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STUDIO KAMADA

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News and updates, May 2008

May 31, 2008 (2nd)

By Wataru Sakai / GGNFS
(88·10¹⁸⁶-7)/9 = 9(7)_186<187> = 3 · 1409 · C184
C184 = P45 · P139
P45 = 558420727813527386131594937710331258974213667_<45>
P139 = 4142346123281926087234853809987716740634386737763126789276317393359104216309692071188150104114601670997665342345732871848423998398042842953_<139>

Number: 97777_186 N=2313171937018636805719843335173356465052703519701390531766685066897983860368530347238651000184002313171937018636805719843335173356465052703519701390531766685066897983860368530347238651 ( 184 digits) SNFS difficulty: 188 digits. Divisors found: r1=558420727813527386131594937710331258974213667 (pp45) r2=4142346123281926087234853809987716740634386737763126789276317393359104216309692071188150104114601670997665342345732871848423998398042842953 (pp139) Version: GGNFS-0.77.1-20060722-nocona Total time: 1038.03 hours. Scaled time: 2089.55 units (timescale=2.013). Factorization parameters were as follows: n: 2313171937018636805719843335173356465052703519701390531766685066897983860368530347238651000184002313171937018636805719843335173356465052703519701390531766685066897983860368530347238651 m: 20000000000000000000000000000000000000 c5: 55 c0: -14 skew: 0.76 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 18500001) Primes: RFBsize:501962, AFBsize:502197, largePrimes:7109241 encountered Relations: rels:7656762, finalFF:1148858 Max relations in full relation-set: 32 Initial matrix: 1004225 x 1148858 with sparse part having weight 131543991. Pruned matrix : 898696 x 903781 with weight 111532419. Total sieving time: 1027.27 hours. Total relation processing time: 0.15 hours. Matrix solve time: 10.30 hours. Time per square root: 0.30 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: 1038.03 hours. --------- CPU info (if available) ----------

May 31, 2008

By Robert Backstrom / GGNFS, Msieve
(31·10¹⁶⁸-13)/9 = 3(4)₁₆₇3_<169> = 36649913 · C161
C161 = P65 · P97
P65 = 19121035045106931156034589094324433473093786433375865827509070283_<65>
P97 = 4915128075224843895655346118121567445584594295484859874268072710814547659240553180841233721217017_<97>

Number: n N=93982336177563216710622053712499793504133132442754896701786016366381127410710209447003174180643878866627717354866420677299955512703248284503279569707148948605811 ( 161 digits) SNFS difficulty: 169 digits. Divisors found: Sat May 31 11:47:02 2008 prp65 factor: 19121035045106931156034589094324433473093786433375865827509070283 Sat May 31 11:47:02 2008 prp97 factor: 4915128075224843895655346118121567445584594295484859874268072710814547659240553180841233721217017 Sat May 31 11:47:02 2008 elapsed time 01:26:56 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 85.06 hours. Scaled time: 71.28 units (timescale=0.838). Factorization parameters were as follows: name: KA_3_4_167_3 n: 93982336177563216710622053712499793504133132442754896701786016366381127410710209447003174180643878866627717354866420677299955512703248284503279569707148948605811 type: snfs deg: 5 c5: 31000 c0: -13 skew: 0.21 m: 1000000000000000000000000000000000 rlim: 3500000 alim: 3500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 5000399) Primes: RFBsize:250150, AFBsize:249832, largePrimes:5816711 encountered Relations: rels:5725824, finalFF:539421 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 84.83 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,48,48,2.5,2.5,100000 total time: 85.06 hours. --------- CPU info (if available) ----------

May 30, 2008 (4th)

By matsui / GGNFS
5·10¹⁷⁶-1 = 4(9)_176<177> = 48409 · 48550259 · C165
C165 = P49 · P117
P49 = 1685407140856189648612097538079896782968048556689_<49>
P117 = 126225619910469676004414039354831078351797442441561563713439568704176968850333129983096588258532811794520832130928061_<117>

N=212741561156104821848315308047573885814443504412799746904803957756367500051206620397368345024193419561880193183093279952257728632311539958871940330087867729139350029 ( 165 digits) SNFS difficulty: 176 digits. Divisors found: r1=1685407140856189648612097538079896782968048556689 (pp49) r2=126225619910469676004414039354831078351797442441561563713439568704176968850333129983096588258532811794520832130928061 (pp117) Version: GGNFS-0.77.1-20060513-prescott Total time: 224.48 hours. Scaled time: 191.48 units (timescale=0.853). Factorization parameters were as follows: n: 212741561156104821848315308047573885814443504412799746904803957756367500051206620397368345024193419561880193183093279952257728632311539958871940330087867729139350029 m: 100000000000000000000000000000000000 c5: 50 c0: -1 skew: 0.46 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 11500001) Primes: RFBsize:501962, AFBsize:501581, largePrimes:6465156 encountered Relations: rels:6924137, finalFF:1134653 Max relations in full relation-set: 28 Initial matrix: 1003608 x 1134653 with sparse part having weight 71856558. Pruned matrix : 891266 x 896348 with weight 54923948. Total sieving time: 201.76 hours. Total relation processing time: 0.44 hours. Matrix solve time: 21.99 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 224.48 hours.

6·10¹⁶⁹+1 = 6(0)₁₆₈1_<170> = 1163 · 50207 · C163
C163 = P45 · P118
P45 = 409692145250436913282056636020822590790365187_<45>
P118 = 2508127593417771961783639597835041387496768657625863183136324428934170806705227815812321776714203987196208985026667903_<118>

N=1027560174309142608757097293901442353677272223690396393496701814419515587240107125888332192941343217411815342435883798768712320331745747155358072952011347141492861 ( 163 digits) SNFS difficulty: 170 digits. Divisors found: r1=409692145250436913282056636020822590790365187 (pp45) r2=2508127593417771961783639597835041387496768657625863183136324428934170806705227815812321776714203987196208985026667903 (pp118) Version: GGNFS-0.77.1-20060513-prescott Total time: 153.02 hours. Scaled time: 177.66 units (timescale=1.161). Factorization parameters were as follows: n: 1027560174309142608757097293901442353677272223690396393496701814419515587240107125888332192941343217411815342435883798768712320331745747155358072952011347141492861 m: 10000000000000000000000000000000000 c5: 3 c0: 5 skew: 1.11 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 7100001) Primes: RFBsize:412849, AFBsize:412211, largePrimes:6020639 encountered Relations: rels:6285070, finalFF:929842 Max relations in full relation-set: 28 Initial matrix: 825125 x 929842 with sparse part having weight 54766796. Pruned matrix : 737962 x 742151 with weight 40674202. Total sieving time: 140.47 hours. Total relation processing time: 0.20 hours. Matrix solve time: 12.05 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 153.02 hours.

May 30, 2008 (3rd)

By Tyler Cadigan / GGNFS, Msieve
(5·10¹⁹⁰+13)/9 = (5)₁₈₉7_<190> = 811 · 907 · 10837804441_<11> · 2785656325929626661973_<22> · 141420727163771568086127494461_<30> · C124
C124 = P59 · P65
P59 = 33459437467275085321414055603258376333697163788226609596037_<59>
P65 = 52868721344425856941945570027921282052374118429357469698868995441_<65>

Number: 55557_190 N=1768957675798608538570697178394242001598658689261756493802670073290117602123758045787374992447868719160331461600669004667317 ( 124 digits) Divisors found: r1=33459437467275085321414055603258376333697163788226609596037 r2=52868721344425856941945570027921282052374118429357469698868995441 Version: Total time: 60.52 hours. Scaled time: 155.16 units (timescale=2.564). Factorization parameters were as follows: name: 55557_190 n: 1768957675798608538570697178394242001598658689261756493802670073290117602123758045787374992447868719160331461600669004667317 skew: 59353.52 # norm 1.07e+017 c5: 491040 c4: 50867111448 c3: -4995511819788260 c2: -163948178132283273278 c1: 9083007404135601852054231 c0: -19006103892754768805129373210 # alpha -6.34 Y1: 76272196706117 Y0: -324577192860632699954327 # Murphy_E 1.84e-010 # M 995658799633167449149780343758990313985724368125209995426425707408614893747362482071898928066623208284832232387742176621524 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5440001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 717956 x 718204 Total sieving time: 60.52 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 60.52 hours. --------- CPU info (if available) ----------

May 30, 2008 (2nd)

By Jo Yeong Uk / GGNFS
(19·10¹⁶⁸+17)/9 = 2(1)₁₆₇3_<169> = C169
C169 = P72 · P97
P72 = 227487177154295025504685455361271692724662216695338616060397175372579537_<72>
P97 = 9280132346445324494177855519611117213830193530355304266419412531346231676756164736608771764227449_<97>

Number: 21113_168 N=2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 ( 169 digits) SNFS difficulty: 171 digits. Divisors found: r1=227487177154295025504685455361271692724662216695338616060397175372579537 (pp72) r2=9280132346445324494177855519611117213830193530355304266419412531346231676756164736608771764227449 (pp97) Version: GGNFS-0.77.1-20050930-nocona Total time: 99.00 hours. Scaled time: 233.44 units (timescale=2.358). Factorization parameters were as follows: n: 2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 m: 10000000000000000000000000000000000 c5: 19 c0: 1700 skew: 2.46 type: snfs Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 49/49 Sieved algebraic special-q in [4000000, 9200001) Primes: RFBsize:539777, AFBsize:539370, largePrimes:9999580 encountered Relations: rels:9956522, finalFF:1241056 Max relations in full relation-set: 28 Initial matrix: 1079214 x 1241056 with sparse part having weight 74507988. Pruned matrix : 936892 x 942352 with weight 53685074. Total sieving time: 92.81 hours. Total relation processing time: 0.18 hours. Matrix solve time: 5.91 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,49,49,2.6,2.6,100000 total time: 99.00 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: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806) Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394) Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 30, 2008

By Sinkiti Sibata / GGNFS
(19·10¹⁶¹+17)/9 = 2(1)₁₆₀3_<162> = 3 · 7 · 36833 · 1060859273_<10> · 14564381097589_<14> · 4408021099498508159119_<22> · C112
C112 = P33 · P79
P33 = 706991398277505775759368626955089_<33>
P79 = 5668225218241225832747085084677390231483282542289051212302192258793615146195383_<79>

Number: 21113_161 N=4007386472796184589094423777355566076795903284996272377907741299098845716620028610166554514234937212618360154087 ( 112 digits) SNFS difficulty: 162 digits. Divisors found: r1=706991398277505775759368626955089 (pp33) r2=5668225218241225832747085084677390231483282542289051212302192258793615146195383 (pp79) Version: GGNFS-0.77.1-20060513-k8 Total time: 83.43 hours. Scaled time: 167.11 units (timescale=2.003). Factorization parameters were as follows: name: 21113_161 n: 4007386472796184589094423777355566076795903284996272377907741299098845716620028610166554514234937212618360154087 m: 100000000000000000000000000000000 c5: 190 c0: 17 skew: 0.62 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, 4950001) Primes: RFBsize:315948, AFBsize:315511, largePrimes:5815229 encountered Relations: rels:5896613, finalFF:711219 Max relations in full relation-set: 28 Initial matrix: 631526 x 711219 with sparse part having weight 50842856. Pruned matrix : 575041 x 578262 with weight 38160172. Total sieving time: 78.98 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.97 hours. Time per square root: 0.24 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: 83.43 hours. --------- CPU info (if available) ----------

May 29, 2008

By Robert Backstrom / GGNFS, Msieve
8·10¹⁷¹-7 = 7(9)₁₇₀3_<172> = 17 · 1151 · C168
C168 = P77 · P92
P77 = 24647086395999836771837331424225869225743402319273339674995455701866527506633_<77>
P92 = 16588234057078252813498282677454365397090590853140579319578237953322061447834122710199965663_<92>

Number: n N=408851637961874584760055194971124853068942607451321101855164307252005928348750447181479020800327081310369499667808044155976899882455154085961056881484131445801604742679 ( 168 digits) SNFS difficulty: 172 digits. Divisors found: Thu May 29 01:44:12 2008 prp77 factor: 24647086395999836771837331424225869225743402319273339674995455701866527506633 Thu May 29 01:44:12 2008 prp92 factor: 16588234057078252813498282677454365397090590853140579319578237953322061447834122710199965663 Thu May 29 01:44:12 2008 elapsed time 02:24:36 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 112.41 hours. Scaled time: 162.21 units (timescale=1.443). Factorization parameters were as follows: name: KA_7_9_170_3 n: 408851637961874584760055194971124853068942607451321101855164307252005928348750447181479020800327081310369499667808044155976899882455154085961056881484131445801604742679 skew: 1.23 deg: 5 c5: 5 c0: -14 m: 20000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5600521) Primes: RFBsize:250150, AFBsize:251001, largePrimes:7971414 encountered Relations: rels:7366966, finalFF:511955 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 112.09 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 112.41 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(19·10¹⁵⁹+17)/9 = 2(1)₁₅₈3_<160> = 12497 · C156
C156 = P60 · P96
P60 = 582369490753755763634044705532923835566861195555346804624251_<60>
P96 = 290072599328501239090268348704294814519427609152777687487796440289248834506309310228248097076379_<96>

Number: n N=168929431952557502689534377139402345451797320245747868377299440754670009691214780436193575346972162207818765392583108835009291118757390662647924390742667129 ( 156 digits) SNFS difficulty: 161 digits. Divisors found: Thu May 29 15:37:16 2008 prp60 factor: 582369490753755763634044705532923835566861195555346804624251 Thu May 29 15:37:16 2008 prp96 factor: 290072599328501239090268348704294814519427609152777687487796440289248834506309310228248097076379 Thu May 29 15:37:16 2008 elapsed time 01:22:49 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 53.77 hours. Scaled time: 94.26 units (timescale=1.753). Factorization parameters were as follows: name: KA_2_1_158_3 n: 168929431952557502689534377139402345451797320245747868377299440754670009691214780436193575346972162207818765392583108835009291118757390662647924390742667129 type: snfs skew: 1.55 deg: 5 c5: 19 c0: 170 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2700281) Primes: RFBsize:216816, AFBsize:217381, largePrimes:7215613 encountered Relations: rels:6592180, finalFF:463705 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 53.51 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 53.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 28, 2008 (4th)

By Jo Yeong Uk / GGNFS
8·10¹⁹⁰-1 = 7(9)_190<191> = 1501424845230313_<16> · 10411475502106841_<17> · 103604998163265343797785903_<27> · C134
C134 = P47 · P88
P47 = 32138196181722492086192711480655875703076973473_<47>
P88 = 1536993045250756022561115557188611458176946430424547082249899017269102518555851907736337_<88>

Number: 79999_190 N=49396184018211872703363301156464019861680357260098919357763832482898095600406839309173237178282301476725054664245512034332052427188401 ( 134 digits) Divisors found: r1=32138196181722492086192711480655875703076973473 (pp47) r2=1536993045250756022561115557188611458176946430424547082249899017269102518555851907736337 (pp88) Version: GGNFS-0.77.1-20050930-nocona Total time: 290.79 hours. Scaled time: 686.84 units (timescale=2.362). Factorization parameters were as follows: name: 79999_190 n: 49396184018211872703363301156464019861680357260098919357763832482898095600406839309173237178282301476725054664245512034332052427188401 skew: 242940.86 # norm 1.21e+18 c5: 85620 c4: -57151682624 c3: -22590728647291809 c2: 2381445185413331717122 c1: 409182909531414672114959920 c0: -32297630581163036627596487351520 # alpha -5.20 Y1: 459331903161439 Y0: -56522857115853633824740049 # Murphy_E 4.45e-11 # M 32787906899257365478808558482535562409527935353125941152465342791486689256008806739515137488792928799075273456259046471198536266016954 type: gnfs rlim: 11000000 alim: 11000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 11000000/11000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved algebraic special-q in [5500000, 10200001) Primes: RFBsize:726517, AFBsize:726481, largePrimes:14857336 encountered Relations: rels:15289846, finalFF:1685493 Max relations in full relation-set: 28 Initial matrix: 1453075 x 1685493 with sparse part having weight 147115281. Pruned matrix : 1241084 x 1248413 with weight 99292092. Polynomial selection time: 19.85 hours. Total sieving time: 255.28 hours. Total relation processing time: 0.34 hours. Matrix solve time: 14.72 hours. Time per square root: 0.59 hours. Prototype def-par.txt line would be: gnfs,133,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,11000000,11000000,28,28,52,52,2.6,2.6,100000 total time: 290.79 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: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806) Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394) Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 28, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(14·10¹⁶⁵-41)/9 = 1(5)₁₆₄1_<166> = 3 · 11 · 59 · 58451 · 5169785550529046037137_<22> · C136
C136 = P63 · P74
P63 = 145830821819731044721528535735047502903441900884043243247216827_<63>
P74 = 18130332859509736343289311799201732135771943135308657063773868356166511517_<74>

Number: n N=2643961340767579204510392201562942474383505436157630831674023493387373870717733728070420140402288953838976680468196570012720491891696559 ( 136 digits) SNFS difficulty: 166 digits. Divisors found: Wed May 28 10:17:40 2008 prp63 factor: 145830821819731044721528535735047502903441900884043243247216827 Wed May 28 10:17:40 2008 prp74 factor: 18130332859509736343289311799201732135771943135308657063773868356166511517 Wed May 28 10:17:40 2008 elapsed time 00:53:14 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.95 hours. Scaled time: 65.76 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_5_164_1 n: 2643961340767579204510392201562942474383505436157630831674023493387373870717733728070420140402288953838976680468196570012720491891696559 skew: 1.24 deg: 5 c5: 14 c0: -41 m: 1000000000000000000000000000000000 type: snfs rlim: 3300000 alim: 3300000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2500339) Primes: RFBsize:236900, AFBsize:237378, largePrimes:7332565 encountered Relations: rels:6804891, finalFF:530984 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 35.79 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,166,5,0,0,0,0,0,0,0,0,3300000,3300000,28,28,48,48,2.5,2.5,100000 total time: 35.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

May 28, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(19·10¹⁴³+17)/9 = 2(1)₁₄₂3_<144> = 3 · 7² · 51721 · 69073 · 445257779 · 44907917730197_<14> · C110
C110 = P34 · P76
P34 = 7235857084230512962952890011521047_<34>
P76 = 2778395777322023419518611783612670148440288856654912472918162716876208274883_<76>

Number: 21113_143 N=20104074768131705952223948574828629453469311264939980616550632557451952625753174430604740451277750586715962501 ( 110 digits) SNFS difficulty: 144 digits. Divisors found: r1=7235857084230512962952890011521047 (pp34) r2=2778395777322023419518611783612670148440288856654912472918162716876208274883 (pp76) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 25.03 hours. Scaled time: 16.95 units (timescale=0.677). Factorization parameters were as follows: name: 21113_143 n: 20104074768131705952223948574828629453469311264939980616550632557451952625753174430604740451277750586715962501 m: 10000000000000000000000000000 c5: 19000 c0: 17 skew: 0.25 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:99493, largePrimes:2950613 encountered Relations: rels:2989844, finalFF:241915 Max relations in full relation-set: 28 Initial matrix: 199581 x 241915 with sparse part having weight 29623414. Pruned matrix : 188729 x 189790 with weight 21916761. Total sieving time: 23.39 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.32 hours. Time per square root: 0.10 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: 25.03 hours. --------- CPU info (if available) ----------

(19·10¹⁵³+17)/9 = 2(1)₁₅₂3_<154> = 631 · 28080280900663_<14> · 15270966995993801_<17> · 297851429000810929_<18> · C104
C104 = P34 · P71
P34 = 1071730829955083205875392845598093_<34>
P71 = 24441526913452149544679014625447927498593580679196528341183377269394693_<71>

Number: 21113_153 N=26194737924323575364340387280235007936643629413751244947257148265834095820142465320158206394355665120449 ( 104 digits) SNFS difficulty: 154 digits. Divisors found: r1=1071730829955083205875392845598093 (pp34) r2=24441526913452149544679014625447927498593580679196528341183377269394693 (pp71) Version: GGNFS-0.77.1-20060513-k8 Total time: 39.96 hours. Scaled time: 80.56 units (timescale=2.016). Factorization parameters were as follows: name: 21113_153 n: 26194737924323575364340387280235007936643629413751244947257148265834095820142465320158206394355665120449 m: 1000000000000000000000000000000 c5: 19000 c0: 17 skew: 0.25 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, 2700001) Primes: RFBsize:176302, AFBsize:175753, largePrimes:5892888 encountered Relations: rels:5941175, finalFF:513449 Max relations in full relation-set: 28 Initial matrix: 352122 x 513449 with sparse part having weight 57240124. Pruned matrix : 298760 x 300584 with weight 34325060. Total sieving time: 38.09 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.54 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 39.96 hours. --------- CPU info (if available) ----------

May 28, 2008

By Tyler Cadigan / GGNFS, Msieve
6·10¹⁹²+7 = 6(0)₁₉₁7_<193> = 13 · 29 · 31 · 3208007417_<10> · 15475455343_<11> · 310826606681_<12> · 40049826089950582237612221318425371_<35> · C123
C123 = P53 · P71
P53 = 10102569630990212054844298716593986140238949067257353_<53>
P71 = 82227811572357690683721133099265358362960911903422547606796172190078277_<71>

Number: 6007_192 N=830712192013686323660709168931323872031297610912396291073166633804134415081608887012251142715040805151323146247750773820781 ( 123 digits) Divisors found: r1=10102569630990212054844298716593986140238949067257353 r2=82227811572357690683721133099265358362960911903422547606796172190078277 Version: Total time: 74.14 hours. Scaled time: 188.47 units (timescale=2.542). Factorization parameters were as follows: name: 6007_192 n: 830712192013686323660709168931323872031297610912396291073166633804134415081608887012251142715040805151323146247750773820781 skew: 77203.59 # norm 1.08e+017 c5: 172080 c4: 14838727404 c3: 1262193336427372 c2: -114796568745882147319 c1: -8195967742681946605855362 c0: -73190742726070200388319319520 # alpha -6.58 Y1: 23760673514311 Y0: -344146629317608937143053 # Murphy_E 1.96e-010 # M 283682133566270285574732015551287576199838655615985021782250332088258772742605296116457305471500075826863743323124395905458 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5800001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 746953 x 747201 Polynomial selection time: 7.91 hours. Total sieving time: 66.23 hours. Total relation processing 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,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 74.14 hours. --------- CPU info (if available) ----------

May 27, 2008 (4th)

By Sinkiti Sibata / GGNFS
(23·10¹⁷⁸+1)/3 = 7(6)₁₇₇7_<179> = 41 · C178
C178 = P45 · P133
P45 = 790936180336816702545701154890239344559082933_<45>
P133 = 2364184046291440600473811766553734828935527300679265758252039337569876107665435775119234232224612425238722596889930956255213593885639_<133>

Number: 76667_178 N=1869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699187 ( 178 digits) SNFS difficulty: 179 digits. Divisors found: r1=790936180336816702545701154890239344559082933 (pp45) r2=2364184046291440600473811766553734828935527300679265758252039337569876107665435775119234232224612425238722596889930956255213593885639 (pp133) Version: GGNFS-0.77.1-20060513-k8 Total time: 423.45 hours. Scaled time: 845.63 units (timescale=1.997). Factorization parameters were as follows: name: 76667_178 n: 1869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699186991869918699187 m: 100000000000000000000000000000000000 c5: 23000 c0: 1 skew: 0.13 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, 16000001) Primes: RFBsize:501962, AFBsize:502881, largePrimes:6769862 encountered Relations: rels:7271637, finalFF:1134889 Max relations in full relation-set: 28 Initial matrix: 1004910 x 1134889 with sparse part having weight 96349025. Pruned matrix : 901341 x 906429 with weight 77225160. Total sieving time: 408.94 hours. Total relation processing time: 0.88 hours. Matrix solve time: 13.25 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: snfs,179,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 423.45 hours. --------- CPU info (if available) ----------

May 27, 2008 (3rd)

By matsui / GGNFS
3·10¹⁷⁵-1 = 2(9)_175<176> = 19 · 1358197 · C169
C169 = P69 · P100
P69 = 127908438358629022538945818383105074917390387700273693347951544125819_<69>
P100 = 9088782074048181389749646028623925455114377328452874707792183747630337777668429784177679834126974147_<100>

N=1162531921673404249588938400262298202380764622820586874789848135742497319298266281269250802040460528495536826821843494295048974176019655779723141472810916546754728201393 ( 169 digits) SNFS difficulty: 175 digits. Divisors found: r1=127908438358629022538945818383105074917390387700273693347951544125819 (pp69) r2=9088782074048181389749646028623925455114377328452874707792183747630337777668429784177679834126974147 (pp100) Version: GGNFS-0.77.1-20060513-prescott Total time: 170.28 hours. Scaled time: 289.65 units (timescale=1.701). Factorization parameters were as follows: n: 1162531921673404249588938400262298202380764622820586874789848135742497319298266281269250802040460528495536826821843494295048974176019655779723141472810916546754728201393 m: 100000000000000000000000000000000000 c5: 3 c0: -1 skew: 0.8 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, 10100001) Primes: RFBsize:501962, AFBsize:501561, largePrimes:6368718 encountered Relations: rels:6829866, finalFF:1143743 Max relations in full relation-set: 28 Initial matrix: 1003588 x 1143743 with sparse part having weight 64710672. Pruned matrix : 882352 x 887433 with weight 47911814. Total sieving time: 156.22 hours. Total relation processing time: 0.35 hours. Matrix solve time: 13.47 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 170.28 hours.

