328293733002387041546989060658107 m: 10000000000000000000000000 c5: 23000 c0: 13 skew: 0.22 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:63628, largePrimes:1510729 encountered Relations: rels:1505111, finalFF:164740 Max relations in full relation-set: 28 Initial matrix: 127646 x 164740 with sparse part having weight 12961919. Pruned matrix : 117224 x 117926 with weight 7554883. Total sieving time: 4.99 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.07 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.15 hours. --------- CPU info (if available) ----------

Aug 5, 2008 (4th)

By Serge Batalov / GMP-ECM, Msieve
(23·10¹¹⁵+13)/9 = 2(5)₁₁₄7_<116> = 3 · 1590765569_<10> · C106
C106 = P41 · P66
P41 = 25989819434052094099886238319121888616577_<41>
P66 = 206041464084329287564612835952629247644214995705639504013510860663_<66>

Number: 25557_115 N=5354980447479447877412865049581996904861673252948384953709366158979594131835599541140507623419977679010551 ( 106 digits) SNFS difficulty: 116 digits. Divisors found: r1=25989819434052094099886238319121888616577 r2=206041464084329287564612835952629247644214995705639504013510860663 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.204). Factorization parameters were as follows: n: 5354980447479447877412865049581996904861673252948384953709366158979594131835599541140507623419977679010551 Y1: 1 Y0: -100000000000000000000000 c5: 23 c0: 13 skew: 0.89 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 72538 x 72764 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.75 hours.

(23·10¹⁷⁶+13)/9 = 2(5)₁₇₅7_<177> = 4567 · C173
C173 = P31 · C143
P31 = 1370850223332403243997479287923_<31>
C143 = [40819182982692297903201245645427546973252118080333946991250896508476928198768851369315568750971333405347653894783379624671217671886324833679377_<143>]
(23·10¹¹⁷+13)/9 = 2(5)₁₁₆7_<118> = 67 · 1069 · C113
C113 = P37 · P77
P37 = 1088529921713480335664455585324748987_<37>
P77 = 32778754467867428138643680913471158736943850231412323569027407329166201609257_<77>

Number: 25557_117 N=35680655034773125330627808882000971134350076868541607522102614461214352310787813349839514618984900877588980572659 ( 113 digits) SNFS difficulty: 118 digits. Divisors found: r1=1088529921713480335664455585324748987 r2=32778754467867428138643680913471158736943850231412323569027407329166201609257 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.287). Factorization parameters were as follows: n: 35680655034773125330627808882000971134350076868541607522102614461214352310787813349839514618984900877588980572659 Y1: 1 Y0: -100000000000000000000000 c5: 2300 c0: 13 skew: 0.36 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 115127 x 115347 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.00 hours.

(23·10¹⁴⁰+13)/9 = 2(5)₁₃₉7_<141> = 383 · 37571 · 60029 · 323957 · 543259 · 1169334002020951974997922683_<28> · C91
C91 = P41 · P50
P41 = 97007064866694932760814312825637589612503_<41>
P50 = 14819598862760793777831985088043035801154127559863_<50>

Mon Aug 4 20:04:31 2008 Msieve v. 1.36 Mon Aug 4 20:04:31 2008 random seeds: 3716472c 5ff7c185 Mon Aug 4 20:04:31 2008 factoring 1437605788178234778599655579349905454752457659865333975172464249220608012494047083105767089 (91 digits) Mon Aug 4 20:04:32 2008 no P-1/P+1/ECM available, skipping Mon Aug 4 20:04:32 2008 commencing quadratic sieve (91-digit input) Mon Aug 4 20:04:32 2008 using multiplier of 1 Mon Aug 4 20:04:32 2008 using 64kb Opteron sieve core Mon Aug 4 20:04:32 2008 sieve interval: 18 blocks of size 65536 Mon Aug 4 20:04:32 2008 processing polynomials in batches of 6 Mon Aug 4 20:04:32 2008 using a sieve bound of 1650079 (62353 primes) Mon Aug 4 20:04:32 2008 using large prime bound of 145206952 (27 bits) Mon Aug 4 20:04:32 2008 using double large prime bound of 491560817809336 (42-49 bits) Mon Aug 4 20:04:32 2008 using trial factoring cutoff of 49 bits Mon Aug 4 20:04:32 2008 polynomial 'A' values have 12 factors Mon Aug 4 21:17:32 2008 62761 relations (17292 full + 45469 combined from 684074 partial), need 62449 Mon Aug 4 21:17:33 2008 begin with 701366 relations Mon Aug 4 21:17:33 2008 reduce to 151346 relations in 10 passes Mon Aug 4 21:17:33 2008 attempting to read 151346 relations Mon Aug 4 21:17:35 2008 recovered 151346 relations Mon Aug 4 21:17:35 2008 recovered 125083 polynomials Mon Aug 4 21:17:35 2008 attempting to build 62761 cycles Mon Aug 4 21:17:35 2008 found 62761 cycles in 6 passes Mon Aug 4 21:17:35 2008 distribution of cycle lengths: Mon Aug 4 21:17:35 2008 length 1 : 17292 Mon Aug 4 21:17:35 2008 length 2 : 12526 Mon Aug 4 21:17:35 2008 length 3 : 11168 Mon Aug 4 21:17:35 2008 length 4 : 8120 Mon Aug 4 21:17:35 2008 length 5 : 5621 Mon Aug 4 21:17:35 2008 length 6 : 3514 Mon Aug 4 21:17:35 2008 length 7 : 2067 Mon Aug 4 21:17:35 2008 length 9+: 2453 Mon Aug 4 21:17:35 2008 largest cycle: 20 relations Mon Aug 4 21:17:35 2008 matrix is 62353 x 62761 (15.8 MB) with weight 3643919 (58.06/col) Mon Aug 4 21:17:35 2008 sparse part has weight 3643919 (58.06/col) Mon Aug 4 21:17:36 2008 filtering completed in 3 passes Mon Aug 4 21:17:36 2008 matrix is 57751 x 57815 (14.6 MB) with weight 3369339 (58.28/col) Mon Aug 4 21:17:36 2008 sparse part has weight 3369339 (58.28/col) Mon Aug 4 21:17:36 2008 saving the first 48 matrix rows for later Mon Aug 4 21:17:37 2008 matrix is 57703 x 57815 (9.2 MB) with weight 2595919 (44.90/col) Mon Aug 4 21:17:37 2008 sparse part has weight 1846004 (31.93/col) Mon Aug 4 21:17:37 2008 matrix includes 64 packed rows Mon Aug 4 21:17:37 2008 using block size 23126 for processor cache size 1024 kB Mon Aug 4 21:17:37 2008 commencing Lanczos iteration Mon Aug 4 21:17:37 2008 memory use: 8.4 MB Mon Aug 4 21:18:00 2008 lanczos halted after 914 iterations (dim = 57701) Mon Aug 4 21:18:00 2008 recovered 16 nontrivial dependencies Mon Aug 4 21:18:01 2008 prp41 factor: 97007064866694932760814312825637589612503 Mon Aug 4 21:18:01 2008 prp50 factor: 14819598862760793777831985088043035801154127559863 Mon Aug 4 21:18:01 2008 elapsed time 01:13:30

