News and updates, July 2008

Since June 16, 2000

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News and updates, July 2008	2008-08-01(Fri) 13:29

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News and updates, July 2008

Jul 31, 2008: By Serge Batalov / pol51, Msieve
(23·10¹⁸⁸-41)/9 = 2(5)₁₈₇1_<189> = 43 · 683 · 1123 · 11003 · 129491 · 13776430890486919_<17> · 1998967854737700046309_<22> · 4118359186990383026851_<22> · C113
C113 = P44 · P69
P44 = 65615481280730819870909029109781563549335597_<44>
P69 = 730790082739108945520358150329693309160286713343015176689118525792073_<69>

Number: 25551_188 N=47951142994111730052600594373683969756210565578842353767390601851826733211778758756378457047403995719847319322581 ( 113 digits) Divisors found: r1=65615481280730819870909029109781563549335597 r2=730790082739108945520358150329693309160286713343015176689118525792073 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: name: 25551_188 n: 47951142994111730052600594373683969756210565578842353767390601851826733211778758756378457047403995719847319322581 skew: 39942.85 # norm 4.55e+15 c5: 34440 c4: 33787766 c3: -289153465319201 c2: 86740494851837328 c1: 170200457961466906677222 c0: 1225255008348063687936417840 # alpha -6.30 Y1: 624020572153 Y0: -4253506998509198027219 # Murphy_E 7.21e-10 # M 13308855079719020252483670510147535496065937586070006992997317244223463936867911346371720820664892712291005385604 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3650001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 7790604 relations (7008594 unique relations and about 7083638 large ideals) Max relations in full relation-set: 20 Initial matrix: 486909 x 487115 (149.7 MB) with weight 49914063 (102.47/col) Pruned matrix : 484228 x 484476 Total sieving time: 12.00 hours. Total relation processing time: 00:06:58 Matrix solve time: 01:06:27 Time per square root: 00:14:26 Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 13.6 hours.
Jul 30, 2008: By Sinkiti Sibata / GMP-ECM, GGNFS
8·10²⁰³-1 = 7(9)₂₀₃_<204> = 139 · 661 · 691 · 221101 · 7609211 · 8030409029_<10> · 58953836021010431_<17> · C158
C158 = P35 · P123
P35 = 15964735925805978713074497549589901_<35>
P123 = 990954857884280807155141937143358514822699724692261377137730212333798710863533568558966350673543013087657806107656416640019_<123>
(23·10¹⁶⁰-41)/9 = 2(5)₁₅₉1_<161> = 3 · 421 · 1303290019_<10> · 16757517846851_<14> · 33410740941589932192257971_<26> · C110
C110 = P51 · P60
P51 = 141201378282839605551482507237147623978827958693229_<51>
P60 = 196384032376405294052137230651200422806370915812525870825887_<60>

Number: 25551_160 N=27729696044290224460609024058949846655012187821821005718326741022823024412724637968075461477077242655504819123 ( 110 digits) Divisors found: r1=141201378282839605551482507237147623978827958693229 (pp51) r2=196384032376405294052137230651200422806370915812525870825887 (pp60) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 34.78 hours. Scaled time: 16.45 units (timescale=0.473). Factorization parameters were as follows: name: 25551_160 n: 27729696044290224460609024058949846655012187821821005718326741022823024412724637968075461477077242655504819123 skew: 19703.02 # norm 2.58e+15 c5: 97200 c4: 2699482653 c3: -193815028071876 c2: -1584280404140977288 c1: 22126732270643781438316 c0: -44916850879699875155644045 # alpha -6.32 Y1: 17675023289 Y0: -778136368901680828542 # Murphy_E 1.04e-09 # M 5474228949482118542256893329492702222648847949467955749282916956767404137793286945529386778071697693401222665 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, 2300001) Primes: RFBsize:230209, AFBsize:230705, largePrimes:7471164 encountered Relations: rels:7388085, finalFF:642533 Max relations in full relation-set: 28 Initial matrix: 460991 x 642533 with sparse part having weight 52550874. Pruned matrix : 312266 x 314634 with weight 26599352. Total sieving time: 30.88 hours. Total relation processing time: 0.45 hours. Matrix solve time: 3.16 hours. Time per square root: 0.28 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: 34.78 hours. --------- CPU info (if available) ----------
(23·10¹⁴⁸-41)/9 = 2(5)₁₄₇1_<149> = 3³ · 17 · 151 · 1283 · 75011929299489064304755445730298699_<35> · C106
C106 = P48 · P59
P48 = 242428544050253915914646918889394792594740748663_<48>
P59 = 15803560686756702280080903994808482373671375272389819798509_<59>

Number: 25551_148 N=3831234208100258225905784789352281618753028879135330243405513044277690944977878017308340945272902471143467 ( 106 digits) SNFS difficulty: 149 digits. Divisors found: r1=242428544050253915914646918889394792594740748663 (pp48) r2=15803560686756702280080903994808482373671375272389819798509 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 42.02 hours. Scaled time: 32.06 units (timescale=0.763). Factorization parameters were as follows: name: 25551_148 n: 3831234208100258225905784789352281618753028879135330243405513044277690944977878017308340945272902471143467 m: 100000000000000000000000000000 c5: 23000 c0: -41 skew: 0.28 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 5650001) Primes: RFBsize:114155, AFBsize:113913, largePrimes:3272514 encountered Relations: rels:3445255, finalFF:267676 Max relations in full relation-set: 28 Initial matrix: 228135 x 267676 with sparse part having weight 36440840. Pruned matrix : 218281 x 219485 with weight 28929745. Total sieving time: 41.16 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.59 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 42.02 hours. --------- CPU info (if available) ----------
Jul 29, 2008 (3rd): By Sinkiti Sibata / GMP-ECM, GGNFS
8·10²¹²-1 = 7(9)₂₁₂_<213> = 4049 · 194729 · 119979793 · 486354823 · C188
C188 = P32 · P157
P32 = 10363055718258968541866287435591_<32>
P157 = 1677885836761735105027686433776347699057186426741928740520860590753000052575004869637655827915676182908115006877848710311065778076524792688071381438849355831_<157>
(23·10¹⁵²-41)/9 = 2(5)₁₅₁1_<153> = 251 · 15727 · 30313 · 103850550449_<12> · 534229782631_<12> · C119
C119 = P35 · P85
P35 = 19790119266604017679102945476566143_<35>
P85 = 1945142794525748056047069045389871786110518491818897667080431528816127400819396477203_<85>

Number: 25551_152 N=38494607894239986573312408816526294980131769999525671688250208724577379801467092036352155350111476847297481563421138029 ( 119 digits) SNFS difficulty: 153 digits. Divisors found: r1=19790119266604017679102945476566143 (pp35) r2=1945142794525748056047069045389871786110518491818897667080431528816127400819396477203 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 43.36 hours. Scaled time: 33.39 units (timescale=0.770). Factorization parameters were as follows: name: 25551_152 n: 38494607894239986573312408816526294980131769999525671688250208724577379801467092036352155350111476847297481563421138029 m: 1000000000000000000000000000000 c5: 2300 c0: -41 skew: 0.45 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:176434, largePrimes:5926245 encountered Relations: rels:5993828, finalFF:528516 Max relations in full relation-set: 28 Initial matrix: 352803 x 528516 with sparse part having weight 59010423. Pruned matrix : 295070 x 296898 with weight 34887846. Total sieving time: 41.80 hours. Total relation processing time: 0.19 hours. Matrix solve time: 1.27 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 43.36 hours. --------- CPU info (if available) ----------
Jul 29, 2008 (2nd): By Sinkiti Sibata / GGNFS
(22·10¹⁸⁶-31)/9 = 2(4)₁₈₅1_<187> = 2609147 · 11184881843_<11> · 20693708759_<11> · 107449652673263951068137572239_<30> · C131
C131 = P60 · P72
P60 = 171456587163938150377867556321935189380057680476175447590519_<60>
P72 = 219711454591472501320115502574137369201432836002086108434234387703221959_<72>

Number: 24441_186 N=37670976165078443863256836601861142328673369625675002713509577133696652081698435733705187027373757745600233596423796059159601006721 ( 131 digits) Divisors found: r1=171456587163938150377867556321935189380057680476175447590519 (pp60) r2=219711454591472501320115502574137369201432836002086108434234387703221959 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 397.44 hours. Scaled time: 398.64 units (timescale=1.003). Factorization parameters were as follows: name: 24441_186 n: 37670976165078443863256836601861142328673369625675002713509577133696652081698435733705187027373757745600233596423796059159601006721 skew: 126850.64 # norm 1.14e+18 c5: 401700 c4: -88329015826 c3: -33312095062761562 c2: 1203702866763267563315 c1: 138153793740909087892531458 c0: -1041535282133753560962272111400 # alpha -5.91 Y1: 97569885487877 Y0: -9872364854022489260068993 # Murphy_E 6.68e-11 # M 633122711962913050141178229451031715178519068215028293487278893698121013088255029031311623901634808174113378784182677589098774524 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, 17640001) Primes: RFBsize:374362, AFBsize:373919, largePrimes:10334820 encountered Relations: rels:12618895, finalFF:844096 Max relations in full relation-set: 28 Initial matrix: 748367 x 844096 with sparse part having weight 133631545. Pruned matrix : 684149 x 687954 with weight 117917272. Total sieving time: 387.86 hours. Total relation processing time: 1.06 hours. Matrix solve time: 7.94 hours. Time per square root: 0.58 hours. Prototype def-par.txt line would be: gnfs,130,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000 total time: 397.44 hours. --------- CPU info (if available) ----------
Jul 29, 2008: By Serge Batalov / pol51, Msieve, GMP-ECM
(23·10¹⁹⁵-41)/9 = 2(5)₁₉₄1_<196> = 158597 · 7029942179561563_<16> · 313306481963429959_<18> · 138881901627091563659_<21> · 337159954666957756609533851017_<30> · C108
C108 = P51 · P57
P51 = 425452593547811250316631268573489297907292332462667_<51>
P57 = 367228525511343637108246350268855498271898118507609664399_<57>

Number: 25551_195 N=156238328603539719034056512317514350799152188699229320945880126217790717414234564344734256456866329066492133 ( 108 digits) Divisors found: r1=425452593547811250316631268573489297907292332462667 r2=367228525511343637108246350268855498271898118507609664399 Version: Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: name: 25551_195 n: 156238328603539719034056512317514350799152188699229320945880126217790717414234564344734256456866329066492133 skew: 18161.46 # norm 6.06e+14 c5: 19440 c4: -1287147529 c3: -42621652708216 c2: 324919101556326086 c1: 4304459856666512446668 c0: 5045724495165348220842000 # alpha -5.28 Y1: 144033260789 Y0: -381083757256829511337 # Murphy_E 1.27e-09 # M 128206860376250402135095926671172746209589861555750814743352707800749867899952792114219665913762911409522204 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1600000, 2900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 372333 x 372574 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,26,26,49,49,2.6,2.6,100000 total time: 11.25 hours.
(23·10¹⁶⁷-41)/9 = 2(5)₁₆₆1_<168> = 43 · 1913 · 202061459 · 8243229814663_<13> · 9719287489760292844376840465897_<31> · C111
C111 = P44 · P67
P44 = 25684063928938037339841953821170973102004701_<44>
P67 = 7471758700860606702764453521083040039688701616397278375982183054061_<67>

Number: 25551_167 N=191905128134502839826363774871925281664941680452003820832204690551782529098643580568564988256211135109759140761 ( 111 digits) Divisors found: r1=25684063928938037339841953821170973102004701 r2=7471758700860606702764453521083040039688701616397278375982183054061 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: name: 25551_167 n: 191905128134502839826363774871925281664941680452003820832204690551782529098643580568564988256211135109759140761 skew: 34967.52 # norm 4.00e+15 c5: 50760 c4: 4857904818 c3: -154098803765337 c2: -4794514057547441483 c1: 129763218046029315253297 c0: -162403929682185181213925415 # alpha -6.94 Y1: 464271068387 Y0: -1304698116443718001226 # Murphy_E 9.82e-10 # M 49869502946388985127326104835168775949738092057117596251976267998101212859840610032696852809604089189634082330 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 3100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 404231 x 404479 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 14.00 hours.
(23·10¹⁴⁶-41)/9 = 2(5)₁₄₅1_<147> = 43 · 6841 · 346043 · 41510532436848216902506677855337901_<35> · C101
C101 = P35 · P67
P35 = 34758835800516322384363626653111027_<35>
P67 = 1739977716010306568378337706839472575468221244846012298568319529657_<67>