May 27, 2008 (2nd)

By Jo Yeong Uk / GMP-ECM
(19·10¹⁶⁰+17)/9 = 2(1)₁₅₉3_<161> = 1091 · 13723 · 321889 · 24546888341483136439651_<23> · C126
C126 = P35 · P91
P35 = 56346892794173538280415510697608311_<35>
P91 = 3167121486201706714211853387395270653867058889451744908587689927499196954815248430586933829_<91>

May 27, 2008

By Robert Backstrom / GGNFS, Msieve
(19·10¹⁵²+17)/9 = 2(1)₁₅₁3_<153> = 3 · C152
C152 = P54 · P99
P54 = 356046920829177338700138389053899011999976498823798123_<54>
P99 = 197643530258564893467617294435465707705350739812651298588563852360274701722217491033354235201386377_<99>

Number: n N=70370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371 ( 152 digits) SNFS difficulty: 153 digits. Divisors found: Tue May 27 02:50:46 2008 prp54 factor: 356046920829177338700138389053899011999976498823798123 Tue May 27 02:50:46 2008 prp99 factor: 197643530258564893467617294435465707705350739812651298588563852360274701722217491033354235201386377 Tue May 27 02:50:46 2008 elapsed time 00:31:20 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 16.60 hours. Scaled time: 30.36 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_1_151_3 n: 70370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371 skew: 0.39 deg: 5 c5: 1900 c0: 17 m: 1000000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1300000) Primes: RFBsize:114155, AFBsize:113552, largePrimes:6914825 encountered Relations: rels:6240853, finalFF:256978 Max relations in full relation-set: 28 Initial matrix: 227774 x 256978 with sparse part having weight 40034553. Pruned matrix : Total sieving time: 16.46 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 16.60 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(16·10¹⁶⁸-61)/9 = 1(7)₁₆₇1_<169> = 97 · 238529 · C161
C161 = P63 · P99
P63 = 276893190703697940414783252826468932935031019517441970031773419_<63>
P99 = 277493155611403703683054353264914582179810037056175052898430042343277972816202057969029288816183393_<99>

Number: n N=76835965255679333973559409330624423751270416654595016187825171305664481341363095091369416050073652795282571393565786043425949148796049816924626372032818926630667 ( 161 digits) SNFS difficulty: 169 digits. Divisors found: Tue May 27 10:02:13 2008 prp63 factor: 276893190703697940414783252826468932935031019517441970031773419 Tue May 27 10:02:13 2008 prp99 factor: 277493155611403703683054353264914582179810037056175052898430042343277972816202057969029288816183393 Tue May 27 10:02:13 2008 elapsed time 01:01:22 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 72.06 hours. Scaled time: 60.46 units (timescale=0.839). Factorization parameters were as follows: name: KA_1_7_167_1 n: 76835965255679333973559409330624423751270416654595016187825171305664481341363095091369416050073652795282571393565786043425949148796049816924626372032818926630667 type: snfs deg: 5 c5: 500 c0: -61 skew: 0.66 m: 2000000000000000000000000000000000 rlim: 3500000 alim: 3500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 4300447) Primes: RFBsize:250150, AFBsize:250362, largePrimes:5832541 encountered Relations: rels:5819193, finalFF:557034 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 71.86 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,48,48,2.5,2.5,100000 total time: 72.06 hours. --------- CPU info (if available) ----------

May 26, 2008 (4th)

By Jo Yeong Uk / GMP-ECM, GGNFS
(19·10¹⁴⁸+17)/9 = 2(1)₁₄₇3_<149> = 36373501 · 102958766380241_<15> · C127
C127 = P32 · P96
P32 = 26224511757071848012274148820403_<32>
P96 = 214958808080422153827853526584090210525279684543816668859493746840385486703480148495405135657631_<96>
(19·10¹⁴²+17)/9 = 2(1)₁₄₁3_<143> = 71 · 7109 · 115015969 · 189613733299_<12> · 322231073053166813_<18> · C100
C100 = P32 · P69
P32 = 11861150895327891743346144866743_<32>
P69 = 501790053285023603948131322212264157408448417965160016833219189411523_<69>

Number: 21113_142 N=5951807539788288225430884682457532216240948269068902899898204239271953616323682713929151105423679589 ( 100 digits) Divisors found: r1=11861150895327891743346144866743 (pp32) r2=501790053285023603948131322212264157408448417965160016833219189411523 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.25 hours. Scaled time: 7.74 units (timescale=2.380). Factorization parameters were as follows: name: 21113_142 n: 5951807539788288225430884682457532216240948269068902899898204239271953616323682713929151105423679589 skew: 7751.50 # norm 1.17e+14 c5: 89760 c4: 286433780 c3: -13296024916531 c2: -35606200466171418 c1: 108194047644569709036 c0: 685898863072462815714288 # alpha -6.78 Y1: 9344433943 Y0: -9211130300927092855 # Murphy_E 3.58e-09 # M 2709477439678778205764349730250602373095667669738940728520330933270108509389153091541589441957421898 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [750000, 1250001) Primes: RFBsize:114155, AFBsize:113795, largePrimes:3865589 encountered Relations: rels:3805363, finalFF:322396 Max relations in full relation-set: 28 Initial matrix: 228035 x 322396 with sparse part having weight 25128749. Pruned matrix : 170035 x 171239 with weight 11283215. Polynomial selection time: 0.25 hours. Total sieving time: 2.79 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.10 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000 total time: 3.25 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: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806) Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394) Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 26, 2008 (3rd)

By Sinkiti Sibata / Msieve, GGNFS
(19·10¹⁰⁵+17)/9 = 2(1)₁₀₄3_<106> = 237581 · 3150047 · C94
C94 = P42 · P52
P42 = 783359782782066587583950077100340582667033_<42>
P52 = 3600983077686881125873890262969601465402154039814123_<52>

Mon May 26 05:54:40 2008 Msieve v. 1.35 Mon May 26 05:54:40 2008 random seeds: a13198c8 f211c8f4 Mon May 26 05:54:40 2008 factoring 2820865321538692810538614558530976382470612956300835716173321479649426366217666289278919907059 (94 digits) Mon May 26 05:54:41 2008 searching for 15-digit factors Mon May 26 05:54:43 2008 commencing quadratic sieve (94-digit input) Mon May 26 05:54:43 2008 using multiplier of 1 Mon May 26 05:54:43 2008 using 64kb Pentium 4 sieve core Mon May 26 05:54:43 2008 sieve interval: 18 blocks of size 65536 Mon May 26 05:54:43 2008 processing polynomials in batches of 6 Mon May 26 05:54:43 2008 using a sieve bound of 2022583 (75294 primes) Mon May 26 05:54:43 2008 using large prime bound of 271026122 (28 bits) Mon May 26 05:54:43 2008 using double large prime bound of 1511541411162932 (42-51 bits) Mon May 26 05:54:43 2008 using trial factoring cutoff of 51 bits Mon May 26 05:54:43 2008 polynomial 'A' values have 12 factors Mon May 26 11:23:20 2008 75572 relations (18222 full + 57350 combined from 1082030 partial), need 75390 Mon May 26 11:23:23 2008 begin with 1100252 relations Mon May 26 11:23:25 2008 reduce to 198215 relations in 11 passes Mon May 26 11:23:25 2008 attempting to read 198215 relations Mon May 26 11:23:31 2008 recovered 198215 relations Mon May 26 11:23:31 2008 recovered 182210 polynomials Mon May 26 11:23:31 2008 attempting to build 75572 cycles Mon May 26 11:23:31 2008 found 75572 cycles in 6 passes Mon May 26 11:23:31 2008 distribution of cycle lengths: Mon May 26 11:23:31 2008 length 1 : 18222 Mon May 26 11:23:31 2008 length 2 : 13030 Mon May 26 11:23:31 2008 length 3 : 12664 Mon May 26 11:23:31 2008 length 4 : 10226 Mon May 26 11:23:31 2008 length 5 : 7717 Mon May 26 11:23:31 2008 length 6 : 5365 Mon May 26 11:23:31 2008 length 7 : 3504 Mon May 26 11:23:31 2008 length 9+: 4844 Mon May 26 11:23:31 2008 largest cycle: 22 relations Mon May 26 11:23:32 2008 matrix is 75294 x 75572 (19.5 MB) with weight 4796606 (63.47/col) Mon May 26 11:23:32 2008 sparse part has weight 4796606 (63.47/col) Mon May 26 11:23:33 2008 filtering completed in 3 passes Mon May 26 11:23:33 2008 matrix is 71948 x 72012 (18.6 MB) with weight 4589082 (63.73/col) Mon May 26 11:23:33 2008 sparse part has weight 4589082 (63.73/col) Mon May 26 11:23:34 2008 saving the first 48 matrix rows for later Mon May 26 11:23:34 2008 matrix is 71900 x 72012 (11.0 MB) with weight 3534900 (49.09/col) Mon May 26 11:23:34 2008 sparse part has weight 2463053 (34.20/col) Mon May 26 11:23:34 2008 matrix includes 64 packed rows Mon May 26 11:23:34 2008 using block size 21845 for processor cache size 512 kB Mon May 26 11:23:34 2008 commencing Lanczos iteration Mon May 26 11:23:34 2008 memory use: 11.1 MB Mon May 26 11:24:28 2008 lanczos halted after 1138 iterations (dim = 71898) Mon May 26 11:24:28 2008 recovered 16 nontrivial dependencies Mon May 26 11:24:29 2008 prp42 factor: 783359782782066587583950077100340582667033 Mon May 26 11:24:29 2008 prp52 factor: 3600983077686881125873890262969601465402154039814123 Mon May 26 11:24:29 2008 elapsed time 05:29:49

(19·10¹³⁷+17)/9 = 2(1)₁₃₆3_<138> = 3 · 7 · 59 · 107 · 3137 · 10378477 · 52018972561_<11> · C111
C111 = P54 · P58
P54 = 257906784564331830598010239861334619288706259471606201_<54>
P58 = 3645720115445636970073274698358696904155253499404580769129_<58>

Number: 21113_137 N=940255952396088864380528059344305845250199889392668041299317576046841164705609190752329635215726376937585768929 ( 111 digits) SNFS difficulty: 138 digits. Divisors found: r1=257906784564331830598010239861334619288706259471606201 (pp54) r2=3645720115445636970073274698358696904155253499404580769129 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 11.28 hours. Scaled time: 22.67 units (timescale=2.010). Factorization parameters were as follows: name: 21113_137 n: 940255952396088864380528059344305845250199889392668041299317576046841164705609190752329635215726376937585768929 m: 1000000000000000000000000000 c5: 1900 c0: 17 skew: 0.39 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1825001) Primes: RFBsize:78498, AFBsize:63278, largePrimes:1661033 encountered Relations: rels:1702175, finalFF:196033 Max relations in full relation-set: 28 Initial matrix: 141843 x 196033 with sparse part having weight 20035278. Pruned matrix : 128428 x 129201 with weight 11672377. Total sieving time: 11.00 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.14 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 11.28 hours. --------- CPU info (if available) ----------

(19·10¹²¹+17)/9 = 2(1)₁₂₀3_<122> = 1609 · 14898491627884431173138326429_<29> · C90
C90 = P38 · P53
P38 = 36218395286981478538085535848918712611_<38>
P53 = 24315518894413952771658466169562042509604178782165703_<53>

Mon May 26 11:50:07 2008 Msieve v. 1.35 Mon May 26 11:50:07 2008 random seeds: d5e0c8e8 ebb720e0 Mon May 26 11:50:07 2008 factoring 880669074925951398734942256801317450090466445248385516105451227031149812348095397237780533 (90 digits) Mon May 26 11:50:08 2008 searching for 15-digit factors Mon May 26 11:50:10 2008 commencing quadratic sieve (90-digit input) Mon May 26 11:50:10 2008 using multiplier of 2 Mon May 26 11:50:10 2008 using 64kb Pentium 4 sieve core Mon May 26 11:50:10 2008 sieve interval: 18 blocks of size 65536 Mon May 26 11:50:10 2008 processing polynomials in batches of 6 Mon May 26 11:50:10 2008 using a sieve bound of 1615001 (61176 primes) Mon May 26 11:50:10 2008 using large prime bound of 135660084 (27 bits) Mon May 26 11:50:10 2008 using double large prime bound of 434924330062824 (42-49 bits) Mon May 26 11:50:10 2008 using trial factoring cutoff of 49 bits Mon May 26 11:50:10 2008 polynomial 'A' values have 12 factors Mon May 26 14:06:03 2008 61929 relations (16287 full + 45642 combined from 670328 partial), need 61272 Mon May 26 14:06:06 2008 begin with 686615 relations Mon May 26 14:06:07 2008 reduce to 151202 relations in 10 passes Mon May 26 14:06:07 2008 attempting to read 151202 relations Mon May 26 14:06:10 2008 recovered 151202 relations Mon May 26 14:06:10 2008 recovered 129702 polynomials Mon May 26 14:06:11 2008 attempting to build 61929 cycles Mon May 26 14:06:11 2008 found 61929 cycles in 5 passes Mon May 26 14:06:11 2008 distribution of cycle lengths: Mon May 26 14:06:11 2008 length 1 : 16287 Mon May 26 14:06:11 2008 length 2 : 11799 Mon May 26 14:06:11 2008 length 3 : 11002 Mon May 26 14:06:11 2008 length 4 : 8442 Mon May 26 14:06:11 2008 length 5 : 5835 Mon May 26 14:06:11 2008 length 6 : 3725 Mon May 26 14:06:11 2008 length 7 : 2334 Mon May 26 14:06:11 2008 length 9+: 2505 Mon May 26 14:06:11 2008 largest cycle: 17 relations Mon May 26 14:06:11 2008 matrix is 61176 x 61929 (15.2 MB) with weight 3728877 (60.21/col) Mon May 26 14:06:11 2008 sparse part has weight 3728877 (60.21/col) Mon May 26 14:06:12 2008 filtering completed in 4 passes Mon May 26 14:06:12 2008 matrix is 57269 x 57333 (14.0 MB) with weight 3437413 (59.96/col) Mon May 26 14:06:12 2008 sparse part has weight 3437413 (59.96/col) Mon May 26 14:06:13 2008 saving the first 48 matrix rows for later Mon May 26 14:06:13 2008 matrix is 57221 x 57333 (8.8 MB) with weight 2690503 (46.93/col) Mon May 26 14:06:13 2008 sparse part has weight 1954397 (34.09/col) Mon May 26 14:06:13 2008 matrix includes 64 packed rows Mon May 26 14:06:13 2008 using block size 21845 for processor cache size 512 kB Mon May 26 14:06:14 2008 commencing Lanczos iteration Mon May 26 14:06:14 2008 memory use: 8.6 MB Mon May 26 14:06:46 2008 lanczos halted after 907 iterations (dim = 57216) Mon May 26 14:06:47 2008 recovered 14 nontrivial dependencies Mon May 26 14:06:47 2008 prp38 factor: 36218395286981478538085535848918712611 Mon May 26 14:06:47 2008 prp53 factor: 24315518894413952771658466169562042509604178782165703 Mon May 26 14:06:47 2008 elapsed time 02:16:40

(19·10¹²⁵+17)/9 = 2(1)₁₂₄3_<126> = 3 · 7 · 1987 · 3727 · 3160957 · 5400152789_<10> · 21795220773379_<14> · C88
C88 = P32 · P57
P32 = 21769371741788386995971686002193_<32>
P57 = 167611083343969985171953195615674438687622824552784462787_<57>

Mon May 26 14:25:38 2008 Msieve v. 1.35 Mon May 26 14:25:38 2008 random seeds: 8498d380 d66b9c6e Mon May 26 14:25:38 2008 factoring 3648787981358758376443619313888158885179582879218339340017561379606686032816905208891891 (88 digits) Mon May 26 14:25:40 2008 searching for 15-digit factors Mon May 26 14:25:42 2008 commencing quadratic sieve (88-digit input) Mon May 26 14:25:42 2008 using multiplier of 11 Mon May 26 14:25:42 2008 using 64kb Pentium 4 sieve core Mon May 26 14:25:42 2008 sieve interval: 13 blocks of size 65536 Mon May 26 14:25:42 2008 processing polynomials in batches of 8 Mon May 26 14:25:42 2008 using a sieve bound of 1517707 (57529 primes) Mon May 26 14:25:42 2008 using large prime bound of 121416560 (26 bits) Mon May 26 14:25:42 2008 using double large prime bound of 356205104400640 (42-49 bits) Mon May 26 14:25:42 2008 using trial factoring cutoff of 49 bits Mon May 26 14:25:42 2008 polynomial 'A' values have 11 factors Mon May 26 15:46:08 2008 57807 relations (16257 full + 41550 combined from 604944 partial), need 57625 Mon May 26 15:46:10 2008 begin with 621201 relations Mon May 26 15:46:11 2008 reduce to 137587 relations in 9 passes Mon May 26 15:46:11 2008 attempting to read 137587 relations Mon May 26 15:46:15 2008 recovered 137587 relations Mon May 26 15:46:15 2008 recovered 113718 polynomials Mon May 26 15:46:15 2008 attempting to build 57807 cycles Mon May 26 15:46:15 2008 found 57807 cycles in 5 passes Mon May 26 15:46:15 2008 distribution of cycle lengths: Mon May 26 15:46:15 2008 length 1 : 16257 Mon May 26 15:46:15 2008 length 2 : 11581 Mon May 26 15:46:15 2008 length 3 : 10022 Mon May 26 15:46:15 2008 length 4 : 7636 Mon May 26 15:46:15 2008 length 5 : 5168 Mon May 26 15:46:15 2008 length 6 : 3243 Mon May 26 15:46:15 2008 length 7 : 1807 Mon May 26 15:46:15 2008 length 9+: 2093 Mon May 26 15:46:15 2008 largest cycle: 16 relations Mon May 26 15:46:15 2008 matrix is 57529 x 57807 (13.6 MB) with weight 3346142 (57.88/col) Mon May 26 15:46:15 2008 sparse part has weight 3346142 (57.88/col) Mon May 26 15:46:16 2008 filtering completed in 3 passes Mon May 26 15:46:16 2008 matrix is 52880 x 52944 (12.6 MB) with weight 3088437 (58.33/col) Mon May 26 15:46:16 2008 sparse part has weight 3088437 (58.33/col) Mon May 26 15:46:17 2008 saving the first 48 matrix rows for later Mon May 26 15:46:17 2008 matrix is 52832 x 52944 (8.7 MB) with weight 2490713 (47.04/col) Mon May 26 15:46:17 2008 sparse part has weight 1970280 (37.21/col) Mon May 26 15:46:17 2008 matrix includes 64 packed rows Mon May 26 15:46:17 2008 using block size 21177 for processor cache size 512 kB Mon May 26 15:46:18 2008 commencing Lanczos iteration Mon May 26 15:46:18 2008 memory use: 8.2 MB Mon May 26 15:46:48 2008 lanczos halted after 837 iterations (dim = 52831) Mon May 26 15:46:48 2008 recovered 17 nontrivial dependencies Mon May 26 15:46:49 2008 prp32 factor: 21769371741788386995971686002193 Mon May 26 15:46:49 2008 prp57 factor: 167611083343969985171953195615674438687622824552784462787 Mon May 26 15:46:49 2008 elapsed time 01:21:11

(19·10¹³²+17)/9 = 2(1)₁₃₁3_<133> = 31 · 911 · 333483323 · 46928703599228182185833657_<26> · C94
C94 = P46 · P48
P46 = 4998028003187250350588924237218853249700597287_<46>
P48 = 955695757724238214604079143204207742822053446549_<48>

Number: 21113_132 N=4776594159633000514124122320061907346291707194004929543799695356781805365347420856122228912563 ( 94 digits) SNFS difficulty: 133 digits. Divisors found: r1=4998028003187250350588924237218853249700597287 (pp46) r2=955695757724238214604079143204207742822053446549 (pp48) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.35 hours. Scaled time: 12.80 units (timescale=2.016). Factorization parameters were as follows: name: 21113_132 n: 4776594159633000514124122320061907346291707194004929543799695356781805365347420856122228912563 m: 100000000000000000000000000 c5: 1900 c0: 17 skew: 0.39 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, 1250001) Primes: RFBsize:63951, AFBsize:63278, largePrimes:1568200 encountered Relations: rels:1587419, finalFF:178535 Max relations in full relation-set: 28 Initial matrix: 127296 x 178535 with sparse part having weight 16438184. Pruned matrix : 115008 x 115708 with weight 8856615. Total sieving time: 6.16 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.35 hours. --------- CPU info (if available) ----------

(19·10¹⁷¹+17)/9 = 2(1)₁₇₀3_<172> = 31633729472340713_<17> · 291104186737583782427_<21> · 6438741037805110785691_<22> · 8577629963433708883037_<22> · C91
C91 = P39 · P52
P39 = 730838499256988735456103400088494610213_<39>
P52 = 5679662912466728551265886075488345660885194579796953_<52>

Mon May 26 16:05:50 2008 Msieve v. 1.35 Mon May 26 16:05:50 2008 random seeds: f9076ce4 4dd5fde8 Mon May 26 16:05:50 2008 factoring 4150916319232761671539358595025702780677783501173809882863812208715661747821991680420080989 (91 digits) Mon May 26 16:05:51 2008 searching for 15-digit factors Mon May 26 16:05:53 2008 commencing quadratic sieve (91-digit input) Mon May 26 16:05:53 2008 using multiplier of 5 Mon May 26 16:05:53 2008 using 64kb Pentium 4 sieve core Mon May 26 16:05:53 2008 sieve interval: 18 blocks of size 65536 Mon May 26 16:05:53 2008 processing polynomials in batches of 6 Mon May 26 16:05:53 2008 using a sieve bound of 1715599 (64706 primes) Mon May 26 16:05:53 2008 using large prime bound of 164697504 (27 bits) Mon May 26 16:05:53 2008 using double large prime bound of 616646889281472 (42-50 bits) Mon May 26 16:05:53 2008 using trial factoring cutoff of 50 bits Mon May 26 16:05:53 2008 polynomial 'A' values have 12 factors Mon May 26 19:12:04 2008 65311 relations (16822 full + 48489 combined from 768000 partial), need 64802 Mon May 26 19:12:07 2008 begin with 784822 relations Mon May 26 19:12:08 2008 reduce to 163602 relations in 10 passes Mon May 26 19:12:08 2008 attempting to read 163602 relations Mon May 26 19:12:13 2008 recovered 163602 relations Mon May 26 19:12:13 2008 recovered 144384 polynomials Mon May 26 19:12:13 2008 attempting to build 65311 cycles Mon May 26 19:12:13 2008 found 65311 cycles in 5 passes Mon May 26 19:12:13 2008 distribution of cycle lengths: Mon May 26 19:12:13 2008 length 1 : 16822 Mon May 26 19:12:13 2008 length 2 : 11982 Mon May 26 19:12:13 2008 length 3 : 11293 Mon May 26 19:12:13 2008 length 4 : 8641 Mon May 26 19:12:13 2008 length 5 : 6470 Mon May 26 19:12:13 2008 length 6 : 4167 Mon May 26 19:12:13 2008 length 7 : 2635 Mon May 26 19:12:13 2008 length 9+: 3301 Mon May 26 19:12:13 2008 largest cycle: 19 relations Mon May 26 19:12:13 2008 matrix is 64706 x 65311 (16.2 MB) with weight 3988777 (61.07/col) Mon May 26 19:12:13 2008 sparse part has weight 3988777 (61.07/col) Mon May 26 19:12:15 2008 filtering completed in 3 passes Mon May 26 19:12:15 2008 matrix is 60989 x 61053 (15.1 MB) with weight 3724320 (61.00/col) Mon May 26 19:12:15 2008 sparse part has weight 3724320 (61.00/col) Mon May 26 19:12:15 2008 saving the first 48 matrix rows for later Mon May 26 19:12:15 2008 matrix is 60941 x 61053 (9.4 MB) with weight 2900914 (47.51/col) Mon May 26 19:12:15 2008 sparse part has weight 2093272 (34.29/col) Mon May 26 19:12:15 2008 matrix includes 64 packed rows Mon May 26 19:12:15 2008 using block size 21845 for processor cache size 512 kB Mon May 26 19:12:16 2008 commencing Lanczos iteration Mon May 26 19:12:16 2008 memory use: 9.3 MB Mon May 26 19:12:54 2008 lanczos halted after 965 iterations (dim = 60941) Mon May 26 19:12:54 2008 recovered 18 nontrivial dependencies Mon May 26 19:12:55 2008 prp39 factor: 730838499256988735456103400088494610213 Mon May 26 19:12:55 2008 prp52 factor: 5679662912466728551265886075488345660885194579796953 Mon May 26 19:12:55 2008 elapsed time 03:07:05

(19·10¹¹⁷+17)/9 = 2(1)₁₁₆3_<118> = 31 · 61 · 61231 · 704964570643_<12> · C98
C98 = P47 · P51
P47 = 63460649118500649720004637763831639443635857911_<47>
P51 = 407545788120013284598901938387320489819499387145561_<51>

Number: 21113_117 N=25863120259606973612140943358534400942067297352716633976505979254681934314828742357338679670383071 ( 98 digits) SNFS difficulty: 118 digits. Divisors found: r1=63460649118500649720004637763831639443635857911 (pp47) r2=407545788120013284598901938387320489819499387145561 (pp51) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.34 hours. Scaled time: 1.58 units (timescale=0.677). Factorization parameters were as follows: name: 21113_117 n: 25863120259606973612140943358534400942067297352716633976505979254681934314828742357338679670383071 m: 100000000000000000000000 c5: 1900 c0: 17 skew: 0.39 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63278, largePrimes:2061617 encountered Relations: rels:2076260, finalFF:171414 Max relations in full relation-set: 28 Initial matrix: 112443 x 171414 with sparse part having weight 13981284. Pruned matrix : 94931 x 95557 with weight 5424242. Total sieving time: 2.10 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.13 hours. Time per square root: 0.05 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: 2.34 hours. --------- CPU info (if available) ----------

May 26, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(8·10¹⁶⁹-17)/9 = (8)₁₆₈7_<169> = 7 · 23 · 347651 · 570290792567_<12> · C150
C150 = P34 · P42 · P75
P34 = 7647057099881162934899256947975591_<34>
P42 = 288971669211010444364343532804847944865909_<42>
P75 = 126017877051932162637963203064793127409653634778576315963511553718382954729_<75>

Number: n N=36415596282124724946851084768003952823187763054201007070477049673615397913960005932770460940694364915011993122433661 ( 116 digits) Divisors found: Mon May 26 03:32:21 2008 prp42 factor: 288971669211010444364343532804847944865909 Mon May 26 03:32:21 2008 prp75 factor: 126017877051932162637963203064793127409653634778576315963511553718382954729 Mon May 26 03:32:21 2008 elapsed time 00:58:59 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 33.79 hours. Scaled time: 60.41 units (timescale=1.788). Factorization parameters were as follows: name: KA_8_168_7 n: 36415596282124724946851084768003952823187763054201007070477049673615397913960005932770460940694364915011993122433661 skew: 32602.77 # norm 9.87e+15 c5: 51240 c4: -17444291338 c3: -204845419034853 c2: 16621713388589075462 c1: 140528977229607893092002 c0: -7240200765027653070058015 # alpha -6.04 Y1: 1095222391577 Y0: -14802594722064352791642 # Murphy_E 4.67e-10 # M 7330779924285220432966678097907383861727993586497700469151769799760136608191069016539989636153384426399706445238266 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 2139990) Primes: RFBsize:315948, AFBsize:315812, largePrimes:6713940 encountered Relations: rels:6667215, finalFF:756278 Max relations in full relation-set: 28 Initial matrix: 631844 x 756278 with sparse part having weight 46156257. Pruned matrix : Total sieving time: 33.56 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 33.79 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(19·10¹¹⁰+17)/9 = 2(1)₁₀₉3_<111> = 3 · 6607 · C107
C107 = P43 · P64
P43 = 2270199252456242699778729641333819680492093_<43>
P64 = 4691606222865481103080585512540588248203889051546135228221187921_<64>

Number: n N=10650880939968271586252515569906216190460174113874734428692352106912421730039408259477882604869134307608653 ( 107 digits) SNFS difficulty: 111 digits. Divisors found: r1=2270199252456242699778729641333819680492093 (pp43) r2=4691606222865481103080585512540588248203889051546135228221187921 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.77 hours. Scaled time: 1.34 units (timescale=1.754). Factorization parameters were as follows: name: KA_2_1_109_3 n: 10650880939968271586252515569906216190460174113874734428692352106912421730039408259477882604869134307608653 type: snfs skew: 0.98 deg: 5 c5: 19 c0: 17 m: 10000000000000000000000 rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:49098, AFBsize:49036, largePrimes:3053133 encountered Relations: rels:2566808, finalFF:139977 Max relations in full relation-set: 28 Initial matrix: 98201 x 139977 with sparse part having weight 6770974. Pruned matrix : 74778 x 75333 with weight 2487548. Total sieving time: 0.67 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.4,2.4,50000 total time: 0.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(16·10¹⁶⁸-43)/9 = 1(7)₁₆₇3_<169> = 3 · 19 · 191 · 1162727 · 32142403 · C151
C151 = P40 · P43 · P69
P40 = 1135576527475659333289157303954971991389_<40>
P43 = 7332359625542663552102105388324769736487451_<43>
P69 = 524750651552389632583331633911460165026537808342751045471152014055281_<69>

Number: n N=3847660490919948366761919261633749695877165825894476197911616472552930306305900066786080295040588420179076778731 ( 112 digits) Divisors found: Mon May 26 10:32:20 2008 prp43 factor: 7332359625542663552102105388324769736487451 Mon May 26 10:32:20 2008 prp69 factor: 524750651552389632583331633911460165026537808342751045471152014055281 Mon May 26 10:32:20 2008 elapsed time 00:41:20 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 18.45 hours. Scaled time: 33.75 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_7_167_3 n: 3847660490919948366761919261633749695877165825894476197911616472552930306305900066786080295040588420179076778731 skew: 36788.59 # norm 6.05e+15 c5: 78000 c4: -5631153824 c3: -347034960848259 c2: 5737219763925262545 c1: 298212253611090490023001 c0: 1359075478596552538555591221 # alpha -6.64 Y1: 390452078753 Y0: -2180828685196191746234 # Murphy_E 7.85e-10 # M 3106697242966918702106236308821846260072575737044410193218342945966571983336045922057382424617833389701926414309 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, 1300000) Primes: RFBsize:250150, AFBsize:249801, largePrimes:6529947 encountered Relations: rels:6131649, finalFF:518517 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 18.27 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 18.45 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(19·10¹¹⁶+17)/9 = 2(1)₁₁₅3_<117> = 3 · 83 · 71527 · 5602253 · C103
C103 = P49 · P54
P49 = 2966325687678056937474314854464720978353817202219_<49>
P54 = 713280224924002374089503089945616997448142074923965033_<54>

Number: n N=2115821453704850469983635766404803392743827058719309562419615688657939260968947379262777059130246008227 ( 103 digits) SNFS difficulty: 117 digits. Divisors found: r1=2966325687678056937474314854464720978353817202219 (pp49) r2=713280224924002374089503089945616997448142074923965033 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.45 hours. Scaled time: 2.53 units (timescale=1.751). Factorization parameters were as follows: name: KA_2_1_115_3 n: 2115821453704850469983635766404803392743827058719309562419615688657939260968947379262777059130246008227 type: snfs skew: 0.62 deg: 5 c5: 190 c0: 17 m: 100000000000000000000000 rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 20000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 240001) Primes: RFBsize:56543, AFBsize:56433, largePrimes:3684144 encountered Relations: rels:3161105, finalFF:179094 Max relations in full relation-set: 28 Initial matrix: 113043 x 179094 with sparse part having weight 10761539. Pruned matrix : 84754 x 85383 with weight 3472881. Total sieving time: 1.29 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.05 hours. Total square root time: 0.03 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,700000,700000,28,28,48,48,2.4,2.4,50000 total time: 1.45 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(19·10¹²⁴+17)/9 = 2(1)₁₂₃3_<125> = 223718153 · 834759311 · C108
C108 = P46 · P62
P46 = 2098106958390013566678652050706071014416820177_<46>
P62 = 53879179111506794848560367490910458372207156743626422470530943_<62>