(23·10¹³⁰+13)/9 = 2(5)₁₂₉7_<131> = 3 · 7 · 1911853405367337457_<19> · C111
C111 = P45 · P67
P45 = 273621240879818118935599372820806523689400881_<45>
P67 = 2326278114029065603348744181689416700387279243410338996591662514801_<67>

Number: 25557_130 N=636519104192195960835737776365832516184927682124212998818556622451324575858446919445568813294192981881484939681 ( 111 digits) SNFS difficulty: 131 digits. Divisors found: r1=273621240879818118935599372820806523689400881 r2=2326278114029065603348744181689416700387279243410338996591662514801 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.313). Factorization parameters were as follows: n: 636519104192195960835737776365832516184927682124212998818556622451324575858446919445568813294192981881484939681 Y1: 1 Y0: -100000000000000000000000000 c5: 23 c0: 13 skew: 0.89 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [400000, 800001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 103517 x 103765 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 1.75 hours.

(23·10¹³⁸+13)/9 = 2(5)₁₃₇7_<139> = 12307410569462018609_<20> · C120
C120 = P30 · P34 · P57
P30 = 507750308517183330272789653297_<30>
P34 = 3474089539882015715274674665350059_<34>
P57 = 117713814807586006583552288564604273462593769995433243151_<57>

#by ECM Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3165820906 Step 1 took 11745ms Step 2 took 11152ms ********** Factor found in step 2: 507750308517183330272789653297 Found probable prime factor of 30 digits: 507750308517183330272789653297 Composite cofactor 408948332722643277879927696871940117264041855347969617854343237250222908088195835079195909 has 90 digits # # then stopped the running snfs-138, and did QS-90 (with Msieve-1.36) # Mon Aug 4 22:13:03 2008 Msieve v. 1.36 Mon Aug 4 22:13:03 2008 random seeds: bac18a9e 3a47e97e Mon Aug 4 22:13:03 2008 factoring 408948332722643277879927696871940117264041855347969617854343237250222908088195835079195909 (90 digits) Mon Aug 4 22:13:04 2008 no P-1/P+1/ECM available, skipping Mon Aug 4 22:13:04 2008 commencing quadratic sieve (90-digit input) Mon Aug 4 22:13:04 2008 using multiplier of 11 Mon Aug 4 22:13:04 2008 using 64kb Opteron sieve core Mon Aug 4 22:13:04 2008 sieve interval: 18 blocks of size 65536 Mon Aug 4 22:13:04 2008 processing polynomials in batches of 6 Mon Aug 4 22:13:04 2008 using a sieve bound of 1578193 (60000 primes) Mon Aug 4 22:13:04 2008 using large prime bound of 126255440 (26 bits) Mon Aug 4 22:13:04 2008 using double large prime bound of 382164232656720 (42-49 bits) Mon Aug 4 22:13:04 2008 using trial factoring cutoff of 49 bits Mon Aug 4 22:13:04 2008 polynomial 'A' values have 12 factors Mon Aug 4 23:37:53 2008 60097 relations (15999 full + 44098 combined from 632948 partial), need 60096 Mon Aug 4 23:37:53 2008 begin with 648947 relations Mon Aug 4 23:37:54 2008 reduce to 146281 relations in 10 passes Mon Aug 4 23:37:54 2008 attempting to read 146281 relations Mon Aug 4 23:37:55 2008 recovered 146281 relations Mon Aug 4 23:37:55 2008 recovered 125898 polynomials Mon Aug 4 23:37:55 2008 attempting to build 60097 cycles Mon Aug 4 23:37:55 2008 found 60097 cycles in 6 passes Mon Aug 4 23:37:55 2008 distribution of cycle lengths: Mon Aug 4 23:37:55 2008 length 1 : 15999 Mon Aug 4 23:37:55 2008 length 2 : 11696 Mon Aug 4 23:37:55 2008 length 3 : 10617 Mon Aug 4 23:37:55 2008 length 4 : 7985 Mon Aug 4 23:37:55 2008 length 5 : 5632 Mon Aug 4 23:37:55 2008 length 6 : 3524 Mon Aug 4 23:37:55 2008 length 7 : 2118 Mon Aug 4 23:37:55 2008 length 9+: 2526 Mon Aug 4 23:37:55 2008 largest cycle: 23 relations Mon Aug 4 23:37:56 2008 matrix is 60000 x 60097 (15.8 MB) with weight 3662551 (60.94/col) Mon Aug 4 23:37:56 2008 sparse part has weight 3662551 (60.94/col) Mon Aug 4 23:37:56 2008 filtering completed in 3 passes Mon Aug 4 23:37:56 2008 matrix is 56117 x 56181 (14.9 MB) with weight 3461219 (61.61/col) Mon Aug 4 23:37:56 2008 sparse part has weight 3461219 (61.61/col) Mon Aug 4 23:37:57 2008 saving the first 48 matrix rows for later Mon Aug 4 23:37:57 2008 matrix is 56069 x 56181 (9.9 MB) with weight 2726773 (48.54/col) Mon Aug 4 23:37:57 2008 sparse part has weight 2024982 (36.04/col) Mon Aug 4 23:37:57 2008 matrix includes 64 packed rows Mon Aug 4 23:37:57 2008 using block size 22472 for processor cache size 1024 kB Mon Aug 4 23:37:57 2008 commencing Lanczos iteration Mon Aug 4 23:37:57 2008 memory use: 8.6 MB Mon Aug 4 23:38:21 2008 lanczos halted after 888 iterations (dim = 56069) Mon Aug 4 23:38:21 2008 recovered 19 nontrivial dependencies Mon Aug 4 23:38:22 2008 prp34 factor: 3474089539882015715274674665350059 Mon Aug 4 23:38:22 2008 prp57 factor: 117713814807586006583552288564604273462593769995433243151 elapsed time 01:25:19

(23·10¹³⁶+13)/9 = 2(5)₁₃₅7_<137> = 3³ · 7 · 260511659 · C126
C126 = P35 · P92
P35 = 35617088186151596018674980636783041_<35>
P92 = 14572630267115638925813556562718250466819225757428431015167830009407651750016178741452169627_<92>

Number: 25557_136 N=519034657328039600210553006352615630158346372995501019534847688559781900082053191302111498978559137446093228922297791128895707 ( 126 digits) SNFS difficulty: 137 digits. Divisors found: r1=35617088186151596018674980636783041 r2=14572630267115638925813556562718250466819225757428431015167830009407651750016178741452169627 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 519034657328039600210553006352615630158346372995501019534847688559781900082053191302111498978559137446093228922297791128895707 Y1: 1 Y0: -1000000000000000000000000000 c5: 230 c0: 13 skew: 0.56 type: snfsFactor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 1625001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 146625 x 146858 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 3.00 hours.