Number: 25551_146 N=60479599727359666560994131358298323344894266838551584001575199716934366999703013872164853960440227739 ( 101 digits) Divisors found: r1=34758835800516322384363626653111027 r2=1739977716010306568378337706839472575468221244846012298568319529657 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.306). Factorization parameters were as follows: name: 25551_146 n: 60479599727359666560994131358298323344894266838551584001575199716934366999703013872164853960440227739 skew: 9581.22 # norm 8.20e+13 c5: 23940 c4: -717855282 c3: -6785777479427 c2: 59164854376037827 c1: 270725537666604462153 c0: -1234452836689798433057766 # alpha -6.03 Y1: 129595215343 Y0: -19077200685863818687 # Murphy_E 3.21e-09 # M 16954413833068882237305959215587452485169461365335948587591155236573028568610291703407904271619835883 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 180427 x 180657 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 5.00 hours.
(23·10¹³⁶-41)/9 = 2(5)₁₃₅1_<137> = 3 · 587 · 5081 · C130
C130 = P64 · P66
P64 = 7220707395104081979889441231486340266276055853078025872679218893_<64>
P66 = 395546029374132684362629681712347760388410687843986837692961179827_<66>

Number: 25551_136 N=2856122139405856309563107813059951282752130483951642176474844660794454712203535608497877323817032394969305938353534250598068871511 ( 130 digits) SNFS difficulty: 137 digits. Divisors found: r1=7220707395104081979889441231486340266276055853078025872679218893 r2=395546029374132684362629681712347760388410687843986837692961179827 Version: Msieve 1.36 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.294). Factorization parameters were as follows: n: 2856122139405856309563107813059951282752130483951642176474844660794454712203535608497877323817032394969305938353534250598068871511 Y1: 1 Y0: -1000000000000000000000000000 c5: 230 c0: -41 skew: 0.71 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 2225001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 167043 x 167264 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 6.60 hours.
(23·10¹²⁸-41)/9 = 2(5)₁₂₇1_<129> = 2455552249163861923_<19> · C111
C111 = P36 · P75
P36 = 183984724928350103604095598822455287_<36>
P75 = 565658580426499955089656149121889215128319053548001037907750693173909533651_<75>

Number: 25551_128 N=104072538323130598266669657959877765401398196056849442449371065528617787768961145538112189660598674708969362837 ( 111 digits) SNFS difficulty: 129 digits. Divisors found: r1=183984724928350103604095598822455287 r2=565658580426499955089656149121889215128319053548001037907750693173909533651 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: n: 104072538323130598266669657959877765401398196056849442449371065528617787768961145538112189660598674708969362837 Y1: 1 Y0: -10000000000000000000000000 c5: 23000 c0: -41 skew: 0.28 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [400000, 1050001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 120882 x 121130 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 2.60 hours.
(23·10¹⁵¹-41)/9 = 2(5)₁₅₀1_<152> = 3 · 7 · 19 · C149
C149 = P42 · P107
P42 = 828705755470883248206443600902260497750813_<42>
P107 = 77288001192943139407705039988537472974515304633897945114412907051296370165896505908384922416246634351671973_<107>

Number: 25551_151 N=64049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049 ( 149 digits) SNFS difficulty: 152 digits. Divisors found: r1=828705755470883248206443600902260497750813 r2=77288001192943139407705039988537472974515304633897945114412907051296370165896505908384922416246634351671973 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.312). Factorization parameters were as follows: n: 64049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049011417432470064049 Y1: 1 Y0: -1000000000000000000000000000000 c5: 230 c0: -41 skew: 0.71 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1200000, 3100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 580869 x 581117 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,52,52,2.5,2.5,100000 total time: 14.25 hours.
(23·10¹⁷⁶-41)/9 = 2(5)₁₇₅1_<177> = 1693 · 40766729 · 6784935167_<10> · 582406709601371_<15> · 64712766329852691432002761083917_<32> · C110
C110 = P39 · P71
P39 = 771073511127576234777110033082908100809_<39>
P71 = 18778663554365193587028132136971846756713170062564978859065837339119323_<71>
Jul 28, 2008 (9th): By Sinkiti Sibata / GGNFS
(23·10¹²⁷-41)/9 = 2(5)₁₂₆1_<128> = 3 · 7 · 13789 · 636704041316348681226905897_<27> · C96
C96 = P40 · P56
P40 = 7221520930973206646401819070774877612779_<40>
P56 = 19194065806847188314532804326356425958335559911996902133_<56>

Number: 25551_127 N=138610347974624100139747647275393532986136399287735632429301347986696578956797567157662333157607 ( 96 digits) SNFS difficulty: 128 digits. Divisors found: r1=7221520930973206646401819070774877612779 (pp40) r2=19194065806847188314532804326356425958335559911996902133 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.25 hours. Scaled time: 4.06 units (timescale=0.774). Factorization parameters were as follows: name: 25551_127 n: 138610347974624100139747647275393532986136399287735632429301347986696578956797567157662333157607 m: 10000000000000000000000000 c5: 2300 c0: -41 skew: 0.45 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:63839, largePrimes:1565208 encountered Relations: rels:1597866, finalFF:199561 Max relations in full relation-set: 28 Initial matrix: 127857 x 199561 with sparse part having weight 16075767. Pruned matrix : 109221 x 109924 with weight 7153577. Total sieving time: 5.11 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.25 hours. --------- CPU info (if available) ----------
Jul 28, 2008 (8th): By Jo Yeong Uk / GGNFS
8·10²³⁷-1 = 7(9)₂₃₇_<238> = 19 · 31 · 569 · 33529 · 441702386307151_<15> · 35149384885764499121265377855887521968365553602811950790861159929701230228471_<77> · C137
C137 = P52 · P86
P52 = 1236107286628145196448639851671015323071433818391231_<52>
P86 = 37096948202534582401901585244832896057767553242001774619573918018896075253502000311741_<86>

Number: 79999_237 N=45855807984819870790284032074741112260037755149041837570580988639808010607112972363240352571450865017457653731943683977750690941100743171 ( 137 digits) SNFS difficulty: 159 digits. Divisors found: r1=1236107286628145196448639851671015323071433818391231 (pp52) r2=37096948202534582401901585244832896057767553242001774619573918018896075253502000311741 (pp86) Version: GGNFS-0.77.1-20050930-nocona Total time: 30.73 hours. Scaled time: 73.26 units (timescale=2.384). Factorization parameters were as follows: n: 45855807984819870790284032074741112260037755149041837570580988639808010607112972363240352571450865017457653731943683977750690941100743171 m: 200000000000000000000000000 c6: 25 c3: 10 c0: 4 skew: 0.74 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, 3900001) Primes: RFBsize:283146, AFBsize:282762, largePrimes:5755281 encountered Relations: rels:5770382, finalFF:637340 Max relations in full relation-set: 28 Initial matrix: 565974 x 637340 with sparse part having weight 42624067. Pruned matrix : 511711 x 514604 with weight 30656236. Total sieving time: 29.14 hours. Total relation processing time: 0.08 hours. Matrix solve time: 1.44 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,159,6,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 30.73 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116) Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)
Jul 28, 2008 (7th): By suberi / GMP-ECM
(4·10²⁰⁵-1)/3 = 1(3)₂₀₅_<206> = 13 · 2722799 · 769133399 · C189
C189 = P35 · P155
P35 = 16552386941879045763447940586089963_<35>
P155 = 29588128831725251679987662009307565255386626445186833657115513568355695849046387928726745167267846248912352318255956907081595132326285283802772607783082707_<155>
Jul 28, 2008 (6th): By Robert Backstrom / GGNFS, Msieve
(22·10¹⁶⁵-13)/9 = 2(4)₁₆₄3_<166> = 7 · 17 · 3191 · C160
C160 = P52 · P109
P52 = 5754480652293022944296874651263801107670250103676807_<52>
P109 = 1118665569732113050387533457391188058592674819391297562139857816414188357774603895007548142093328554147528381_<109>

Number: n N=6437339377409796050458206890820675914782501321849119884034257179315892240109247501361350975154503460216218525433781576978435790904683193657699160307599483959467 ( 160 digits) SNFS difficulty: 166 digits. Divisors found: Mon Jul 28 17:54:55 2008 prp52 factor: 5754480652293022944296874651263801107670250103676807 Mon Jul 28 17:54:55 2008 prp109 factor: 1118665569732113050387533457391188058592674819391297562139857816414188357774603895007548142093328554147528381 Mon Jul 28 17:54:55 2008 elapsed time 02:54:38 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 40.31 hours. Scaled time: 52.76 units (timescale=1.309). Factorization parameters were as follows: name: KA_2_4_164_3 n: 6437339377409796050458206890820675914782501321849119884034257179315892240109247501361350975154503460216218525433781576978435790904683193657699160307599483959467 type: snfs skew: 0.90 deg: 5 c5: 22 c0: -13 m: 1000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2300000) Primes: RFBsize:348513, AFBsize:348457, largePrimes:9839460 encountered Relations: rels:9290956, finalFF:745978 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 39.81 hours. Total relation processing time: 0.49 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,50,50,2.5,2.5,100000 total time: 40.31 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(23·10¹²⁵-41)/9 = 2(5)₁₂₄1_<126> = 43 · C124
C124 = P42 · P83
P42 = 249348569303014160413787592148654698519463_<42>
P83 = 23834716483005383332708850249577163177780742690701649474076750209456743894544822939_<83>

Number: n N=5943152454780361757105943152454780361757105943152454780361757105943152454780361757105943152454780361757105943152454780361757 ( 124 digits) SNFS difficulty: 126 digits. Divisors found: r1=249348569303014160413787592148654698519463 (pp42) r2=23834716483005383332708850249577163177780742690701649474076750209456743894544822939 (pp83) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.59 hours. Scaled time: 2.90 units (timescale=1.818). Factorization parameters were as follows: name: KA_2_5_124_1 n: 5943152454780361757105943152454780361757105943152454780361757105943152454780361757105943152454780361757105943152454780361757 skew: 1.12 deg: 5 c5: 23 c0: -41 m: 10000000000000000000000000 type: snfs rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 320001) Primes: RFBsize:56543, AFBsize:56629, largePrimes:5090222 encountered Relations: rels:4337119, finalFF:156374 Max relations in full relation-set: 48 Initial matrix: 113237 x 156374 with sparse part having weight 17243698. Pruned matrix : 101383 x 102013 with weight 7505512. Total sieving time: 1.44 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.05 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,700000,700000,28,28,50,50,2.5,2.5,50000 total time: 1.59 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(28·10¹⁶⁹-1)/9 = 3(1)₁₆₉_<170> = 569 · 66874311668453_<14> · C153
C153 = P65 · P89
P65 = 44747666732132274776543864200416504217245710983578615464026424207_<65>
P89 = 18271471956786769290650039107080148906269339162611613818652179674703425122513940651184189_<89>

Number: n N=817605737827795112675191444680284193664087344513277738051760753443865670302478953404332802895920027643909527487197553597209356778647497395851301805263123 ( 153 digits) SNFS difficulty: 171 digits. Divisors found: Mon Jul 28 21:12:01 2008 prp65 factor: 44747666732132274776543864200416504217245710983578615464026424207 Mon Jul 28 21:12:01 2008 prp89 factor: 18271471956786769290650039107080148906269339162611613818652179674703425122513940651184189 Mon Jul 28 21:12:01 2008 elapsed time 02:26:33 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 48.38 hours. Scaled time: 88.49 units (timescale=1.829). Factorization parameters were as follows: name: KA_3_1_169 n: 817605737827795112675191444680284193664087344513277738051760753443865670302478953404332802895920027643909527487197553597209356778647497395851301805263123 skew: 0.81 deg: 5 c5: 14 c0: -5 m: 10000000000000000000000000000000000 type: snfs rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 3100001) Primes: RFBsize:412849, AFBsize:414176, largePrimes:9904175 encountered Relations: rels:9455000, finalFF:839308 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 48.10 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,171,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,50,50,2.5,2.5,100000 total time: 48.38 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 28, 2008 (5th): By Sinkiti Sibata / GGNFS
(23·10¹²⁹-41)/9 = 2(5)₁₂₈1_<130> = 347 · 1399 · 59004638297548789745241165391_<29> · C95
C95 = P36 · P60
P36 = 145724632415306209970889384614530979_<36>
P60 = 612236216310466332533975530312917979837581554624783714920903_<60>