Number: n N=113044280606194274951039755402217484921209733464583986651108663909704532766448392160888427078429686945236911 ( 108 digits) SNFS difficulty: 126 digits. Divisors found: r1=2098106958390013566678652050706071014416820177 (pp46) r2=53879179111506794848560367490910458372207156743626422470530943 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.99 hours. Scaled time: 3.63 units (timescale=1.823). Factorization parameters were as follows: name: KA_2_1_123_3 n: 113044280606194274951039755402217484921209733464583986651108663909704532766448392160888427078429686945236911 skew: 1.55 deg: 5 c5: 19 c0: 170 m: 10000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 400001) Primes: RFBsize:78498, AFBsize:78541, largePrimes:4987460 encountered Relations: rels:4343076, finalFF:223428 Max relations in full relation-set: 48 Initial matrix: 157104 x 223428 with sparse part having weight 18618193. Pruned matrix : 128827 x 129676 with weight 6954852. Total sieving time: 1.80 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.07 hours. Total square root time: 0.05 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 1.99 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(19·10¹⁴⁵+17)/9 = 2(1)₁₄₄3_<146> = 28447 · 41017 · C137
C137 = P35 · P102
P35 = 78028900325725980152501066021599909_<35>
P102 = 231875700865027574418442587619581173200268280817376948139532338530122326771487269224347720783283635043_<102>
(19·10¹⁴⁰+17)/9 = 2(1)₁₃₉3_<141> = 3⁴ · 103142892767_<12> · C128
C128 = P37 · P92
P37 = 1338967039267258903607662253178789037_<37>
P92 = 18871954411427858011578814863318916834385230348366099626180972019620251580610578675135514787_<92>

May 26, 2008

The factor table of 211...113 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 25, 2008

By Sinkiti Sibata / GGNFS
6·10¹⁶⁴+1 = 6(0)₁₆₃1_<165> = 127301 · 9028519 · 731813929840206967957739_<24> · C129
C129 = P48 · P82
P48 = 369270152835869755547632504844697137215152321611_<48>
P82 = 1931781669601575696400721360944887567321529473091599594216511185010148045718575651_<82>

Number: 60001_164 N=713349312379305508790666689367172868406630219599967618257841050319008187812555276771966182501762848278868158748777307060785693761 ( 129 digits) SNFS difficulty: 165 digits. Divisors found: r1=369270152835869755547632504844697137215152321611 (pp48) r2=1931781669601575696400721360944887567321529473091599594216511185010148045718575651 (pp82) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 109.83 hours. Scaled time: 74.35 units (timescale=0.677). Factorization parameters were as follows: name: 60001_164 n: 713349312379305508790666689367172868406630219599967618257841050319008187812555276771966182501762848278868158748777307060785693761 m: 1000000000000000000000000000000000 c5: 3 c0: 5 skew: 1.11 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:347746, largePrimes:5774254 encountered Relations: rels:5921824, finalFF:793765 Max relations in full relation-set: 28 Initial matrix: 696324 x 793765 with sparse part having weight 43434956. Pruned matrix : 618590 x 622135 with weight 30984281. Total sieving time: 93.90 hours. Total relation processing time: 0.36 hours. Matrix solve time: 15.32 hours. Time per square root: 0.25 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: 109.83 hours. --------- CPU info (if available) ----------

May 22, 2008

By Wataru Sakai / GGNFS
(10¹⁷⁵+53)/9 = (1)₁₇₄7_<175> = 7 · 193 · 3954197657_<10> · C162
C162 = P37 · P125
P37 = 2610737759979808348888414895912745601_<37>
P125 = 79667376637152748251187653628669585032369930493112417006130329078837954943743446933778194805256207158514266300958092844163331_<125>

Number: 11117_175 N=207990628425147882873116937733374674024084023398128816882295841907268463261365926197669521747703201029768219977406412612707085785431852504776846402074903895756931 ( 162 digits) SNFS difficulty: 175 digits. Divisors found: r1=2610737759979808348888414895912745601 (pp37) r2=79667376637152748251187653628669585032369930493112417006130329078837954943743446933778194805256207158514266300958092844163331 (pp125) Version: GGNFS-0.77.1-20060722-nocona Total time: 229.61 hours. Scaled time: 462.67 units (timescale=2.015). Factorization parameters were as follows: n: 207990628425147882873116937733374674024084023398128816882295841907268463261365926197669521747703201029768219977406412612707085785431852504776846402074903895756931 m: 100000000000000000000000000000000000 c5: 1 c0: 53 skew: 2.21 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, 11500001) Primes: RFBsize:501962, AFBsize:502556, largePrimes:6722972 encountered Relations: rels:7341404, finalFF:1276844 Max relations in full relation-set: 32 Initial matrix: 1004582 x 1276844 with sparse part having weight 84011642. Pruned matrix : 767989 x 773075 with weight 63465184. Total sieving time: 223.38 hours. Total relation processing time: 0.10 hours. Matrix solve time: 5.93 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 229.61 hours.

May 21, 2008

By Robert Backstrom / GGNFS, Msieve
(5·10¹⁶⁵-41)/9 = (5)₁₆₄1_<165> = 19 · 23 · 6579711991137624748790221_<25> · C138
C138 = P68 · P70
P68 = 21083373136695693791397262348539885288424420557620875447965111556739_<68>
P70 = 9164295383350239108257431989856648493254559513704497509580294208734917_<70>

Number: n N=193214259102070796294938693019973703949380505820952443293645400138485561727618230806612603709067289274548366084025358207192680957655955663 ( 138 digits) SNFS difficulty: 165 digits. Divisors found: Wed May 21 17:27:32 2008 prp68 factor: 21083373136695693791397262348539885288424420557620875447965111556739 Wed May 21 17:27:32 2008 prp70 factor: 9164295383350239108257431989856648493254559513704497509580294208734917 Wed May 21 17:27:32 2008 elapsed time 00:46:27 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 30.38 hours. Scaled time: 55.56 units (timescale=1.829). Factorization parameters were as follows: name: KA_5_164_1 n: 193214259102070796294938693019973703949380505820952443293645400138485561727618230806612603709067289274548366084025358207192680957655955663 skew: 1.52 deg: 5 c5: 5 c0: -41 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3200000) Primes: RFBsize:230209, AFBsize:230198, largePrimes:8031343 encountered Relations: rels:7742603, finalFF:745531 Max relations in full relation-set: 28 Initial matrix: 460472 x 745531 with sparse part having weight 73265518. Pruned matrix : Total sieving time: 30.20 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 30.38 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

May 20, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(5·10¹⁶⁸-23)/9 = (5)₁₆₇3_<168> = 127709 · 3157451059191428479609_<22> · C142
C142 = P37 · P49 · P56
P37 = 4534229354659272615202786707505221491_<37>
P49 = 5307729004237646738094282755789801851124238131627_<49>
P56 = 57247580658584769147297015573859650130443012417569320109_<56>

Number: n N=303854644284004501603054739515143078103688249906898718160532334889375027156095800934456094438098839987343 ( 105 digits) Divisors found: Wed May 21 00:10:06 2008 prp49 factor: 5307729004237646738094282755789801851124238131627 Wed May 21 00:10:06 2008 prp56 factor: 57247580658584769147297015573859650130443012417569320109 Wed May 21 00:10:06 2008 elapsed time 00:25:35 (Msieve 1.35) Version: GGNFS-0.77.1-20051202-athlon Total time: 9.19 hours. Scaled time: 13.30 units (timescale=1.447). Factorization parameters were as follows: name: n n: 303854644284004501603054739515143078103688249906898718160532334889375027156095800934456094438098839987343 skew: 4247.77 # norm 1.75e+13 c5: 55080 c4: 365730018 c3: -2888912593427 c2: -4861785643557040 c1: 22243646095735652084 c0: 22141020713593788522960 # alpha -3.84 Y1: 103926725093 Y0: -88783796969622700957 # Murphy_E 2.08e-09 # M 123198688195128300348499142709450541348104311857436014602214916670286578204588240644864396042236949963164 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 special-q in [100000, 1300000) Primes: RFBsize:183072, AFBsize:182479, largePrimes:4258432 encountered Relations: rels:4351739, finalFF:511925 Max relations in full relation-set: 28 Initial matrix: 365631 x 511925 with sparse part having weight 32012362. Pruned matrix : Total sieving time: 9.03 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. 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: 9.19 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 20, 2008

By Robert Backstrom / GGNFS, Msieve
(52·10¹⁶⁸-7)/9 = 5(7)_168<169> = 2273 · 4327 · C162
C162 = P68 · P95
P68 = 20752002809996857119171828649866996717199970697800523504969822088337_<68>
P95 = 28308345385696301109711060065796518182592934915052319190743442789270172132944796227018696827351_<95>

Number: n N=587454862990331204679340078964552962269954511449433145032585048015227824203092906924250259883817922025511831629019452313797736511559038665815896458549823159705287 ( 162 digits) SNFS difficulty: 171 digits. Divisors found: Tue May 20 09:17:49 2008 prp68 factor: 20752002809996857119171828649866996717199970697800523504969822088337 Tue May 20 09:17:49 2008 prp95 factor: 28308345385696301109711060065796518182592934915052319190743442789270172132944796227018696827351 Tue May 20 09:17:49 2008 elapsed time 01:32:25 (Msieve 1.35) Version: GGNFS-0.77.1-20051202-athlon Total time: 84.28 hours. Scaled time: 154.14 units (timescale=1.829). Factorization parameters were as follows: name: KA_5_7_168 n: 587454862990331204679340078964552962269954511449433145032585048015227824203092906924250259883817922025511831629019452313797736511559038665815896458549823159705287 skew: 1.68 deg: 5 c5: 13 c0: -175 m: 10000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5601451) Primes: RFBsize:250150, AFBsize:250051, largePrimes:8242669 encountered Relations: rels:7702797, finalFF:542216 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 83.96 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 84.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

May 19, 2008 (4th)

By Wataru Sakai / GGNFS
(10¹⁷⁴+53)/9 = (1)₁₇₃7_<174> = 3² · 24256521885311_<14> · C159
C159 = P43 · P52 · P65
P43 = 2027653539543295031938083824511414251255561_<43>
P52 = 8392517209536205849446943360188330150487682685953111_<52>
P65 = 29908901503673913152403882822870481251319731298983207281605651573_<65>

Number: 11117 N=508963282976766783534262853063054603099914669847218516424297079463077466707163153543756764845578381588268013787077522720355911520232708905656308189050983576283 ( 159 digits) SNFS difficulty: 175 digits. Divisors found: r1=2027653539543295031938083824511414251255561 (pp43) r2=8392517209536205849446943360188330150487682685953111 (pp52) r3=29908901503673913152403882822870481251319731298983207281605651573 (pp65) Version: GGNFS-0.77.1-20060722-nocona Total time: 269.79 hours. Scaled time: 543.10 units (timescale=2.013). Factorization parameters were as follows: n: 508963282976766783534262853063054603099914669847218516424297079463077466707163153543756764845578381588268013787077522720355911520232708905656308189050983576283 m: 100000000000000000000000000000000000 c5: 1 c0: 530 skew: 3.51 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, 12900001) Primes: RFBsize:501962, AFBsize:502251, largePrimes:6702326 encountered Relations: rels:7292639, finalFF:1245904 Max relations in full relation-set: 32 Initial matrix: 1004277 x 1245904 with sparse part having weight 85068839. Pruned matrix : 795304 x 800389 with weight 63132763. Total sieving time: 263.47 hours. Total relation processing time: 0.11 hours. Matrix solve time: 6.01 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 269.79 hours. --------- CPU info (if available) ----------

May 19, 2008 (3rd)

By Jo Yeong Uk / GGNFS
8·10¹⁸²-1 = 7(9)_182<183> = 6689 · 45833 · 64965178089572382042423526852742694223_<38> · C137
C137 = P46 · P92
P46 = 2829679223950790825954049626119361318023850447_<46>
P92 = 14194910762760110159567326572030778175180115767221826639366766883637151712659720504442682567_<92>

Number: 79999_182 N=40167044071217756780187592392246187076622588646967716036404892251010744662016892972703963262216033825927684995558723281578766771102057449 ( 137 digits) SNFS difficulty: 182 digits. Divisors found: r1=2829679223950790825954049626119361318023850447 (pp46) r2=14194910762760110159567326572030778175180115767221826639366766883637151712659720504442682567 (pp92) Version: GGNFS-0.77.1-20050930-nocona Total time: 198.43 hours. Scaled time: 470.07 units (timescale=2.369). Factorization parameters were as follows: n: 40167044071217756780187592392246187076622588646967716036404892251010744662016892972703963262216033825927684995558723281578766771102057449 m: 2000000000000000000000000000000000000 c5: 25 c0: -1 skew: 0.53 type: snfs 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, 8700001) Primes: RFBsize:664579, AFBsize:664195, largePrimes:11026461 encountered Relations: rels:11383611, finalFF:1565933 Max relations in full relation-set: 28 Initial matrix: 1328838 x 1565933 with sparse part having weight 91203312. Pruned matrix : 1110337 x 1117045 with weight 59728587. Total sieving time: 189.97 hours. Total relation processing time: 0.22 hours. Matrix solve time: 8.13 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000 total time: 198.43 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806) Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394) Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 19, 2008 (2nd)

By Robert Backstrom / GGNFS
(17·10¹⁶³-53)/9 = 1(8)₁₆₂3_<164> = 13 · 1733 · 23472466891217_<14> · C146
C146 = P47 · P99
P47 = 37464998032005354061197314116355187433310192513_<47>
P99 = 953410757092344732158061608063141390017470114019584701189414810489033337617424683715457001145387587_<99>

Number: n N=35719532138157430052106995256408556683128572464714853419483400421642599338267848370829079226006677548827900672142510416094914152945325824970536131 ( 146 digits) SNFS difficulty: 164 digits. Divisors found: r1=37464998032005354061197314116355187433310192513 (pp47) r2=953410757092344732158061608063141390017470114019584701189414810489033337617424683715457001145387587 (pp99) Version: GGNFS-0.77.1-20051202-athlon Total time: 62.14 hours. Scaled time: 113.65 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_8_162_3 n: 35719532138157430052106995256408556683128572464714853419483400421642599338267848370829079226006677548827900672142510416094914152945325824970536131 skew: 0.32 deg: 5 c5: 17000 c0: -53 m: 100000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 4000001) Primes: RFBsize:230209, AFBsize:230502, largePrimes:7910428 encountered Relations: rels:7389998, finalFF:540625 Max relations in full relation-set: 48 Initial matrix: 460778 x 540625 with sparse part having weight 70572678. Pruned matrix : 433405 x 435772 with weight 49582594. Total sieving time: 58.94 hours. Total relation processing time: 0.29 hours. Matrix solve time: 2.75 hours. Total square root time: 0.16 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 62.14 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

May 19, 2008

Msieve 1.36 has been released. The option "ECM=1" seems not to work with the latest GMP-ECM 6.2 on Cygwin.
HOW TO for Japanese

May 18, 2008 (2nd)

By Wataru Sakai / GGNFS
(10¹⁹²+53)/9 = (1)₁₉₁7_<192> = 3² · C191
C191 = P83 · P108
P83 = 14123720387393002847291410763872967484180831506670434762025325964606545058458745507_<83>
P108 = 874109559926262470155627544776491563984637426442504930902793822720147512252658789539043366361166147669006359_<108>

Number: 11117_192 N=12345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679013 ( 191 digits) SNFS difficulty: 192 digits. Divisors found: r1=14123720387393002847291410763872967484180831506670434762025325964606545058458745507 (pp83) r2=874109559926262470155627544776491563984637426442504930902793822720147512252658789539043366361166147669006359 (pp108) Version: GGNFS-0.77.1-20060722-nocona Total time: 1917.76 hours. Scaled time: 3607.30 units (timescale=1.881). Factorization parameters were as follows: n: 12345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679013 m: 100000000000000000000000000000000000000 c5: 100 c0: 53 skew: 0.88 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, 33200001) Primes: RFBsize:501962, AFBsize:501086, largePrimes:7793203 encountered Relations: rels:8555123, finalFF:1127939 Max relations in full relation-set: 32 Initial matrix: 1003112 x 1127939 with sparse part having weight 174268786. Pruned matrix : 926899 x 931978 with weight 156610693. Total sieving time: 1901.26 hours. Total relation processing time: 0.23 hours. Matrix solve time: 15.94 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,192,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1917.76 hours. --------- CPU info (if available) ----------

10¹⁷⁹-9 = (9)₁₇₈1_<179> = 569 · 8951 · 944482695820147111_<18> · C155
C155 = P51 · P104
P51 = 546906270091264303592773419636796433846880957980999_<51>
P104 = 38010997664106318499368894010475771853596823493322466917536870017901952887416421331572081502939677862201_<104>

Number: 99991_179 N=20788452954924146764603039522194137117407445350777136241530147122589364351329595415517377430574666346326413082578657526895364119580095412547818049498318799 ( 155 digits) SNFS difficulty: 180 digits. Divisors found: r1=546906270091264303592773419636796433846880957980999 (pp51) r2=38010997664106318499368894010475771853596823493322466917536870017901952887416421331572081502939677862201 (pp104) Version: GGNFS-0.77.1-20060722-nocona Total time: 378.09 hours. Scaled time: 732.36 units (timescale=1.937). Factorization parameters were as follows: n: 20788452954924146764603039522194137117407445350777136241530147122589364351329595415517377430574666346326413082578657526895364119580095412547818049498318799 m: 1000000000000000000000000000000000000 c5: 1 c0: -90 skew: 2.46 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, ) Primes: RFBsize:501962, AFBsize:502106, largePrimes:6681820 encountered Relations: rels:7298544, finalFF:1280046 Max relations in full relation-set: 32 Initial matrix: 1004132 x 1280046 with sparse part having weight 79504127. Pruned matrix : 763803 x 768887 with weight 58674310. Total sieving time: 372.79 hours. Total relation processing time: 0.11 hours. Matrix solve time: 5.00 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 378.09 hours. --------- CPU info (if available) ----------

May 18, 2008

GMP-ECM 6.2 has been released.
HOW TO for Japanese

May 17, 2008 (3rd)

By Wataru Sakai / GGNFS
10¹⁸⁵-9 = (9)₁₈₄1_<185> = 43 · 68239 · C179
C179 = P46 · P62 · P72
P46 = 2538313576960440629507448895847540063266132079_<46>
P62 = 29377049543046125556029128856057470051512089568061282636870001_<62>
P72 = 457030771896922620319211488891391699946102749496004569879285614325665077_<72>

Number: 99991_185 N=34079945417559419236834150286424901261878138975972616082258082655454819023561851863338055677770026483525583985424688943818187580790770605501798228319957522756031553939863209915083 ( 179 digits) SNFS difficulty: 185 digits. Divisors found: r1=2538313576960440629507448895847540063266132079 (pp46) r2=29377049543046125556029128856057470051512089568061282636870001 (pp62) r3=457030771896922620319211488891391699946102749496004569879285614325665077 (pp72) Version: GGNFS-0.77.1-20060722-nocona Total time: 551.24 hours. Scaled time: 1091.46 units (timescale=1.980). Factorization parameters were as follows: n: 34079945417559419236834150286424901261878138975972616082258082655454819023561851863338055677770026483525583985424688943818187580790770605501798228319957522756031553939863209915083 m: 10000000000000000000000000000000000000 c5: 1 c0: -9 skew: 1.55 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, 10800001) Primes: RFBsize:501962, AFBsize:501561, largePrimes:6796158 encountered Relations: rels:7433227, finalFF:1293690 Max relations in full relation-set: 32 Initial matrix: 1003587 x 1293690 with sparse part having weight 91676647. Pruned matrix : 758115 x 763196 with weight 74168224. Total sieving time: 544.72 hours. Total relation processing time: 0.12 hours. Matrix solve time: 6.19 hours. Time per square root: 0.21 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: 551.24 hours. --------- CPU info (if available) ----------

May 17, 2008 (2nd)

By matsui / GMP-ECM, GGNFS
4·10¹⁹⁵+3 = 4(0)₁₉₄3_<196> = 334619 · C191
C191 = P34 · C157
P34 = 1899148878726749048488989889567829_<34>
C157 = [6294342673917283095296597333781389878764955396535221356317197348749861635004950569207387365842036953134093517964225806435213623451826519913911915772485876053_<157>]
(31·10¹⁷⁹-13)/9 = 3(4)₁₇₈3_<180> = 11 · C179
C179 = P68 · P112
P68 = 30083976209855206209867424244392759793889864427042762736211518417297_<68>
P112 = 1040857468264898047169776135475785954744385602127018579283000666366877231179930173843719367433591547037710900129_<112>

N=31313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313 ( 179 digits) SNFS difficulty: 181 digits. Divisors found: r1=30083976209855206209867424244392759793889864427042762736211518417297 (pp68) r2=1040857468264898047169776135475785954744385602127018579283000666366877231179930173843719367433591547037710900129 (pp112) Version: GGNFS-0.77.1-20060513-prescott Total time: 488.40 hours. Scaled time: 829.79 units (timescale=1.699). Factorization parameters were as follows: n: 31313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313 m: 1000000000000000000000000000000000000 c5: 31 c0: -130 skew: 1.33 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, 10000001) Primes: RFBsize:501962, AFBsize:503087, largePrimes:6595694 encountered Relations: rels:7075180, finalFF:1156780 Max relations in full relation-set: 28 Initial matrix: 1005114 x 1156780 with sparse part having weight 74860798. Pruned matrix : 877750 x 882839 with weight 57165750. Total sieving time: 473.22 hours. Total relation processing time: 0.16 hours. Matrix solve time: 14.75 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 488.40 hours.

May 17, 2008

(17·10¹⁵¹+1)/9 = 1(8)₁₅₀9_<152> = 1999 · 23053 · 136739 · 3036797 · 10115327 · 241307805079199_<15> · C111
C111 = P44 · P68
P44 = 16052814829035632996593744878571920614918011_<44>
P68 = 25191586207757365324351562684284330771481754244914451059244679310463_<68>

Number: 18889_151 N=404395868642816960618253208929134675199315393867524038135573530299426396894733529649892305557335362882759449093 ( 111 digits) SNFS difficulty: 152 digits. Divisors found: r1=16052814829035632996593744878571920614918011 (pp44) r2=25191586207757365324351562684284330771481754244914451059244679310463 (pp68) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 34.49 hours. Scaled time: 23.32 units (timescale=0.676). Factorization parameters were as follows: name: 18889_151 n: 404395868642816960618253208929134675199315393867524038135573530299426396894733529649892305557335362882759449093 m: 1000000000000000000000000000000 c5: 170 c0: 1 skew: 0.36 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:176638, largePrimes:5642853 encountered Relations: rels:5669604, finalFF:579959 Max relations in full relation-set: 28 Initial matrix: 353007 x 579959 with sparse part having weight 52116995. Pruned matrix : 262184 x 264013 with weight 25401214. Total sieving time: 31.27 hours. Total relation processing time: 0.23 hours. Matrix solve time: 2.85 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 34.49 hours. --------- CPU info (if available) ----------

(5·10¹⁹⁵+7)/3 = 1(6)₁₉₄9_<196> = C196
C196 = P56 · P140
P56 = 70933856352032678645751387076184010145835868792093142469_<56>
P140 = 23496067355978549054213838968500546792259877842124452223684145406670771881352881209782499995258163300154998364416791685762865175855683321801_<140>

Number: 16669_195 N=1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 ( 196 digits) SNFS difficulty: 195 digits. Divisors found: r1=70933856352032678645751387076184010145835868792093142469 (pp56) r2=23496067355978549054213838968500546792259877842124452223684145406670771881352881209782499995258163300154998364416791685762865175855683321801 (pp140) Version: GGNFS-0.77.1-20060513-k8 Total time: 2741.50 hours. Scaled time: 5510.41 units (timescale=2.010). Factorization parameters were as follows: name: 16669_195 n: 1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 m: 1000000000000000000000000000000000000000 c5: 5 c0: 7 skew: 1.07 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, 37900000 ) Primes: RFBsize:501962, AFBsize:501136, largePrimes:8055645 encountered Relations: rels:8992598, finalFF:1135865 Max relations in full relation-set: 28 Initial matrix: 1003163 x 1135865 with sparse part having weight 171400953. Pruned matrix : 919129 x 924208 with weight 156929395. Total sieving time: 2711.16 hours. Total relation processing time: 3.34 hours. Matrix solve time: 26.46 hours. Time per square root: 0.54 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 2741.50 hours. --------- CPU info (if available) ----------

May 16, 2008 (3rd)

By Makoto Kamada / GMP-ECM
2·10¹⁹³-7 = 1(9)₁₉₂3_<194> = 13 · 19 · 59 · 107 · C188
C188 = P34 · C154
P34 = 5988949810510825396976938071071359_<34>
C154 = [2141640541578786521330418665807384878608009014861807243660439094425838336861612412560917549794060720323430428012100399379490077809110556314251517234498057_<154>]

May 16, 2008 (2nd)

By Jo Yeong Uk / GGNFS
(17·10¹⁶⁷+1)/9 = 1(8)₁₆₆9_<168> = 3 · 439 · 1869749428162746085682491_<25> · 163609302509880042320150939_<27> · C114
C114 = P47 · P67
P47 = 67491671682398385317058511254298691184136924241_<47>
P67 = 6946708088484961654717938698979654691930307591413856517996301354013_<67>

Number: 18889_167 N=468844941581488303298926571089388851951033336400850491856810847637557401770554274615923511541962492525097502329133 ( 114 digits) Divisors found: r1=67491671682398385317058511254298691184136924241 (pp47) r2=6946708088484961654717938698979654691930307591413856517996301354013 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.62 hours. Scaled time: 41.71 units (timescale=2.367). Factorization parameters were as follows: name: 18889_167 n: 468844941581488303298926571089388851951033336400850491856810847637557401770554274615923511541962492525097502329133 skew: 46684.93 # norm 8.48e+15 c5: 25920 c4: -676451736 c3: 130428591787688 c2: 3765533627980100596 c1: 36339129263182235163297 c0: -2557412519550371046968785290 # alpha -7.07 Y1: 636525890843 Y0: -7103609029808023059391 # Murphy_E 6.52e-10 # M 180139406609668129580026728876662211747894112506436949390916334295806210579842840786329647593722407771469041647991 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, 2730001) Primes: RFBsize:250150, AFBsize:251199, largePrimes:7420613 encountered Relations: rels:7298007, finalFF:609288 Max relations in full relation-set: 28 Initial matrix: 501430 x 609288 with sparse part having weight 49346372. Pruned matrix : 410627 x 413198 with weight 29226622. Polynomial selection time: 1.18 hours. Total sieving time: 15.33 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.87 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: 17.62 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: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806) Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394) Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 16, 2008

By Robert Backstrom / GGNFS, Msieve
(16·10¹⁶⁴+11)/9 = 1(7)₁₆₃9_<165> = 8837 · 591781793 · C152
C152 = P60 · P92
P60 = 819054711215580220780088216797582579278329688084587866978373_<60>
P92 = 41504779040362072486741147317329424235777767852517739678824079973857105583247144975259600203_<92>

Number: n N=33994684810970224044938855284325010320587366934543670749637725820422739011723947723559014858582979941037256593746246806758495085353818012064597627409719 ( 152 digits) SNFS difficulty: 166 digits. Divisors found: Fri May 16 01:29:50 2008 prp60 factor: 819054711215580220780088216797582579278329688084587866978373 Fri May 16 01:29:50 2008 prp92 factor: 41504779040362072486741147317329424235777767852517739678824079973857105583247144975259600203 Fri May 16 01:29:50 2008 elapsed time 01:08:56 (Msieve 1.35) Version: GGNFS-0.77.1-20051202-athlon Total time: 51.96 hours. Scaled time: 73.43 units (timescale=1.413). Factorization parameters were as follows: name: KA_1_7_163_9 n: 33994684810970224044938855284325010320587366934543670749637725820422739011723947723559014858582979941037256593746246806758495085353818012064597627409719 skew: 1.47 deg: 5 c5: 1 c0: 220 m: 2000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3400223) Primes: RFBsize:230209, AFBsize:230048, largePrimes:7594820 encountered Relations: rels:7045114, finalFF:515446 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 51.77 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 51.96 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