(17·10¹⁸⁹+1)/9 = 1(8)₁₈₈9_<190> = 59 · 71 · 1617391 · 12524207 · 3607698986231981_<16> · 370127884625109553441_<21> · C137
C137 = P31 · P36 · P71
P31 = 1756706333511604963524042522871_<31>
P36 = 668814360582016023721300568011912207_<36>
P71 = 14188743452434643875801927553951755349395681019380535143529908397628329_<71>
(23·10¹⁷¹+13)/9 = 2(5)₁₇₀7_<172> = 47 · 89 · 224293807 · C160
C160 = P30 · P130
P30 = 420665653593367124551131807829_<30>
P130 = 6475049984190779352600188491788559885012137408499137509465838676005670925080692961463905247359951019310758928110457579498055421593_<130>
(23·10¹³⁷+13)/9 = 2(5)₁₃₆7_<138> = 1193 · C135
C135 = P53 · P82
P53 = 24825801948309814186567834093884243731110843768686833_<53>
P82 = 8628625030368435551953354953972853797741901598228835301547475858040231276993102253_<82>

Number: 25557_137 N=214212536090155536928378504237682779174816056626618236006333240197448076743969451429635838688646735587221756542795939275402812703734749 ( 135 digits) SNFS difficulty: 138 digits. Divisors found: r1=24825801948309814186567834093884243731110843768686833 r2=8628625030368435551953354953972853797741901598228835301547475858040231276993102253 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.946). Factorization parameters were as follows: n: 214212536090155536928378504237682779174816056626618236006333240197448076743969451429635838688646735587221756542795939275402812703734749 Y1: 1 Y0: -1000000000000000000000000000 c5: 2300 c0: 13 skew: 0.36 type: snfsFactor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 2450001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 172185 x 172417 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.25 hours.

(23·10¹⁹¹+13)/9 = 2(5)₁₉₀7_<192> = 17 · 61 · 600577511 · C180
C180 = P33 · P147
P33 = 581223556439835774287202811285249_<33>
P147 = 705983086990766454288312162598464346964091589028038512031272672754584909109068532226533435641467045849482264569501155389959859487896366390090168799_<147>

Aug 5, 2008 (3rd)

Factorizations of 255...557 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 5, 2008 (2nd)

By Serge Batalov / GMP-ECM
(8·10¹⁷⁹-17)/9 = (8)₁₇₈7_<179> = 3² · 193 · 15809 · 552241 · 1674912378443233_<16> · 3436763031126603253_<19> · C133
C133 = P30 · P103
P30 = 681730178728744701011924498497_<30>
P103 = 1493689791486146713478996194570842049379770863848290072870963693810359525801102136426038074592658672243_<103>
(43·10¹⁸⁷-7)/9 = 4(7)_187<188> = 157 · 167 · 857 · 398681 · 15621247 · 153367745358551_<15> · 38912178926543071_<17> · C137
C137 = P33 · P105
P33 = 563109820432391065038572286966239_<33>
P105 = 101595641665225801482855126843463077933095944176748411552258185690480521896642701682667226673118857591243_<105>
(67·10¹⁷⁹+23)/9 = 7(4)₁₇₈7_<180> = 3 · 11 · 127721089 · 12689264677_<11> · 11278525964270232939888763_<26> · C136
C136 = P31 · P105
P31 = 1503577311371110536299145909067_<31>
P105 = 820807237203065576049616360230827773873672515282532295733748443458210584183593438540403638917367057872443_<105>
(10¹⁸¹+11)/3 = (3)₁₈₀7_<181> = 7 · 17 · 37426643 · 314567063 · 5853728102221_<13> · 954343568843543_<15> · C135
C135 = P30 · P33 · P74
P30 = 105981447101665873606353102413_<30>
P33 = 173528881158073536221773584328933_<33>
P74 = 23157877513186904238703485740025834562034755077344962107936455349631017881_<74>

Aug 5, 2008

By matsui / GGNFS
(2·10¹⁸⁵+1)/3 = (6)₁₈₄7_<185> = 21143 · C181
C181 = P81 · P100
P81 = 900453601285265582520047067012732576071069650788340131680486043607858213615331267_<81>
P100 = 3501714962000928317461759364309288753778079923142299914269367242522743703784043573496181765706887407_<100>

N=3153131848208232827255671695911964558798026139463021646250137949518359110186192435636696148449447413643601507197023443535291428211070645919059105456494663324346907565939869775654669 ( 181 digits) SNFS difficulty: 185 digits. Divisors found: r1=900453601285265582520047067012732576071069650788340131680486043607858213615331267 (pp81) r2=3501714962000928317461759364309288753778079923142299914269367242522743703784043573496181765706887407 (pp100) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 298.03 hours. Scaled time: 848.78 units (timescale=2.848). Factorization parameters were as follows: n: 3153131848208232827255671695911964558798026139463021646250137949518359110186192435636696148449447413643601507197023443535291428211070645919059105456494663324346907565939869775654669 m: 10000000000000000000000000000000000000 c5: 2 c0: 1 skew: 0.87 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10800001) Primes: RFBsize:501962, AFBsize:501936, largePrimes:6574782 encountered Relations: rels:7037035, finalFF:1136338 Max relations in full relation-set: 28 Initial matrix: 1003963 x 1136338 with sparse part having weight 79195228. Pruned matrix : 896127 x 901210 with weight 62006881. Total sieving time: 291.34 hours. Total relation processing time: 0.13 hours. Matrix solve time: 6.33 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 298.03 hours.