Number: 25551_129 N=89217897573180606659720594531071090386214846727194734208262478987142825655424436387351428154037 ( 95 digits) SNFS difficulty: 131 digits. Divisors found: r1=145724632415306209970889384614530979 (pp36) r2=612236216310466332533975530312917979837581554624783714920903 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.18 hours. Scaled time: 4.01 units (timescale=0.774). Factorization parameters were as follows: name: 25551_129 n: 89217897573180606659720594531071090386214846727194734208262478987142825655424436387351428154037 m: 100000000000000000000000000 c5: 23 c0: -410 skew: 1.78 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:64059, largePrimes:1499300 encountered Relations: rels:1490747, finalFF:160397 Max relations in full relation-set: 28 Initial matrix: 128075 x 160397 with sparse part having weight 12552187. Pruned matrix : 119298 x 120002 with weight 7667375. Total sieving time: 5.02 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.08 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.18 hours. --------- CPU info (if available) ----------
(23·10¹¹⁶-41)/9 = 2(5)₁₁₅1_<117> = 17 · 192406883 · C107
C107 = P38 · P70
P38 = 20871150723274008192701347204335976081_<38>
P70 = 3743427330215324631982859564971087424753593345379490493751515455230261_<70>

Number: 25551_116 N=78129636030547262195749898698837870196137347232609306808107078432860782708361889269454031878999438043387141 ( 107 digits) SNFS difficulty: 117 digits. Divisors found: r1=20871150723274008192701347204335976081 (pp38) r2=3743427330215324631982859564971087424753593345379490493751515455230261 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.23 hours. Scaled time: 1.73 units (timescale=0.774). Factorization parameters were as follows: name: 25551_116 n: 78129636030547262195749898698837870196137347232609306808107078432860782708361889269454031878999438043387141 m: 100000000000000000000000 c5: 230 c0: -41 skew: 0.71 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:63644, largePrimes:2232224 encountered Relations: rels:2412467, finalFF:298474 Max relations in full relation-set: 28 Initial matrix: 112809 x 298474 with sparse part having weight 28115143. Pruned matrix : 79906 x 80534 with weight 5836660. Total sieving time: 2.12 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.23 hours. --------- CPU info (if available) ----------
(23·10¹²³-41)/9 = 2(5)₁₂₂1_<124> = 1453 · 1801 · 9391 · 6693819476983_<13> · C101
C101 = P45 · P56
P45 = 637191652502528066422659078234237565527319133_<45>
P56 = 24380919769593584418550698024252096421356470057475816983_<56>

Number: 25551_123 N=15535318557518891893677625380007670301471136199536056513238867420641462692932163565132174374942235739 ( 101 digits) SNFS difficulty: 124 digits. Divisors found: r1=637191652502528066422659078234237565527319133 (pp45) r2=24380919769593584418550698024252096421356470057475816983 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.15 hours. Scaled time: 3.19 units (timescale=0.768). Factorization parameters were as follows: name: 25551_123 n: 15535318557518891893677625380007670301471136199536056513238867420641462692932163565132174374942235739 m: 1000000000000000000000000 c5: 23000 c0: -41 skew: 0.28 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:49098, AFBsize:63559, largePrimes:2391319 encountered Relations: rels:2706287, finalFF:384069 Max relations in full relation-set: 28 Initial matrix: 112724 x 384069 with sparse part having weight 40247857. Pruned matrix : 85697 x 86324 with weight 9432873. Total sieving time: 4.00 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.15 hours. --------- CPU info (if available) ----------
(23·10¹³³-41)/9 = 2(5)₁₃₂1_<134> = 3 · 7 · 19 · 1406343509201398365268977301_<28> · C104
C104 = P39 · P66
P39 = 131983281958163855510539651678444328449_<39>
P66 = 345065940183956376607582992204291886943136677148509477565980637101_<66>

Number: 25551_133 N=45542935277458017797569348660685401934522573265115886086415534445131430705420105041865756177125119186349 ( 104 digits) SNFS difficulty: 134 digits. Divisors found: r1=131983281958163855510539651678444328449 (pp39) r2=345065940183956376607582992204291886943136677148509477565980637101 (pp66) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 10.59 hours. Scaled time: 5.01 units (timescale=0.473). Factorization parameters were as follows: name: 25551_133 n: 45542935277458017797569348660685401934522573265115886086415534445131430705420105041865756177125119186349 m: 100000000000000000000000000 c5: 23000 c0: -41 skew: 0.28 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, 1450001) Primes: RFBsize:78498, AFBsize:63559, largePrimes:1565148 encountered Relations: rels:1564919, finalFF:169848 Max relations in full relation-set: 28 Initial matrix: 142124 x 169848 with sparse part having weight 15160791. Pruned matrix : 133632 x 134406 with weight 10401980. Total sieving time: 10.13 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.31 hours. Time per square root: 0.04 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: 10.59 hours. --------- CPU info (if available) ----------
Jul 28, 2008 (4th): By Serge Batalov / GMP-ECM, Msieve, pol51
8·10²⁴⁴-1 = 7(9)₂₄₄_<245> = 89 · 1278578053639_<13> · 108861017508663575689495374381113_<33> · C199
C199 = P36 · C164
P36 = 142573390866785288763609707121204263_<36>
C164 = [45296210130250230198807436160507101560969066892484152346441941909506494187913106289607271581488076574862891981551400056470584444467889627923713436760753843396214751_<164>]
8·10²⁴⁰-1 = 7(9)₂₄₀_<241> = 7 · 23 · 167 · 1063 · 1327 · 53831 · 2010123697_<10> · 14590058377_<11> · 967282300096325356931642416182002212551860417333658191869546350550040969_<72> · C135
C135 = P56 · P80
P56 = 12638631559884545162091883790692457456172929864285579791_<56>
P80 = 10928936369148320848662567406798716031938309146132546684068294609008875247151417_<80>

Number: 79999_240 N=138126800111087979621904572738473262040684851838378352665408113514452160684022609766361862880248315626676076038065194239443863012213847 ( 135 digits) SNFS difficulty: 162 digits. Divisors found: r1=12638631559884545162091883790692457456172929864285579791 r2=10928936369148320848662567406798716031938309146132546684068294609008875247151417 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 138126800111087979621904572738473262040684851838378352665408113514452160684022609766361862880248315626676076038065194239443863012213847 Y1: 1 Y0: -1000000000000000000000000000 c6: 1 c3: 5 c0: 25 skew: 1.7 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2500000, 6000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 808067 x 808315 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.25 hours. * 4 dep Prototype def-par.txt line would be: snfs,162,6,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000 total time: 25.90 hours.
(23·10¹³⁴-41)/9 = 2(5)₁₃₃1_<135> = 83 · C133
C133 = P62 · P71
P62 = 61675709953442697785653352579529799727020527376375559085086927_<62>
P71 = 49922126545103830085717272367270909155555235254621911382926371134183211_<71>

Number: 25551_134 N=3078982597054886211512717536813922356091030789825970548862115127175368139223560910307898259705488621151271753681392235609103078982597 ( 133 digits) SNFS difficulty: 136 digits. Divisors found: r1=61675709953442697785653352579529799727020527376375559085086927 r2=49922126545103830085717272367270909155555235254621911382926371134183211 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.303). Factorization parameters were as follows: n: 3078982597054886211512717536813922356091030789825970548862115127175368139223560910307898259705488621151271753681392235609103078982597 Y1: 1 Y0: -1000000000000000000000000000 c5: 23 c0: -410 skew: 1.78 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 1625001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 145782 x 146030 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 4.5 hours.
(23·10¹⁷⁰-41)/9 = 2(5)₁₆₉1_<171> = 47 · 167 · 1233615293_<10> · 645304315442331619894177_<24> · 8914696587075694200020688570908983_<34> · C100
C100 = P39 · P62
P39 = 285490091589476305221345080451232055137_<39>
P62 = 16070488449447674612650589351851462929548050466307798710623429_<62>

Number: 25551_170 N=4587965219320437679186724585504871860492353253197962059126245596532976638080543930484448622172004773 ( 100 digits) Divisors found: r1=285490091589476305221345080451232055137 r2=16070488449447674612650589351851462929548050466307798710623429 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: name: 25551_170 n: 4587965219320437679186724585504871860492353253197962059126245596532976638080543930484448622172004773 skew: 4343.54 # norm 1.85e+14 c5: 102600 c4: -2099554410 c3: 313677236699 c2: -32073952736029022 c1: -22993856991668603067 c0: 77448256609396649268195 # alpha -6.35 Y1: 13929288857 Y0: -8513290624657879186 # Murphy_E 3.34e-09 # M 881146291402212354249118032869459916813881084351627622763479243021417493888375943481775157365108946 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 4089960 relations Max relations in full relation-set: Initial matrix: Pruned matrix : 188015 x 188257 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 2.80 hours.
(23·10¹⁴⁴-41)/9 = 2(5)₁₄₃1_<145> = C145
C145 = P53 · P93
P53 = 11328951549049208258659188667017358765383634275585517_<53>
P93 = 225577410627202540610471998982892547446702289733649826841945206400113122054353971517703547003_<93>

Number: 25551_144 N=2555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551 ( 145 digits) SNFS difficulty: 146 digits. Divisors found: r1=11328951549049208258659188667017358765383634275585517 r2=225577410627202540610471998982892547446702289733649826841945206400113122054353971517703547003 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 2555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551 Y1: 1 Y0: -100000000000000000000000000000 c5: 23 c0: -410 skew: 1.78 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved rational special-q in [750000, 2750001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 3186702 relations Max relations in full relation-set: Initial matrix: Pruned matrix : 255651 x 255899 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 7.02 hours.
Jul 28, 2008 (3rd): By Sinkiti Sibata / GGNFS
(23·10¹²¹-41)/9 = 2(5)₁₂₀1_<122> = 3³ · 7² · 107 · 242689 · 2785847 · 774795187 · C96
C96 = P48 · P48
P48 = 552729096969604125117866209022368136492287800707_<48>
P48 = 623498064629031326448330932831149966744250542153_<48>

Number: 25551_121 N=344625522224700355890781569301728917200166256280370455883285888961664239432175325341492766702171 ( 96 digits) SNFS difficulty: 122 digits. Divisors found: r1=552729096969604125117866209022368136492287800707 (pp48) r2=623498064629031326448330932831149966744250542153 (pp48) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.99 hours. Scaled time: 1.42 units (timescale=0.473). Factorization parameters were as follows: name: 25551_121 n: 344625522224700355890781569301728917200166256280370455883285888961664239432175325341492766702171 m: 1000000000000000000000000 c5: 230 c0: -41 skew: 0.71 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63644, largePrimes:2079639 encountered Relations: rels:2058172, finalFF:128435 Max relations in full relation-set: 28 Initial matrix: 112809 x 128435 with sparse part having weight 11139017. Pruned matrix : 108190 x 108818 with weight 8118576. Total sieving time: 2.71 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.17 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.99 hours. --------- CPU info (if available) ----------
Jul 28, 2008 (2nd): By Serge Batalov / GMP-ECM, Msieve, pol51
8·10²⁴⁴-1 = 7(9)₂₄₄_<245> = 89 · 1278578053639_<13> · C231
C231 = P33 · C199
P33 = 108861017508663575689495374381113_<33>
C199 = [6458034271684205445370439176812586281872425037340884899946467880064597890608060770039709215095343983538806570804236640838846920029060722859175686181158626178828082778050969836074995833443582884683513_<199>]
8·10²⁴¹-1 = 7(9)₂₄₁_<242> = 149 · 24421 · 31350871 · 1697371865690194829_<19> · C210
C210 = P31 · C180
P31 = 4084686957513171056405214141139_<31>
C180 = [101147437776188067596893019641822094170077201992981329794320726118257488337588143534303319427488460340571418858976260720363458708418693527978581840212562659143024599069105778741431_<180>]
(23·10¹¹⁴-41)/9 = 2(5)₁₁₃1_<115> = 12671 · 3204884250067103630129_<22> · C89
C89 = P27 · P62
P27 = 725788414881940170954537007_<27>
P62 = 86706579727612278786969624143583485674657111291579725893503327_<62>
(23·10¹⁵³-41)/9 = 2(5)₁₅₂1_<154> = 157 · 1511 · 71889401 · 6594980699_<10> · 10359967718793949674331_<23> · 126119780815898289136469561_<27> · C83
C83 = P41 · P42
P41 = 50235185876494027386262953460826258885293_<41>
P42 = 346173000949072010309520257023196154046249_<42>