May 15, 2008 (4th)

By Strohl philippe / GMP-ECM, Msieve
(10¹⁹⁸+71)/9 = (1)₁₉₇9_<198> = 4001 · 5031332503_<10> · 58763767963_<11> · 13275389735735891_<17> · 1080515019909211499629_<22> · C136
C136 = P41 · P42 · P55
P41 = 10069084871636180530120147336924416212569_<41>
P42 = 372936171880615158098090212029283260211837_<42>
P55 = 1743788007353172537521605567071655468363222761077697113_<55>

May 15, 2008 (3rd)

By Jo Yeong Uk / GGNFS
(17·10¹⁶⁰+1)/9 = 1(8)₁₅₉9_<161> = 13 · 2776731921313909477_<19> · 23804872312724088177544609_<26> · C116
C116 = P49 · P67
P49 = 3019027540589841111615402443598033601002863914943_<49>
P67 = 7281086248778730252929784206334560094320704875958402009234594411847_<67>

Number: 18889_160 N=21981799910472962006573451120284964892454411201578582142123383849630370984496422039098541921072986649975632919529721 ( 116 digits) SNFS difficulty: 161 digits. Divisors found: r1=3019027540589841111615402443598033601002863914943 (pp49) r2=7281086248778730252929784206334560094320704875958402009234594411847 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.37 hours. Scaled time: 58.03 units (timescale=2.381). Factorization parameters were as follows: n: 21981799910472962006573451120284964892454411201578582142123383849630370984496422039098541921072986649975632919529721 m: 100000000000000000000000000000000 c5: 17 c0: 1 skew: 0.57 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:282982, largePrimes:5612739 encountered Relations: rels:5636302, finalFF:651682 Max relations in full relation-set: 28 Initial matrix: 566193 x 651682 with sparse part having weight 40463301. Pruned matrix : 498218 x 501112 with weight 27564761. Total sieving time: 23.12 hours. Total relation processing time: 0.08 hours. Matrix solve time: 1.14 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 24.37 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806) Calibrating delay using timer specific routine.. 5344.78 BogoMIPS (lpj=2672394) Calibrating delay using timer specific routine.. 5344.44 BogoMIPS (lpj=2672223) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672388)

May 15, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(17·10¹⁵⁰+1)/9 = 1(8)₁₄₉9_<151> = 12599100967_<11> · 232362627870787_<15> · C126
C126 = P50 · P77
P50 = 12255622955186676467421637879285692660200973908309_<50>
P77 = 52645976406605495742233878007732625356159233240897545278160906703716316402849_<77>

Number: 18889_150 N=645209236947010492147224285543187145714532531053986933972672816337481145452624873946152946638065994199823548790633407632372341 ( 126 digits) SNFS difficulty: 151 digits. Divisors found: r1=12255622955186676467421637879285692660200973908309 (pp50) r2=52645976406605495742233878007732625356159233240897545278160906703716316402849 (pp77) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 27.02 hours. Scaled time: 18.02 units (timescale=0.667). Factorization parameters were as follows: name: 18889_150 n: 645209236947010492147224285543187145714532531053986933972672816337481145452624873946152946638065994199823548790633407632372341 m: 1000000000000000000000000000000 c5: 17 c0: 1 skew: 0.57 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 1900001) Primes: RFBsize:176302, AFBsize:176118, largePrimes:5313564 encountered Relations: rels:5181418, finalFF:453835 Max relations in full relation-set: 28 Initial matrix: 352485 x 453835 with sparse part having weight 36996961. Pruned matrix : 294072 x 295898 with weight 21718071. Total sieving time: 23.62 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.06 hours. Time per square root: 0.15 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: 27.02 hours. --------- CPU info (if available) ----------

May 15, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(17·10¹⁵⁶+1)/9 = 1(8)₁₅₅9_<157> = 1570653419_<10> · 413097321610859_<15> · 67407421335827431871_<20> · C113
C113 = P43 · P71
P43 = 1683915841330240179281702206131814655635817_<43>
P71 = 25647531544462176640389814319070297296091174784612085044944710867824487_<71>

Number: n N=43188284658736900485468870637293355701575449624772259430741937853997084709199848904019254042856968584304546850879 ( 113 digits) SNFS difficulty: 157 digits. Divisors found: r1=1683915841330240179281702206131814655635817 (pp43) r2=25647531544462176640389814319070297296091174784612085044944710867824487 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 18.48 hours. Scaled time: 33.68 units (timescale=1.823). Factorization parameters were as follows: name: KA_1_8_155_9 n: 43188284658736900485468870637293355701575449624772259430741937853997084709199848904019254042856968584304546850879 skew: 0.36 deg: 5 c5: 170 c0: 1 m: 10000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:148933, AFBsize:149105, largePrimes:6785053 encountered Relations: rels:6136287, finalFF:337877 Max relations in full relation-set: 48 Initial matrix: 298105 x 337877 with sparse part having weight 40377415. Pruned matrix : 280312 x 281866 with weight 28247297. Total sieving time: 17.45 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.83 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 18.48 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(13·10¹⁶⁸+23)/9 = 1(4)₁₆₇7_<169> = 6197231736504198581_<19> · 6827481749527884299_<19> · C131
C131 = P57 · P75
P57 = 125991706661408379069740433560492000863719150637957632449_<57>
P75 = 270957140149426777544289571433775011527741409316792143226462515238075645737_<75>

Number: n N=34138352519520697488492384808044363669564458449619491153150511809519512581286624284223734680550286431913886638391088083143379719913 ( 131 digits) SNFS difficulty: 169 digits. Divisors found: Thu May 15 13:35:04 2008 prp57 factor: 125991706661408379069740433560492000863719150637957632449 Thu May 15 13:35:04 2008 prp75 factor: 270957140149426777544289571433775011527741409316792143226462515238075645737 Thu May 15 13:35:04 2008 elapsed time 01:35:31 (Msieve 1.35) Version: GGNFS-0.77.1-20050930-k8 Total time: 71.47 hours. Scaled time: 60.11 units (timescale=0.841). Factorization parameters were as follows: name: KA_1_4_167_7 n: 34138352519520697488492384808044363669564458449619491153150511809519512581286624284223734680550286431913886638391088083143379719913 type: snfs deg: 5 c5: 13000 c0: 23 skew: 0.28 m: 1000000000000000000000000000000000 rlim: 3400000 alim: 3400000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 9101657) Primes: RFBsize:243539, AFBsize:243864, largePrimes:6295660 encountered Relations: rels:6358983, finalFF:386411 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 71.23 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,48,48,2.5,2.5,100000 total time: 71.47 hours. --------- CPU info (if available) ----------

(17·10¹⁶⁶+1)/9 = 1(8)₁₆₅9_<167> = 13 · 745033 · 7085413956200779_<16> · 671347539145262415473123_<24> · C120
C120 = P33 · P87
P33 = 878173932625410668935107562634861_<33>
P87 = 466868291565041584191404564367635894529401621360028875543317445660814498485125130692393_<87>

May 14, 2008 (3rd)

By Sinkiti Sibata / GGNFS
(17·10¹³⁶+1)/9 = 1(8)₁₃₅9_<137> = 13 · 131 · 683 · 456409592321987984917_<21> · C110
C110 = P45 · P66
P45 = 135271113016603325460958519014799560369771317_<45>
P66 = 263033602744615290623211932004282702100555610794776909675214160549_<66>

Number: 18889_136 N=35580848204031197632957661319571263404262342057907723715152309747795286599815779076172254024688540843253173033 ( 110 digits) SNFS difficulty: 137 digits. Divisors found: r1=135271113016603325460958519014799560369771317 (pp45) r2=263033602744615290623211932004282702100555610794776909675214160549 (pp66) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 8.98 hours. Scaled time: 6.08 units (timescale=0.677). Factorization parameters were as follows: name: 18889_136 n: 35580848204031197632957661319571263404262342057907723715152309747795286599815779076172254024688540843253173033 m: 1000000000000000000000000000 c5: 170 c0: 1 skew: 0.36 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, 1300001) Primes: RFBsize:78498, AFBsize:63758, largePrimes:1536783 encountered Relations: rels:1537478, finalFF:174059 Max relations in full relation-set: 28 Initial matrix: 142323 x 174059 with sparse part having weight 14424184. Pruned matrix : 132346 x 133121 with weight 9309259. Total sieving time: 8.46 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.37 hours. Time per square root: 0.06 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: 8.98 hours. --------- CPU info (if available) ----------

May 14, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve
(17·10¹⁴⁶+1)/9 = 1(8)₁₄₅9_<147> = 3² · 7 · 171598487 · C137
C137 = P40 · P97
P40 = 3210829111399465992677672913074119450171_<40>
P97 = 5441707777847825911517573089597079709549116073352279752874414335353976222031085839213018547986339_<97>

Number: n N=17472393748842697564100529228848415796336457975702693130378453345976558074187660708043800543522486486548479317292793680457479225899213969 ( 137 digits) SNFS difficulty: 147 digits. Divisors found: r1=3210829111399465992677672913074119450171 (pp40) r2=5441707777847825911517573089597079709549116073352279752874414335353976222031085839213018547986339 (pp97) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.41 hours. Scaled time: 11.66 units (timescale=1.818). Factorization parameters were as follows: name: KA_1_8_145_9 n: 17472393748842697564100529228848415796336457975702693130378453345976558074187660708043800543522486486548479317292793680457479225899213969 skew: 0.36 deg: 5 c5: 170 c0: 1 m: 100000000000000000000000000000 type: snfs rlim: 1600000 alim: 1600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:121127, AFBsize:121025, largePrimes:6566213 encountered Relations: rels:5867774, finalFF:300967 Max relations in full relation-set: 48 Initial matrix: 242219 x 300967 with sparse part having weight 33169592. Pruned matrix : 220316 x 221591 with weight 18533404. Total sieving time: 5.78 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.40 hours. Total square root time: 0.11 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,48,48,2.5,2.5,100000 total time: 6.41 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

May 14, 2008

By Jo Yeong Uk / GGNFS
(17·10¹⁵⁵+1)/9 = 1(8)₁₅₄9_<156> = 3² · 233707265677436331129169_<24> · C131
C131 = P43 · P89
P43 = 7432798877836175924862195765978994856188367_<43>
P89 = 12082013223071163764032145160054775612064289873932471918156403070758301397897940923198927_<89>

Number: 18889_155 N=89803174326445185097380030661135204861505848627374060515671755601306327312337475431786542613761787651305075448165637035599724282209 ( 131 digits) SNFS difficulty: 156 digits. Divisors found: r1=7432798877836175924862195765978994856188367 (pp43) r2=12082013223071163764032145160054775612064289873932471918156403070758301397897940923198927 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.92 hours. Scaled time: 37.90 units (timescale=2.380). Factorization parameters were as follows: n: 89803174326445185097380030661135204861505848627374060515671755601306327312337475431786542613761787651305075448165637035599724282209 m: 10000000000000000000000000000000 c5: 17 c0: 1 skew: 0.57 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:216621, largePrimes:5652876 encountered Relations: rels:5672516, finalFF:606082 Max relations in full relation-set: 28 Initial matrix: 433502 x 606082 with sparse part having weight 47143850. Pruned matrix : 323248 x 325479 with weight 29229758. Total sieving time: 15.24 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.58 hours. Time per square root: 0.04 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: 15.92 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: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.38 BogoMIPS (lpj=2672192) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672358)

May 13, 2008 (3rd)

By Sinkiti Sibata / GGNFS
(17·10¹³⁸+1)/9 = 1(8)₁₃₇9_<139> = 4510061376844003663_<19> · C120
C120 = P50 · P71
P50 = 31840264865105550282268277463062426428832090106619_<50>
P71 = 13153680477112431114501007873566580075045768560448657392843078514243637_<71>

Number: 18889_138 N=418816670342227751757005180681984987355373125957642242039607767360886430241132243704166233930906908148091812021472333303 ( 120 digits) SNFS difficulty: 139 digits. Divisors found: r1=31840264865105550282268277463062426428832090106619 (pp50) r2=13153680477112431114501007873566580075045768560448657392843078514243637 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 13.84 hours. Scaled time: 9.37 units (timescale=0.677). Factorization parameters were as follows: name: 18889_138 n: 418816670342227751757005180681984987355373125957642242039607767360886430241132243704166233930906908148091812021472333303 m: 1000000000000000000000000000 c5: 17000 c0: 1 skew: 0.14 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, 1900001) Primes: RFBsize:78498, AFBsize:63878, largePrimes:1627941 encountered Relations: rels:1648597, finalFF:175753 Max relations in full relation-set: 28 Initial matrix: 142443 x 175753 with sparse part having weight 18062658. Pruned matrix : 133976 x 134752 with weight 12318345. Total sieving time: 13.17 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.49 hours. Time per square root: 0.07 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: 13.84 hours. --------- CPU info (if available) ----------

(17·10¹³³+1)/9 = 1(8)₁₃₂9_<134> = 107 · 227 · 4813 · 685170157317962653049_<21> · C105
C105 = P37 · P69
P37 = 1234014527104641903445029379611028313_<37>
P69 = 191100667533990229020460551789426582958270387694681889491226478787821_<69>

Number: 18889_133 N=235820999876338346487677767402600117955663203582401779655854919539426132493778302474140196027811550575973 ( 105 digits) SNFS difficulty: 134 digits. Divisors found: r1=1234014527104641903445029379611028313 (pp37) r2=191100667533990229020460551789426582958270387694681889491226478787821 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 7.65 hours. Scaled time: 5.18 units (timescale=0.677). Factorization parameters were as follows: name: 18889_133 n: 235820999876338346487677767402600117955663203582401779655854919539426132493778302474140196027811550575973 m: 100000000000000000000000000 c5: 17000 c0: 1 skew: 0.14 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, 1150001) Primes: RFBsize:78498, AFBsize:63878, largePrimes:1524268 encountered Relations: rels:1529587, finalFF:179780 Max relations in full relation-set: 28 Initial matrix: 142443 x 179780 with sparse part having weight 13890647. Pruned matrix : 129461 x 130237 with weight 8271331. Total sieving time: 7.21 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.30 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 7.65 hours. --------- CPU info (if available) ----------

May 13, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve
(17·10¹⁴⁸+1)/9 = 1(8)₁₄₇9_<149> = 13 · 23 · 79 · 2579 · C141
C141 = P39 · P50 · P54
P39 = 125681550014263882017357848163817899931_<39>
P50 = 20778615782132915248991027933944063474034054154181_<50>
P54 = 118732236759698250781220009050291048271486353167257761_<54>

Number: n N=310067887339372044057852532081215001964982278863308124029803280292445671423201078818835634127341864552129161310084319113472281721057927336871 ( 141 digits) SNFS difficulty: 151 digits. Divisors found: r1=125681550014263882017357848163817899931 (pp39) r2=20778615782132915248991027933944063474034054154181 (pp50) r3=118732236759698250781220009050291048271486353167257761 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 10.43 hours. Scaled time: 19.02 units (timescale=1.823). Factorization parameters were as follows: name: KA_1_8_147_9 n: 310067887339372044057852532081215001964982278863308124029803280292445671423201078818835634127341864552129161310084319113472281721057927336871 skew: 1.43 deg: 5 c5: 17 c0: 100 m: 1000000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 750001) Primes: RFBsize:114155, AFBsize:114282, largePrimes:6189604 encountered Relations: rels:5491469, finalFF:264671 Max relations in full relation-set: 48 Initial matrix: 228504 x 264671 with sparse part having weight 29914799. Pruned matrix : 213309 x 214515 with weight 19462184. Total sieving time: 9.85 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.39 hours. Total square root time: 0.07 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 10.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(13·10¹⁷⁰+23)/9 = 1(4)₁₆₉7_<171> = 3² · 7² · C168
C168 = P42 · P126
P42 = 446315784615474862410026239878656530619417_<42>
P126 = 733871474114925252241865494143887940469879995924979497675057972980625973036265099361056138544027803999139735087936933070351151_<126>

Number: n N=327538422776518014613252708490803728898966994205089443184681279919375157470395565633660871756109851347946586041824137062232300327538422776518014613252708490803728898967 ( 168 digits) SNFS difficulty: 171 digits. Divisors found: Tue May 13 13:00:56 2008 prp42 factor: 446315784615474862410026239878656530619417 Tue May 13 13:00:56 2008 prp126 factor: 733871474114925252241865494143887940469879995924979497675057972980625973036265099361056138544027803999139735087936933070351151 Tue May 13 13:00:56 2008 elapsed time 01:20:02 (Msieve 1.35) Version: GGNFS-0.77.1-20051202-athlon Total time: 62.30 hours. Scaled time: 113.95 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_4_169_7 n: 327538422776518014613252708490803728898966994205089443184681279919375157470395565633660871756109851347946586041824137062232300327538422776518014613252708490803728898967 skew: 1.12 deg: 5 c5: 13 c0: 23 m: 10000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4100573) Primes: RFBsize:250150, AFBsize:249461, largePrimes:7723547 encountered Relations: rels:7159466, finalFF:540371 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 62.05 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 62.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(17·10¹⁵⁷+1)/9 = 1(8)₁₅₆9_<158> = 31 · 89 · 4993 · C151
C151 = P68 · P84
P68 = 10389319827483729125541276705287706636888901647006845589895676437721_<68>
P84 = 131979363484273526432917168541620540675529931962287016158799908174443540210525526807_<84>

Number: n N=1371175817865845012948456863812954583599996783382846088829463742090604184668894472478134040711645734175645025100300906146378680706732730562830651486847 ( 151 digits) SNFS difficulty: 158 digits. Divisors found: Tue May 13 23:42:18 2008 prp68 factor: 10389319827483729125541276705287706636888901647006845589895676437721 Tue May 13 23:42:18 2008 prp84 factor: 131979363484273526432917168541620540675529931962287016158799908174443540210525526807 Tue May 13 23:42:18 2008 elapsed time 00:51:03 (Msieve 1.35) Version: GGNFS-0.77.1-20051202-athlon Total time: 27.44 hours. Scaled time: 39.71 units (timescale=1.447). Factorization parameters were as follows: name: KA_1_8_156_9 n: 1371175817865845012948456863812954583599996783382846088829463742090604184668894472478134040711645734175645025100300906146378680706732730562830651486847 skew: 0.23 deg: 5 c5: 1700 c0: 1 m: 10000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1300001) Primes: RFBsize:203362, AFBsize:203472, largePrimes:7091762 encountered Relations: rels:6614208, finalFF:513664 Max relations in full relation-set: 28 Initial matrix: 406901 x 513664 with sparse part having weight 38635564. Pruned matrix : Total sieving time: 27.25 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 27.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 13, 2008

By Jo Yeong Uk / GGNFS
(17·10¹⁵⁸+1)/9 = 1(8)₁₅₇9_<159> = 3 · 7² · 5088556838519157777959041_<25> · 773952255048761259605344760131_<30> · C102
C102 = P50 · P53
P50 = 16713340926956566201930088601647275580275612424791_<50>
P53 = 19521671710027297651795646344507570669558565769398567_<53>

Number: 18889_158 N=326272354753809409783926743501951526769302667744497378253582147117816704691884198427382049596590674497 ( 102 digits) Divisors found: r1=16713340926956566201930088601647275580275612424791 (pp50) r2=19521671710027297651795646344507570669558565769398567 (pp53) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.34 hours. Scaled time: 10.10 units (timescale=2.324). Factorization parameters were as follows: name: 18889_158 n: 326272354753809409783926743501951526769302667744497378253582147117816704691884198427382049596590674497 skew: 9707.57 # norm 1.66e+14 c5: 58140 c4: -1204082396 c3: -16047945750919 c2: 95250222814570675 c1: 627468897543127179213 c0: -2238096650248582827457545 # alpha -5.97 Y1: 22959935999 Y0: -22378083790384944344 # Murphy_E 2.69e-09 # M 198217674374385453969471597599128458274937908501156646603931004074576906134386477000765936111891797998 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1500001) Primes: RFBsize:135072, AFBsize:135135, largePrimes:4297434 encountered Relations: rels:4209433, finalFF:333131 Max relations in full relation-set: 28 Initial matrix: 270296 x 333131 with sparse part having weight 25414943. Pruned matrix : 224093 x 225508 with weight 14231777. Polynomial selection time: 0.31 hours. Total sieving time: 3.72 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.18 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 4.34 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: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.38 BogoMIPS (lpj=2672192) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672358)

(17·10¹⁴³+1)/9 = 1(8)₁₄₂9_<144> = 3 · 899753171 · 82020986669_<11> · C123
C123 = P42 · P82
P42 = 651294001984968690031508343706506092549381_<42>
P82 = 1309965033693254983247199110421891812341830657407559148798183964348719311977188577_<82>

Number: 18889_143 N=853172369254454387976182331880392282540220002760894331827020690232607449767249084940972241338131506687593970016650921620837 ( 123 digits) SNFS difficulty: 146 digits. Divisors found: r1=651294001984968690031508343706506092549381 (pp42) r2=1309965033693254983247199110421891812341830657407559148798183964348719311977188577 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 7.26 hours. Scaled time: 17.35 units (timescale=2.389). Factorization parameters were as follows: n: 853172369254454387976182331880392282540220002760894331827020690232607449767249084940972241338131506687593970016650921620837 m: 100000000000000000000000000000 c5: 17 c0: 100 skew: 1.43 type: snfs 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, 1425001) Primes: RFBsize:135072, AFBsize:135058, largePrimes:3620149 encountered Relations: rels:3640316, finalFF:341971 Max relations in full relation-set: 28 Initial matrix: 270197 x 341971 with sparse part having weight 29294147. Pruned matrix : 237673 x 239087 with weight 16973507. Total sieving time: 6.98 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.21 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 7.26 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: 8047200k/8912896k available (2439k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.38 BogoMIPS (lpj=2672192) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672358)

May 12, 2008 (3rd)

By Wataru Sakai / GGNFS
10¹⁸¹-9 = (9)₁₈₀1_<181> = 613 · 4721990197_<10> · C169
C169 = P78 · P92
P78 = 118046288030005689138006772776064145473173086074955176614021148886231992477409_<78>
P92 = 29265915150079883819125682044728327718073357005292178916251770323960139756081440411297901759_<92>

Number: 99991 N=3454732649268037140651629992081894263362774944623633726957884046515864376096038447979084779442532000245131642678651564893028283221292314837219802797322498616193908862431 ( 169 digits) SNFS difficulty: 181 digits. Divisors found: r1=118046288030005689138006772776064145473173086074955176614021148886231992477409 (pp78) r2=29265915150079883819125682044728327718073357005292178916251770323960139756081440411297901759 (pp92) Version: GGNFS-0.77.1-20060722-nocona Total time: 438.14 hours. Scaled time: 880.23 units (timescale=2.009). Factorization parameters were as follows: n: 3454732649268037140651629992081894263362774944623633726957884046515864376096038447979084779442532000245131642678651564893028283221292314837219802797322498616193908862431 m: 1000000000000000000000000000000000000 c5: 10 c0: -9 skew: 0.98 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 9400001) Primes: RFBsize:501962, AFBsize:501581, largePrimes:6755535 encountered Relations: rels:7413387, finalFF:1315241 Max relations in full relation-set: 32 Initial matrix: 1003610 x 1315241 with sparse part having weight 83791927. Pruned matrix : 736585 x 741667 with weight 65509568. Total sieving time: 433.29 hours. Total relation processing time: 0.11 hours. Matrix solve time: 4.53 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 438.14 hours. --------- CPU info (if available) ----------

May 12, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(43·10¹⁶³-7)/9 = 4(7)_163<164> = 17 · 665881683559_<12> · 3731199745103581640718101353_<28> · C124
C124 = P61 · P63
P61 = 4940707832454493415501651784634079823643014735022300729459783_<61>
P63 = 228950862555947401946978886763873337701268538465930614150009641_<63>

Number: 47777_163 N=1131179319877381526484592406638873153964107702611935425473131250001541648222905288588232080460486389335504040917062171767903 ( 124 digits) SNFS difficulty: 164 digits. Divisors found: r1=4940707832454493415501651784634079823643014735022300729459783 (pp61) r2=228950862555947401946978886763873337701268538465930614150009641 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 181.33 hours. Scaled time: 122.58 units (timescale=0.676). Factorization parameters were as follows: name: 47777_163 n: 1131179319877381526484592406638873153964107702611935425473131250001541648222905288588232080460486389335504040917062171767903 m: 100000000000000000000000000000000 c5: 43000 c0: -7 skew: 0.17 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, 6700001) Primes: RFBsize:348513, AFBsize:348291, largePrimes:6066233 encountered Relations: rels:6239037, finalFF:799065 Max relations in full relation-set: 28 Initial matrix: 696871 x 799065 with sparse part having weight 64573761. Pruned matrix : 622367 x 625915 with weight 49390580. Total sieving time: 156.93 hours. Total relation processing time: 0.57 hours. Matrix solve time: 23.53 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 181.33 hours. --------- CPU info (if available) ----------

(17·10¹¹⁹+1)/9 = 1(8)₁₁₈9_<120> = 3² · 29 · 47 · 71 · 2417 · 44567363 · C103
C103 = P41 · P62
P41 = 86639197230970329577098695493425102913119_<41>
P62 = 23238157441907373887888004008759141749503788540363070255980273_<62>

Number: 18889_119 N=2013335305893753905147239573058748417504252779225347674038251424889645608319577440321753664083296901487 ( 103 digits) SNFS difficulty: 121 digits. Divisors found: r1=86639197230970329577098695493425102913119 (pp41) r2=23238157441907373887888004008759141749503788540363070255980273 (pp62) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.07 hours. Scaled time: 1.40 units (timescale=0.676). Factorization parameters were as follows: name: 18889_119 n: 2013335305893753905147239573058748417504252779225347674038251424889645608319577440321753664083296901487 m: 1000000000000000000000000 c5: 17 c0: 10 skew: 0.9 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63823, largePrimes:2084723 encountered Relations: rels:2152414, finalFF:219464 Max relations in full relation-set: 28 Initial matrix: 112986 x 219464 with sparse part having weight 18433757. Pruned matrix : 86159 x 86787 with weight 4759705. Total sieving time: 1.86 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.11 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.07 hours. --------- CPU info (if available) ----------

May 12, 2008

By Robert Backstrom / GGNFS, Msieve
(17·10¹⁵⁹-53)/9 = 1(8)₁₅₈3_<160> = 7 · 733 · C156
C156 = P47 · P109
P47 = 64373087450280690223885039799015227383176824847_<47>
P109 = 5718736130150877068395855148563309851888644433107510229967183373492458900540607629747479591403697254369712119_<109>

Number: n N=368132701011282184542757530479222157257627926113601420559128608241841529699647025704324476493644297191364039931570627341432252755581541393273999003876220793 ( 156 digits) SNFS difficulty: 161 digits. Divisors found: Mon May 12 02:28:47 2008 prp47 factor: 64373087450280690223885039799015227383176824847 Mon May 12 02:28:47 2008 prp109 factor: 5718736130150877068395855148563309851888644433107510229967183373492458900540607629747479591403697254369712119 Mon May 12 02:28:47 2008 elapsed time 01:46:51 (Msieve 1.35) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.79 hours. Scaled time: 65.47 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_8_158_3 n: 368132701011282184542757530479222157257627926113601420559128608241841529699647025704324476493644297191364039931570627341432252755581541393273999003876220793 skew: 1.99 deg: 5 c5: 17 c0: -530 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2400169) Primes: RFBsize:216816, AFBsize:217351, largePrimes:7254373 encountered Relations: rels:6651059, finalFF:451072 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 35.61 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 35.79 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(16·10¹⁷⁰+11)/9 = 1(7)₁₆₉9_<171> = 97 · C169
C169 = P48 · P121
P48 = 544927506016603202875320936707390870032381644203_<48>
P121 = 3363310854033769132027671298925141168506829437495958093452712839551811960294973871579104443447473715330880252358213138169_<121>