Aug 4, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(23·10¹⁶⁴-41)/9 = 2(5)₁₆₃1_<165> = 17 · 14783 · 6954611 · C153
C153 = P39 · P40 · P75
P39 = 127092897952617830861128387381793123491_<39>
P40 = 5984338350534202483602163442377911766177_<40>
P75 = 192248766671982198740268835298401979782919136451461142361013167032834159033_<75>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 146218049130642441234495363713913754675210966706539923532522558284754745799883843367386080454093351306607004960263989647786921657401273701595788872021931 (153 digits) Using B1=4366000, B2=8561918830, polynomial Dickson(6), sigma=1627898278 Step 1 took 52484ms Step 2 took 17660ms ********** Factor found in step 2: 5984338350534202483602163442377911766177 Found probable prime factor of 40 digits: 5984338350534202483602163442377911766177 Composite cofactor 24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203 has 113 digits Number: n N=24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203 ( 113 digits) Divisors found: Mon Aug 4 22:19:36 2008 prp39 factor: 127092897952617830861128387381793123491 Mon Aug 4 22:19:36 2008 prp75 factor: 192248766671982198740268835298401979782919136451461142361013167032834159033 Mon Aug 4 22:19:36 2008 elapsed time 00:39:09 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 21.39 hours. Scaled time: 17.93 units (timescale=0.838). Factorization parameters were as follows: name: KA_2_5_163_1 n: 24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203 skew: 22181.66 # norm 3.00e+15 c5: 92520 c4: -6744153222 c3: -45832076939516 c2: 3355354381773925699 c1: 26376496291199123709754 c0: 55897100324407256183969376 # alpha -5.88 Y1: 32923335533 Y0: -3050351678222518898863 # Murphy_E 7.42e-10 # M 24431814637208274680734783426277441947002447691196750391363360992421760360967572735589642666701638520266722683606 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1500001) Primes: RFBsize:250150, AFBsize:249815, largePrimes:6780508 encountered Relations: rels:6430342, finalFF:544879 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 21.19 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 21.39 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

(2·10¹⁹¹+61)/9 = (2)₁₉₀9_<191> = 17 · C190
C190 = P35 · C156
P35 = 10852771508056059135206234116514171_<35>
C156 = [120447531905866413108914601272250048343140105606651999784883636087529705448811959016585189877632383393661040361642471439530256902961775524681574643452982847_<156>]

Aug 4, 2008 (2nd)

By Serge Batalov / GMP-ECM, pol51, Msieve
(43·10¹⁹³-7)/9 = 4(7)_193<194> = 919 · 445461301538551_<15> · 893558958002816352193_<21> · 4284288203992414224517391893_<28> · C128
C128 = P33 · P96
P33 = 150826515975256399552220025155339_<33>
P96 = 202125386244925252749734893061275680905056146225460546218343135651883483612166284107990237484503_<96>
(10¹⁸⁴+71)/9 = (1)₁₈₃9_<184> = 3 · 29 · 199 · 1697 · 919179139 · 1299592780666421554668910151_<28> · 9343168720031962523222369884197334253_<37> · C103
C103 = P40 · P64
P40 = 1586931314118813407557567732512708559877_<40>
P64 = 2135224521200188890616493683567821754642212756737532735710790131_<64>

Number: 11119_184 N=3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887 ( 103 digits) Divisors found: r1=1586931314118813407557567732512708559877 r2=2135224521200188890616493683567821754642212756737532735710790131 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.316). Factorization parameters were as follows: name: 11119_184 n: 3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887 skew: 31960.24 # norm 9.10e+13 c5: 480 c4: -138581412 c3: -2970890933000 c2: 125334112112828449 c1: 728602337992886243758 c0: -14786800388206937397895095 # alpha -5.22 Y1: 7082309663 Y0: -93272580525981859492 # Murphy_E 2.34e-09 # M 3088295724384864144699871818544359448147530931965530510173465076385594779988601548584947108074515787463 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 273090 x 273338 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.90 hours.

(16·10¹⁹⁹-43)/9 = 1(7)₁₉₈3_<200> = 13² · 197 · 41046419 · 3191682259_<10> · 200516406221467309_<18> · C161
C161 = P40 · P56 · P66
P40 = 4390892260316240532684572528091436747139_<40>
P56 = 23900525030689996426582940228851626653088952483784974829_<56>
P66 = 193695479051958499150090176237277153417415656132662983103787245979_<66>

# first ECM # Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1416775493 Step 1 took 24354ms Step 2 took 19253ms ********** Factor found in step 2: 4390892260316240532684572528091436747139 Found probable prime factor of 40 digits: 4390892260316240532684572528091436747139 Composite cofactor 4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591 has 121 digits # # then Msieve-1.36/gnfs-121 # Number: 17773_199 N=4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591 ( 121 digits) Divisors found: r1=23900525030689996426582940228851626653088952483784974829 r2=193695479051958499150090176237277153417415656132662983103787245979 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.299). Factorization parameters were as follows: name: 17773_199 n: 4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591 skew: 43909.78 # norm 6.12e+16 c5: 13800 c4: 29054540302 c3: -1619554790749659 c2: -70244931498683416923 c1: 55355974140314250897651 c0: 1392762997799671933665557405 # alpha -5.70 Y1: 9197936842171 Y0: -201892988572876655833536 # Murphy_E 2.30e-10 # M 4486796550059614013416217299982389050995435682256387198880252966082610771759153383949597551122257473790454129900955193894 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 9500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 830699 x 830947 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000 total time: 2.5 days

(16·10²¹⁴-61)/9 = 1(7)₂₁₃1_<215> = 13 · 863 · 18661 · 369819256019_<12> · 584833068852155422531_<21> · 4516565897012282883697690057920883_<34> · C140
C140 = P53 · P88
P53 = 16814750565378686502204377710527501824320586545945603_<53>
P88 = 5169733908173540534007921788791377675334362229095173255753307146459503895142109161685829_<88>