Sun Jul 27 11:25:56 2008 Msieve v. 1.36 Sun Jul 27 11:25:56 2008 random seeds: 42d2437e c33efa51 Sun Jul 27 11:25:56 2008 factoring 17390065048100375790461411356970700872395622645753315257013857083257878410307915957 (83 digits) Sun Jul 27 11:25:57 2008 no P-1/P+1/ECM available, skipping Sun Jul 27 11:25:57 2008 commencing quadratic sieve (83-digit input) Sun Jul 27 11:25:57 2008 using multiplier of 13 Sun Jul 27 11:25:57 2008 using 64kb Opteron sieve core Sun Jul 27 11:25:57 2008 sieve interval: 6 blocks of size 65536 Sun Jul 27 11:25:57 2008 processing polynomials in batches of 17 Sun Jul 27 11:25:57 2008 using a sieve bound of 1356389 (52353 primes) Sun Jul 27 11:25:57 2008 using large prime bound of 123431399 (26 bits) Sun Jul 27 11:25:57 2008 using trial factoring cutoff of 27 bits Sun Jul 27 11:25:57 2008 polynomial 'A' values have 11 factors Sun Jul 27 11:42:17 2008 52737 relations (28001 full + 24736 combined from 268831 partial), need 52449 Sun Jul 27 11:42:17 2008 begin with 296832 relations Sun Jul 27 11:42:17 2008 reduce to 74247 relations in 2 passes Sun Jul 27 11:42:17 2008 attempting to read 74247 relations Sun Jul 27 11:42:18 2008 recovered 74247 relations Sun Jul 27 11:42:18 2008 recovered 64353 polynomials Sun Jul 27 11:42:18 2008 attempting to build 52737 cycles Sun Jul 27 11:42:18 2008 found 52737 cycles in 1 passes Sun Jul 27 11:42:18 2008 distribution of cycle lengths: Sun Jul 27 11:42:18 2008 length 1 : 28001 Sun Jul 27 11:42:18 2008 length 2 : 24736 Sun Jul 27 11:42:18 2008 largest cycle: 2 relations Sun Jul 27 11:42:18 2008 matrix is 52353 x 52737 (8.1 MB) with weight 1696688 (32.17/col) Sun Jul 27 11:42:18 2008 sparse part has weight 1696688 (32.17/col) Sun Jul 27 11:42:19 2008 filtering completed in 3 passes Sun Jul 27 11:42:19 2008 matrix is 36662 x 36726 (6.1 MB) with weight 1317403 (35.87/col) Sun Jul 27 11:42:19 2008 sparse part has weight 1317403 (35.87/col) Sun Jul 27 11:42:19 2008 saving the first 48 matrix rows for later Sun Jul 27 11:42:19 2008 matrix is 36614 x 36726 (4.1 MB) with weight 989538 (26.94/col) Sun Jul 27 11:42:19 2008 sparse part has weight 717356 (19.53/col) Sun Jul 27 11:42:19 2008 matrix includes 64 packed rows Sun Jul 27 11:42:19 2008 using block size 14690 for processor cache size 1024 kB Sun Jul 27 11:42:19 2008 commencing Lanczos iteration Sun Jul 27 11:42:19 2008 memory use: 4.1 MB Sun Jul 27 11:42:26 2008 lanczos halted after 581 iterations (dim = 36608) Sun Jul 27 11:42:26 2008 recovered 14 nontrivial dependencies Sun Jul 27 11:42:26 2008 prp41 factor: 50235185876494027386262953460826258885293 Sun Jul 27 11:42:26 2008 prp42 factor: 346173000949072010309520257023196154046249 Sun Jul 27 11:42:26 2008 elapsed time 00:16:30
(23·10¹²⁴-41)/9 = 2(5)₁₂₃1_<125> = 3 · 47 · 3643631 · 17073588094550355706752106093964111_<35> · C82
C82 = P36 · P47
P36 = 155830978679555689187019330766573207_<36>
P47 = 18696194936136122483576503549609207686186338653_<47>

Sun Jul 27 11:25:25 2008 Msieve v. 1.36 Sun Jul 27 11:25:25 2008 random seeds: 795a1938 d119b872 Sun Jul 27 11:25:25 2008 factoring 2913446354481845142744359062908868931976606350837226718898980159766073710818270171 (82 digits) Sun Jul 27 11:25:26 2008 no P-1/P+1/ECM available, skipping Sun Jul 27 11:25:26 2008 commencing quadratic sieve (82-digit input) Sun Jul 27 11:25:26 2008 using multiplier of 1 Sun Jul 27 11:25:26 2008 using 64kb Opteron sieve core Sun Jul 27 11:25:26 2008 sieve interval: 6 blocks of size 65536 Sun Jul 27 11:25:26 2008 processing polynomials in batches of 17 Sun Jul 27 11:25:26 2008 using a sieve bound of 1337729 (51471 primes) Sun Jul 27 11:25:26 2008 using large prime bound of 125746526 (26 bits) Sun Jul 27 11:25:26 2008 using trial factoring cutoff of 27 bits Sun Jul 27 11:25:26 2008 polynomial 'A' values have 10 factors Sun Jul 27 11:46:04 2008 51676 relations (25977 full + 25699 combined from 278377 partial), need 51567 Sun Jul 27 11:46:05 2008 begin with 304354 relations Sun Jul 27 11:46:05 2008 reduce to 74155 relations in 2 passes Sun Jul 27 11:46:05 2008 attempting to read 74155 relations Sun Jul 27 11:46:06 2008 recovered 74155 relations Sun Jul 27 11:46:06 2008 recovered 65726 polynomials Sun Jul 27 11:46:06 2008 attempting to build 51676 cycles Sun Jul 27 11:46:07 2008 found 51676 cycles in 1 passes Sun Jul 27 11:46:07 2008 distribution of cycle lengths: Sun Jul 27 11:46:07 2008 length 1 : 25977 Sun Jul 27 11:46:07 2008 length 2 : 25699 Sun Jul 27 11:46:07 2008 largest cycle: 2 relations Sun Jul 27 11:46:07 2008 matrix is 51471 x 51676 (7.7 MB) with weight 1608107 (31.12/col) Sun Jul 27 11:46:07 2008 sparse part has weight 1608107 (31.12/col) Sun Jul 27 11:46:08 2008 filtering completed in 3 passes Sun Jul 27 11:46:08 2008 matrix is 37409 x 37473 (6.1 MB) with weight 1301480 (34.73/col) Sun Jul 27 11:46:08 2008 sparse part has weight 1301480 (34.73/col) Sun Jul 27 11:46:08 2008 saving the first 48 matrix rows for later Sun Jul 27 11:46:08 2008 matrix is 37361 x 37473 (4.6 MB) with weight 1010936 (26.98/col) Sun Jul 27 11:46:08 2008 sparse part has weight 827779 (22.09/col) Sun Jul 27 11:46:08 2008 matrix includes 64 packed rows Sun Jul 27 11:46:08 2008 using block size 14989 for processor cache size 1024 kB Sun Jul 27 11:46:09 2008 commencing Lanczos iteration Sun Jul 27 11:46:09 2008 memory use: 4.4 MB Sun Jul 27 11:46:22 2008 lanczos halted after 593 iterations (dim = 37361) Sun Jul 27 11:46:22 2008 recovered 18 nontrivial dependencies Sun Jul 27 11:46:23 2008 prp36 factor: 155830978679555689187019330766573207 Sun Jul 27 11:46:23 2008 prp47 factor: 18696194936136122483576503549609207686186338653 Sun Jul 27 11:46:23 2008 elapsed time 00:20:58
(23·10¹⁷⁰-41)/9 = 2(5)₁₆₉1_<171> = 47 · 167 · 1233615293_<10> · 645304315442331619894177_<24> · C134
C134 = P34 · C100
P34 = 8914696587075694200020688570908983_<34>
C100 = [4587965219320437679186724585504871860492353253197962059126245596532976638080543930484448622172004773_<100>]
(23·10¹⁴⁶-41)/9 = 2(5)₁₄₅1_<147> = 43 · 6841 · 346043 · C136
C136 = P35 · C101
P35 = 41510532436848216902506677855337901_<35>
C101 = [60479599727359666560994131358298323344894266838551584001575199716934366999703013872164853960440227739_<101>]
(23·10¹⁹⁵-41)/9 = 2(5)₁₉₄1_<196> = 158597 · 7029942179561563_<16> · 313306481963429959_<18> · 138881901627091563659_<21> · C137
C137 = P30 · C108
P30 = 337159954666957756609533851017_<30>
C108 = [156238328603539719034056512317514350799152188699229320945880126217790717414234564344734256456866329066492133_<108>]
(23·10¹⁴⁸-41)/9 = 2(5)₁₄₇1_<149> = 3³ · 17 · 151 · 1283 · C141
C141 = P35 · C106
P35 = 75011929299489064304755445730298699_<35>
C106 = [3831234208100258225905784789352281618753028879135330243405513044277690944977878017308340945272902471143467_<106>]
(23·10¹⁵⁷-41)/9 = 2(5)₁₅₆1_<158> = 3² · 7 · 14776651 · 63748651 · C141
C141 = P30 · P111
P30 = 973336363550106887302722574739_<30>
P111 = 442420062949587264507358090096128210983570197191636875054556465288607675852564435098117942495764116067637731443_<111>
(23·10¹⁰⁶-41)/9 = 2(5)₁₀₅1_<107> = 3 · 89 · 304585559 · 183954605179_<12> · C85
C85 = P32 · P54
P32 = 12361526776253110052746469951419_<32>
P54 = 138191705900215663268288927238977959384385858170547267_<54>

Sun Jul 27 11:50:55 2008 Msieve v. 1.36 Sun Jul 27 11:50:55 2008 random seeds: 2bb3be20 caa580c6 Sun Jul 27 11:50:55 2008 factoring 1708260472741610815635081495099835617949910688096929711288607302314546926614133221873 (85 digits) Sun Jul 27 11:50:55 2008 no P-1/P+1/ECM available, skipping Sun Jul 27 11:50:55 2008 commencing quadratic sieve (85-digit input) Sun Jul 27 11:50:55 2008 using multiplier of 1 Sun Jul 27 11:50:56 2008 using 64kb Opteron sieve core Sun Jul 27 11:50:56 2008 sieve interval: 6 blocks of size 65536 Sun Jul 27 11:50:56 2008 processing polynomials in batches of 17 Sun Jul 27 11:50:56 2008 using a sieve bound of 1409879 (54118 primes) Sun Jul 27 11:50:56 2008 using large prime bound of 118429836 (26 bits) Sun Jul 27 11:50:56 2008 using trial factoring cutoff of 27 bits Sun Jul 27 11:50:56 2008 polynomial 'A' values have 11 factors Sun Jul 27 12:27:36 2008 54264 relations (27466 full + 26798 combined from 283153 partial), need 54214 Sun Jul 27 12:27:36 2008 begin with 310619 relations Sun Jul 27 12:27:36 2008 reduce to 77728 relations in 2 passes Sun Jul 27 12:27:36 2008 attempting to read 77728 relations Sun Jul 27 12:27:37 2008 recovered 77728 relations Sun Jul 27 12:27:37 2008 recovered 72460 polynomials Sun Jul 27 12:27:37 2008 attempting to build 54264 cycles Sun Jul 27 12:27:37 2008 found 54264 cycles in 1 passes Sun Jul 27 12:27:37 2008 distribution of cycle lengths: Sun Jul 27 12:27:37 2008 length 1 : 27466 Sun Jul 27 12:27:37 2008 length 2 : 26798 Sun Jul 27 12:27:37 2008 largest cycle: 2 relations Sun Jul 27 12:27:37 2008 matrix is 54118 x 54264 (8.2 MB) with weight 1722644 (31.75/col) Sun Jul 27 12:27:37 2008 sparse part has weight 1722644 (31.75/col) Sun Jul 27 12:27:38 2008 filtering completed in 3 passes Sun Jul 27 12:27:38 2008 matrix is 39821 x 39884 (6.6 MB) with weight 1398732 (35.07/col) Sun Jul 27 12:27:38 2008 sparse part has weight 1398732 (35.07/col) Sun Jul 27 12:27:38 2008 saving the first 48 matrix rows for later Sun Jul 27 12:27:38 2008 matrix is 39773 x 39884 (4.2 MB) with weight 1024154 (25.68/col) Sun Jul 27 12:27:38 2008 sparse part has weight 701631 (17.59/col) Sun Jul 27 12:27:38 2008 matrix includes 64 packed rows Sun Jul 27 12:27:38 2008 using block size 15953 for processor cache size 1024 kB Sun Jul 27 12:27:38 2008 commencing Lanczos iteration Sun Jul 27 12:27:38 2008 memory use: 4.3 MB Sun Jul 27 12:27:46 2008 lanczos halted after 631 iterations (dim = 39770) Sun Jul 27 12:27:46 2008 recovered 14 nontrivial dependencies Sun Jul 27 12:27:46 2008 prp32 factor: 12361526776253110052746469951419 Sun Jul 27 12:27:46 2008 prp54 factor: 138191705900215663268288927238977959384385858170547267 Sun Jul 27 12:27:46 2008 elapsed time 00:36:51
(23·10¹¹⁰-41)/9 = 2(5)₁₀₉1_<111> = 52498139 · 68759837 · C95
C95 = P43 · P53
P43 = 1171236310664623846065075156444685421318659_<43>
P53 = 60445232405964426967246594540875308055954431145200123_<53>