Number: n N=1832760595647193585337915234822451317296678121420389461626575028636884306987399770904925544100801832760595647193585337915234822451317296678121420389461626575028636884307 ( 169 digits) SNFS difficulty: 171 digits. Divisors found: Mon May 12 13:11:07 2008 prp48 factor: 544927506016603202875320936707390870032381644203 Mon May 12 13:11:07 2008 prp121 factor: 3363310854033769132027671298925141168506829437495958093452712839551811960294973871579104443447473715330880252358213138169 Mon May 12 13:11:07 2008 elapsed time 01:00:41 (Msieve 1.35) Version: GGNFS-0.77.1-20050930-k8 Total time: 45.52 hours. Scaled time: 38.20 units (timescale=0.839). Factorization parameters were as follows: name: KA_1_7_169_9 n: 1832760595647193585337915234822451317296678121420389461626575028636884306987399770904925544100801832760595647193585337915234822451317296678121420389461626575028636884307 type: snfs deg: 5 c5: 1 c0: 22 skew: 1.86 m: 20000000000000000000000000000000000 rlim: 3500000 alim: 3500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 5399990) Primes: RFBsize:250150, AFBsize:250502, largePrimes:6093794 encountered Relations: rels:6215521, finalFF:628867 Max relations in full relation-set: 28 Initial matrix: 500716 x 628867 with sparse part having weight 69517955. Pruned matrix : Total sieving time: 45.32 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,48,48,2.5,2.5,100000 total time: 45.52 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... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

(17·10¹⁵⁴+1)/9 = 1(8)₁₅₃9_<155> = 13 · 71 · C152
C152 = P75 · P78
P75 = 140600607147819071282411043598609766109102241498072762816470647254054550719_<75>
P78 = 145551777955531635886729066649473155038928609925267339235336817734887886875397_<78>

Number: n N=20464668351992295654267485253400746358492837366076802696521006380161309738774527506921873119056217647766943541591428915372577344408330323823281569760443 ( 152 digits) SNFS difficulty: 156 digits. Divisors found: Mon May 12 18:53:45 2008 prp75 factor: 140600607147819071282411043598609766109102241498072762816470647254054550719 Mon May 12 18:53:45 2008 prp78 factor: 145551777955531635886729066649473155038928609925267339235336817734887886875397 Mon May 12 18:53:45 2008 elapsed time 00:43:24 (Msieve 1.35) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.12 hours. Scaled time: 27.69 units (timescale=1.448). Factorization parameters were as follows: name: KA_1_8_153_9 n: 20464668351992295654267485253400746358492837366076802696521006380161309738774527506921873119056217647766943541591428915372577344408330323823281569760443 skew: 0.90 deg: 5 c5: 17 c0: 10 m: 10000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 900000) Primes: RFBsize:203362, AFBsize:203567, largePrimes:6640756 encountered Relations: rels:6105592, finalFF:466574 Max relations in full relation-set: 28 Initial matrix: 406994 x 466574 with sparse part having weight 28924041. Pruned matrix : 355349 x 357447 with weight 18031557. Total sieving time: 18.96 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 19.12 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 11, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve
(17·10¹³²+1)/9 = 1(8)₁₃₁9_<133> = 8803 · 29339 · 78461252861251661_<17> · C107
C107 = P33 · P75
P33 = 764434950764564155154419754456677_<33>
P75 = 121936753814368589908864502423562855042102683681063541354324629952254041961_<75>

Number: 18889_132 N=93212716398477633470908531852402735461671942666641846206285286787028561038608429955683517892828816714623597 ( 107 digits) SNFS difficulty: 133 digits. Divisors found: r1=764434950764564155154419754456677 (pp33) r2=121936753814368589908864502423562855042102683681063541354324629952254041961 (pp75) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.63 hours. Scaled time: 4.49 units (timescale=0.677). Factorization parameters were as follows: name: 18889_132 n: 93212716398477633470908531852402735461671942666641846206285286787028561038608429955683517892828816714623597 m: 100000000000000000000000000 c5: 1700 c0: 1 skew: 0.23 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:63983, largePrimes:1499560 encountered Relations: rels:1488645, finalFF:158343 Max relations in full relation-set: 28 Initial matrix: 128001 x 158343 with sparse part having weight 12844094. Pruned matrix : 119794 x 120498 with weight 8038832. Total sieving time: 6.24 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.26 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.63 hours. --------- CPU info (if available) ----------

(17·10¹¹³+1)/9 = 1(8)₁₁₂9_<114> = 3 · 53 · 89 · 2220046208670695120267_<22> · C88
C88 = P35 · P54
P35 = 18762080918146736784154405984746413_<35>
P54 = 320461795922942801708809319235463489099097846767274609_<54>

Sun May 11 03:36:19 2008 Msieve v. 1.35 Sun May 11 03:36:19 2008 random seeds: 9a6638be 9dc82e78 Sun May 11 03:36:19 2008 factoring 6012530146280878871724387278640046283639523062843790961849685220400824632099961998727517 (88 digits) Sun May 11 03:36:21 2008 searching for 15-digit factors Sun May 11 03:36:23 2008 commencing quadratic sieve (88-digit input) Sun May 11 03:36:23 2008 using multiplier of 13 Sun May 11 03:36:23 2008 using 64kb Pentium 4 sieve core Sun May 11 03:36:23 2008 sieve interval: 14 blocks of size 65536 Sun May 11 03:36:23 2008 processing polynomials in batches of 8 Sun May 11 03:36:23 2008 using a sieve bound of 1524241 (58000 primes) Sun May 11 03:36:23 2008 using large prime bound of 121939280 (26 bits) Sun May 11 03:36:23 2008 using double large prime bound of 358970217792320 (42-49 bits) Sun May 11 03:36:23 2008 using trial factoring cutoff of 49 bits Sun May 11 03:36:23 2008 polynomial 'A' values have 11 factors Sun May 11 04:48:35 2008 58535 relations (17055 full + 41480 combined from 603615 partial), need 58096 Sun May 11 04:48:38 2008 begin with 620670 relations Sun May 11 04:48:38 2008 reduce to 137330 relations in 11 passes Sun May 11 04:48:38 2008 attempting to read 137330 relations Sun May 11 04:48:42 2008 recovered 137330 relations Sun May 11 04:48:42 2008 recovered 107941 polynomials Sun May 11 04:48:42 2008 attempting to build 58535 cycles Sun May 11 04:48:42 2008 found 58534 cycles in 4 passes Sun May 11 04:48:42 2008 distribution of cycle lengths: Sun May 11 04:48:42 2008 length 1 : 17055 Sun May 11 04:48:42 2008 length 2 : 11927 Sun May 11 04:48:42 2008 length 3 : 10231 Sun May 11 04:48:42 2008 length 4 : 7473 Sun May 11 04:48:42 2008 length 5 : 4986 Sun May 11 04:48:42 2008 length 6 : 3101 Sun May 11 04:48:42 2008 length 7 : 1787 Sun May 11 04:48:42 2008 length 9+: 1974 Sun May 11 04:48:42 2008 largest cycle: 16 relations Sun May 11 04:48:43 2008 matrix is 58000 x 58534 (13.8 MB) with weight 3393855 (57.98/col) Sun May 11 04:48:43 2008 sparse part has weight 3393855 (57.98/col) Sun May 11 04:48:44 2008 filtering completed in 4 passes Sun May 11 04:48:44 2008 matrix is 52822 x 52886 (12.6 MB) with weight 3079016 (58.22/col) Sun May 11 04:48:44 2008 sparse part has weight 3079016 (58.22/col) Sun May 11 04:48:44 2008 saving the first 48 matrix rows for later Sun May 11 04:48:44 2008 matrix is 52774 x 52886 (9.2 MB) with weight 2535293 (47.94/col) Sun May 11 04:48:44 2008 sparse part has weight 2089021 (39.50/col) Sun May 11 04:48:44 2008 matrix includes 64 packed rows Sun May 11 04:48:44 2008 using block size 21154 for processor cache size 512 kB Sun May 11 04:48:45 2008 commencing Lanczos iteration Sun May 11 04:48:45 2008 memory use: 8.3 MB Sun May 11 04:49:16 2008 lanczos halted after 836 iterations (dim = 52774) Sun May 11 04:49:17 2008 recovered 18 nontrivial dependencies Sun May 11 04:49:17 2008 prp35 factor: 18762080918146736784154405984746413 Sun May 11 04:49:17 2008 prp54 factor: 320461795922942801708809319235463489099097846767274609 Sun May 11 04:49:17 2008 elapsed time 01:12:58

(17·10¹²⁹+1)/9 = 1(8)₁₂₈9_<130> = 852239 · 273146271888899_<15> · 30492449909076721_<17> · C93
C93 = P31 · P62
P31 = 6729959298046035632672774532523_<31>
P62 = 39540756448263316717593054313840418944154669628044642036622503_<62>

Sun May 11 05:52:11 2008 Msieve v. 1.35 Sun May 11 05:52:11 2008 random seeds: 8b66ad6c bf0aea57 Sun May 11 05:52:11 2008 factoring 266107681510763448035340107082246050075465189572361909539503641703667818407790475101647165069 (93 digits) Sun May 11 05:52:13 2008 searching for 15-digit factors Sun May 11 05:52:14 2008 commencing quadratic sieve (93-digit input) Sun May 11 05:52:15 2008 using multiplier of 5 Sun May 11 05:52:15 2008 using 64kb Pentium 4 sieve core Sun May 11 05:52:15 2008 sieve interval: 18 blocks of size 65536 Sun May 11 05:52:15 2008 processing polynomials in batches of 6 Sun May 11 05:52:15 2008 using a sieve bound of 1909319 (71765 primes) Sun May 11 05:52:15 2008 using large prime bound of 231027599 (27 bits) Sun May 11 05:52:15 2008 using double large prime bound of 1133952533144101 (42-51 bits) Sun May 11 05:52:15 2008 using trial factoring cutoff of 51 bits Sun May 11 05:52:15 2008 polynomial 'A' values have 12 factors Sun May 11 10:31:39 2008 72146 relations (17646 full + 54500 combined from 969220 partial), need 71861 Sun May 11 10:31:44 2008 begin with 986866 relations Sun May 11 10:31:45 2008 reduce to 186840 relations in 11 passes Sun May 11 10:31:45 2008 attempting to read 186840 relations Sun May 11 10:31:51 2008 recovered 186840 relations Sun May 11 10:31:51 2008 recovered 170297 polynomials Sun May 11 10:31:51 2008 attempting to build 72146 cycles Sun May 11 10:31:51 2008 found 72146 cycles in 5 passes Sun May 11 10:31:51 2008 distribution of cycle lengths: Sun May 11 10:31:51 2008 length 1 : 17646 Sun May 11 10:31:51 2008 length 2 : 12583 Sun May 11 10:31:51 2008 length 3 : 12249 Sun May 11 10:31:51 2008 length 4 : 9903 Sun May 11 10:31:51 2008 length 5 : 7433 Sun May 11 10:31:51 2008 length 6 : 4817 Sun May 11 10:31:51 2008 length 7 : 3200 Sun May 11 10:31:51 2008 length 9+: 4315 Sun May 11 10:31:51 2008 largest cycle: 22 relations Sun May 11 10:31:51 2008 matrix is 71765 x 72146 (18.0 MB) with weight 4433526 (61.45/col) Sun May 11 10:31:51 2008 sparse part has weight 4433526 (61.45/col) Sun May 11 10:31:53 2008 filtering completed in 3 passes Sun May 11 10:31:53 2008 matrix is 68458 x 68522 (17.1 MB) with weight 4218924 (61.57/col) Sun May 11 10:31:53 2008 sparse part has weight 4218924 (61.57/col) Sun May 11 10:31:53 2008 saving the first 48 matrix rows for later Sun May 11 10:31:54 2008 matrix is 68410 x 68522 (10.0 MB) with weight 3180791 (46.42/col) Sun May 11 10:31:54 2008 sparse part has weight 2218415 (32.38/col) Sun May 11 10:31:54 2008 matrix includes 64 packed rows Sun May 11 10:31:54 2008 using block size 21845 for processor cache size 512 kB Sun May 11 10:31:54 2008 commencing Lanczos iteration Sun May 11 10:31:54 2008 memory use: 10.3 MB Sun May 11 10:32:41 2008 lanczos halted after 1084 iterations (dim = 68410) Sun May 11 10:32:41 2008 recovered 18 nontrivial dependencies Sun May 11 10:32:42 2008 prp31 factor: 6729959298046035632672774532523 Sun May 11 10:32:42 2008 prp62 factor: 39540756448263316717593054313840418944154669628044642036622503 Sun May 11 10:32:42 2008 elapsed time 04:40:31

(17·10¹⁴⁰+1)/9 = 1(8)₁₃₉9_<141> = 3 · 7 · 3023 · 7121 · 142888091809_<12> · 959922253880171_<15> · 43808521896921204679_<20> · C86
C86 = P30 · P56
P30 = 887678841787165579554448685089_<30>
P56 = 78336004908801861872486359113613068126829797389465976247_<56>

un May 11 10:42:17 2008 Msieve v. 1.35 Sun May 11 10:42:17 2008 random seeds: 9850883f 57e30385 Sun May 11 10:42:17 2008 factoring 69537214107678954149627935760226226356182538302600223483249920864963697363052857080983 (86 digits) Sun May 11 10:42:18 2008 searching for 15-digit factors Sun May 11 10:42:20 2008 commencing quadratic sieve (86-digit input) Sun May 11 10:42:20 2008 using multiplier of 7 Sun May 11 10:42:20 2008 using 64kb Pentium 4 sieve core Sun May 11 10:42:20 2008 sieve interval: 9 blocks of size 65536 Sun May 11 10:42:20 2008 processing polynomials in batches of 12 Sun May 11 10:42:20 2008 using a sieve bound of 1466053 (56000 primes) Sun May 11 10:42:20 2008 using large prime bound of 117284240 (26 bits) Sun May 11 10:42:20 2008 using double large prime bound of 334681134421600 (41-49 bits) Sun May 11 10:42:20 2008 using trial factoring cutoff of 49 bits Sun May 11 10:42:20 2008 polynomial 'A' values have 11 factors Sun May 11 11:33:39 2008 56345 relations (16828 full + 39517 combined from 574612 partial), need 56096 Sun May 11 11:33:42 2008 begin with 591440 relations Sun May 11 11:33:42 2008 reduce to 130331 relations in 10 passes Sun May 11 11:33:42 2008 attempting to read 130331 relations Sun May 11 11:33:46 2008 recovered 130331 relations Sun May 11 11:33:46 2008 recovered 102621 polynomials Sun May 11 11:33:46 2008 attempting to build 56345 cycles Sun May 11 11:33:46 2008 found 56344 cycles in 4 passes Sun May 11 11:33:46 2008 distribution of cycle lengths: Sun May 11 11:33:46 2008 length 1 : 16828 Sun May 11 11:33:46 2008 length 2 : 11654 Sun May 11 11:33:46 2008 length 3 : 10013 Sun May 11 11:33:46 2008 length 4 : 7125 Sun May 11 11:33:46 2008 length 5 : 4675 Sun May 11 11:33:46 2008 length 6 : 2828 Sun May 11 11:33:46 2008 length 7 : 1601 Sun May 11 11:33:46 2008 length 9+: 1620 Sun May 11 11:33:46 2008 largest cycle: 18 relations Sun May 11 11:33:46 2008 matrix is 56000 x 56344 (12.4 MB) with weight 3029132 (53.76/col) Sun May 11 11:33:46 2008 sparse part has weight 3029132 (53.76/col) Sun May 11 11:33:47 2008 filtering completed in 3 passes Sun May 11 11:33:47 2008 matrix is 50377 x 50441 (11.2 MB) with weight 2735941 (54.24/col) Sun May 11 11:33:47 2008 sparse part has weight 2735941 (54.24/col) Sun May 11 11:33:47 2008 saving the first 48 matrix rows for later Sun May 11 11:33:47 2008 matrix is 50329 x 50441 (6.9 MB) with weight 2087392 (41.38/col) Sun May 11 11:33:48 2008 sparse part has weight 1507293 (29.88/col) Sun May 11 11:33:48 2008 matrix includes 64 packed rows Sun May 11 11:33:48 2008 using block size 20176 for processor cache size 512 kB Sun May 11 11:33:48 2008 commencing Lanczos iteration Sun May 11 11:33:48 2008 memory use: 7.0 MB Sun May 11 11:34:14 2008 lanczos halted after 798 iterations (dim = 50327) Sun May 11 11:34:14 2008 recovered 16 nontrivial dependencies Sun May 11 11:34:16 2008 prp30 factor: 887678841787165579554448685089 Sun May 11 11:34:16 2008 prp56 factor: 78336004908801861872486359113613068126829797389465976247 Sun May 11 11:34:16 2008 elapsed time 00:51:59

May 11, 2008 (2nd)

By Robert Backstrom / GGNFS
(17·10¹¹⁵+1)/9 = 1(8)₁₁₄9_<116> = 4519 · C112
C112 = P38 · P74
P38 = 85206749882772292395357406238644765829_<38>
P74 = 49055767028910420725937601905379783432564947652856091509002810221880045139_<74>

Number: n N=4179882471539917877603206215731110619360232106414890216616262201568685304024980944653438568021440338324604755231 ( 112 digits) SNFS difficulty: 116 digits. Divisors found: r1=85206749882772292395357406238644765829 (pp38) r2=49055767028910420725937601905379783432564947652856091509002810221880045139 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.05 hours. Scaled time: 1.53 units (timescale=1.453). Factorization parameters were as follows: name: KA_1_8_114_9 n: 4179882471539917877603206215731110619360232106414890216616262201568685304024980944653438568021440338324604755231 skew: 0.90 deg: 5 c5: 17 c0: 1 m: 100000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:78498, AFBsize:78436, largePrimes:3886230 encountered Relations: rels:3300843, finalFF:184286 Max relations in full relation-set: 28 Initial matrix: 156999 x 184286 with sparse part having weight 7862251. Pruned matrix : 129226 x 130074 with weight 4084209. Total sieving time: 0.86 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 1.05 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(17·10¹³⁴+1)/9 = 1(8)₁₃₃9_<135> = 3 · 7 · 409 · 1301 · C128
C128 = P38 · P91
P38 = 12714871233905837021626832695666376227_<38>
P91 = 1329457769065054174158179915996114710331432479966297431062804648433587475807882771460823363_<91>

Number: n N=16903884344577886690498956031018070938463188923151073763072432517978449357170634202219835990360450574429289316652620035949391401 ( 128 digits) SNFS difficulty: 136 digits. Divisors found: r1=12714871233905837021626832695666376227 (pp38) r2=1329457769065054174158179915996114710331432479966297431062804648433587475807882771460823363 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.82 hours. Scaled time: 5.52 units (timescale=1.447). Factorization parameters were as follows: name: KA_1_8_133_9 n: 16903884344577886690498956031018070938463188923151073763072432517978449357170634202219835990360450574429289316652620035949391401 skew: 0.90 deg: 5 c5: 17 c0: 10 m: 1000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 420001) Primes: RFBsize:148933, AFBsize:148425, largePrimes:5309234 encountered Relations: rels:4787842, finalFF:368807 Max relations in full relation-set: 28 Initial matrix: 297423 x 368807 with sparse part having weight 17430308. Pruned matrix : 230148 x 231699 with weight 8092085. Total sieving time: 3.08 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.59 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000 total time: 3.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 11, 2008

By Robert Backstrom / GGNFS
(17·10¹⁰⁴+1)/9 = 1(8)₁₀₃9_<105> = 3 · 7 · 23 · C102
C102 = P48 · P55
P48 = 265864911884614770878329372513092064450057351103_<48>
P55 = 1470951173457249660790510390603202909803884594187358861_<55>

Number: n N=391074304117782378651943869335173682999769956291695422130204738900391074304117782378651943869335173683 ( 102 digits) SNFS difficulty: 106 digits. Divisors found: r1=265864911884614770878329372513092064450057351103 (pp48) r2=1470951173457249660790510390603202909803884594187358861 (pp55) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.65 hours. Scaled time: 0.78 units (timescale=1.187). Factorization parameters were as follows: name: KA_1_8_103_9 n: 391074304117782378651943869335173682999769956291695422130204738900391074304117782378651943869335173683 skew: 0.90 deg: 5 c5: 17 c0: 10 m: 1000000000000000000000 type: snfs rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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: 48/48 Sieved algebraic special-q in [100000, 140001) Primes: RFBsize:63951, AFBsize:63823, largePrimes:3718009 encountered Relations: rels:3165750, finalFF:190127 Max relations in full relation-set: 28 Initial matrix: 127839 x 190127 with sparse part having weight 7841354. Pruned matrix : 76058 x 76761 with weight 2308544. Total sieving time: 0.56 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,106,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000 total time: 0.65 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 10, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve
(17·10¹⁶⁵-53)/9 = 1(8)₁₆₄3_<166> = 7 · 29 · C163
C163 = P77 · P87
P77 = 43402480428621987030205003566889274936988593086053286493942371994002021584433_<77>
P87 = 214385705193492725009349612317191476170118142711660225267764600968001857107379610049417_<87>

Number: n N=9304871373836891078270388615216201423097974822112753147235905856595511767925561029009304871373836891078270388615216201423097974822112753147235905856595511767925561 ( 163 digits) SNFS difficulty: 166 digits. Divisors found: Sat May 10 22:25:30 2008 prp77 factor: 43402480428621987030205003566889274936988593086053286493942371994002021584433 Sat May 10 22:25:30 2008 prp87 factor: 214385705193492725009349612317191476170118142711660225267764600968001857107379610049417 Sat May 10 22:25:30 2008 elapsed time 01:40:15 (Msieve 1.35) Version: GGNFS-0.77.1-20051202-athlon Total time: 63.69 hours. Scaled time: 92.60 units (timescale=1.454). Factorization parameters were as follows: name: KA_1_8_164_3 n: 9304871373836891078270388615216201423097974822112753147235905856595511767925561029009304871373836891078270388615216201423097974822112753147235905856595511767925561 skew: 1.26 deg: 5 c5: 17 c0: -53 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3400001) Primes: RFBsize:216816, AFBsize:215951, largePrimes:7486111 encountered Relations: rels:6868633, finalFF:449713 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 63.43 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 63.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 10, 2008

The factor table of 188...889 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 9, 2008 (4th)

By Wataru Sakai / GGNFS
(7·10¹⁹⁶-43)/9 = (7)₁₉₅3_<196> = 3² · 773 · 1283808358934056767222095093_<28> · 2620302803462725418522123017_<28> · C138
C138 = P64 · P74
P64 = 3543854126479629404194342535389768714682873298488000234516262161_<64>
P74 = 93779089025421898269355240230012909396341206292481875062343831519528856229_<74>

Number: template N=332339411620241921667758139292075249481033920519211972712773710323231368221675760778894882184866260658051286208269366836796238604641850869 ( 138 digits) Divisors found: r1=3543854126479629404194342535389768714682873298488000234516262161 (pp64) r2=93779089025421898269355240230012909396341206292481875062343831519528856229 (pp74) Version: GGNFS-0.77.1-20060722-nocona Total time: 2441.17 hours. Scaled time: 4906.75 units (timescale=2.010). Factorization parameters were as follows: name: template n: 332339411620241921667758139292075249481033920519211972712773710323231368221675760778894882184866260658051286208269366836796238604641850869 skew: 633970.78 # norm 2.37e+19 c5: 139560 c4: 459904593894 c3: -126980206595135003 c2: -161343727948017254210674 c1: 28008909286869388566227571068 c0: 7362373410681343420678015225067305 # alpha -5.99 Y1: 524199648991469 Y0: -298788360335374199376115932 # Murphy_E 2.20e-11 # M 1149381156828760038636208504312778076181482399815369717819531744821170386726634917697242824590468521180129638888519451984000293384578269 type: gnfs rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 60000 Factor 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, 38880001) Primes: RFBsize:374362, AFBsize:374845, largePrimes:11794582 encountered Relations: rels:17293160, finalFF:861795 Max relations in full relation-set: 32 Initial matrix: 749287 x 861795 with sparse part having weight 177161076. Pruned matrix : 694434 x 698244 with weight 162974487. Total sieving time: 2429.94 hours. Total relation processing time: 1.60 hours. Matrix solve time: 9.05 hours. Time per square root: 0.58 hours. Prototype def-par.txt line would be: gnfs,137,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000 total time: 2441.17 hours. --------- CPU info (if available) ----------

May 9, 2008 (3rd)

By Jo Yeong Uk / GGNFS
(14·10¹⁷⁷+31)/9 = 1(5)₁₇₆9_<178> = C178
C178 = P70 · P109
P70 = 1096328539362005176413092222756577932801642557082525242167262230187171_<70>
P109 = 1418877188457386922625323450174283086499815757388954272526173072437542925270309130364696618460095061630075629_<109>

Number: 15559_177 N=1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559 ( 178 digits) SNFS difficulty: 178 digits. Divisors found: r1=1096328539362005176413092222756577932801642557082525242167262230187171 (pp70) r2=1418877188457386922625323450174283086499815757388954272526173072437542925270309130364696618460095061630075629 (pp109) Version: GGNFS-0.77.1-20050930-nocona Total time: 219.39 hours. Scaled time: 522.80 units (timescale=2.383). Factorization parameters were as follows: n: 1555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559 m: 200000000000000000000000000000000000 c5: 175 c0: 124 skew: 0.93 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [4500000, 8700001) Primes: RFBsize:602489, AFBsize:602061, largePrimes:11158562 encountered Relations: rels:11397768, finalFF:1426718 Max relations in full relation-set: 28 Initial matrix: 1204617 x 1426718 with sparse part having weight 98668142. Pruned matrix : 1013971 x 1020058 with weight 71526964. Total sieving time: 210.79 hours. Total relation processing time: 0.24 hours. Matrix solve time: 8.25 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,178,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.6,2.6,100000 total time: 219.39 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.48 BogoMIPS (lpj=2672242) Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672351)

May 9, 2008 (2nd)

By Robert Backstrom / GMP-ECM, Msieve
(4·10¹⁶⁹+17)/3 = 1(3)₁₆₈9_<170> = 787 · 540101 · 1340039 · 33282371 · 1228724437_<10> · 16622933878153_<14> · C125
C125 = P35 · P43 · P48
P35 = 54993925552292230908242328636465353_<35>
P43 = 2748027937502551074896604229460386066456913_<43>
P48 = 227855381034873924333702464731031467728937974797_<48>

Fri May 9 04:21:35 2008 Fri May 9 04:21:35 2008 Fri May 9 04:21:35 2008 Msieve v. 1.34 Fri May 9 04:21:35 2008 random seeds: 691b551c 6b560d30 Fri May 9 04:21:35 2008 factoring 12530661861321035695461437620308285858371167816021440960712419669439223860277708341 (83 digits) Fri May 9 04:21:35 2008 no P-1/P+1/ECM available, skipping Fri May 9 04:21:35 2008 commencing quadratic sieve (83-digit input) Fri May 9 04:21:35 2008 using multiplier of 61 Fri May 9 04:21:35 2008 using 64kb Opteron sieve core Fri May 9 04:21:35 2008 sieve interval: 6 blocks of size 65536 Fri May 9 04:21:35 2008 processing polynomials in batches of 17 Fri May 9 04:21:35 2008 using a sieve bound of 1359329 (52059 primes) Fri May 9 04:21:35 2008 using large prime bound of 125058268 (26 bits) Fri May 9 04:21:35 2008 using trial factoring cutoff of 27 bits Fri May 9 04:21:35 2008 polynomial 'A' values have 11 factors Fri May 9 04:35:11 2008 52262 relations (27275 full + 24987 combined from 270355 partial), need 52155 Fri May 9 04:35:11 2008 begin with 297630 relations Fri May 9 04:35:11 2008 reduce to 74125 relations in 2 passes Fri May 9 04:35:11 2008 attempting to read 74125 relations Fri May 9 04:35:12 2008 recovered 74125 relations Fri May 9 04:35:12 2008 recovered 66164 polynomials Fri May 9 04:35:12 2008 attempting to build 52262 cycles Fri May 9 04:35:12 2008 found 52262 cycles in 1 passes Fri May 9 04:35:12 2008 distribution of cycle lengths: Fri May 9 04:35:12 2008 length 1 : 27275 Fri May 9 04:35:12 2008 length 2 : 24987 Fri May 9 04:35:12 2008 largest cycle: 2 relations Fri May 9 04:35:12 2008 matrix is 52059 x 52262 (7.2 MB) with weight 1681414 (32.17/col) Fri May 9 04:35:12 2008 sparse part has weight 1681414 (32.17/col) Fri May 9 04:35:12 2008 filtering completed in 4 passes Fri May 9 04:35:12 2008 matrix is 44666 x 44730 (6.1 MB) with weight 1410257 (31.53/col) Fri May 9 04:35:12 2008 sparse part has weight 1410257 (31.53/col) Fri May 9 04:35:12 2008 saving the first 48 matrix rows for later Fri May 9 04:35:12 2008 matrix is 44618 x 44730 (3.7 MB) with weight 1022140 (22.85/col) Fri May 9 04:35:12 2008 sparse part has weight 706896 (15.80/col) Fri May 9 04:35:12 2008 matrix includes 64 packed rows Fri May 9 04:35:12 2008 commencing Lanczos iteration Fri May 9 04:35:12 2008 memory use: 5.4 MB Fri May 9 04:35:43 2008 lanczos halted after 707 iterations (dim = 44606) Fri May 9 04:35:44 2008 recovered 12 nontrivial dependencies Fri May 9 04:35:44 2008 prp35 factor: 54993925552292230908242328636465353 Fri May 9 04:35:44 2008 prp48 factor: 227855381034873924333702464731031467728937974797 Fri May 9 04:35:44 2008 elapsed time 00:14:09