# gnfs,140 # pol51 polynomial selection time: 2 or 3 days (while ECM was run for a week or two) # Number: 17771_214 N=86927786155318407263273710266523202940690097929584601977940218641236715258445415008714444666356629075405450626239173034367866144188409959887 ( 140 digits) Divisors found: r1=16814750565378686502204377710527501824320586545945603 r2=5169733908173540534007921788791377675334362229095173255753307146459503895142109161685829 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.735). Factorization parameters were as follows: name: 17771_214 n: 86927786155318407263273710266523202940690097929584601977940218641236715258445415008714444666356629075405450626239173034367866144188409959887 skew: 267143.89 # norm 1.97e+19 c5: 698880 c4: -1489690686532 c3: -176616113976832028 c2: 103006324549653347616719 c1: 3712851734270791622017222272 c0: -432658741100514020527612440105864 # alpha -6.29 Y1: 13968147388773457 Y0: -659105787539946137530863055 # Murphy_E 1.94e-11 # M 49579079600743972072443184556436418407617530021357634358500716158197635856463288739352084719618552259657530257163309696054721363836328031333 type: gnfs rlim: 12000000 alim: 12000000 lpbr: 27 lpba: 27 mfbr: 54 mfba: 54 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [6000000, 37700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 16715895 relations #### (beware of huge redundancy! up to 25-30% in the end) 12175171 unique relations and about 10717437 large ideals Max relations in full relation-set: 20 Initial matrix: Pruned matrix : 2296340 x 2296588 (this one, Lanczos = 31hrs) Pruned matrix : 1881104 x 1881352 (with most oversieving, Lanczos = 15hrs, -> ...Sun Aug 3 03:17:51 2008 lanczos error: only trivial dependencies found !! tried twice) Pruned matrix : 2052464 x 2052685 (alternative run with oversieving and pruning, Lanczos = 19hrs, still running for studying purposes) Total sieving time: 17 days Total relation processing time: 2.00 hours. Matrix solve time: 31.00 hours. Time per square root: 1.60 hours. * 3 deps Prototype def-par.txt line would be: gnfs,139,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12000000,12000000,27,27,54,54,2.6,2.6,100000 total time: 19 days # in retrospect, obervations - rlim/alim should be higher still # 28 bit would have been probably better in terms of redundancy of sieving

Note: C140 is the largest composite number factored by GNFS so far in our tables.

Aug 4, 2008

By Tyler Cadigan / Msieve, GGNFS
(5·10¹⁹⁸-11)/3 = 1(6)₁₉₇3_<199> = 17 · 73 · 14417612748337_<14> · 15591863092514077_<17> · 2050925281672230869_<19> · 798492457907659976598191_<24> · C124
C124 = P59 · P65
P59 = 58029655586752866277654340982152770761209260744213665747727_<59>
P65 = 62865872733823391060391929387855942847658010265702276841724324879_<65>

Number: 16663_198 N=3648084942904409231781740133863005618024633980723139006909650256997407933041732927137820715390571584310230633883275803800033 ( 124 digits) Divisors found: r1=58029655586752866277654340982152770761209260744213665747727 r2=62865872733823391060391929387855942847658010265702276841724324879 Version: Total time: 82.43 hours. Scaled time: 205.57 units (timescale=2.494). Factorization parameters were as follows: name: 16663_198 n: 3648084942904409231781740133863005618024633980723139006909650256997407933041732927137820715390571584310230633883275803800033 skew: 212888.11 # norm 1.22e+017 c5: 10740 c4: 7370305606 c3: -2467585952064540 c2: -248933528645380281069 c1: 34811739326102006425315528 c0: 1611754352640371786855945807871 # alpha -5.96 Y1: 22584968622799 Y0: -805768826493317965725508 # Murphy_E 1.69e-010 # M 2314935598007029659498302023408434039733754485237880886588822343019923669131832398564903343895745163314827211213456861106685 type: gnfs rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [2700000, 6700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 715840 x 716088 Total sieving time: 82.43 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: gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5, total time: 82.43 hours. --------- CPU info (if available) ----------

Aug 3, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(23·10¹⁶⁶-41)/9 = 2(5)₁₆₅1_<167> = 3² · C166
C166 = P72 · P94
P72 = 643496646045034314863036088356290602835699348302317420935391877062800651_<72>
P94 = 4412620003991111484688047460906035814232134281081696744784440167395589300355555901131709979989_<94>

Number: n N=2839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839 ( 166 digits) SNFS difficulty: 167 digits. Divisors found: Sun Aug 3 15:17:18 2008 prp72 factor: 643496646045034314863036088356290602835699348302317420935391877062800651 Sun Aug 3 15:17:18 2008 prp94 factor: 4412620003991111484688047460906035814232134281081696744784440167395589300355555901131709979989 Sun Aug 3 15:17:18 2008 elapsed time 01:27:42 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 88.42 hours. Scaled time: 74.18 units (timescale=0.839). Factorization parameters were as follows: name: KA_2_5_165_1 n: 2839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839 type: snfs deg: 5 c5: 230 c0: -41 skew: 0.71 m: 1000000000000000000000000000000000 rlim: 5800000 alim: 5800000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 4600001) Primes: RFBsize:399993, AFBsize:399420, largePrimes:5834136 encountered Relations: rels:5996928, finalFF:828084 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 88.21 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,167,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,48,48,2.5,2.5,100000 total time: 88.42 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

Aug 3, 2008 (2nd)

By suberi / GMP-ECM
(46·10¹⁶⁷-1)/9 = 5(1)_167<168> = 70626533 · 213771611 · 38387318408683_<14> · C138
C138 = P41 · P98
P41 = 10652708041146778174216248100844005311463_<41>
P98 = 82784609590842840754482542867744143167470530984746443938052838133532893663609041186948295276030693_<98>
(46·10¹⁷⁴-1)/9 = 5(1)_174<175> = 35159 · 58943237 · 1746625507597_<13> · C151
C151 = P30 · C121
P30 = 248922781670497343680620477691_<30>
C121 = [5672576765062949804877898588549304541456787458112679112216952341251445580533290906546230462728475408918734991394065086371_<121>]

Aug 3, 2008

By Serge Batalov / GMP-ECM, Msieve, pol51
(4·10¹⁹⁰+23)/9 = (4)₁₈₉7_<190> = 9569335559270336914133_<22> · 2204456588025119545885777787_<28> · C141
C141 = P33 · P108
P33 = 914614705542996095283314411688089_<33>
P108 = 230354111071823462818299073248460216708575614431593821351666507826249002338559777821243718681313328757074913_<108>
3·10¹⁸¹-7 = 2(9)₁₈₀3_<182> = 1936760724982998289_<19> · 68808646991249141025719_<23> · C141
C141 = P37 · P105
P37 = 1724512309637715528857993530467193207_<37>
P105 = 130537703533059377398780785440600547165396660129485394210598345885209061956376547057033455498259978403289_<105>
(16·10¹⁹⁶+11)/9 = 1(7)₁₉₅9_<197> = 10099 · 160006301767452572991787889_<27> · 888035983002108169065398017_<27> · C140
C140 = P31 · P53 · P57
P31 = 4803801617306383518347006989561_<31>
P53 = 14715761835396161314812187666323650894319358275041849_<53>
P57 = 175252263317018383575140193534337967914768654073004843553_<57>
(22·10¹⁸¹+41)/9 = 2(4)₁₈₀9_<182> = 23897095845197_<14> · 776272617318286786491553225607_<30> · C139
C139 = P34 · P36 · P69
P34 = 1769770208978296859658331890070637_<34>
P36 = 894919377524823262965410505209487619_<36>
P69 = 831993602705134771540965249704583123198561362548116161848843063999477_<69>