Number: 25551_110 N=70795651000427540270331785995431991726223223369658715988001782164765787215865399899805108995057 ( 95 digits) SNFS difficulty: 111 digits. Divisors found: r1=1171236310664623846065075156444685421318659 r2=60445232405964426967246594540875308055954431145200123 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.176). Factorization parameters were as follows: n: 70795651000427540270331785995431991726223223369658715988001782164765787215865399899805108995057 Y1: 1 Y0: -10000000000000000000000 c5: 23 c0: -41 skew: 1.12 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 2.8M relations Max relations in full relation-set: Initial matrix: Pruned matrix : 66260 x 66481 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.05 hours.
(23·10¹⁸⁰-41)/9 = 2(5)₁₇₉1_<181> = 17 · 160625847619_<12> · 23288197500401_<14> · 10538502885230213_<17> · 14005677645847267_<17> · 452648203174615703323010093477_<30> · C93
C93 = P36 · P57
P36 = 818721351585225269696284670558586233_<36>
P57 = 734691701926879427540330661208791006085582518574130629367_<57>

Number: 25551_180 N=601507783200024177533706526882724961664302389935805095370359219106224905189670063398031704511 ( 93 digits) Divisors found: r1=818721351585225269696284670558586233 r2=734691701926879427540330661208791006085582518574130629367 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: name: 25551_180 n: 601507783200024177533706526882724961664302389935805095370359219106224905189670063398031704511 skew: 9274.72 # norm 5.56e+12 c5: 960 c4: 51491975 c3: -375693115044 c2: -3597295424721214 c1: 12421001845831235314 c0: 64030193958855804894760 # alpha -4.84 Y1: 14132136997 Y0: -910587610201992171 # Murphy_E 7.07e-09 # M 172801455112640510589520181640160855778357793905387688415191739720540490264493458130883360178 type: gnfs rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 109001 x 109222 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,92,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 1.60 hours.
(23·10¹⁴³-41)/9 = 2(5)₁₄₂1_<144> = 557 · 171012781 · 136207903799352110227_<21> · C113
C113 = P33 · P80
P33 = 538844847458477932858080232424621_<33>
P80 = 36554051399146403713935390141869213541499333355306590438897345084105764804979409_<80>
(23·10¹³⁸-41)/9 = 2(5)₁₃₇1_<139> = C139
C139 = P35 · P105
P35 = 17609003514447728631938833758128093_<35>
P105 = 145127778153873886153305871603820300439044982225316042826202236046692596812484867625963184012287196067307_<105>
(23·10¹⁷⁶-41)/9 = 2(5)₁₇₅1_<177> = 1693 · 40766729 · 6784935167_<10> · 582406709601371_<15> · C141
C141 = P32 · C110
P32 = 64712766329852691432002761083917_<32>
C110 = [14479730041147820385756519417126351350432451092133329416395602786113828306192530413105615533147360150563832307_<110>]
Jul 28, 2008: Factorizations of 255...551 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.
Jul 27, 2008 (4th): By Serge Batalov / GMP-ECM
8·10²⁴⁹-1 = 7(9)₂₄₉_<250> = 139 · 6513641919379205078817101_<25> · 30704788883921543079717165000137354872639579175495937407099_<59> · C165
C165 = P30 · P135
P30 = 444308886544865560271771281999_<30>
P135 = 647679560070206617765843309810908725678476935981017638468004383156312447877119496409280870778743697648282559776979950903559036235285741_<135>
8·10²⁴⁶-1 = 7(9)₂₄₆_<247> = 7² · 4519 · 234721 · 227403769 · 423619321 · 91904895863405227344778390349737714039_<38> · 982772344963126877180586765965485256911_<39> · C143
C143 = P36 · P107
P36 = 727185362958603102583458640927672321_<36>
P107 = 24327052797346741204514652628175478116899457476934725356694836765790319302103867872875822020632685040373489_<107>
Jul 27, 2008 (3rd): By Jo Yeong Uk / GGNFS
8·10²³¹-1 = 7(9)₂₃₁_<232> = 331 · 1549 · 2719 · 3296551 · 180273339366603915157042541456190941_<36> · 336541551884960929475454162660123389_<36> · C146
C146 = P68 · P78
P68 = 86993443529090471243193900012390628379624840454127261893376643990701_<68>
P78 = 329825971258905280264523732622444591114643795678979992003823731515025390553941_<78>

Number: 79999_231 N=28692697005138993302709192211409576219617822299744756725421307261784974933066555140257538805109891878235215013147269934963361194111890447242902641 ( 146 digits) SNFS difficulty: 156 digits. Divisors found: r1=86993443529090471243193900012390628379624840454127261893376643990701 (pp68) r2=329825971258905280264523732622444591114643795678979992003823731515025390553941 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.78 hours. Scaled time: 59.18 units (timescale=2.388). Factorization parameters were as follows: n: 28692697005138993302709192211409576219617822299744756725421307261784974933066555140257538805109891878235215013147269934963361194111890447242902641 m: 100000000000000000000000000 c6: 1 c3: 5 c0: 25 skew: 1.71 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3100001) Primes: RFBsize:216816, AFBsize:216710, largePrimes:5807273 encountered Relations: rels:5811297, finalFF:564255 Max relations in full relation-set: 28 Initial matrix: 433591 x 564255 with sparse part having weight 50527041. Pruned matrix : 358974 x 361205 with weight 33138080. Total sieving time: 23.66 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.98 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,156,6,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 24.78 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: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116) Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)
Jul 27, 2008 (2nd): By Sinkiti Sibata / GGNFS
(22·10¹⁶²+23)/9 = 2(4)₁₆₁7_<163> = 1978727 · 1171413239_<10> · 1087986601832676187_<19> · C129
C129 = P55 · P75
P55 = 1030690545220291183793531315683239605395413174248632823_<55>
P75 = 940442666446536063195756357805894289825335687502835965056411741932351986299_<75>

Number: 24447_162 N=969305364628204696618841104157701934175888050442734215063287899040826831867856381020984867573714343451139369729680252409177692077 ( 129 digits) SNFS difficulty: 163 digits. Divisors found: r1=1030690545220291183793531315683239605395413174248632823 (pp55) r2=940442666446536063195756357805894289825335687502835965056411741932351986299 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 95.03 hours. Scaled time: 72.98 units (timescale=0.768). Factorization parameters were as follows: name: 24447_162 n: 969305364628204696618841104157701934175888050442734215063287899040826831867856381020984867573714343451139369729680252409177692077 m: 100000000000000000000000000000000 c5: 2200 c0: 23 skew: 0.4 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, 5350001) Primes: RFBsize:315948, AFBsize:315882, largePrimes:6095209 encountered Relations: rels:6363736, finalFF:864607 Max relations in full relation-set: 28 Initial matrix: 631897 x 864607 with sparse part having weight 68497139. Pruned matrix : 463354 x 466577 with weight 52859718. Total sieving time: 90.96 hours. Total relation processing time: 0.28 hours. Matrix solve time: 3.65 hours. Time per square root: 0.13 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: 95.03 hours. --------- CPU info (if available) ----------
Jul 27, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(85·10¹⁸²+41)/9 = 9(4)₁₈₁9_<183> = 13 · 103 · C180
C180 = P36 · C145
P36 = 104574808336266590413440953679885241_<36>
C145 = [6744795118571178385715723334774127654765899499968956986278497873607085936148420292629447731798091830209139268833767631800242442027606210314918251_<145>]
(71·10¹⁶⁹-17)/9 = 7(8)₁₆₈7_<170> = 7 · 11 · 2517919 · 22273117 · C155
C155 = P53 · P103
P53 = 11409640629076421191434060010145846556226043653471327_<53>
P103 = 1601144010506807619000508842408173481687372550772951863625802499128877259926572721944100979348066363311_<103>

Number: n N=18268477755280836423775397397311493833809308462958858798539984335848791528224787061958360337859405752134076680695538897022388485946815868458429689903283697 ( 155 digits) SNFS difficulty: 171 digits. Divisors found: Sun Jul 27 06:14:21 2008 prp53 factor: 11409640629076421191434060010145846556226043653471327 Sun Jul 27 06:14:21 2008 prp103 factor: 1601144010506807619000508842408173481687372550772951863625802499128877259926572721944100979348066363311 Sun Jul 27 06:14:21 2008 elapsed time 04:24:45 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 81.67 hours. Scaled time: 117.77 units (timescale=1.442). Factorization parameters were as follows: name: KA_7_8_168_7 n: 18268477755280836423775397397311493833809308462958858798539984335848791528224787061958360337859405752134076680695538897022388485946815868458429689903283697 skew: 1.19 deg: 5 c5: 71 c0: -170 m: 10000000000000000000000000000000000 type: snfs rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 3900001) Primes: RFBsize:425648, AFBsize:425813, largePrimes:10128244 encountered Relations: rels:9731875, finalFF:881380 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 81.20 hours. Total relation processing time: 0.47 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,50,50,2.5,2.5,100000 total time: 81.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(68·10¹⁶⁹+13)/9 = 7(5)₁₆₈7_<170> = 7 · 11 · 474977 · C163
C163 = P32 · P46 · P86
P32 = 12564720581656893961516793698787_<32>
P46 = 7968617766944774753846532883783787495699428027_<46>
P86 = 20633232290617592691462578937718847171342995492350851612982494029893918840047147814217_<86>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 2065870518448222210720184306273737972536019599351086981014324864658670295574819372813802017742419067114789223438694886786057516429723926086907873394376951391291033 (163 digits) Using B1=290000, B2=172085560, polynomial Dickson(3), sigma=929903015 Step 1 took 3703ms Step 2 took 1859ms ********** Factor found in step 2: 12564720581656893961516793698787 Found probable prime factor of 32 digits: 12564720581656893961516793698787 Composite cofactor 164418341420513981191767033032572250364100248544748569751915035921047786398535014962302739673567607106739107738403172999090158859859 has 132 digits GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 164418341420513981191767033032572250364100248544748569751915035921047786398535014962302739673567607106739107738403172999090158859859 (132 digits) Using B1=3744000, B2=8561285470, polynomial Dickson(6), sigma=1706818246 Step 1 took 36187ms Step 2 took 15657ms ********** Factor found in step 2: 7968617766944774753846532883783787495699428027 Found probable prime factor of 46 digits: 7968617766944774753846532883783787495699428027 Probable prime cofactor 20633232290617592691462578937718847171342995492350851612982494029893918840047147814217 has 86 digits
Jul 26, 2008 (5th): By Robert Backstrom / GGNFS, Msieve
(35·10¹⁶⁹-53)/9 = 3(8)₁₆₈3_<170> = 3³ · 11² · 661 · 2207 · 7726057 · C154
C154 = P65 · P89
P65 = 59462556413862442092449340501731601838252568471681890551614913937_<65>
P89 = 17761151691851101595704380123061264611926150229274494050475365714951019876727414514520043_<89>

Number: n N=1056123484451864485860196229763977615884332123194476548802930056924154205342208938356587023654483801371879875439683279449403528714039431756768156306539291 ( 154 digits) SNFS difficulty: 170 digits. Divisors found: Sat Jul 26 20:46:42 2008 prp65 factor: 59462556413862442092449340501731601838252568471681890551614913937 Sat Jul 26 20:46:42 2008 prp89 factor: 17761151691851101595704380123061264611926150229274494050475365714951019876727414514520043 Sat Jul 26 20:46:42 2008 elapsed time 03:16:11 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 75.91 hours. Scaled time: 132.69 units (timescale=1.748). Factorization parameters were as follows: name: KA_3_8_168_3 n: 1056123484451864485860196229763977615884332123194476548802930056924154205342208938356587023654483801371879875439683279449403528714039431756768156306539291 type: snfs skew: 1.72 deg: 5 c5: 7 c0: -106 m: 10000000000000000000000000000000000 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 qintsize: 100000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2500001) Primes: RFBsize:412849, AFBsize:412531, largePrimes:10050797 encountered Relations: rels:9692589, finalFF:916683 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 75.46 hours. Total relation processing time: 0.45 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,50,50,2.6,2.6,100000 total time: 75.91 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 26, 2008 (4th): By Wataru Sakai / GGNFS
(31·10¹⁸⁹-13)/9 = 3(4)₁₈₈3_<190> = 11 · C189
C189 = P47 · P51 · P93
P47 = 18960275308406929724116517425722392691269164543_<47>
P51 = 148127824952087837453635732252173826200808100223731_<51>
P93 = 111492387161833705684170668928437133194092717290960694048484857650925015218158645936453543861_<93>