May 9, 2008

By Justin Card / GGNFS
(17·10¹⁶¹-53)/9 = 1(8)₁₆₀3_<162> = 3 · 19 · 43 · 254355202674105893_<18> · 3287574485420198704133928558179_<31> · C110
C110 = P37 · P74
P37 = 6592109827352816863838466122643365447_<37>
P74 = 13980491502316873967791731851571399701122210654779288236879044841952532537_<74>

Number: worktodo N=92160935423645611317768122235971519726726074113585668724342529983025445149705393998167342865053046962449049039 ( 110 digits) Divisors found: r1=6592109827352816863838466122643365447 r2=13980491502316873967791731851571399701122210654779288236879044841952532537 Version: Total time: 24.24 hours. Scaled time: 48.91 units (timescale=2.018). Factorization parameters were as follows: name: worktodo n: 92160935423645611317768122235971519726726074113585668724342529983025445149705393998167342865053046962449049039 skew: 33082.85 # norm 4.09e+15 c5: 12600 c4: 2267365945 c3: -155321015926195 c2: -2349240279840559620 c1: 12982214017744131860983 c0: -31622288422337636799496945 # alpha -6.00 Y1: 379217522827 Y0: -1488782601061726047438 # Murphy_E 9.05e-10 # M 6562666969988531225364949784099942114382953390221344757651863751224118313342204937610904748802425250931949588 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, 2400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 407644 x 407892 Total sieving time: 24.24 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 24.24 hours. --------- CPU info (if available) ----------

May 8, 2008 (4th)

By Jo Yeong Uk / GGNFS
8·10¹⁸¹-1 = 7(9)_181<182> = 7821454222070056969_<19> · C164
C164 = P51 · P113
P51 = 788439573104899094381095893696862654025503474927799_<51>
P113 = 12972810228209453983816901634265018328778556886502519239281435619824317355319728543086413776308502828632117225329_<113>

Number: 79999_181 N=10228276958300330498080736507519279486105205969987660391195978740025086788072414219094013040085242030630292224665357961760845294364879206193081236289180022489020871 ( 164 digits) SNFS difficulty: 182 digits. Divisors found: r1=788439573104899094381095893696862654025503474927799 (pp51) r2=12972810228209453983816901634265018328778556886502519239281435619824317355319728543086413776308502828632117225329 (pp113) Version: GGNFS-0.77.1-20050930-nocona Total time: 191.88 hours. Scaled time: 453.03 units (timescale=2.361). Factorization parameters were as follows: n: 10228276958300330498080736507519279486105205969987660391195978740025086788072414219094013040085242030630292224665357961760845294364879206193081236289180022489020871 m: 2000000000000000000000000000000000000 c5: 5 c0: -2 skew: 0.83 type: snfs 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, 8600001) Primes: RFBsize:664579, AFBsize:664045, largePrimes:11037168 encountered Relations: rels:11404548, finalFF:1577413 Max relations in full relation-set: 28 Initial matrix: 1328689 x 1577413 with sparse part having weight 92971068. Pruned matrix : 1097910 x 1104617 with weight 60006284. Total sieving time: 183.42 hours. Total relation processing time: 0.21 hours. Matrix solve time: 8.15 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000 total time: 191.88 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.48 BogoMIPS (lpj=2672242) Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672351)

May 8, 2008 (3rd)

By Justin Card / GGNFS
(17·10¹⁵⁰-53)/9 = 1(8)₁₄₉3_<151> = 139 · 1109 · 19867 · 53699 · C137
C137 = P56 · P81
P56 = 58524777302241362713821490265536758164758485666839114161_<56>
P81 = 196255486079589701227585169591220827496285377009347149826952814709503321846950741_<81>

Number: 18883_150 N=11485808617151117068599663545151818379779946947029462334170568301636248776109389736647593871953122496252803763639449645494895547442543301 ( 137 digits) SNFS difficulty: 151 digits. Divisors found: r1=58524777302241362713821490265536758164758485666839114161 r2=196255486079589701227585169591220827496285377009347149826952814709503321846950741 Version: Total time: 21.46 hours. Scaled time: 43.31 units (timescale=2.018). Factorization parameters were as follows: n: 11485808617151117068599663545151818379779946947029462334170568301636248776109389736647593871953122496252803763639449645494895547442543301 m: 1000000000000000000000000000000 c5: 17 c0: -53 Y1: 1 Y0: -1000000000000000000000000000000 skew: 1.26 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, 1200000) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 336747 x 336995 Total sieving time: 21.46 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.29 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 21.46 hours. --------- CPU info (if available) ----------

May 8, 2008 (2nd)

By Robert Backstrom / GMP-ECM, Msieve
(14·10¹⁹⁵+31)/9 = 1(5)₁₉₄9_<196> = 3517 · 72959 · 119831 · 174723560293_<12> · 29908448484246570631_<20> · 296464817923705928738027_<24> · C128
C128 = P38 · P90
P38 = 67438308398974187180622772855468793089_<38>
P90 = 484216870346117642180865357051076528493767653821960944086179418529064377186836629909208187_<90>
(4·10¹⁸⁸+11)/3 = 1(3)₁₈₇7_<189> = 647 · 3129923 · 26842061 · 6040965932401_<13> · 14857068261935316657329056727_<29> · C131
C131 = P34 · P98
P34 = 1736857011312162555994210469872451_<34>
P98 = 15735529880735063854034395949750241973639121882661501326917621354847802201149038459287456328343941_<98>
(11·10¹⁸²+61)/9 = 1(2)₁₈₁9_<183> = 3 · 5287159 · 6837552090639889_<16> · 215270056119179928842411146396979_<33> · C127
C127 = P39 · P41 · P48
P39 = 386743518904360880703905991006429255227_<39>
P41 = 15816269637526716768726379630499787809243_<41>
P48 = 855845109201103507837814977690861986896119008947_<48>

Thu May 8 22:23:43 2008 Thu May 8 22:23:43 2008 Thu May 8 22:23:43 2008 Msieve v. 1.34 Thu May 8 22:23:43 2008 random seeds: 447cc43b 31aa6ae9 Thu May 8 22:23:43 2008 factoring 13536277015083150708358105307944157502727791650822840210249683528781966042510629446297121 (89 digits) Thu May 8 22:23:43 2008 no P-1/P+1/ECM available, skipping Thu May 8 22:23:43 2008 commencing quadratic sieve (89-digit input) Thu May 8 22:23:44 2008 using multiplier of 1 Thu May 8 22:23:44 2008 using 64kb Opteron sieve core Thu May 8 22:23:44 2008 sieve interval: 14 blocks of size 65536 Thu May 8 22:23:44 2008 processing polynomials in batches of 8 Thu May 8 22:23:44 2008 using a sieve bound of 1520879 (58333 primes) Thu May 8 22:23:44 2008 using large prime bound of 121670320 (26 bits) Thu May 8 22:23:44 2008 using double large prime bound of 357546364197680 (42-49 bits) Thu May 8 22:23:44 2008 using trial factoring cutoff of 49 bits Thu May 8 22:23:44 2008 polynomial 'A' values have 11 factors Thu May 8 23:01:20 2008 58833 relations (15979 full + 42854 combined from 614451 partial), need 58429 Thu May 8 23:01:20 2008 begin with 630430 relations Thu May 8 23:01:20 2008 reduce to 142082 relations in 9 passes Thu May 8 23:01:20 2008 attempting to read 142082 relations Thu May 8 23:01:21 2008 recovered 142082 relations Thu May 8 23:01:21 2008 recovered 118230 polynomials Thu May 8 23:01:21 2008 attempting to build 58833 cycles Thu May 8 23:01:21 2008 found 58833 cycles in 5 passes Thu May 8 23:01:21 2008 distribution of cycle lengths: Thu May 8 23:01:21 2008 length 1 : 15979 Thu May 8 23:01:21 2008 length 2 : 11357 Thu May 8 23:01:21 2008 length 3 : 10582 Thu May 8 23:01:21 2008 length 4 : 7805 Thu May 8 23:01:21 2008 length 5 : 5245 Thu May 8 23:01:21 2008 length 6 : 3550 Thu May 8 23:01:21 2008 length 7 : 2031 Thu May 8 23:01:21 2008 length 9+: 2284 Thu May 8 23:01:21 2008 largest cycle: 18 relations Thu May 8 23:01:22 2008 matrix is 58333 x 58833 (14.0 MB) with weight 3422665 (58.18/col) Thu May 8 23:01:22 2008 sparse part has weight 3422665 (58.18/col) Thu May 8 23:01:22 2008 filtering completed in 3 passes Thu May 8 23:01:22 2008 matrix is 54281 x 54344 (12.9 MB) with weight 3170823 (58.35/col) Thu May 8 23:01:22 2008 sparse part has weight 3170823 (58.35/col) Thu May 8 23:01:22 2008 saving the first 48 matrix rows for later Thu May 8 23:01:22 2008 matrix is 54233 x 54344 (8.9 MB) with weight 2545096 (46.83/col) Thu May 8 23:01:22 2008 sparse part has weight 2008783 (36.96/col) Thu May 8 23:01:22 2008 matrix includes 64 packed rows Thu May 8 23:01:22 2008 using block size 21737 for processor cache size 1024 kB Thu May 8 23:01:23 2008 commencing Lanczos iteration Thu May 8 23:01:23 2008 memory use: 8.4 MB Thu May 8 23:01:41 2008 lanczos halted after 859 iterations (dim = 54229) Thu May 8 23:01:41 2008 recovered 14 nontrivial dependencies Thu May 8 23:01:42 2008 prp41 factor: 15816269637526716768726379630499787809243 Thu May 8 23:01:42 2008 prp48 factor: 855845109201103507837814977690861986896119008947 Thu May 8 23:01:42 2008 elapsed time 00:37:59

May 8, 2008

By Robert Backstrom / GGNFS, Msieve
(25·10¹⁸⁵-1)/3 = 8(3)_185<186> = 877 · 1380443 · 216888485620043_<15> · 323366540549594477093_<21> · C142
C142 = P60 · P83
P60 = 880905126532956667848805335238198593911413113053283385249717_<60>
P83 = 11141405152029028996571436570066231843415229390926814860984551946924997119693480441_<83>

Number: n N=9814520915203067108861318616106861980723536434273639929210502060032509597936265847719548119380237456211747556776071673719211139066269640285197 ( 142 digits) SNFS difficulty: 186 digits. Divisors found: Thu May 8 01:31:10 2008 prp60 factor: 880905126532956667848805335238198593911413113053283385249717 Thu May 8 01:31:10 2008 prp83 factor: 11141405152029028996571436570066231843415229390926814860984551946924997119693480441 Thu May 8 01:31:10 2008 elapsed time 02:13:43 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 80.43 hours. Scaled time: 67.16 units (timescale=0.835). Factorization parameters were as follows: name: KA_8_3_185 n: 9814520915203067108861318616106861980723536434273639929210502060032509597936265847719548119380237456211747556776071673719211139066269640285197 type: snfs deg: 5 c5: 25 c0: -1 skew: 0.53 m: 10000000000000000000000000000000000000 rlim: 7000000 alim: 7000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 9999990) Primes: RFBsize:476648, AFBsize:475734, largePrimes:6401443 encountered Relations: rels:6804178, finalFF:1070473 Max relations in full relation-set: 28 Initial matrix: 952446 x 1070473 with sparse part having weight 65768427. Pruned matrix : Total sieving time: 80.22 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,186,5,0,0,0,0,0,0,0,0,7000000,7000000,27,27,48,48,2.5,2.5,100000 total time: 80.43 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

May 7, 2008

By Jo Yeong Uk / GMP-ECM, GGNFS
(17·10¹⁶¹-53)/9 = 1(8)₁₆₀3_<162> = 3 · 19 · 43 · 254355202674105893_<18> · C141
C141 = P31 · C110
P31 = 3287574485420198704133928558179_<31>
C110 = [92160935423645611317768122235971519726726074113585668724342529983025445149705393998167342865053046962449049039_<110>]
(17·10¹⁶⁴-53)/9 = 1(8)₁₆₃3_<165> = 3 · 3162156699067_<13> · 262881178953307_<15> · 105290032030122334034954183_<27> · C111
C111 = P55 · P57
P55 = 1216259663201331434035013956830378303572945186485863881_<55>
P57 = 591464542648869639542420113968295913254867921520280460903_<57>

Number: 18883_164 N=719374465437643719673155958990646694072313754932899142898045569823974710056813761548010949545481947900800344543 ( 111 digits) Divisors found: r1=1216259663201331434035013956830378303572945186485863881 (pp55) r2=591464542648869639542420113968295913254867921520280460903 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.70 hours. Scaled time: 37.30 units (timescale=2.376). Factorization parameters were as follows: name: 18883_164 n: 719374465437643719673155958990646694072313754932899142898045569823974710056813761548010949545481947900800344543 skew: 18557.77 # norm 3.73e+15 c5: 64800 c4: 11133954640 c3: -106032251608850 c2: -5726041892371431773 c1: 10229939804823287742570 c0: -4521566322811507267369192 # alpha -6.05 Y1: 2901225613 Y0: -1618363130240665777689 # Murphy_E 8.01e-10 # M 111225469245920816024952471555682815374427338915935731619376144303250142866072342485964589906349848316772010006 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:175934, largePrimes:7511808 encountered Relations: rels:7245607, finalFF:405867 Max relations in full relation-set: 28 Initial matrix: 352312 x 405867 with sparse part having weight 38930358. Pruned matrix : 317084 x 318909 with weight 27771207. Polynomial selection time: 0.84 hours. Total sieving time: 14.07 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.57 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000 total time: 15.70 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.48 BogoMIPS (lpj=2672242) Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672351)

May 6, 2008 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM
(17·10¹⁴⁹-53)/9 = 1(8)₁₄₈3_<150> = 3² · 131 · 255137 · 3375511 · C135
C135 = P40 · P95
P40 = 5388930257121078729270880943678492107897_<40>
P95 = 34520499532221180433112166674230849735039209965903167809354543240545253834351079688548856476663_<95>

Number: 18883_149 N=186028564420120763869411900228851597728893983321120725406369201290270575424216972614176528429421435137778820470318466817128999458507711 ( 135 digits) SNFS difficulty: 151 digits. Divisors found: r1=5388930257121078729270880943678492107897 (pp40) r2=34520499532221180433112166674230849735039209965903167809354543240545253834351079688548856476663 (pp95) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.38 hours. Scaled time: 36.40 units (timescale=2.367). Factorization parameters were as follows: n: 186028564420120763869411900228851597728893983321120725406369201290270575424216972614176528429421435137778820470318466817128999458507711 m: 1000000000000000000000000000000 c5: 17 c0: -530 skew: 1.99 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:176478, largePrimes:5642114 encountered Relations: rels:5569954, finalFF:478847 Max relations in full relation-set: 28 Initial matrix: 352845 x 478847 with sparse part having weight 44707797. Pruned matrix : 304861 x 306689 with weight 25872555. Total sieving time: 14.76 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.51 hours. Time per square root: 0.04 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: 15.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹⁵⁷-53)/9 = 1(8)₁₅₆3_<158> = 13 · 103 · 1606069667_<10> · 96829103143_<11> · C134
C134 = P40 · P95
P40 = 7966230062417543067682362213686161549493_<40>
P95 = 11386826441643864898561421221923570419394152237250887959212635282363431012333153776133535984209_<95>

May 6, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(64·10¹⁶⁶+53)/9 = 7(1)₁₆₅7_<167> = 17 · 19 · 5483057904307_<13> · 125102202163039_<15> · C138
C138 = P57 · P82
P57 = 189017252553419561480806004528870537398168187166973127563_<57>
P82 = 1698031369177711247850014025611530461767387472590376241897452371528925800729051521_<82>

Number: n N=320957224151492255429082127231488936975920891075446305694396741711567954921815157690547768799927437761891217541762696415656265015932173323 ( 138 digits) SNFS difficulty: 167 digits. Divisors found: Tue May 06 11:05:04 2008 prp57 factor: 189017252553419561480806004528870537398168187166973127563 Tue May 06 11:05:04 2008 prp82 factor: 1698031369177711247850014025611530461767387472590376241897452371528925800729051521 Tue May 06 11:05:04 2008 elapsed time 02:14:27 (Msieve 1.34) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 95.69 hours. Scaled time: 123.35 units (timescale=1.289). Factorization parameters were as follows: name: KA_7_1_165_7 n: 320957224151492255429082127231488936975920891075446305694396741711567954921815157690547768799927437761891217541762696415656265015932173323 skew: 0.61 deg: 5 c5: 640 c0: 53 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4100293) Primes: RFBsize:216816, AFBsize:215751, largePrimes:7744522 encountered Relations: rels:7160434, finalFF:475852 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 95.27 hours. Total relation processing time: 0.42 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 95.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 6, 2008 (2nd)

By matsui / GGNFS
10¹⁷⁷-9 = (9)₁₇₆1_<177> = 1321 · 2376752857145462309881481_<25> · C150
C150 = P60 · P91
P60 = 166539912927088863044604457888822597127041055210868917788027_<60>
P91 = 1912470850607748174543437500075957519331332156283120157980757697449058309385972258440240133_<91>

N=318502728935809954002509561087485010327351554728615657106064751195435717694394036448608577571954357904487482813391637647426139449497421967533072287591 ( 150 digits) SNFS difficulty: 177 digits. Divisors found: r1=166539912927088863044604457888822597127041055210868917788027 (pp60) r2=1912470850607748174543437500075957519331332156283120157980757697449058309385972258440240133 (pp91) Version: GGNFS-0.77.1-20060513-prescott Total time: 284.83 hours. Scaled time: 483.93 units (timescale=1.699). Factorization parameters were as follows: n: 318502728935809954002509561087485010327351554728615657106064751195435717694394036448608577571954357904487482813391637647426139449497421967533072287591 m: 100000000000000000000000000000000000 c5: 100 c0: -9 skew: 0.62 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, 14800001) Primes: RFBsize:501962, AFBsize:501986, largePrimes:6735594 encountered Relations: rels:7221193, finalFF:1133995 Max relations in full relation-set: 28 Initial matrix: 1004012 x 1133995 with sparse part having weight 89857824. Pruned matrix : 899749 x 904833 with weight 71278579. Total sieving time: 266.47 hours. Total relation processing time: 0.17 hours. Matrix solve time: 17.92 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,177,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 284.83 hours.

May 6, 2008

By Justin Card / GGNFS
(10¹⁶⁴+71)/9 = (1)₁₆₃9_<164> = 19² · 7831997 · 2098626111640319124673_<22> · C133
C133 = P47 · P86
P47 = 28129977390358023629213634794275869491272177939_<47>
P86 = 66569197414739914752363340066606515578290318079885508716380491999752942375601583635281_<86>

Number: 11119_164 N=1872590018170913600366772304304121841458097175167099440399150522128818251133408166221876789031838225191954311628349902030957910265859 ( 133 digits) SNFS difficulty: 165 digits. Divisors found: r1=28129977390358023629213634794275869491272177939 (pp47) r2=66569197414739914752363340066606515578290318079885508716380491999752942375601583635281 (pp86) Version: GGNFS-0.77.1-20060722-k8 Total time: 107.01 hours. Scaled time: 215.94 units (timescale=2.018). Factorization parameters were as follows: n: 1872590018170913600366772304304121841458097175167099440399150522128818251133408166221876789031838225191954311628349902030957910265859 m: 1000000000000000000000000000000000 c5: 1 c0: 710 skew: 3.72 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, 6000001) Primes: RFBsize:348513, AFBsize:349267, largePrimes:5903324 encountered Relations: rels:6042140, finalFF:784177 Max relations in full relation-set: 32 Initial matrix: 697844 x 784177 with sparse part having weight 53680249. Pruned matrix : 633863 x 637416 with weight 40023983. Total sieving time: 99.60 hours. Total relation processing time: 0.12 hours. Matrix solve time: 7.19 hours. Time per square root: 0.10 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: 107.01 hours. --------- CPU info (if available) ----------

May 5, 2008 (4th)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve
(17·10¹⁵⁶-53)/9 = 1(8)₁₅₅3_<157> = C157
C157 = P77 · P80
P77 = 94115205417543442260889014109032287575728859357342112763830605058897534630713_<77>
P80 = 20069965108281988776637007571562300370718669072099530779317161803679127900838091_<80>

Number: n N=1888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 ( 157 digits) SNFS difficulty: 157 digits. Divisors found: r1=94115205417543442260889014109032287575728859357342112763830605058897534630713 (pp77) r2=20069965108281988776637007571562300370718669072099530779317161803679127900838091 (pp80) Version: GGNFS-0.77.1-20051202-athlon Total time: 31.24 hours. Scaled time: 56.95 units (timescale=1.823). Factorization parameters were as follows: name: KA_1_8_155_3 n: 1888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 skew: 0.79 deg: 5 c5: 170 c0: -53 m: 10000000000000000000000000000000 type: snfs rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 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: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2200001) Primes: RFBsize:135072, AFBsize:135633, largePrimes:7506713 encountered Relations: rels:6975775, finalFF:328656 Max relations in full relation-set: 48 Initial matrix: 270772 x 328656 with sparse part having weight 59693763. Pruned matrix : 260051 x 261468 with weight 42450536. Total sieving time: 29.78 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.14 hours. Total square root time: 0.16 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000 total time: 31.24 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(4·10¹⁶⁸-7)/3 = 1(3)₁₆₇1_<169> = 59 · 2383 · C163
C163 = P35 · P47 · P82
P35 = 40023304173544835675150634644920757_<35>
P47 = 87704264899678723077483412253836681182971817527_<47>
P82 = 2701649657888416586918373900392021989279527982766201328562651932265680628922403757_<82>

Number: n N=236946197261572085292838556629037751292137492986711183144801139487713250729956995533124609056643740923364539938459175868023248939 ( 129 digits) SNFS difficulty: 168 digits. Divisors found: Mon May 05 12:27:06 2008 prp47 factor: 87704264899678723077483412253836681182971817527 Mon May 05 12:27:06 2008 prp82 factor: 2701649657888416586918373900392021989279527982766201328562651932265680628922403757 Mon May 05 12:27:06 2008 elapsed time 01:48:02 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 70.29 hours. Scaled time: 123.78 units (timescale=1.761). Factorization parameters were as follows: name: KA_1_3_167_1 n: 236946197261572085292838556629037751292137492986711183144801139487713250729956995533124609056643740923364539938459175868023248939 type: snfs skew: 0.56 deg: 5 c5: 125 c0: -7 m: 2000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3299990) Primes: RFBsize:230209, AFBsize:229892, largePrimes:7666340 encountered Relations: rels:7167828, finalFF:516796 Max relations in full relation-set: 28 Initial matrix: 460166 x 516796 with sparse part having weight 46524840. Pruned matrix : Total sieving time: 70.00 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,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000 total time: 70.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 5, 2008 (3rd)

By Jo Yeong Uk / GGNFS
(17·10¹⁴⁵-53)/9 = 1(8)₁₄₄3_<146> = 13 · 1693 · 21139 · 152839 · C132
C132 = P33 · P99
P33 = 906712254747545828169857551757513_<33>
P99 = 292966518254180953679091271458567512967760755284807647661567847660425624429080931183692604031429719_<99>

Number: 18883_145 N=265636332331786455948599830433367466549294462972153747320203357415347232538865457535237362193153091325035833595006246655618589728847 ( 132 digits) SNFS difficulty: 146 digits. Divisors found: r1=906712254747545828169857551757513 (pp33) r2=292966518254180953679091271458567512967760755284807647661567847660425624429080931183692604031429719 (pp99) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.04 hours. Scaled time: 21.60 units (timescale=2.388). Factorization parameters were as follows: n: 265636332331786455948599830433367466549294462972153747320203357415347232538865457535237362193153091325035833595006246655618589728847 m: 100000000000000000000000000000 c5: 17 c0: -53 skew: 1.26 type: snfs 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, 1575001) Primes: RFBsize:135072, AFBsize:134618, largePrimes:3865067 encountered Relations: rels:4038075, finalFF:449877 Max relations in full relation-set: 28 Initial matrix: 269755 x 449877 with sparse part having weight 41845575. Pruned matrix : 210461 x 211873 with weight 18696046. Total sieving time: 8.75 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.22 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 9.04 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹⁵⁴-53)/9 = 1(8)₁₅₃3_<155> = 971 · 102437 · 371631714756730591_<18> · 101739334408004478253_<21> · C109
C109 = P37 · P73
P37 = 1274109118835390829488419042276855939_<37>
P73 = 3942049247854730324039591295348901289336792997888410316410784299138286157_<73>

Number: 18883_154 N=5022600893589905636339499417613746611203498473826015438112127303240501238047489385556412100188188698846936423 ( 109 digits) Divisors found: r1=1274109118835390829488419042276855939 (pp37) r2=3942049247854730324039591295348901289336792997888410316410784299138286157 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.95 hours. Scaled time: 28.49 units (timescale=2.385). Factorization parameters were as follows: name: 18883_154 n: 5022600893589905636339499417613746611203498473826015438112127303240501238047489385556412100188188698846936423 skew: 13374.50 # norm 5.43e+14 c5: 30720 c4: 173704624 c3: -7232247169672 c2: -374569345942660446 c1: -1059675685050481945127 c0: 22995021347564797885400 # alpha -5.17 Y1: 208977619037 Y0: -696147622413157774917 # Murphy_E 1.15e-09 # M 4860478897446311097949180415020740955658616983891812118048734381297380893306393968043407480884279029213211245 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1200000, 1860001) Primes: RFBsize:176302, AFBsize:176443, largePrimes:7604035 encountered Relations: rels:7511229, finalFF:560575 Max relations in full relation-set: 28 Initial matrix: 352821 x 560575 with sparse part having weight 54604718. Pruned matrix : 235491 x 237319 with weight 27052759. Polynomial selection time: 0.71 hours. Total sieving time: 10.66 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.36 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000 total time: 11.95 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

May 5, 2008 (2nd)

By Sinkiti Sibata / Msieve
(17·10¹⁴⁰-53)/9 = 1(8)₁₃₉3_<141> = 3² · 31 · 43 · 89 · 10416211045177969_<17> · 2199553991945068036403_<22> · C97
C97 = P29 · P69
P29 = 38770123268705413047738066497_<29>
P69 = 199160022643799127833796061370630292550733822605403852646915352573069_<69>