#ecm: # Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1689418823 Step 1 took 18414ms Step 2 took 16307ms ********** Factor found in step 2: 894919377524823262965410505209487619 Found probable prime factor of 36 digits: 894919377524823262965410505209487619 Composite cofactor 1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849 has 103 digits # #then pol51, and Msieve/gnfs-103 # Number: 24449_181 N=1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849 ( 103 digits) Divisors found: r1=1769770208978296859658331890070637 r2=831993602705134771540965249704583123198561362548116161848843063999477 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.725). Factorization parameters were as follows: name: 24449_181 n: 1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849 skew: 12109.92 # norm 1.11e+14 c5: 13800 c4: 229021120 c3: -5546394553982 c2: 39015717440707647 c1: 265001117184500868642 c0: -1409292541606116852827712 # alpha -5.56 Y1: 57257448043 Y0: -40330119583764690079 # Murphy_E 2.48e-09 # M 555219686948494539915267439001639650635907604410780913489476571794940846402885098730478554425179319560 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 231148 x 231396 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 4.50 hours.

(23·10¹⁸⁵+1)/3 = 7(6)₁₈₄7_<186> = 11 · 409 · 3919 · 9019884346492579823_<19> · 81540614634217442591_<20> · C140
C140 = P33 · P108
P33 = 334871162855198257095061908037933_<33>
P108 = 176547927865901998870134175492592669582800548196356188701886100127196219234273530578226419288591470033352403_<108>
(10¹⁸⁴+71)/9 = (1)₁₈₃9_<184> = 3 · 29 · 199 · 1697 · 919179139 · 1299592780666421554668910151_<28> · C140
C140 = P37 · C103
P37 = 9343168720031962523222369884197334253_<37>
C103 = [3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887_<103>]
6·10¹⁸⁹+1 = 6(0)₁₈₈1_<190> = 42589 · 5780291335866737_<16> · 107788304148617970061487122159_<30> · C141
C141 = P30 · P41 · P71
P30 = 174013302696433020274845304681_<30>
P41 = 18309085696764041534162136664724986762411_<41>
P71 = 70971393580825121102733841341176453634821357709829428898091709401554553_<71>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2803236752 Step 1 took 20722ms Step 2 took 16429ms ********** Factor found in step 2: 174013302696433020274845304681 Found probable prime factor of 30 digits: 174013302696433020274845304681 Composite cofactor 1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283 has 112 digits # # then Msieve/gnfs-112 # Number: 60001_189 N=1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283 ( 112 digits) Divisors found: r1=18309085696764041534162136664724986762411 r2=70971393580825121102733841341176453634821357709829428898091709401554553 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.188). Factorization parameters were as follows: name: 60001_189 n: 1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283 skew: 52578.04 # norm 2.72e+15 c5: 16440 c4: 1619746172 c3: -135511103262470 c2: -4014692173401370183 c1: 183805157963031787936530 c0: 1031049847200277256970651600 # alpha -5.96 Y1: 828435965947 Y0: -2396440646982282764377 # Murphy_E 7.97e-10 # M 1136488550539358265641494014969627028960530201153737973603644946454438107607609201185415837558953909792296923205 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3550001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 437477 x 437725 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 16.0 hours.

Aug 2, 2008 (3rd)

By Serge Batalov / GMP-ECM
(23·10¹⁹⁴+1)/3 = 7(6)₁₉₃7_<195> = 13 · 139 · 78459255911_<11> · 234102535388474561689151_<24> · C158
C158 = P32 · C126
P32 = 28755254470177769678351594744207_<32>
C126 = [803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803_<126>]
(5·10¹⁹⁸-23)/9 = (5)₁₉₇3_<198> = 79 · 1787 · 92166227 · 62964716122813547478189355909_<29> · C156
C156 = P33 · C124
P33 = 119356565544646731891786102577789_<33>
C124 = [5681466871324695058688910174023721450274408912155790860885985665340075745372042729625565314195995410292414361378012735405343_<124>]
(43·10¹⁹³-7)/9 = 4(7)_193<194> = 919 · 445461301538551_<15> · 893558958002816352193_<21> · C156
C156 = P28 · C128
P28 = 4284288203992414224517391893_<28>
C128 = [30485867797475088755064300991906426987241836546815788111296849337158228409230973644957546968604924308437984135196279273180211517_<128>]

Aug 2, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(23·10¹⁵⁴-41)/9 = 2(5)₁₅₃1_<155> = 3 · 91411 · 125717 · 99479243282099_<14> · C130
C130 = P33 · P47 · P51
P33 = 340181494077011694290357817506041_<33>
P47 = 69952169448817622365476237996541279017803003027_<47>
P51 = 313131860083472179775867830221927950460921636582587_<51>

Number: 25551_154 N=7451421490539368400745666140791923586210703006310976378376855205625717878891916365540177939686299220679430926588394932343158718809 ( 130 digits) SNFS difficulty: 156 digits. Divisors found: r1=340181494077011694290357817506041 (pp33) r2=69952169448817622365476237996541279017803003027 (pp47) r3=313131860083472179775867830221927950460921636582587 (pp51) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 57.77 hours. Scaled time: 27.27 units (timescale=0.472). Factorization parameters were as follows: name: 25551_154 n: 7451421490539368400745666140791923586210703006310976378376855205625717878891916365540177939686299220679430926588394932343158718809 m: 10000000000000000000000000000000 c5: 23 c0: -410 skew: 1.78 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:216777, largePrimes:5650674 encountered Relations: rels:5572838, finalFF:509244 Max relations in full relation-set: 28 Initial matrix: 433658 x 509244 with sparse part having weight 42472284. Pruned matrix : 400314 x 402546 with weight 29842667. Total sieving time: 51.37 hours. Total relation processing time: 0.28 hours. Matrix solve time: 5.99 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 57.77 hours. --------- CPU info (if available) ----------

(23·10¹⁷⁹-41)/9 = 2(5)₁₇₈1_<180> = 311 · 605993 · 9486007 · 14509530323_<11> · 29282668291_<11> · 62155026673_<11> · 348398479188686501_<18> · C116
C116 = P55 · P61
P55 = 4498980788192811699189568905957540794386101261910526893_<55>
P61 = 3453371022627095076155775850110344684731257028691845350307583_<61>