Number: 34443_189 N=313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313 ( 189 digits) SNFS difficulty: 191 digits. Divisors found: r1=18960275308406929724116517425722392691269164543 (pp47) r2=148127824952087837453635732252173826200808100223731 (pp51) r3=111492387161833705684170668928437133194092717290960694048484857650925015218158645936453543861 (pp93) Version: GGNFS-0.77.1-20060722-nocona Total time: 1502.39 hours. Scaled time: 2836.51 units (timescale=1.888). Factorization parameters were as follows: n: 313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313 m: 100000000000000000000000000000000000000 c5: 31 c0: -130 skew: 1.33 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, 25500001) Primes: RFBsize:501962, AFBsize:503087, largePrimes:7478270 encountered Relations: rels:8154107, finalFF:1168778 Max relations in full relation-set: 32 Initial matrix: 1005114 x 1168778 with sparse part having weight 159477313. Pruned matrix : 892881 x 897970 with weight 142693512. Total sieving time: 1489.05 hours. Total relation processing time: 0.17 hours. Matrix solve time: 12.84 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1502.39 hours. --------- CPU info (if available) ----------
Jul 26, 2008 (3rd): By Jo Yeong Uk / GGNFS
8·10²²⁸-1 = 7(9)₂₂₈_<229> = 7 · 71 · 3449 · 4847041 · 15820639 · 17076769 · 18395633 · 130854596492286412438405476816657478703173293235697757911_<57> · C139
C139 = P43 · P96
P43 = 1528903929139327175345777358726109783347673_<43>
P96 = 968389496066443829563630012210817722372169284170780283664563868997439143831062269183972619538007_<96>

Number: 79999_228 N=1480574505473238989199098674408682671411071598963681517151759583539213670859023764835487170244141115567827261158255099210189135575118507711 ( 139 digits) SNFS difficulty: 153 digits. Divisors found: r1=1528903929139327175345777358726109783347673 (pp43) r2=968389496066443829563630012210817722372169284170780283664563868997439143831062269183972619538007 (pp96) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.80 hours. Scaled time: 49.37 units (timescale=2.374). Factorization parameters were as follows: n: 1480574505473238989199098674408682671411071598963681517151759583539213670859023764835487170244141115567827261158255099210189135575118507711 m: 20000000000000000000000000 c6: 25 c3: 10 c0: 4 skew: 0.74 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, 2600001) Primes: RFBsize:176302, AFBsize:175893, largePrimes:5789972 encountered Relations: rels:5766761, finalFF:478712 Max relations in full relation-set: 28 Initial matrix: 352261 x 478712 with sparse part having weight 49162015. Pruned matrix : 300961 x 302786 with weight 30294030. Total sieving time: 20.06 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.60 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,153,6,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 20.80 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: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116) Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)
Jul 26, 2008 (2nd): By matsui / GGNFS
(14·10¹⁷⁹+31)/9 = 1(5)₁₇₈9_<180> = 3² · 937 · C176
C176 = P45 · P49 · P83
P45 = 175295153066532340613622437887691574772872821_<45>
P49 = 8441086165595067651650397848876928006494892885709_<49>
P83 = 12466231410440518465524895241428903373602741675890690732557533120565315438138006407_<83>

N=18446051886108805354625347510441782942672305888243277072875080701477001726023426485895358182800374191338261064337193828478068961882551352490875792192049751637087104892156475223 ( 176 digits) SNFS difficulty: 180 digits. Divisors found: r1=175295153066532340613622437887691574772872821 (pp45) r2=8441086165595067651650397848876928006494892885709 (pp49) r3=12466231410440518465524895241428903373602741675890690732557533120565315438138006407 (pp83) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 315.32 hours. Scaled time: 610.14 units (timescale=1.935). Factorization parameters were as follows: n: 18446051886108805354625347510441782942672305888243277072875080701477001726023426485895358182800374191338261064337193828478068961882551352490875792192049751637087104892156475223 m: 1000000000000000000000000000000000000 c5: 7 c0: 155 skew: 1.86 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, 10200001) Primes: RFBsize:501962, AFBsize:499942, largePrimes:6632716 encountered Relations: rels:7100185, finalFF:1147043 Max relations in full relation-set: 28 Initial matrix: 1001969 x 1147043 with sparse part having weight 77618795. Pruned matrix : 881350 x 886423 with weight 59827143. Total sieving time: 308.53 hours. Total relation processing time: 0.13 hours. Matrix solve time: 6.25 hours. Time per square root: 0.40 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: 315.32 hours.
Jul 26, 2008: By Robert Backstrom / GGNFS, GMP-ECM, Msieve
8·10²³⁴-1 = 7(9)₂₃₄_<235> = 7 · 127 · 359 · 967 · 46271 · 18821440207_<11> · 6017479539201391_<16> · 3860717760049320127_<19> · 948031877361413200744641307998671084939526110708897790110817166822633_<69> · C109
C109 = P45 · P64
P45 = 282121745180560667036164213290041989056941689_<45>
P64 = 4790307443776610893726570695190991776424749473108915987693203239_<64>

Number: n N=1351449895989687962880757239485494608558029508437965645529620904507286128520390416692603853519156577248930671 ( 109 digits) Divisors found: r1=282121745180560667036164213290041989056941689 (pp45) r2=4790307443776610893726570695190991776424749473108915987693203239 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 11.28 hours. Scaled time: 20.56 units (timescale=1.823). Factorization parameters were as follows: name: KA_7_9_234 n: 1351449895989687962880757239485494608558029508437965645529620904507286128520390416692603853519156577248930671 skew: 23681.14 # norm 8.45e+14 c5: 35400 c4: 909978134 c3: -10843425355649 c2: -859297610146079263 c1: 1071555635925958284545 c0: 159770744406752924182690785 # alpha -5.97 Y1: 174057782899 Y0: -520425527026525197052 # Murphy_E 1.21e-09 # M 430725653313612678331739255995629435060729388392356940731188563969563801629981448267959244966784299042202987 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 [100000, 1500001) Primes: RFBsize:230209, AFBsize:230422, largePrimes:6728311 encountered Relations: rels:6387483, finalFF:548322 Max relations in full relation-set: 48 Initial matrix: 460713 x 548322 with sparse part having weight 36052224. Pruned matrix : 375310 x 377677 with weight 17297185. Polynomial selection time: 1.36 hours. Total sieving time: 8.95 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.69 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 11.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
2·10¹⁸³-7 = 1(9)₁₈₂3_<184> = 811 · 2624277319_<10> · 2755493291_<10> · 101591439292081_<15> · 16322026806562391_<17> · C132
C132 = P40 · P46 · P47
P40 = 6162314909610575169723533703783208734587_<40>
P46 = 2296936960460684436839110679001518570233133723_<46>
P47 = 14530343872204972792659597373865720056086160057_<47>

Sat Jul 26 07:08:12 2008 Sat Jul 26 07:08:12 2008 Sat Jul 26 07:08:12 2008 Msieve v. 1.36 Sat Jul 26 07:08:12 2008 random seeds: 6c176500 b95488c8 Sat Jul 26 07:08:12 2008 factoring 33375283888271021987099616586864311324910632800353159555401618973887857681828893792862302211 (92 digits) Sat Jul 26 07:08:12 2008 searching for 15-digit factors Sat Jul 26 07:08:13 2008 commencing quadratic sieve (92-digit input) Sat Jul 26 07:08:13 2008 using multiplier of 3 Sat Jul 26 07:08:13 2008 using 64kb Opteron sieve core Sat Jul 26 07:08:13 2008 sieve interval: 18 blocks of size 65536 Sat Jul 26 07:08:13 2008 processing polynomials in batches of 6 Sat Jul 26 07:08:13 2008 using a sieve bound of 1816147 (68235 primes) Sat Jul 26 07:08:13 2008 using large prime bound of 197960023 (27 bits) Sat Jul 26 07:08:13 2008 using double large prime bound of 858695942807652 (42-50 bits) Sat Jul 26 07:08:13 2008 using trial factoring cutoff of 50 bits Sat Jul 26 07:08:13 2008 polynomial 'A' values have 12 factors Sat Jul 26 07:29:14 2008 Sat Jul 26 07:29:14 2008 Sat Jul 26 07:29:14 2008 Msieve v. 1.36 Sat Jul 26 07:29:14 2008 random seeds: ae82c9e0 243e55c6 Sat Jul 26 07:29:14 2008 factoring 33375283888271021987099616586864311324910632800353159555401618973887857681828893792862302211 (92 digits) Sat Jul 26 07:29:14 2008 searching for 15-digit factors Sat Jul 26 07:29:15 2008 commencing quadratic sieve (92-digit input) Sat Jul 26 07:29:15 2008 using multiplier of 3 Sat Jul 26 07:29:15 2008 using 64kb Opteron sieve core Sat Jul 26 07:29:15 2008 sieve interval: 18 blocks of size 65536 Sat Jul 26 07:29:15 2008 processing polynomials in batches of 6 Sat Jul 26 07:29:15 2008 using a sieve bound of 1816147 (68235 primes) Sat Jul 26 07:29:15 2008 using large prime bound of 197960023 (27 bits) Sat Jul 26 07:29:15 2008 using double large prime bound of 858695942807652 (42-50 bits) Sat Jul 26 07:29:15 2008 using trial factoring cutoff of 50 bits Sat Jul 26 07:29:15 2008 polynomial 'A' values have 12 factors Sat Jul 26 07:29:15 2008 restarting with 3580 full and 178004 partial relations Sat Jul 26 08:43:06 2008 68500 relations (16968 full + 51532 combined from 874683 partial), need 68331 Sat Jul 26 08:43:08 2008 begin with 891651 relations Sat Jul 26 08:43:08 2008 reduce to 174938 relations in 12 passes Sat Jul 26 08:43:08 2008 attempting to read 174938 relations Sat Jul 26 08:43:10 2008 recovered 174938 relations Sat Jul 26 08:43:10 2008 recovered 157541 polynomials Sat Jul 26 08:43:10 2008 attempting to build 68500 cycles Sat Jul 26 08:43:10 2008 found 68500 cycles in 6 passes Sat Jul 26 08:43:11 2008 distribution of cycle lengths: Sat Jul 26 08:43:11 2008 length 1 : 16968 Sat Jul 26 08:43:11 2008 length 2 : 12406 Sat Jul 26 08:43:11 2008 length 3 : 11767 Sat Jul 26 08:43:11 2008 length 4 : 9209 Sat Jul 26 08:43:11 2008 length 5 : 7086 Sat Jul 26 08:43:11 2008 length 6 : 4525 Sat Jul 26 08:43:11 2008 length 7 : 2793 Sat Jul 26 08:43:11 2008 length 9+: 3746 Sat Jul 26 08:43:11 2008 largest cycle: 20 relations Sat Jul 26 08:43:11 2008 matrix is 68235 x 68500 (17.0 MB) with weight 4195226 (61.24/col) Sat Jul 26 08:43:11 2008 sparse part has weight 4195226 (61.24/col) Sat Jul 26 08:43:11 2008 filtering completed in 3 passes Sat Jul 26 08:43:11 2008 matrix is 64825 x 64889 (16.2 MB) with weight 3993054 (61.54/col) Sat Jul 26 08:43:11 2008 sparse part has weight 3993054 (61.54/col) Sat Jul 26 08:43:12 2008 saving the first 48 matrix rows for later Sat Jul 26 08:43:12 2008 matrix is 64777 x 64889 (9.5 MB) with weight 3068327 (47.29/col) Sat Jul 26 08:43:12 2008 sparse part has weight 2106581 (32.46/col) Sat Jul 26 08:43:12 2008 matrix includes 64 packed rows Sat Jul 26 08:43:12 2008 using block size 25955 for processor cache size 1024 kB Sat Jul 26 08:43:12 2008 commencing Lanczos iteration Sat Jul 26 08:43:12 2008 memory use: 9.7 MB Sat Jul 26 08:43:37 2008 lanczos halted after 1025 iterations (dim = 64774) Sat Jul 26 08:43:38 2008 recovered 16 nontrivial dependencies Sat Jul 26 08:43:38 2008 prp46 factor: 2296936960460684436839110679001518570233133723 Sat Jul 26 08:43:38 2008 prp47 factor: 14530343872204972792659597373865720056086160057 Sat Jul 26 08:43:38 2008 elapsed time 01:14:24
Jul 25, 2008 (7th): By Robert Backstrom / GGNFS, Msieve
(2·10¹⁶⁹+1)/3 = (6)₁₆₈7_<169> = 7 · 766169 · 5025529 · C156
C156 = P46 · P111
P46 = 1261440917199733159119900387950410686385690243_<46>
P111 = 196081864308815835019995393044774169560246557899424260150099777307102229210524305885773367324515406034150789967_<111>