Sun May 4 20:45:00 2008 Msieve v. 1.35 Sun May 4 20:45:00 2008 random seeds: dc0174df bdb499f0 Sun May 4 20:45:00 2008 factoring 7721458628098253520507907794388559567326852814475284956638057016810555515872552885560367973369293 (97 digits) Sun May 4 20:45:02 2008 searching for 15-digit factors Sun May 4 20:45:04 2008 commencing quadratic sieve (97-digit input) Sun May 4 20:45:04 2008 using multiplier of 53 Sun May 4 20:45:04 2008 using 64kb Pentium 4 sieve core Sun May 4 20:45:04 2008 sieve interval: 18 blocks of size 65536 Sun May 4 20:45:04 2008 processing polynomials in batches of 6 Sun May 4 20:45:04 2008 using a sieve bound of 2401409 (88235 primes) Sun May 4 20:45:04 2008 using large prime bound of 360211350 (28 bits) Sun May 4 20:45:04 2008 using double large prime bound of 2522337833647050 (43-52 bits) Sun May 4 20:45:04 2008 using trial factoring cutoff of 52 bits Sun May 4 20:45:04 2008 polynomial 'A' values have 13 factors Mon May 5 05:41:31 2008 88780 relations (22380 full + 66400 combined from 1309522 partial), need 88331 Mon May 5 05:41:37 2008 begin with 1331902 relations Mon May 5 05:41:38 2008 reduce to 228356 relations in 11 passes Mon May 5 05:41:39 2008 attempting to read 228356 relations Mon May 5 05:41:46 2008 recovered 228356 relations Mon May 5 05:41:46 2008 recovered 214407 polynomials Mon May 5 05:41:47 2008 attempting to build 88780 cycles Mon May 5 05:41:47 2008 found 88780 cycles in 6 passes Mon May 5 05:41:47 2008 distribution of cycle lengths: Mon May 5 05:41:47 2008 length 1 : 22380 Mon May 5 05:41:47 2008 length 2 : 15920 Mon May 5 05:41:47 2008 length 3 : 15021 Mon May 5 05:41:47 2008 length 4 : 11905 Mon May 5 05:41:47 2008 length 5 : 8961 Mon May 5 05:41:47 2008 length 6 : 5950 Mon May 5 05:41:47 2008 length 7 : 3672 Mon May 5 05:41:47 2008 length 9+: 4971 Mon May 5 05:41:47 2008 largest cycle: 19 relations Mon May 5 05:41:47 2008 matrix is 88235 x 88780 (23.4 MB) with weight 5776404 (65.06/col) Mon May 5 05:41:48 2008 sparse part has weight 5776404 (65.06/col) Mon May 5 05:41:49 2008 filtering completed in 3 passes Mon May 5 05:41:49 2008 matrix is 83760 x 83824 (22.1 MB) with weight 5457471 (65.11/col) Mon May 5 05:41:49 2008 sparse part has weight 5457471 (65.11/col) Mon May 5 05:41:50 2008 saving the first 48 matrix rows for later Mon May 5 05:41:50 2008 matrix is 83712 x 83824 (12.8 MB) with weight 4196289 (50.06/col) Mon May 5 05:41:50 2008 sparse part has weight 2865457 (34.18/col) Mon May 5 05:41:50 2008 matrix includes 64 packed rows Mon May 5 05:41:50 2008 using block size 21845 for processor cache size 512 kB Mon May 5 05:41:51 2008 commencing Lanczos iteration Mon May 5 05:41:51 2008 memory use: 12.9 MB Mon May 5 05:43:03 2008 lanczos halted after 1326 iterations (dim = 83712) Mon May 5 05:43:04 2008 recovered 18 nontrivial dependencies Mon May 5 05:43:05 2008 prp29 factor: 38770123268705413047738066497 Mon May 5 05:43:05 2008 prp69 factor: 199160022643799127833796061370630292550733822605403852646915352573069 Mon May 5 05:43:05 2008 elapsed time 08:58:05

May 5, 2008

By Jo Yeong Uk / GGNFS
(17·10¹⁴³-53)/9 = 1(8)₁₄₂3_<144> = 3 · 19 · 82003 · 33747234085323696229891580573_<29> · C109
C109 = P54 · P55
P54 = 284184304370485849583806799703613180155918074201814599_<54>
P55 = 4213699332694306433921848962284585352045581816321987099_<55>

Number: 18883_143 N=1197467213688111895850772536711179223052372690430306061875255929817187752960564141361063736311640807267858301 ( 109 digits) SNFS difficulty: 146 digits. Divisors found: r1=284184304370485849583806799703613180155918074201814599 (pp54) r2=4213699332694306433921848962284585352045581816321987099 (pp55) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.08 hours. Scaled time: 23.75 units (timescale=2.356). Factorization parameters were as follows: n: 1197467213688111895850772536711179223052372690430306061875255929817187752960564141361063736311640807267858301 m: 100000000000000000000000000000 c5: 17 c0: -5300 skew: 3.15 type: snfs 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, 1650001) Primes: RFBsize:135072, AFBsize:135378, largePrimes:3801778 encountered Relations: rels:3847640, finalFF:337434 Max relations in full relation-set: 28 Initial matrix: 270517 x 337434 with sparse part having weight 31669794. Pruned matrix : 247287 x 248703 with weight 19935634. Total sieving time: 9.72 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.28 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 10.08 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

May 4, 2008 (3rd)

By Jo Yeong Uk / GGNFS
(17·10¹³⁹-53)/9 = 1(8)₁₃₈3_<140> = 13 · 109363 · 10038594233_<11> · 1303876585637_<13> · C112
C112 = P46 · P66
P46 = 1093771935863111803994728995558734837426133433_<46>
P66 = 928018175045653313023689862079602922263543547526513521806182993649_<66>

Number: 18883_139 N=1015040235835836378728631986726903634233303583621327606120724533258279780022125161642706618871835169922865567017 ( 112 digits) SNFS difficulty: 141 digits. Divisors found: r1=1093771935863111803994728995558734837426133433 (pp46) r2=928018175045653313023689862079602922263543547526513521806182993649 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.77 hours. Scaled time: 16.07 units (timescale=2.374). Factorization parameters were as follows: n: 1015040235835836378728631986726903634233303583621327606120724533258279780022125161642706618871835169922865567017 m: 10000000000000000000000000000 c5: 17 c0: -530 skew: 1.99 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1250001) Primes: RFBsize:114155, AFBsize:114172, largePrimes:3312330 encountered Relations: rels:3279076, finalFF:271361 Max relations in full relation-set: 28 Initial matrix: 228392 x 271361 with sparse part having weight 24091352. Pruned matrix : 211946 x 213151 with weight 15991644. Total sieving time: 6.51 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.19 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.77 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹⁷⁸-53)/9 = 1(8)₁₇₇3_<179> = 149 · 71023 · 2981057 · 738493163 · 18978130740089_<14> · 43743537687611_<14> · 93010512334718522114163289_<26> · C104
C104 = P38 · P66
P38 = 40841462947354589786207930836285747643_<38>
P66 = 257100965516938781704461385818273110825314784282900274223801951843_<66>

Number: 18883_178 N=10500379556889145330246585114238768457291202943488725603741369894166236710397268265106651792985936756049 ( 104 digits) Divisors found: r1=40841462947354589786207930836285747643 (pp38) r2=257100965516938781704461385818273110825314784282900274223801951843 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.95 hours. Scaled time: 11.76 units (timescale=2.378). Factorization parameters were as follows: name: 18883_178 n: 10500379556889145330246585114238768457291202943488725603741369894166236710397268265106651792985936756049 skew: 14873.58 # norm 2.30e+14 c5: 16860 c4: 394657478 c3: 691223280664 c2: -129661333066021771 c1: 933196451921052844674 c0: 2280582783604846240475616 # alpha -6.26 Y1: 55451588929 Y0: -57394135822956993649 # Murphy_E 2.25e-09 # M 6839246963409309748766842326136220909111860140739734615850387672023936970225800943518710329636436932672 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1620001) Primes: RFBsize:135072, AFBsize:135010, largePrimes:4383712 encountered Relations: rels:4338342, finalFF:345714 Max relations in full relation-set: 28 Initial matrix: 270166 x 345714 with sparse part having weight 28239737. Pruned matrix : 220167 x 221581 with weight 15602253. Polynomial selection time: 0.39 hours. Total sieving time: 4.23 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.20 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 4.95 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

May 4, 2008 (2nd)

By Sinkiti Sibata / Msieve
(17·10¹⁸⁹-53)/9 = 1(8)₁₈₈3_<190> = 7 · 1487 · 37763269 · 107409211127_<12> · 1892069578404541_<16> · 3090777110713708539900218209_<28> · 18308463842770442763352292651_<29> · C96
C96 = P34 · P63
P34 = 3425376722500250431425989302857061_<34>
P63 = 121989164029539344478888387906348661308781361217618006478634011_<63>

Sat May 3 19:48:17 2008 Msieve v. 1.35 Sat May 3 19:48:17 2008 random seeds: 695a6d9a 2c707a77 Sat May 3 19:48:17 2008 factoring 417858842864048922896196337118593534562428072576844463940803492716857825203006427509934866101671 (96 digits) Sat May 3 19:48:19 2008 searching for 15-digit factors Sat May 3 19:48:21 2008 commencing quadratic sieve (96-digit input) Sat May 3 19:48:21 2008 using multiplier of 1 Sat May 3 19:48:21 2008 using 64kb Pentium 4 sieve core Sat May 3 19:48:21 2008 sieve interval: 18 blocks of size 65536 Sat May 3 19:48:21 2008 processing polynomials in batches of 6 Sat May 3 19:48:21 2008 using a sieve bound of 2257987 (83529 primes) Sat May 3 19:48:21 2008 using large prime bound of 338698050 (28 bits) Sat May 3 19:48:21 2008 using double large prime bound of 2257682284654350 (43-52 bits) Sat May 3 19:48:21 2008 using trial factoring cutoff of 52 bits Sat May 3 19:48:21 2008 polynomial 'A' values have 12 factors Sun May 4 04:33:19 2008 83830 relations (19972 full + 63858 combined from 1268871 partial), need 83625 Sun May 4 04:33:24 2008 begin with 1288843 relations Sun May 4 04:33:26 2008 reduce to 222077 relations in 11 passes Sun May 4 04:33:26 2008 attempting to read 222077 relations Sun May 4 04:33:33 2008 recovered 222077 relations Sun May 4 04:33:33 2008 recovered 209059 polynomials Sun May 4 04:33:33 2008 attempting to build 83830 cycles Sun May 4 04:33:34 2008 found 83830 cycles in 6 passes Sun May 4 04:33:34 2008 distribution of cycle lengths: Sun May 4 04:33:34 2008 length 1 : 19972 Sun May 4 04:33:34 2008 length 2 : 14020 Sun May 4 04:33:34 2008 length 3 : 14057 Sun May 4 04:33:34 2008 length 4 : 11320 Sun May 4 04:33:34 2008 length 5 : 8801 Sun May 4 04:33:34 2008 length 6 : 6050 Sun May 4 04:33:34 2008 length 7 : 3976 Sun May 4 04:33:34 2008 length 9+: 5634 Sun May 4 04:33:34 2008 largest cycle: 19 relations Sun May 4 04:33:34 2008 matrix is 83529 x 83830 (23.4 MB) with weight 5800295 (69.19/col) Sun May 4 04:33:34 2008 sparse part has weight 5800295 (69.19/col) Sun May 4 04:33:36 2008 filtering completed in 3 passes Sun May 4 04:33:36 2008 matrix is 80180 x 80244 (22.5 MB) with weight 5574830 (69.47/col) Sun May 4 04:33:36 2008 sparse part has weight 5574830 (69.47/col) Sun May 4 04:33:37 2008 saving the first 48 matrix rows for later Sun May 4 04:33:37 2008 matrix is 80132 x 80244 (16.0 MB) with weight 4623887 (57.62/col) Sun May 4 04:33:37 2008 sparse part has weight 3724238 (46.41/col) Sun May 4 04:33:37 2008 matrix includes 64 packed rows Sun May 4 04:33:37 2008 using block size 21845 for processor cache size 512 kB Sun May 4 04:33:38 2008 commencing Lanczos iteration Sun May 4 04:33:38 2008 memory use: 14.4 MB Sun May 4 04:34:57 2008 lanczos halted after 1270 iterations (dim = 80131) Sun May 4 04:34:57 2008 recovered 17 nontrivial dependencies Sun May 4 04:34:59 2008 prp34 factor: 3425376722500250431425989302857061 Sun May 4 04:34:59 2008 prp63 factor: 121989164029539344478888387906348661308781361217618006478634011 Sun May 4 04:34:59 2008 elapsed time 08:46:42

(17·10¹³⁰-53)/9 = 1(8)₁₂₉3_<131> = 59 · 433 · 479 · 12851536795962440562749361929843_<32> · C93
C93 = P44 · P50
P44 = 11614451771081002807800660499716452065000621_<44>
P50 = 10341349396259693395744386085621912743878339580497_<50>

Sun May 4 06:17:09 2008 Msieve v. 1.35 Sun May 4 06:17:09 2008 random seeds: fc847c7a fd7eb40d Sun May 4 06:17:09 2008 factoring 120109103810755855073665089276825555209639255049591698558354393477251802397035257825184488637 (93 digits) Sun May 4 06:17:11 2008 searching for 15-digit factors Sun May 4 06:17:13 2008 commencing quadratic sieve (93-digit input) Sun May 4 06:17:13 2008 using multiplier of 13 Sun May 4 06:17:13 2008 using 64kb Pentium 4 sieve core Sun May 4 06:17:13 2008 sieve interval: 18 blocks of size 65536 Sun May 4 06:17:13 2008 processing polynomials in batches of 6 Sun May 4 06:17:13 2008 using a sieve bound of 1852271 (69412 primes) Sun May 4 06:17:13 2008 using large prime bound of 209306623 (27 bits) Sun May 4 06:17:13 2008 using double large prime bound of 949312700295976 (42-50 bits) Sun May 4 06:17:13 2008 using trial factoring cutoff of 50 bits Sun May 4 06:17:13 2008 polynomial 'A' values have 12 factors Sun May 4 09:46:15 2008 69873 relations (18535 full + 51338 combined from 881173 partial), need 69508 Sun May 4 09:46:19 2008 begin with 899708 relations Sun May 4 09:46:20 2008 reduce to 174000 relations in 11 passes Sun May 4 09:46:20 2008 attempting to read 174000 relations Sun May 4 09:46:25 2008 recovered 174000 relations Sun May 4 09:46:25 2008 recovered 154249 polynomials Sun May 4 09:46:25 2008 attempting to build 69873 cycles Sun May 4 09:46:25 2008 found 69873 cycles in 6 passes Sun May 4 09:46:25 2008 distribution of cycle lengths: Sun May 4 09:46:25 2008 length 1 : 18535 Sun May 4 09:46:25 2008 length 2 : 12855 Sun May 4 09:46:25 2008 length 3 : 12103 Sun May 4 09:46:25 2008 length 4 : 9383 Sun May 4 09:46:25 2008 length 5 : 6738 Sun May 4 09:46:25 2008 length 6 : 4286 Sun May 4 09:46:25 2008 length 7 : 2636 Sun May 4 09:46:25 2008 length 9+: 3337 Sun May 4 09:46:25 2008 largest cycle: 18 relations Sun May 4 09:46:26 2008 matrix is 69412 x 69873 (17.2 MB) with weight 4220263 (60.40/col) Sun May 4 09:46:26 2008 sparse part has weight 4220263 (60.40/col) Sun May 4 09:46:27 2008 filtering completed in 3 passes Sun May 4 09:46:27 2008 matrix is 65252 x 65314 (16.1 MB) with weight 3954945 (60.55/col) Sun May 4 09:46:27 2008 sparse part has weight 3954945 (60.55/col) Sun May 4 09:46:28 2008 saving the first 48 matrix rows for later Sun May 4 09:46:28 2008 matrix is 65204 x 65314 (9.4 MB) with weight 3024807 (46.31/col) Sun May 4 09:46:28 2008 sparse part has weight 2081515 (31.87/col) Sun May 4 09:46:28 2008 matrix includes 64 packed rows Sun May 4 09:46:28 2008 using block size 21845 for processor cache size 512 kB Sun May 4 09:46:28 2008 commencing Lanczos iteration Sun May 4 09:46:28 2008 memory use: 9.6 MB Sun May 4 09:47:10 2008 lanczos halted after 1032 iterations (dim = 65202) Sun May 4 09:47:11 2008 recovered 16 nontrivial dependencies Sun May 4 09:47:11 2008 prp44 factor: 11614451771081002807800660499716452065000621 Sun May 4 09:47:11 2008 prp50 factor: 10341349396259693395744386085621912743878339580497 Sun May 4 09:47:11 2008 elapsed time 03:30:02

May 4, 2008

By Robert Backstrom / GGNFS, GMP-ECM
(17·10¹³⁸-53)/9 = 1(8)₁₃₇3_<139> = 1187 · 1979 · 100520408961365189_<18> · C115
C115 = P41 · P75
P41 = 52269084438711395174858006507068213911373_<41>
P75 = 153042044567989424299284094191024360306276834800651709136147324967796139843_<75>

Number: n N=7999367550197271822646360963644905153246648798556416044418272601732208581583503314076806099132800234363381916134439 ( 115 digits) SNFS difficulty: 139 digits. Divisors found: Sun May 4 03:10:23 2008 prp41 factor: 52269084438711395174858006507068213911373 Sun May 4 03:10:23 2008 prp75 factor: 153042044567989424299284094191024360306276834800651709136147324967796139843 Sun May 4 03:10:23 2008 elapsed time 00:13:11 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 5.83 hours. Scaled time: 4.89 units (timescale=0.839). Factorization parameters were as follows: name: KA_1_8_137_3 n: 7999367550197271822646360963644905153246648798556416044418272601732208581583503314076806099132800234363381916134439 type: snfs deg: 5 c5: 17000 c0: -53 skew: 0.32 m: 1000000000000000000000000000 rlim: 1100000 alim: 1100000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved special-q in [100000, 2349990) Primes: RFBsize:85714, AFBsize:85954, largePrimes:1723644 encountered Relations: rels:1751737, finalFF:207968 Max relations in full relation-set: 28 Initial matrix: 171735 x 207968 with sparse part having weight 17947252. Pruned matrix : Total sieving time: 5.74 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1100000,1100000,25,25,43,43,2.5,2.5,75000 total time: 5.83 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 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

6·10¹⁶⁵-7 = 5(9)₁₆₄3_<166> = 13 · 79 · 113 · 7235159683_<10> · 782556346460516558455522307_<27> · C124
C124 = P56 · P69
P56 = 89114521059015530309415870009443429755507579670159234491_<56>
P69 = 102468445422444548672703238249307270954451352766414703365751873047633_<69>

Number: n N=9131426437483018250616136976167125291747020858040915201947647855343618380368524095147817529154557716728675938758146459509803 ( 124 digits) SNFS difficulty: 165 digits. Divisors found: Sun May 04 04:55:30 2008 prp56 factor: 89114521059015530309415870009443429755507579670159234491 Sun May 04 04:55:30 2008 prp69 factor: 102468445422444548672703238249307270954451352766414703365751873047633 Sun May 04 04:55:30 2008 elapsed time 01:53:48 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 63.25 hours. Scaled time: 91.53 units (timescale=1.447). Factorization parameters were as follows: name: KA_5_9_164_3 n: 9131426437483018250616136976167125291747020858040915201947647855343618380368524095147817529154557716728675938758146459509803 skew: 1.03 deg: 5 c5: 6 c0: -7 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3300149) Primes: RFBsize:216816, AFBsize:217096, largePrimes:7508847 encountered Relations: rels:6918012, finalFF:470957 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 62.98 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 63.25 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(17·10¹⁴⁸-53)/9 = 1(8)₁₄₇3_<149> = 599 · 1523 · 5449 · C139
C139 = P66 · P74
P66 = 196920964872399960571095869962957319355465848009092572272618008697_<66>
P74 = 19296161407988911730535538884844824784794847267080297111232954814015304743_<74>

Number: n N=3799818722794744250790994913866933739151845029327254261031147177170091191856457432267665149073674412679857372535547483357901361918279349871 ( 139 digits) SNFS difficulty: 149 digits. Divisors found: Sun May 04 15:08:17 2008 prp66 factor: 196920964872399960571095869962957319355465848009092572272618008697 Sun May 04 15:08:17 2008 prp74 factor: 19296161407988911730535538884844824784794847267080297111232954814015304743 Sun May 04 15:08:17 2008 elapsed time 00:32:29 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 12.67 hours. Scaled time: 23.17 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_8_147_3 n: 3799818722794744250790994913866933739151845029327254261031147177170091191856457432267665149073674412679857372535547483357901361918279349871 skew: 0.32 deg: 5 c5: 17000 c0: -53 m: 100000000000000000000000000000 type: snfs rlim: 1600000 alim: 1600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2700001) Primes: RFBsize:121127, AFBsize:121430, largePrimes:7338873 encountered Relations: rels:6686800, finalFF:246342 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 12.49 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,48,48,2.5,2.5,100000 total time: 12.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

May 3, 2008 (4th)

By Justin Card / GGNFS
4·10¹⁶⁴+3 = 4(0)₁₆₃3_<165> = 13 · 11467 · 9523399993242554891943426601_<28> · C132
C132 = P56 · P76
P56 = 31445722457122043977687400352333915199796312519950578127_<56>
P76 = 8960107578000945594964516537852622453791282510444775001014858922521752127659_<76>

May 3, 2008 (3rd)

By Sinkiti Sibata / Msieve
(17·10¹⁰⁹-53)/9 = 1(8)₁₀₈3_<110> = 13 · 29 · 127² · 1489 · 6379 · C96
C96 = P33 · P64
P33 = 133163092855224104302363788449929_<33>
P64 = 2455989164158808006628046290075502317087684176170758096093506249_<64>

Sat May 3 07:03:12 2008 Msieve v. 1.35 Sat May 3 07:03:12 2008 random seeds: 6f29155d 3913c6e4 Sat May 3 07:03:12 2008 factoring 327047113118303586290974817149111522786499532420335382905249154650071096486259467066566385106321 (96 digits) Sat May 3 07:03:13 2008 searching for 15-digit factors Sat May 3 07:03:15 2008 commencing quadratic sieve (96-digit input) Sat May 3 07:03:16 2008 using multiplier of 1 Sat May 3 07:03:16 2008 using 64kb Pentium 4 sieve core Sat May 3 07:03:16 2008 sieve interval: 18 blocks of size 65536 Sat May 3 07:03:16 2008 processing polynomials in batches of 6 Sat May 3 07:03:16 2008 using a sieve bound of 2253037 (83529 primes) Sat May 3 07:03:16 2008 using large prime bound of 337955550 (28 bits) Sat May 3 07:03:16 2008 using double large prime bound of 2248781238410700 (43-51 bits) Sat May 3 07:03:16 2008 using trial factoring cutoff of 51 bits Sat May 3 07:03:16 2008 polynomial 'A' values have 12 factors Sat May 3 14:08:38 2008 83700 relations (20716 full + 62984 combined from 1232784 partial), need 83625 Sat May 3 14:08:43 2008 begin with 1253500 relations Sat May 3 14:08:44 2008 reduce to 217266 relations in 13 passes Sat May 3 14:08:44 2008 attempting to read 217266 relations Sat May 3 14:08:51 2008 recovered 217266 relations Sat May 3 14:08:51 2008 recovered 202315 polynomials Sat May 3 14:08:52 2008 attempting to build 83700 cycles Sat May 3 14:08:52 2008 found 83700 cycles in 5 passes Sat May 3 14:08:52 2008 distribution of cycle lengths: Sat May 3 14:08:52 2008 length 1 : 20716 Sat May 3 14:08:52 2008 length 2 : 14681 Sat May 3 14:08:52 2008 length 3 : 14201 Sat May 3 14:08:52 2008 length 4 : 11285 Sat May 3 14:08:52 2008 length 5 : 8445 Sat May 3 14:08:52 2008 length 6 : 5713 Sat May 3 14:08:52 2008 length 7 : 3597 Sat May 3 14:08:52 2008 length 9+: 5062 Sat May 3 14:08:52 2008 largest cycle: 20 relations Sat May 3 14:08:52 2008 matrix is 83529 x 83700 (22.5 MB) with weight 5575853 (66.62/col) Sat May 3 14:08:52 2008 sparse part has weight 5575853 (66.62/col) Sat May 3 14:08:54 2008 filtering completed in 3 passes Sat May 3 14:08:54 2008 matrix is 79665 x 79729 (21.6 MB) with weight 5347576 (67.07/col) Sat May 3 14:08:54 2008 sparse part has weight 5347576 (67.07/col) Sat May 3 14:08:55 2008 saving the first 48 matrix rows for later Sat May 3 14:08:55 2008 matrix is 79617 x 79729 (14.8 MB) with weight 4376564 (54.89/col) Sat May 3 14:08:55 2008 sparse part has weight 3401479 (42.66/col) Sat May 3 14:08:55 2008 matrix includes 64 packed rows Sat May 3 14:08:55 2008 using block size 21845 for processor cache size 512 kB Sat May 3 14:08:56 2008 commencing Lanczos iteration Sat May 3 14:08:56 2008 memory use: 13.6 MB Sat May 3 14:10:09 2008 lanczos halted after 1261 iterations (dim = 79617) Sat May 3 14:10:10 2008 recovered 17 nontrivial dependencies Sat May 3 14:10:12 2008 prp33 factor: 133163092855224104302363788449929 Sat May 3 14:10:12 2008 prp64 factor: 2455989164158808006628046290075502317087684176170758096093506249 Sat May 3 14:10:12 2008 elapsed time 07:07:00

(17·10¹¹⁴-53)/9 = 1(8)₁₁₃3_<115> = 23 · 135963488010063195216983_<24> · C90
C90 = P44 · P47
P44 = 45407051110420976718615060333667020841308287_<44>
P47 = 13302491197732416716475505613313966954879008701_<47>

Sat May 3 14:29:59 2008 Msieve v. 1.35 Sat May 3 14:29:59 2008 random seeds: 06c7da98 e99f005e Sat May 3 14:29:59 2008 factoring 604026897711361001042648778953029296818263452928596668891224289618648285800606122496405187 (90 digits) Sat May 3 14:30:01 2008 searching for 15-digit factors Sat May 3 14:30:03 2008 commencing quadratic sieve (90-digit input) Sat May 3 14:30:03 2008 using multiplier of 3 Sat May 3 14:30:03 2008 using 64kb Pentium 4 sieve core Sat May 3 14:30:03 2008 sieve interval: 18 blocks of size 65536 Sat May 3 14:30:03 2008 processing polynomials in batches of 6 Sat May 3 14:30:03 2008 using a sieve bound of 1617893 (61176 primes) Sat May 3 14:30:03 2008 using large prime bound of 135903012 (27 bits) Sat May 3 14:30:03 2008 using double large prime bound of 436327220460936 (42-49 bits) Sat May 3 14:30:03 2008 using trial factoring cutoff of 49 bits Sat May 3 14:30:03 2008 polynomial 'A' values have 12 factors Sat May 3 16:46:42 2008 61740 relations (16397 full + 45343 combined from 662542 partial), need 61272 Sat May 3 16:46:45 2008 begin with 678939 relations Sat May 3 16:46:45 2008 reduce to 150588 relations in 11 passes Sat May 3 16:46:45 2008 attempting to read 150588 relations Sat May 3 16:46:49 2008 recovered 150588 relations Sat May 3 16:46:49 2008 recovered 129378 polynomials Sat May 3 16:46:50 2008 attempting to build 61740 cycles Sat May 3 16:46:50 2008 found 61740 cycles in 5 passes Sat May 3 16:46:50 2008 distribution of cycle lengths: Sat May 3 16:46:50 2008 length 1 : 16397 Sat May 3 16:46:50 2008 length 2 : 11886 Sat May 3 16:46:50 2008 length 3 : 10898 Sat May 3 16:46:50 2008 length 4 : 8182 Sat May 3 16:46:50 2008 length 5 : 5849 Sat May 3 16:46:50 2008 length 6 : 3702 Sat May 3 16:46:50 2008 length 7 : 2260 Sat May 3 16:46:50 2008 length 9+: 2566 Sat May 3 16:46:50 2008 largest cycle: 18 relations Sat May 3 16:46:50 2008 matrix is 61176 x 61740 (14.9 MB) with weight 3662101 (59.31/col) Sat May 3 16:46:50 2008 sparse part has weight 3662101 (59.31/col) Sat May 3 16:46:51 2008 filtering completed in 4 passes Sat May 3 16:46:51 2008 matrix is 57220 x 57284 (13.8 MB) with weight 3399691 (59.35/col) Sat May 3 16:46:51 2008 sparse part has weight 3399691 (59.35/col) Sat May 3 16:46:52 2008 saving the first 48 matrix rows for later Sat May 3 16:46:52 2008 matrix is 57172 x 57284 (8.5 MB) with weight 2623647 (45.80/col) Sat May 3 16:46:52 2008 sparse part has weight 1877380 (32.77/col) Sat May 3 16:46:52 2008 matrix includes 64 packed rows Sat May 3 16:46:52 2008 using block size 21845 for processor cache size 512 kB Sat May 3 16:46:52 2008 commencing Lanczos iteration Sat May 3 16:46:52 2008 memory use: 8.4 MB Sat May 3 16:47:25 2008 lanczos halted after 906 iterations (dim = 57172) Sat May 3 16:47:25 2008 recovered 18 nontrivial dependencies Sat May 3 16:47:27 2008 prp44 factor: 45407051110420976718615060333667020841308287 Sat May 3 16:47:27 2008 prp47 factor: 13302491197732416716475505613313966954879008701 Sat May 3 16:47:27 2008 elapsed time 02:17:28

(17·10¹¹⁶-53)/9 = 1(8)₁₁₅3_<117> = 3 · 3238037953_<10> · 200976479996422199_<18> · C89
C89 = P35 · P55
P35 = 40639575279507524445937749287780453_<35>
P55 = 2380722773741498849314583916531534950249488824911854571_<55>