Number: 25551_179 N=15536649885301064370678981856573830216220820743461352404945988973856041528897128938405796842530844335414223143329619 ( 116 digits) Divisors found: r1=4498980788192811699189568905957540794386101261910526893 (pp55) r2=3453371022627095076155775850110344684731257028691845350307583 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 47.90 hours. Scaled time: 36.41 units (timescale=0.760). Factorization parameters were as follows: name: 25551_179 n: 15536649885301064370678981856573830216220820743461352404945988973856041528897128938405796842530844335414223143329619 skew: 29412.77 # norm 3.98e+15 c5: 13440 c4: 7304861420 c3: -37829521335628 c2: -4586753777585773893 c1: 32509909704735860085894 c0: 381949982671101480999382968 # alpha -5.47 Y1: 523520788439 Y0: -16315113794246774390069 # Murphy_E 4.96e-10 # M 2833285247338597467203869810197414061555862670509082923762924242923193033919568095952457100773799659651415061182693 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, 3630001) Primes: RFBsize:315948, AFBsize:316793, largePrimes:7713552 encountered Relations: rels:7941927, finalFF:902430 Max relations in full relation-set: 28 Initial matrix: 632821 x 902430 with sparse part having weight 72590726. Pruned matrix : 404955 x 408183 with weight 39044189. Total sieving time: 45.03 hours. Total relation processing time: 0.38 hours. Matrix solve time: 2.20 hours. Time per square root: 0.30 hours. 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: 47.90 hours. --------- CPU info (if available) ----------

Aug 2, 2008

By Robert Backstrom / GMP-ECM
(23·10¹⁶⁹-41)/9 = 2(5)₁₆₈1_<170> = 3 · 7 · 19 · C167
C167 = P38 · P129
P38 = 99115019415880121677092502404222247027_<38>
P129 = 646208937806761842825739606924013230081780096425955573149216008366271383509656353669041781599017902484058310271913115315734810187_<129>

Aug 1, 2008 (6th)

By Robert Backstrom / GGNFS, Msieve
(82·10¹⁸⁷-1)/9 = 9(1)_187<188> = 7 · 13 · C187
C187 = P73 · P114
P73 = 3026480116245698243462872523183807295562073549268169183952528712774717527_<73>
P114 = 330820280578284578811104218819679244326107204280567814363792995482310812487533307731049138903576211787733292120323_<114>

Number: n N=1001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221 ( 187 digits) SNFS difficulty: 188 digits. Divisors found: Fri Aug 01 22:10:03 2008 prp73 factor: 3026480116245698243462872523183807295562073549268169183952528712774717527 Fri Aug 01 22:10:03 2008 prp114 factor: 330820280578284578811104218819679244326107204280567814363792995482310812487533307731049138903576211787733292120323 Fri Aug 01 22:10:03 2008 elapsed time 06:58:34 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 125.80 hours. Scaled time: 258.01 units (timescale=2.051). Factorization parameters were as follows: name: KA_9_1_187 n: 1001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221 type: snfs skew: 0.16 deg: 5 c5: 8200 c0: -1 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 9300001) Primes: RFBsize:602489, AFBsize:603036, largePrimes:10948587 encountered Relations: rels:10948800, finalFF:1233699 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 125.35 hours. Total relation processing time: 0.45 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000 total time: 125.80 hours. --------- CPU info (if available) ----------

Aug 1, 2008 (5th)

By Serge Batalov / Msieve
(22·10²⁰⁰-31)/9 = 2(4)₁₉₉1_<201> = C201
C201 = P53 · P70 · P79
P53 = 47713862744287860379304252114030623412334743979315223_<53>
P70 = 2395392072792774623211423837351600973074529935809359597689484971362983_<70>
P79 = 2138744897728437264421864974178897354836969223259709418858727405909337720973849_<79>

# ok, dudes! If there's a thing called a nice split, # there must be a thing called an ugly split. Well, it's OK. # Doing a full 43M ECM wouldn't have helped -- # SNFS-201 is easier than GNFS-149 # # C201 = P53 . P70 . P79 (no smaller factors!) # # plain SNFS, 29-bit LPs, 1 CPU, 2Gb of memory, 23 days # Number: 24441_200 N=244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 ( 201 digits) SNFS difficulty: 201 digits. Divisors found: r1=47713862744287860379304252114030623412334743979315223 r2=2395392072792774623211423837351600973074529935809359597689484971362983 r3=2138744897728437264421864974178897354836969223259709418858727405909337720973849 Version: Msieve 1.36 Total time: 23 days Scaled time: ? units (timescale=2.738). Factorization parameters were as follows: n: 244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 name: 24441_200 #res: 1872 Y0: -10000000000000000000000000000000000000000 Y1: 1 c5: 22 c0: -31 skew: 1.07 type: snfs lpbr: 29 lpba: 29 mfbr: 57 mfba: 57 rlambda: 2.5 alambda: 2.5 rlim: 16000000 alim: 16000000 Factor base limits: 16000000/16000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 57/57 Sieved rational special-q in [8000000, 16900001) Relations: 40323955 relations 37001703 unique relations and about 33452936 large ideals Max relations in full relation-set: 20 Initial matrix: 3454542 x 3455788 (1045.7 MB) with weight 328806948 (95.15/col) sparse part has weight 236099120 (68.32/col) Pruned matrix : 3395676 x 3395924 (991.3 MB) with weight 250430313 (73.74/col) sparse part has weight 225898752 (66.52/col) Total sieving time: exactly 20 days on 1cpu. Total relation processing time: 2.00 hours. Matrix solve time: 67.50 hours. (a bit under 3 days) Time per square root: 1.11 hours. Times 5. (One Newton failed to converge.) elapsed time 05:35:31 Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,16000000,16000000,29,29,57,57,2.5,2.5,100000 total time: 23 days.

Aug 1, 2008 (4th)

By Serge Batalov / GMP-ECM
(5·10¹⁹⁸-23)/9 = (5)₁₉₇3_<198> = 79 · 1787 · 92166227 · C185
C185 = P29 · C156
P29 = 62964716122813547478189355909_<29>
C156 = [678120373017004965696027723355266137898901427492400737189655707913532453650073593892558088509716301805095025038393270924775790361244152143461824320103726627_<156>]
(8·10²⁰⁰+7)/3 = 2(6)₁₉₉9_<201> = 10181399 · 126355837 · 36206518457_<11> · 28184782664921_<14> · C162
C162 = P30 · P132
P30 = 697368348053808161867372475367_<30>
P132 = 291274374180553751645366386448159892837438428245940571965196990275330307174828818699791027080461993416672152709678515211741667562337_<132>

Aug 1, 2008 (3rd)

By Sinkiti Sibata / GGNFS, GMP-ECM
(23·10¹⁵⁶-41)/9 = 2(5)₁₅₅1_<157> = 109 · 1949 · 615887 · 79671967 · C138
C138 = P60 · P78
P60 = 568072473549876077847951681943235841700911865100362592901083_<60>
P78 = 431555511214783572160697906549520112228842379475734051031125209152188991775173_<78>