Number: n N=247345686759946268316263131816608663902423313937075401253427394805496653944142877381675229300044388850675738926738552046324162639205415759533671843014191981 ( 156 digits) SNFS difficulty: 170 digits. Divisors found: Sat Jul 26 00:24:03 2008 prp46 factor: 1261440917199733159119900387950410686385690243 Sat Jul 26 00:24:03 2008 prp111 factor: 196081864308815835019995393044774169560246557899424260150099777307102229210524305885773367324515406034150789967 Sat Jul 26 00:24:03 2008 elapsed time 02:24:18 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 53.75 hours. Scaled time: 70.47 units (timescale=1.311). Factorization parameters were as follows: name: KA_6_168_7 n: 247345686759946268316263131816608663902423313937075401253427394805496653944142877381675229300044388850675738926738552046324162639205415759533671843014191981 skew: 1.38 deg: 5 c5: 1 c0: 5 m: 10000000000000000000000000000000000 type: snfs rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2100001) Primes: RFBsize:412849, AFBsize:412271, largePrimes:9846876 encountered Relations: rels:9579900, finalFF:971104 Max relations in full relation-set: 28 Initial matrix: 825184 x 971103 with sparse part having weight 57456378. Pruned matrix : Total sieving time: 53.39 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,50,50,2.5,2.5,100000 total time: 53.75 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 25, 2008 (6th): By Kenji Ibusuki / GGNFS
5·10¹⁹⁰-7 = 4(9)₁₈₉3_<191> = 19 · 43 · C188
C188 = P37 · P67 · P86
P37 = 1765787545312409783860474993038088441_<37>
P67 = 1221634377469420523013631539626062841035324877347830895794628620683_<67>
P86 = 28370582518084984958701082392541132842482155696727816580550567234311865111305350903443_<86>

Number: 49993_190 N=61199510403916768665850673194614443084455324357405140758873929008567931456548347613219094247246022031823745410036719706242350061199510403916768665850673194614443084455324357405140758873929 ( 188 digits) SNFS difficulty: 190 digits. Divisors found: r1=1765787545312409783860474993038088441 (pp37) r2=1221634377469420523013631539626062841035324877347830895794628620683 (pp67) r3=28370582518084984958701082392541132842482155696727816580550567234311865111305350903443 (pp86) Version: GGNFS-0.77.1 Total time: 476.75 hours. Scaled time: 1380.66 units (timescale=2.896). Factorization parameters were as follows: n: 61199510403916768665850673194614443084455324357405140758873929008567931456548347613219094247246022031823745410036719706242350061199510403916768665850673194614443084455324357405140758873929 m: 100000000000000000000000000000000000000 type: snfs skew: 1.070 c0: -7 c5: 5 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 29/29 Sieved special-q in [3700000, 11800001) Relations: rels:18218529, finalFF:1213632 Initial matrix: 1003163 x 1213632 with sparse part having weight 169464967. Pruned matrix : 952997 x 958076 with weight 121817026. Total sieving time: 462.13 hours. Total relation processing time: 0.88 hours. Matrix solve time: 13.50 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,29,29,51,51,2.6,2.6,100000 total time: 476.75 hours. --------- CPU info (if available) ----------
Jul 25, 2008 (5th): By suberi / GMP-ECM
(4·10²⁴³-1)/3 = 1(3)₂₄₃_<244> = 31 · 83 · 157 · 131231 · 299197 · 1442216753248456277_<19> · 4038335633468132831_<19> · C191
C191 = P35 · P156
P35 = 35657045111837177984079582344894317_<35>
P156 = 404787718601259261978273194650372481814255336058492445066139143092845027355459172172060392549607938205765428041891254949939762856614330735166038645561890001_<156>
(4·10²⁴⁵-1)/3 = 1(3)₂₄₅_<246> = 293 · 4428013 · 436570924477_<12> · 197820650760877883_<18> · 1940832977077439598289_<22> · 245134337177055685486188936209_<30> · C157
C157 = P31 · C127
P31 = 1675203063576126721567576664071_<31>
C127 = [1493055747910029065087937422859586920491486247404972020337179301095994338939893155969148811179362195548241166474252224587374317_<127>]
Jul 25, 2008 (4th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(2·10¹⁶⁹-17)/3 = (6)₁₆₈1_<169> = 238729 · 571138289 · C155
C155 = P41 · P44 · P72
P41 = 11817386542506337749843599398989802401983_<41>
P44 = 13085479642349468381361523918766801187989977_<44>
P72 = 316192233564917210640549980219740383800204370022180000336001159014458091_<72>

Number: n N=48894756307188046205660588215055908169171174475099021113090591883003280000280409811352237979810160283919583949322319878169034135110728714578780893777197581 ( 155 digits) SNFS difficulty: 170 digits. Divisors found: Fri Jul 25 11:48:36 2008 prp41 factor: 11817386542506337749843599398989802401983 Fri Jul 25 11:48:36 2008 prp44 factor: 13085479642349468381361523918766801187989977 Fri Jul 25 11:48:36 2008 prp72 factor: 316192233564917210640549980219740383800204370022180000336001159014458091 Fri Jul 25 11:48:36 2008 elapsed time 02:12:34 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 45.36 hours. Scaled time: 76.02 units (timescale=1.676). Factorization parameters were as follows: name: KA_6_168_1 n: 48894756307188046205660588215055908169171174475099021113090591883003280000280409811352237979810160283919583949322319878169034135110728714578780893777197581 skew: 2.43 deg: 5 c5: 1 c0: -85 m: 10000000000000000000000000000000000 type: snfs rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2600001) Primes: RFBsize:412849, AFBsize:413336, largePrimes:9838235 encountered Relations: rels:9447054, finalFF:885558 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 45.07 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,170,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,50,50,2.5,2.5,100000 total time: 45.36 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
8·10²¹⁹-1 = 7(9)₂₁₉_<220> = 19 · 29 · 61 · 91734541 · 1119024901_<10> · 589635422899_<12> · 100236345329109106048850820884161_<33> · 5936402484004975288098822472966741469_<37> · C118
C118 = P32 · P86
P32 = 78804181274997851192664174029191_<32>
P86 = 83859934851872620017547819860052379897723933994052604566651127218360972849629908176429_<86>
Jul 25, 2008 (3rd): By Jo Yeong Uk / GGNFS, GMP-ECM
8·10²¹³-1 = 7(9)₂₁₃_<214> = 311 · 14341 · 49801 · 118018309 · 812126836567325311_<18> · 48223863818791257229_<20> · 15900386507052020800133836615165276113430575119_<47> · C111
C111 = P42 · P70
P42 = 173118702419871755400126634132558566548011_<42>
P70 = 2830904217224319706645261082037462977679894136530963560822965061287591_<70>

Number: 79999_213 N=490082464760816993503044892873304511247077521030235243425978837079485571213821882640228393121233082755780031501 ( 111 digits) SNFS difficulty: 144 digits. Divisors found: r1=173118702419871755400126634132558566548011 (pp42) r2=2830904217224319706645261082037462977679894136530963560822965061287591 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.44 hours. Scaled time: 24.97 units (timescale=2.392). Factorization parameters were as follows: n: 490082464760816993503044892873304511247077521030235243425978837079485571213821882640228393121233082755780031501 m: 1000000000000000000000000 c6: 1 c3: 5 c0: 25 skew: 1.71 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1550001) Primes: RFBsize:114155, AFBsize:113645, largePrimes:3474537 encountered Relations: rels:3489348, finalFF:285283 Max relations in full relation-set: 28 Initial matrix: 227865 x 285283 with sparse part having weight 27887141. Pruned matrix : 209026 x 210229 with weight 17824594. Total sieving time: 10.16 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.19 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,144,6,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 10.44 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: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116) Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)
8·10²¹⁶-1 = 7(9)₂₁₆_<217> = 7 · 10337 · 113209 · 14053183457400553_<17> · 1539265796448195743859457_<25> · 125696116580006172197631576931601768549558111_<45> · C123
C123 = P36 · P88
P36 = 147283812222899232001715996680222327_<36>
P88 = 2438660054892819457675742999944584962791806880889823383873998562744490822150544305736417_<88>
Jul 25, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(22·10¹⁶⁸+41)/9 = 2(4)₁₆₇9_<169> = 7 · 31 · 82189 · C162
C162 = P43 · P119
P43 = 2899543658506815033242105025684834449702477_<43>
P119 = 47269073375747822390380499935334445424904739368471132437674465794253492151242396483956332265049621005799300244584991649_<119>

Number: n N=137058741950142926413591313022560984084757574577851131616469494271994331848507452416459940031691843703418912251112149144183098966311067137682739252527847579614573 ( 162 digits) SNFS difficulty: 169 digits. Divisors found: Fri Jul 25 01:46:01 2008 prp43 factor: 2899543658506815033242105025684834449702477 Fri Jul 25 01:46:01 2008 prp119 factor: 47269073375747822390380499935334445424904739368471132437674465794253492151242396483956332265049621005799300244584991649 Fri Jul 25 01:46:01 2008 elapsed time 02:23:22 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 54.93 hours. Scaled time: 100.46 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_4_167_9 n: 137058741950142926413591313022560984084757574577851131616469494271994331848507452416459940031691843703418912251112149144183098966311067137682739252527847579614573 skew: 0.57 deg: 5 c5: 1375 c0: 82 m: 2000000000000000000000000000000000 type: snfs rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 3200001) Primes: RFBsize:399993, AFBsize:399636, largePrimes:10053706 encountered Relations: rels:9578110, finalFF:811962 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 54.61 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,169,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000 total time: 54.93 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 25, 2008: By Jo Yeong Uk / GGNFS
8·10²⁰⁷-1 = 7(9)₂₀₇_<208> = 31 · 439 · 212039 · 995881 · 4155919 · 35458744861_<11> · 339679388641_<12> · 2626410054718091_<16> · 7442213814490672036679386751621599_<34> · C115
C115 = P42 · P73
P42 = 541832960047230906014967345407576299650631_<42>
P73 = 5251106845463258052650105055200096921760782933920709388847288619870698129_<73>

Number: 79999_207 N=2845222765601634215803869063836629035398868860105421171772198973101369113582035289814048310534414748999136765369399 ( 115 digits) SNFS difficulty: 138 digits. Divisors found: r1=541832960047230906014967345407576299650631 (pp42) r2=5251106845463258052650105055200096921760782933920709388847288619870698129 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.37 hours. Scaled time: 12.78 units (timescale=2.379). Factorization parameters were as follows: n: 2845222765601634215803869063836629035398868860105421171772198973101369113582035289814048310534414748999136765369399 m: 100000000000000000000000 c6: 4 c3: 2 c0: 1 skew: 0.79 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [650000, 1800001) Primes: RFBsize:100021, AFBsize:99911, largePrimes:2422278 encountered Relations: rels:2600965, finalFF:242584 Max relations in full relation-set: 28 Initial matrix: 199997 x 242584 with sparse part having weight 25213545. Pruned matrix : 185672 x 186735 with weight 17433607. Total sieving time: 5.15 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.15 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,138,6,0,0,0,0,0,0,0,0,1300000,1300000,25,25,47,47,2.3,2.3,50000 total time: 5.37 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: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116) Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)
Jul 24, 2008 (3rd): By Sinkiti Sibata / GGNFS
(22·10¹⁶⁰+41)/9 = 2(4)₁₅₉9_<161> = 2609 · 6053 · 133979 · 3698763923775038153208904926649_<31> · C118
C118 = P46 · P73
P46 = 2175120316596344341395729390310266840279264737_<46>
P73 = 1436014378583454632133875028269996384218596726067989942997243612917575231_<73>