Sat May 3 17:04:10 2008 Msieve v. 1.35 Sat May 3 17:04:10 2008 random seeds: f1ace691 41f2247d Sat May 3 17:04:10 2008 factoring 96751562383105601979686446490891285119918160039771268179072666138270111858671872512500663 (89 digits) Sat May 3 17:04:12 2008 searching for 15-digit factors Sat May 3 17:04:14 2008 commencing quadratic sieve (89-digit input) Sat May 3 17:04:14 2008 using multiplier of 3 Sat May 3 17:04:14 2008 using 64kb Pentium 4 sieve core Sat May 3 17:04:14 2008 sieve interval: 17 blocks of size 65536 Sat May 3 17:04:14 2008 processing polynomials in batches of 6 Sat May 3 17:04:14 2008 using a sieve bound of 1550147 (59333 primes) Sat May 3 17:04:14 2008 using large prime bound of 124011760 (26 bits) Sat May 3 17:04:14 2008 using double large prime bound of 370026785535040 (42-49 bits) Sat May 3 17:04:14 2008 using trial factoring cutoff of 49 bits Sat May 3 17:04:14 2008 polynomial 'A' values have 11 factors Sat May 3 19:36:18 2008 59471 relations (15268 full + 44203 combined from 634222 partial), need 59429 Sat May 3 19:36:20 2008 begin with 649490 relations Sat May 3 19:36:21 2008 reduce to 147167 relations in 10 passes Sat May 3 19:36:21 2008 attempting to read 147167 relations Sat May 3 19:36:25 2008 recovered 147167 relations Sat May 3 19:36:25 2008 recovered 129612 polynomials Sat May 3 19:36:25 2008 attempting to build 59471 cycles Sat May 3 19:36:25 2008 found 59471 cycles in 5 passes Sat May 3 19:36:25 2008 distribution of cycle lengths: Sat May 3 19:36:25 2008 length 1 : 15268 Sat May 3 19:36:25 2008 length 2 : 10961 Sat May 3 19:36:25 2008 length 3 : 10382 Sat May 3 19:36:25 2008 length 4 : 8027 Sat May 3 19:36:25 2008 length 5 : 5917 Sat May 3 19:36:25 2008 length 6 : 3876 Sat May 3 19:36:25 2008 length 7 : 2292 Sat May 3 19:36:25 2008 length 9+: 2748 Sat May 3 19:36:25 2008 largest cycle: 18 relations Sat May 3 19:36:25 2008 matrix is 59333 x 59471 (14.9 MB) with weight 3656207 (61.48/col) Sat May 3 19:36:25 2008 sparse part has weight 3656207 (61.48/col) Sat May 3 19:36:26 2008 filtering completed in 3 passes Sat May 3 19:36:26 2008 matrix is 55994 x 56058 (14.1 MB) with weight 3478766 (62.06/col) Sat May 3 19:36:26 2008 sparse part has weight 3478766 (62.06/col) Sat May 3 19:36:27 2008 saving the first 48 matrix rows for later Sat May 3 19:36:27 2008 matrix is 55946 x 56058 (10.5 MB) with weight 2924982 (52.18/col) Sat May 3 19:36:27 2008 sparse part has weight 2418502 (43.14/col) Sat May 3 19:36:27 2008 matrix includes 64 packed rows Sat May 3 19:36:27 2008 using block size 21845 for processor cache size 512 kB Sat May 3 19:36:28 2008 commencing Lanczos iteration Sat May 3 19:36:28 2008 memory use: 9.4 MB Sat May 3 19:37:04 2008 lanczos halted after 886 iterations (dim = 55944) Sat May 3 19:37:04 2008 recovered 16 nontrivial dependencies Sat May 3 19:37:05 2008 prp35 factor: 40639575279507524445937749287780453 Sat May 3 19:37:05 2008 prp55 factor: 2380722773741498849314583916531534950249488824911854571 Sat May 3 19:37:05 2008 elapsed time 02:32:55

May 3, 2008 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM
(17·10¹¹¹-53)/9 = 1(8)₁₁₀3_<112> = 7 · 741937667 · C102
C102 = P47 · P56
P47 = 21406727974433936850882602900693924335418266933_<47>
P56 = 16989893695587092805835674132504936884778981121981724779_<56>

Number: 18883_111 N=363698032655983000887109927310470195159725284363099792950451819884850031842151060166176791870362432807 ( 102 digits) SNFS difficulty: 112 digits. Divisors found: r1=21406727974433936850882602900693924335418266933 (pp47) r2=16989893695587092805835674132504936884778981121981724779 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.78 hours. Scaled time: 1.86 units (timescale=2.379). Factorization parameters were as follows: n: 363698032655983000887109927310470195159725284363099792950451819884850031842151060166176791870362432807 m: 10000000000000000000000 c5: 170 c0: -53 skew: 0.79 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 360001) Primes: RFBsize:30757, AFBsize:30774, largePrimes:1077150 encountered Relations: rels:997972, finalFF:91744 Max relations in full relation-set: 28 Initial matrix: 61598 x 91744 with sparse part having weight 4823069. Pruned matrix : 54393 x 54764 with weight 2049154. Total sieving time: 0.76 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.78 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹²⁶-53)/9 = 1(8)₁₂₅3_<127> = 2539 · 333367 · 641721697 · C109
C109 = P36 · P73
P36 = 727894902607689657739464596480166721_<36>
P73 = 4777555082205456186505940897215974516974069492382172337337363813495100943_<73>

Number: 18883_126 N=3477557991264813287478908886327964502328581041382834256329695746849099622706974067359408570904712197364317903 ( 109 digits) SNFS difficulty: 127 digits. Divisors found: r1=727894902607689657739464596480166721 (pp36) r2=4777555082205456186505940897215974516974069492382172337337363813495100943 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.08 hours. Scaled time: 4.96 units (timescale=2.382). Factorization parameters were as follows: n: 3477557991264813287478908886327964502328581041382834256329695746849099622706974067359408570904712197364317903 m: 10000000000000000000000000 c5: 170 c0: -53 skew: 0.79 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [400000, 920001) Primes: RFBsize:63951, AFBsize:63898, largePrimes:1458294 encountered Relations: rels:1439137, finalFF:156132 Max relations in full relation-set: 28 Initial matrix: 127916 x 156132 with sparse part having weight 10680678. Pruned matrix : 119166 x 119869 with weight 6532998. Total sieving time: 2.01 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000 total time: 2.08 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹²⁸-53)/9 = 1(8)₁₂₇3_<129> = 3 · 313 · 2045697173576072885436493_<25> · C101
C101 = P46 · P56
P46 = 4004240923599095557112102414494870267401405247_<46>
P56 = 24557224171047782792269547057638686525422784224174595907_<56>

Number: 18883_128 N=98333041995706407541101587203287053374224097813765416091275589460900030276042794110046704210174524029 ( 101 digits) SNFS difficulty: 131 digits. Divisors found: r1=4004240923599095557112102414494870267401405247 (pp46) r2=24557224171047782792269547057638686525422784224174595907 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.88 hours. Scaled time: 6.86 units (timescale=2.385). Factorization parameters were as follows: n: 98333041995706407541101587203287053374224097813765416091275589460900030276042794110046704210174524029 m: 100000000000000000000000000 c5: 17 c0: -5300 skew: 3.15 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 1200001) Primes: RFBsize:78498, AFBsize:78786, largePrimes:1601165 encountered Relations: rels:1619904, finalFF:194549 Max relations in full relation-set: 28 Initial matrix: 157351 x 194549 with sparse part having weight 13099468. Pruned matrix : 144276 x 145126 with weight 7867622. Total sieving time: 2.78 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 2.88 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹³³-53)/9 = 1(8)₁₃₂3_<134> = 13 · 9293 · 8751737149_<10> · 27537178718993_<14> · C105
C105 = P34 · P72
P34 = 3764382625358250645569863551537179_<34>
P72 = 172345383011769458501536322137290527842023267217164289309509635505102629_<72>

Number: 18883_133 N=648773965370217964813793670013617787398115175546853715736855115418235213719596637355092244272371104143591 ( 105 digits) SNFS difficulty: 136 digits. Divisors found: r1=3764382625358250645569863551537179 (pp34) r2=172345383011769458501536322137290527842023267217164289309509635505102629 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.61 hours. Scaled time: 8.59 units (timescale=2.377). Factorization parameters were as follows: n: 648773965370217964813793670013617787398115175546853715736855115418235213719596637355092244272371104143591 m: 1000000000000000000000000000 c5: 17 c0: -5300 skew: 3.15 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1450001) Primes: RFBsize:107126, AFBsize:107538, largePrimes:2291876 encountered Relations: rels:2382392, finalFF:248342 Max relations in full relation-set: 28 Initial matrix: 214731 x 248342 with sparse part having weight 19852549. Pruned matrix : 203707 x 204844 with weight 13784270. Total sieving time: 3.40 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.15 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.61 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: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

(17·10¹⁴²-53)/9 = 1(8)₁₄₁3_<143> = 1067029 · 1527173 · 244863342785827_<15> · 180280219243349327_<18> · C99
C99 = P31 · P68
P31 = 5812880350102104118685752874347_<31>
P68 = 45172977411817853583314487385516736976079129109325013547106832353973_<68>
(17·10¹³⁵-53)/9 = 1(8)₁₃₄3_<136> = 7 · 12526489 · 6994006470802381_<16> · C112
C112 = P40 · P73
P40 = 1347794481418895554693419393197617111453_<40>
P73 = 2285226791368354411931518719607928339055696989105013365535936167657426597_<73>

Number: 18883_135 N=3080016058196877858823811294679731916589946298223632245279662342289283579816083683606578447554446986742515515441 ( 112 digits) SNFS difficulty: 136 digits. Divisors found: r1=1347794481418895554693419393197617111453 (pp40) r2=2285226791368354411931518719607928339055696989105013365535936167657426597 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.16 hours. Scaled time: 7.54 units (timescale=2.386). Factorization parameters were as follows: n: 3080016058196877858823811294679731916589946298223632245279662342289283579816083683606578447554446986742515515441 m: 1000000000000000000000000000 c5: 17 c0: -53 skew: 1.26 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1350001) Primes: RFBsize:107126, AFBsize:106848, largePrimes:2339441 encountered Relations: rels:2497590, finalFF:307796 Max relations in full relation-set: 28 Initial matrix: 214039 x 307796 with sparse part having weight 24583959. Pruned matrix : 182104 x 183238 with weight 11697085. Total sieving time: 3.00 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.16 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)

May 3, 2008

By Robert Backstrom / Msieve, GGNFS
(17·10¹⁰⁷-53)/9 = 1(8)₁₀₆3_<108> = 3 · 19 · 9789899963_<10> · 1060679948543_<13> · C84
C84 = P41 · P43
P41 = 93231858661753747555233330990664897834019_<41>
P43 = 3422981886629292384067736826750714955820389_<43>

Sat May 03 01:00:14 2008 Sat May 03 01:00:14 2008 Sat May 03 01:00:14 2008 Msieve v. 1.34 Sat May 03 01:00:14 2008 random seeds: 58766b18 0f915d74 Sat May 03 01:00:14 2008 factoring 319130963455965377482501772162273692026572248526301173912434143259339755923298013391 (84 digits) Sat May 03 01:00:14 2008 searching for 15-digit factors Sat May 03 01:00:15 2008 commencing quadratic sieve (84-digit input) Sat May 03 01:00:15 2008 using multiplier of 3 Sat May 03 01:00:15 2008 using 64kb Opteron sieve core Sat May 03 01:00:15 2008 sieve interval: 6 blocks of size 65536 Sat May 03 01:00:15 2008 processing polynomials in batches of 17 Sat May 03 01:00:15 2008 using a sieve bound of 1398737 (53529 primes) Sat May 03 01:00:15 2008 using large prime bound of 120291382 (26 bits) Sat May 03 01:00:15 2008 using trial factoring cutoff of 27 bits Sat May 03 01:00:15 2008 polynomial 'A' values have 11 factors Sat May 03 01:20:55 2008 53671 relations (27000 full + 26671 combined from 282540 partial), need 53625 Sat May 03 01:20:55 2008 begin with 309539 relations Sat May 03 01:20:55 2008 reduce to 76978 relations in 2 passes Sat May 03 01:20:55 2008 attempting to read 76978 relations Sat May 03 01:20:56 2008 recovered 76978 relations Sat May 03 01:20:56 2008 recovered 71187 polynomials Sat May 03 01:20:56 2008 attempting to build 53671 cycles Sat May 03 01:20:56 2008 found 53671 cycles in 1 passes Sat May 03 01:20:56 2008 distribution of cycle lengths: Sat May 03 01:20:56 2008 length 1 : 27000 Sat May 03 01:20:56 2008 length 2 : 26671 Sat May 03 01:20:56 2008 largest cycle: 2 relations Sat May 03 01:20:56 2008 matrix is 53529 x 53671 (7.4 MB) with weight 1729380 (32.22/col) Sat May 03 01:20:56 2008 sparse part has weight 1729380 (32.22/col) Sat May 03 01:20:56 2008 filtering completed in 4 passes Sat May 03 01:20:56 2008 matrix is 46544 x 46608 (6.3 MB) with weight 1475595 (31.66/col) Sat May 03 01:20:56 2008 sparse part has weight 1475595 (31.66/col) Sat May 03 01:20:57 2008 saving the first 48 matrix rows for later Sat May 03 01:20:57 2008 matrix is 46496 x 46608 (4.1 MB) with weight 1106357 (23.74/col) Sat May 03 01:20:57 2008 sparse part has weight 783710 (16.81/col) Sat May 03 01:20:57 2008 matrix includes 64 packed rows Sat May 03 01:20:57 2008 commencing Lanczos iteration Sat May 03 01:20:57 2008 memory use: 5.8 MB Sat May 03 01:21:31 2008 lanczos halted after 736 iterations (dim = 46489) Sat May 03 01:21:31 2008 recovered 14 nontrivial dependencies Sat May 03 01:21:31 2008 prp41 factor: 93231858661753747555233330990664897834019 Sat May 03 01:21:31 2008 prp43 factor: 3422981886629292384067736826750714955820389 Sat May 03 01:21:31 2008 elapsed time 00:21:17

(17·10¹⁰⁶-53)/9 = 1(8)₁₀₅3_<107> = C107
C107 = P49 · P58
P49 = 8630106820148450673420782464300565409835605393871_<49>
P58 = 2188720172592715591130753702142474055753413658268136225373_<58>

Number: n N=18888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 ( 107 digits) SNFS difficulty: 107 digits. Divisors found: r1=8630106820148450673420782464300565409835605393871 (pp49) r2=2188720172592715591130753702142474055753413658268136225373 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.68 hours. Scaled time: 1.24 units (timescale=1.823). Factorization parameters were as follows: name: KA_1_8_105_3 n: 18888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 skew: 0.79 deg: 5 c5: 170 c0: -53 m: 1000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:49098, AFBsize:49096, largePrimes:3980929 encountered Relations: rels:3421632, finalFF:187238 Max relations in full relation-set: 48 Initial matrix: 98261 x 187238 with sparse part having weight 13120897. Pruned matrix : 67652 x 68207 with weight 2699659. Total sieving time: 0.61 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.01 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,107,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 0.68 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(17·10¹⁰⁴-53)/9 = 1(8)₁₀₃3_<105> = 3³ · 139 · 1215463 · C95
C95 = P32 · P64
P32 = 15853792454098265153552008138381_<32>
P64 = 2611878293362696035834569502178477397915530892823191844676083137_<64>

Number: n N=41408176378336565319566253850826344214275710089439512380007961638247320706460090919410156581197 ( 95 digits) SNFS difficulty: 106 digits. Divisors found: r1=15853792454098265153552008138381 (pp32) r2=2611878293362696035834569502178477397915530892823191844676083137 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.60 hours. Scaled time: 1.09 units (timescale=1.823). Factorization parameters were as follows: name: KA_1_8_103_3 n: 41408176378336565319566253850826344214275710089439512380007961638247320706460090919410156581197 skew: 1.99 deg: 5 c5: 17 c0: -530 m: 1000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:49098, AFBsize:49241, largePrimes:3709422 encountered Relations: rels:3117179, finalFF:145044 Max relations in full relation-set: 48 Initial matrix: 98404 x 145044 with sparse part having weight 9101580. Pruned matrix : 76838 x 77394 with weight 2816172. Total sieving time: 0.53 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.02 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,106,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 0.60 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(23·10¹⁶⁴+1)/3 = 7(6)₁₆₃7_<165> = 13 · 86369 · 41704840921_<11> · 118056872720744949209_<21> · C129
C129 = P51 · P79
P51 = 111436804245982124976494018826930500402933157080689_<51>
P79 = 1244511588556699658378674981796798862545904148539310114593089804716974603547991_<79>

Number: n N=138684394275849187828660560710673371912849390957781872773628671686689559292146610064299317211442794052605863374723378423270845799 ( 129 digits) SNFS difficulty: 166 digits. Divisors found: Sat May 03 10:40:40 2008 prp51 factor: 111436804245982124976494018826930500402933157080689 Sat May 03 10:40:40 2008 prp79 factor: 1244511588556699658378674981796798862545904148539310114593089804716974603547991 Sat May 03 10:40:40 2008 elapsed time 01:03:58 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.14 hours. Scaled time: 38.67 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_6_163_7 n: 138684394275849187828660560710673371912849390957781872773628671686689559292146610064299317211442794052605863374723378423270845799 skew: 0.85 deg: 5 c5: 23 c0: 10 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3300000) Primes: RFBsize:216816, AFBsize:217411, largePrimes:7366557 encountered Relations: rels:6789767, finalFF:477036 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 20.99 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 21.14 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

4·10¹⁶⁷-3 = 3(9)₁₆₆7_<168> = 13 · 17 · 139 · 4421 · 7873915303_<10> · C150
C150 = P54 · P96
P54 = 618273762409165239603405636857538455481103354894431607_<54>
P96 = 605007623043639365025444446465689291883809981765758204992885675613074765084447457982884602953543_<96>

Number: n N=374060339385416889430110381945106309862426286979244992667492320805419072529582709129344665255156355799651740239660308846387388622669297398516411833601 ( 150 digits) SNFS difficulty: 167 digits. Divisors found: Sat May 3 12:45:02 2008 prp54 factor: 618273762409165239603405636857538455481103354894431607 Sat May 3 12:45:02 2008 prp96 factor: 605007623043639365025444446465689291883809981765758204992885675613074765084447457982884602953543 Sat May 3 12:45:02 2008 elapsed time 00:55:23 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 25.57 hours. Scaled time: 21.45 units (timescale=0.839). Factorization parameters were as follows: name: KA_3_9_166_7 n: 374060339385416889430110381945106309862426286979244992667492320805419072529582709129344665255156355799651740239660308846387388622669297398516411833601 type: snfs deg: 5 c5: 25 c0: -6 skew: 0.75 m: 2000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3300203) Primes: RFBsize:216816, AFBsize:215956, largePrimes:5607000 encountered Relations: rels:5453742, finalFF:481499 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 25.40 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,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 25.57 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

(17·10¹¹²-53)/9 = 1(8)₁₁₁3_<113> = 223 · 4001 · C107
C107 = P49 · P58
P49 = 8549198048140881562228719565616138334096186877231_<49>
P58 = 2476324871342590569760961715536698238992882278782339631491_<58>

Number: n N=21170591756644794954724198870561383072268803750731475078415249202148889783035058375416111094299170598481421 ( 107 digits) SNFS difficulty: 113 digits. Divisors found: r1=8549198048140881562228719565616138334096186877231 (pp49) r2=2476324871342590569760961715536698238992882278782339631491 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.93 hours. Scaled time: 1.70 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_8_111_3 n: 21170591756644794954724198870561383072268803750731475078415249202148889783035058375416111094299170598481421 skew: 0.50 deg: 5 c5: 1700 c0: -53 m: 10000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:49098, AFBsize:49416, largePrimes:4169529 encountered Relations: rels:3562039, finalFF:164380 Max relations in full relation-set: 48 Initial matrix: 98581 x 164380 with sparse part having weight 14493062. Pruned matrix : 78682 x 79238 with weight 3965425. Total sieving time: 0.84 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.02 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 0.93 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(17·10¹²⁷-53)/9 = 1(8)₁₂₆3_<128> = 13 · 4003 · 540251 · C117
C117 = P51 · P67
P51 = 328798120789209691542180686790545783365122362891647_<51>
P67 = 2043396115186747802808184830871608870858489870879968003790681182801_<67>

Number: n N=671864802701374144242485442869363565197753682139350317263751143697120621763729277444117459175771975912204400562963247 ( 117 digits) SNFS difficulty: 128 digits. Divisors found: Sat May 3 20:42:58 2008 prp51 factor: 328798120789209691542180686790545783365122362891647 Sat May 3 20:42:58 2008 prp67 factor: 2043396115186747802808184830871608870858489870879968003790681182801 Sat May 3 20:42:58 2008 elapsed time 00:05:26 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 2.68 hours. Scaled time: 2.25 units (timescale=0.839). Factorization parameters were as follows: name: KA_1_8_126_3 n: 671864802701374144242485442869363565197753682139350317263751143697120621763729277444117459175771975912204400562963247 type: snfs deg: 5 c5: 1700 c0: -53 skew: 0.50 m: 10000000000000000000000000 rlim: 800000 alim: 800000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved special-q in [100000, 521243) Primes: RFBsize:63951, AFBsize:64318, largePrimes:1526929 encountered Relations: rels:1490361, finalFF:138680 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 2.62 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.5,2.5,50000 total time: 2.68 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

May 2, 2008 (3rd)

By Robert Backstrom / GMP-ECM
(16·10¹⁸⁵+11)/9 = 1(7)₁₈₄9_<186> = 7 · C185
C185 = P29 · C156
P29 = 26956598084950821289292271647_<29>
C156 = [942137628672209731441123765840597029595643313299719206072714213145836957181250058636962835363668375659087382552918820565633591241200675392898887129525086251_<156>]

May 2, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(13·10¹⁶²+23)/9 = 1(4)₁₆₁7_<163> = 48440917801958347097_<20> · 170569706737281090797_<21> · C123
C123 = P37 · P86
P37 = 4896627844567999141056381026425997699_<37>
P86 = 35701747916582274558191451115278830078250818431335984974373036683747660077947671049617_<86>

Number: 14447_162 N=174818172948084317069323230611457205447676147430883678288697651601550278437647590631488396130094047936924771876587756831283 ( 123 digits) SNFS difficulty: 163 digits. Divisors found: r1=4896627844567999141056381026425997699 (pp37) r2=35701747916582274558191451115278830078250818431335984974373036683747660077947671049617 (pp86) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 134.15 hours. Scaled time: 90.82 units (timescale=0.677). Factorization parameters were as follows: name: 14447_162 n: 174818172948084317069323230611457205447676147430883678288697651601550278437647590631488396130094047936924771876587756831283 m: 100000000000000000000000000000000 c5: 1300 c0: 23 skew: 0.45 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, 5550001) Primes: RFBsize:315948, AFBsize:315066, largePrimes:5940702 encountered Relations: rels:6062603, finalFF:735486 Max relations in full relation-set: 28 Initial matrix: 631081 x 735486 with sparse part having weight 58557622. Pruned matrix : 557419 x 560638 with weight 43543481. Total sieving time: 115.98 hours. Total relation processing time: 0.49 hours. Matrix solve time: 17.44 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 134.15 hours. --------- CPU info (if available) ----------

May 2, 2008

The factor table of 188...883 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 1, 2008

By Robert Backstrom / GMP-ECM, Msieve
(17·10¹⁷⁹-71)/9 = 1(8)₁₇₈1_<180> = 7 · 11 · 103 · 239 · 9930637 · 14023579 · 1231364489_<10> · 684907717263391040869653253_<27> · C123
C123 = P40 · P42 · P43
P40 = 1187282062146192125179089986736275870419_<40>
P42 = 375284494633543979200133045260994522261009_<42>
P43 = 1904194805934835770754653293450160027271669_<43>

Thu May 01 01:02:37 2008 Thu May 01 01:02:37 2008 Thu May 01 01:02:37 2008 Msieve v. 1.34 Thu May 01 01:02:37 2008 random seeds: 9e84d5d0 7d88e2a1 Thu May 01 01:02:37 2008 factoring 714614785429074193724941033575218868394451441841244639514764707813514033355369054021 (84 digits) Thu May 01 01:02:37 2008 searching for 15-digit factors Thu May 01 01:02:38 2008 commencing quadratic sieve (84-digit input) Thu May 01 01:02:38 2008 using multiplier of 29 Thu May 01 01:02:38 2008 using 64kb Opteron sieve core Thu May 01 01:02:38 2008 sieve interval: 6 blocks of size 65536 Thu May 01 01:02:38 2008 processing polynomials in batches of 17 Thu May 01 01:02:38 2008 using a sieve bound of 1405787 (53824 primes) Thu May 01 01:02:38 2008 using large prime bound of 119491895 (26 bits) Thu May 01 01:02:38 2008 using double large prime bound of 346106003521495 (41-49 bits) Thu May 01 01:02:38 2008 using trial factoring cutoff of 49 bits Thu May 01 01:02:38 2008 polynomial 'A' values have 11 factors Thu May 01 01:25:48 2008 54118 relations (15886 full + 38232 combined from 576589 partial), need 53920 Thu May 01 01:25:48 2008 begin with 592474 relations Thu May 01 01:25:49 2008 reduce to 127260 relations in 11 passes Thu May 01 01:25:49 2008 attempting to read 127260 relations Thu May 01 01:25:50 2008 recovered 127260 relations Thu May 01 01:25:50 2008 recovered 105898 polynomials Thu May 01 01:25:50 2008 attempting to build 54118 cycles Thu May 01 01:25:50 2008 found 54117 cycles in 5 passes Thu May 01 01:25:50 2008 distribution of cycle lengths: Thu May 01 01:25:50 2008 length 1 : 15886 Thu May 01 01:25:50 2008 length 2 : 10845 Thu May 01 01:25:50 2008 length 3 : 9537 Thu May 01 01:25:50 2008 length 4 : 6918 Thu May 01 01:25:50 2008 length 5 : 4661 Thu May 01 01:25:50 2008 length 6 : 2830 Thu May 01 01:25:50 2008 length 7 : 1579 Thu May 01 01:25:50 2008 length 9+: 1861 Thu May 01 01:25:50 2008 largest cycle: 18 relations Thu May 01 01:25:50 2008 matrix is 53824 x 54117 (11.4 MB) with weight 2766188 (51.11/col) Thu May 01 01:25:50 2008 sparse part has weight 2766188 (51.11/col) Thu May 01 01:25:51 2008 filtering completed in 3 passes Thu May 01 01:25:51 2008 matrix is 49265 x 49329 (10.4 MB) with weight 2532773 (51.34/col) Thu May 01 01:25:51 2008 sparse part has weight 2532773 (51.34/col) Thu May 01 01:25:51 2008 saving the first 48 matrix rows for later Thu May 01 01:25:51 2008 matrix is 49217 x 49329 (5.6 MB) with weight 1835858 (37.22/col) Thu May 01 01:25:51 2008 sparse part has weight 1172093 (23.76/col) Thu May 01 01:25:51 2008 matrix includes 64 packed rows Thu May 01 01:25:51 2008 commencing Lanczos iteration Thu May 01 01:25:51 2008 memory use: 7.5 MB Thu May 01 01:26:37 2008 lanczos halted after 779 iterations (dim = 49213) Thu May 01 01:26:37 2008 recovered 16 nontrivial dependencies Thu May 01 01:26:38 2008 prp42 factor: 375284494633543979200133045260994522261009 Thu May 01 01:26:38 2008 prp43 factor: 1904194805934835770754653293450160027271669 Thu May 01 01:26:38 2008 elapsed time 00:24:01

(2·10¹⁷³+61)/9 = (2)₁₇₂9_<173> = 24029 · 783927755987291861663_<21> · 79938271189022562029053_<23> · C125
C125 = P39 · P87
P39 = 121842971281799818523533840048423370159_<39>
P87 = 121121297489504812466235866743869623924667673289246788407622284113444086914024115748701_<87>
(71·10¹⁹⁰-17)/9 = 7(8)₁₈₉7_<191> = 15073 · 19403 · 89882231 · 27578264513_<11> · 1005770645897839_<16> · 11369559029669171813_<20> · C130
C130 = P38 · P93
P38 = 54199323118774369622038618504219850957_<38>
P93 = 175577976731131661812043593232506970976847183659624924342240801835328186189054850754452122509_<93>