Number: 25551_156 N=245154806729863389877554529829728473478831042552701224896737949891351647068415901547655165076105391748463107205434374654549956804164212359 ( 138 digits) SNFS difficulty: 157 digits. Divisors found: r1=568072473549876077847951681943235841700911865100362592901083 (pp60) r2=431555511214783572160697906549520112228842379475734051031125209152188991775173 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 60.42 hours. Scaled time: 46.29 units (timescale=0.766). Factorization parameters were as follows: name: 25551_156 n: 245154806729863389877554529829728473478831042552701224896737949891351647068415901547655165076105391748463107205434374654549956804164212359 m: 10000000000000000000000000000000 c5: 230 c0: -41 skew: 0.71 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3600001) Primes: RFBsize:216816, AFBsize:216312, largePrimes:5870783 encountered Relations: rels:5897251, finalFF:541008 Max relations in full relation-set: 28 Initial matrix: 433195 x 541008 with sparse part having weight 56507710. Pruned matrix : 387613 x 389842 with weight 39426318. Total sieving time: 57.85 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.25 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 60.42 hours. --------- CPU info (if available) ----------

8·10²⁰⁶-1 = 7(9)_206<207> = 2844937 · 95500513 · 69076890761242761822409_<23> · C170
C170 = P47 · P124
P47 = 41135749498277498847659154913591669404231513839_<47>
P124 = 1036237806348703114978686943063529149880910428973216429428407074021642801060804673132690587919795720559017683362400311580929_<124>

Factor79991_206 Input number is 42626418822604840172098173334880818320537225294947181741042961592958391680695314798229314971658518580998472053287968986315776968375378540443044665760795283585213031976431 Run 1845 out of 2350: Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1065804300 Step 1 took 66862ms Step 2 took 21278ms ********** Factor found in step 2: 41135749498277498847659154913591669404231513839 Found probable prime factor of 47 digits: 41135749498277498847659154913591669404231513839 Probable prime cofactor 1036237806348703114978686943063529149880910428973216429428407074021642801060804673132690587919795720559017683362400311580929 has 124 digits

Aug 1, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve
(8·10¹⁸⁶+7)/3 = 2(6)₁₈₅9_<187> = 19 · C186
C186 = P64 · P122
P64 = 9461561365491417751494369249651340254835341510781699493399324537_<64>
P122 = 14833796640042493150323341558774456583384342378431564682298156460186483076837772252833910763261999400743782662308014748023_<122>

Number: n N=140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140351 ( 186 digits) SNFS difficulty: 186 digits. Divisors found: Fri Aug 01 04:57:51 2008 prp64 factor: 9461561365491417751494369249651340254835341510781699493399324537 Fri Aug 01 04:57:51 2008 prp122 factor: 14833796640042493150323341558774456583384342378431564682298156460186483076837772252833910763261999400743782662308014748023 Fri Aug 01 04:57:51 2008 elapsed time 08:20:34 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 75.43 hours. Scaled time: 98.52 units (timescale=1.306). Factorization parameters were as follows: name: KA_2_6_185_9 n: 140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140351 type: snfs skew: 0.61 deg: 5 c5: 80 c0: 7 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 6350001) Primes: RFBsize:602489, AFBsize:603715, largePrimes:10590638 encountered Relations: rels:10590627, finalFF:1235224 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 74.89 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,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000 total time: 75.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(23·10¹⁵⁸-41)/9 = 2(5)₁₅₇1_<159> = 203982161 · C151
C151 = P66 · P85
P66 = 171689635527179533850177211158120096687991880816145824295203094123_<66>
P85 = 7297079191886613832743568747111087572188527660082593836965018158316475096972563946317_<85>

Number: n N=1252832866867978497176307273044114654494495504219879088130434874427845460248632014225771221021408610116428541785845457120907526592757077201253670194991 ( 151 digits) SNFS difficulty: 159 digits. Divisors found: Fri Aug 1 10:14:11 2008 prp66 factor: 171689635527179533850177211158120096687991880816145824295203094123 Fri Aug 1 10:14:11 2008 prp85 factor: 7297079191886613832743568747111087572188527660082593836965018158316475096972563946317 Fri Aug 1 10:14:11 2008 elapsed time 00:58:14 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 35.26 hours. Scaled time: 29.51 units (timescale=0.837). Factorization parameters were as follows: name: KA_2_5_157_1 n: 1252832866867978497176307273044114654494495504219879088130434874427845460248632014225771221021408610116428541785845457120907526592757077201253670194991 type: snfs deg: 5 c5: 23000 c0: -41 skew: 0.28 m: 10000000000000000000000000000000 rlim: 5500000 alim: 5500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2100001) Primes: RFBsize:380800, AFBsize:381098, largePrimes:5429667 encountered Relations: rels:5543974, finalFF:780100 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 35.09 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.5,2.5,100000 total time: 35.26 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

Aug 1, 2008

By Tyler Cadigan / Msieve, GGNFS
(10¹⁹⁸+53)/9 = (1)₁₉₇7_<198> = 3 · 11618966467_<11> · 272033009875993867_<18> · 30874217309083734095351287845727_<32> · C138
C138 = P49 · P89
P49 = 9453997590293827952520076434647256044623334210059_<49>
P89 = 40145390515984245549625564941684431539990421548183675478964571944721581807941671195434707_<89>

Number: 11117_198 N=379534425199519751802558862062259553534112280564965144585212678040651849592463853984445240166695146589693057988042923980473715294957117713 ( 138 digits) Divisors found: r1=9453997590293827952520076434647256044623334210059 r2=40145390515984245549625564941684431539990421548183675478964571944721581807941671195434707 Version: Total time: 621.18 hours. Scaled time: 1600.17 units (timescale=2.576). Factorization parameters were as follows: name: 11117_198 n: 379534425199519751802558862062259553534112280564965144585212678040651849592463853984445240166695146589693057988042923980473715294957117713 skew: 113421.69 # norm 6.07e+018 c5: 4597020 c4: 112946341846 c3: -142581740199761914 c2: 9306396615802705483023 c1: 924174800200196017988522392 c0: -13806708124835709986443831217980 # alpha -5.94 Y1: 6237782020208299 Y0: -152529859043766825334703079 # Murphy_E 2.62e-011 # M 105204987891615758404166717436433383277087204802518042147842137078868339598661102665100403548164843043068382038692909504027948782527384386 type: gnfs rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [2700000, 13700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1309332 x 1309580 Total sieving time: 621.18 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: gnfs,137,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5, total time: 621.18 hours. --------- CPU info (if available) ----------