Number: 24449_160 N=3123504049781346520649845866412023805576131973733178763648331210776077464897935701049859097482628566670996489562929247 ( 118 digits) SNFS difficulty: 161 digits. Divisors found: r1=2175120316596344341395729390310266840279264737 (pp46) r2=1436014378583454632133875028269996384218596726067989942997243612917575231 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 70.37 hours. Scaled time: 54.82 units (timescale=0.779). Factorization parameters were as follows: name: 24449_160 n: 3123504049781346520649845866412023805576131973733178763648331210776077464897935701049859097482628566670996489562929247 m: 100000000000000000000000000000000 c5: 22 c0: 41 skew: 1.13 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, 4300001) Primes: RFBsize:283146, AFBsize:282794, largePrimes:5837251 encountered Relations: rels:5919740, finalFF:686098 Max relations in full relation-set: 28 Initial matrix: 566006 x 686098 with sparse part having weight 53196518. Pruned matrix : 483417 x 486311 with weight 38131690. Total sieving time: 67.10 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.94 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 70.37 hours. --------- CPU info (if available) ----------
Jul 24, 2008 (2nd): Factorizations of 799...99 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.
Note the algebraic factorization 8·10^3k-1 = (2·10^k-1)(4·10^2k+2·10^k+1).
"Efforts by ECM" section was added in "Contribution and Reservation" pages.
Jul 24, 2008: By Jo Yeong Uk / GGNFS
(4·10²³⁵-1)/3 = 1(3)₂₃₅_<236> = 13 · 67 · 677 · 7079 · 48775637 · 7554172820434544567959_<22> · 17218527001291015325523195827_<29> · 6303239909341182749584186343717_<31> · 103002075143888028035790451977073523_<36> · C102
C102 = P46 · P57
P46 = 1989378140372439563653744711213759800430408243_<46>
P57 = 389804622956411924070438346247626600778953706285860014157_<57>

Number: 13333_235 N=775468795925606718265168401955990662675462021136190876422142039835490928358779949182032553037269496151 ( 102 digits) Divisors found: r1=1989378140372439563653744711213759800430408243 (pp46) r2=389804622956411924070438346247626600778953706285860014157 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.05 hours. Scaled time: 9.64 units (timescale=2.380). Factorization parameters were as follows: name: 13333_235 n: 775468795925606718265168401955990662675462021136190876422142039835490928358779949182032553037269496151 skew: 7498.52 # norm 1.34e+14 c5: 31320 c4: 1422114954 c3: -74642879737 c2: -36382164166013463 c1: 102204763625923220477 c0: -178970016479028225265815 # alpha -5.96 Y1: 4898667461 Y0: -30112573504914213526 # Murphy_E 2.76e-09 # M 715234690321575102484757119045421095899911177627116595345331779978125106824482793025729130387051609948 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [750000, 1350001) Primes: RFBsize:114155, AFBsize:114862, largePrimes:4398781 encountered Relations: rels:4343529, finalFF:318275 Max relations in full relation-set: 28 Initial matrix: 229097 x 318275 with sparse part having weight 27359727. Pruned matrix : 184410 x 185619 with weight 13182842. Polynomial selection time: 0.31 hours. Total sieving time: 3.52 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,49,49,2.6,2.6,50000 total time: 4.05 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: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116) Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)
Jul 23, 2008: By Sinkiti Sibata / GGNFS
(22·10¹⁴⁸+41)/9 = 2(4)₁₄₇9_<149> = 5063780237_<10> · 28583166325918913_<17> · C123
C123 = P41 · P82
P41 = 17402239799437999024534166513064894599063_<41>
P82 = 9704872554934624715117145597971219813583628402942201073104426199442049345595512483_<82>

Number: 24449_148 N=168886519423956864772830398013728626154547408630592155514741531403323179695674542221418226218787968070077564086556296603429 ( 123 digits) SNFS difficulty: 149 digits. Divisors found: r1=17402239799437999024534166513064894599063 (pp41) r2=9704872554934624715117145597971219813583628402942201073104426199442049345595512483 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 38.93 hours. Scaled time: 30.29 units (timescale=0.778). Factorization parameters were as follows: name: 24449_148 n: 168886519423956864772830398013728626154547408630592155514741531403323179695674542221418226218787968070077564086556296603429 m: 200000000000000000000000000000 c5: 1375 c0: 82 skew: 0.57 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 5250001) Primes: RFBsize:114155, AFBsize:114334, largePrimes:3203085 encountered Relations: rels:3335826, finalFF:257222 Max relations in full relation-set: 28 Initial matrix: 228555 x 257222 with sparse part having weight 34263507. Pruned matrix : 221405 x 222611 with weight 28567526. Total sieving time: 38.06 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.62 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 38.93 hours. --------- CPU info (if available) ----------
Jul 22, 2008 (4th): By Robert Backstrom / GMP-ECM
(8·10¹⁶⁹-71)/9 = (8)₁₆₈1_<169> = 89 · 463 · 673 · 419791 · C156
C156 = P41 · P116
P41 = 47781549603347332166946262947607610229479_<41>
P116 = 15979679407133185494514008168674390360680444782139128263236808135037861497132308268172748142259881307507065765651839_<116>
Jul 22, 2008 (3rd): By suberi / GMP-ECM
(4·10²³⁵-1)/3 = 1(3)₂₃₅_<236> = 13 · 67 · 677 · 7079 · 48775637 · 7554172820434544567959_<22> · 17218527001291015325523195827_<29> · 6303239909341182749584186343717_<31> · C137
C137 = P36 · C102
P36 = 103002075143888028035790451977073523_<36>
C102 = [775468795925606718265168401955990662675462021136190876422142039835490928358779949182032553037269496151_<102>]
Jul 22, 2008 (2nd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(22·10¹⁵⁵+41)/9 = 2(4)₁₅₄9_<156> = 3 · 31129227631_<11> · 1579287976025387_<16> · C130
C130 = P47 · P83
P47 = 45999919755091463993377327103075511881496406927_<47>
P83 = 36030655935244507282549301863752200400900959948706991027890149836194085839645629857_<83>

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM] Input number is 1657407281744557318977622952657209008164750830211547757484769227847986576290000102482091734717402424938133879682164532903292819439 (130 digits) Using B1=3870000, B2=5773430343, polynomial Dickson(6), sigma=219387156 Step 1 took 51500ms Step 2 took 25750ms ********** Factor found in step 2: 45999919755091463993377327103075511881496406927 Found probable prime factor of 47 digits: 45999919755091463993377327103075511881496406927 Probable prime cofactor 36030655935244507282549301863752200400900959948706991027890149836194085839645629857 has 83 digits
7·10¹⁶⁹-9 = 6(9)₁₆₈1_<170> = 208699 · 241417849 · C157
C157 = P42 · P115
P42 = 260261239348850539688922265966919165310599_<42>
P115 = 5338248691337501107137922770641624082752782783076792345043666099791736776212975427477023032244417290856029907636859_<115>

Number: n N=1389339220359877542274357801042835125646101146451738583460851033141648832587493612920864982552675488236762722326237405531715310872085039395485860784835768541 ( 157 digits) SNFS difficulty: 170 digits. Divisors found: Tue Jul 22 11:26:18 2008 prp42 factor: 260261239348850539688922265966919165310599 Tue Jul 22 11:26:18 2008 prp115 factor: 5338248691337501107137922770641624082752782783076792345043666099791736776212975427477023032244417290856029907636859 Tue Jul 22 11:26:18 2008 elapsed time 04:16:58 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 76.95 hours. Scaled time: 111.43 units (timescale=1.448). Factorization parameters were as follows: name: KA_6_9_168_1 n: 1389339220359877542274357801042835125646101146451738583460851033141648832587493612920864982552675488236762722326237405531715310872085039395485860784835768541 skew: 1.67 deg: 5 c5: 7 c0: -90 m: 10000000000000000000000000000000000 type: snfs rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 3500001) Primes: RFBsize:425648, AFBsize:426372, largePrimes:10109777 encountered Relations: rels:9700992, finalFF:871192 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 76.51 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,50,50,2.5,2.5,100000 total time: 76.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(22·10¹⁵⁸+41)/9 = 2(4)₁₅₇9_<159> = 3² · 23 · 6473 · 8629 · C149
C149 = P61 · P89
P61 = 1105326103418514975838635653554146491496662790047875884527581_<61>
P89 = 19127284756894328245610160409392789398531145245398183946272241072229624360054573707039191_<89>

Number: n N=21141887129314365340413439278686685605805369645401750927238009940322413589021656829320590485472112245817998315002378156081032695372500342703287426971 ( 149 digits) SNFS difficulty: 159 digits. Divisors found: r1=1105326103418514975838635653554146491496662790047875884527581 (pp61) r2=19127284756894328245610160409392789398531145245398183946272241072229624360054573707039191 (pp89) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.64 hours. Scaled time: 46.74 units (timescale=1.823). Factorization parameters were as follows: name: KA_2_4_157_9 n: 21141887129314365340413439278686685605805369645401750927238009940322413589021656829320590485472112245817998315002378156081032695372500342703287426971 skew: 0.57 deg: 5 c5: 1375 c0: 82 m: 20000000000000000000000000000000 type: snfs rlim: 3800000 alim: 3800000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:269987, AFBsize:269724, largePrimes:9478739 encountered Relations: rels:8787558, finalFF:611556 Max relations in full relation-set: 48 Initial matrix: 539777 x 611556 with sparse part having weight 54924569. Pruned matrix : 481221 x 483983 with weight 35223051. Total sieving time: 23.38 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.00 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,50,50,2.5,2.5,100000 total time: 25.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(22·10¹⁵⁰+41)/9 = 2(4)₁₄₉9_<151> = 7 · 23476275923_<11> · C140
C140 = P50 · P90
P50 = 16097965590711520018626138438225266068918017570413_<50>
P90 = 924021191327169870580703157780617527631433867785181172624034019357349260873271768572067393_<90>

Number: n N=14874861343073046583956967287786005221131697004818390945830695295766361927386448243115974657528153010128905799588150001926913642418358843309 ( 140 digits) SNFS difficulty: 151 digits. Divisors found: Tue Jul 22 16:05:34 2008 prp50 factor: 16097965590711520018626138438225266068918017570413 Tue Jul 22 16:05:34 2008 prp90 factor: 924021191327169870580703157780617527631433867785181172624034019357349260873271768572067393 Tue Jul 22 16:05:34 2008 elapsed time 00:49:27 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.87 hours. Scaled time: 44.79 units (timescale=1.731). Factorization parameters were as follows: name: KA_2_4_149_9 n: 14874861343073046583956967287786005221131697004818390945830695295766361927386448243115974657528153010128905799588150001926913642418358843309 type: snfs skew: 1.13 deg: 5 c5: 22 c0: 41 m: 1000000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 1200001) Primes: RFBsize:148933, AFBsize:148322, largePrimes:6170485 encountered Relations: rels:5474077, finalFF:325172 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 25.66 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,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,50,50,2.3,2.3,100000 total time: 25.87 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 22, 2008: By Sinkiti Sibata / GGNFS
(22·10¹⁴³+41)/9 = 2(4)₁₄₂9_<144> = 3 · 97 · 2457442313_<10> · C132
C132 = P61 · P71
P61 = 6803073944175257199768043132997513943459774741129425881805173_<61>
P71 = 50245672019300841540350636053956247113188991898199365782683211009817511_<71>

Number: 24449_143 N=341825022122081335958998419546470762029091886554630659976017195508658914361214371124388440953080000138856974651484571068809985784403 ( 132 digits) SNFS difficulty: 144 digits. Divisors found: r1=6803073944175257199768043132997513943459774741129425881805173 (pp61) r2=50245672019300841540350636053956247113188991898199365782683211009817511 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.21 hours. Scaled time: 15.56 units (timescale=0.770). Factorization parameters were as follows: name: 24449_143 n: 341825022122081335958998419546470762029091886554630659976017195508658914361214371124388440953080000138856974651484571068809985784403 m: 20000000000000000000000000000 c5: 1375 c0: 82 skew: 0.57 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, 2950001) Primes: RFBsize:100021, AFBsize:100230, largePrimes:2954435 encountered Relations: rels:3008883, finalFF:265588 Max relations in full relation-set: 28 Initial matrix: 200317 x 265588 with sparse part having weight 31931584. Pruned matrix : 184165 x 185230 with weight 21048063. Total sieving time: 19.70 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.33 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 20.21 hours. --------- CPU info (if available) ----------
(22·10¹⁷³+41)/9 = 2(4)₁₇₂9_<174> = 3 · C173
C173 = P70 · P104
P70 = 7247333544342156249361332950765992322106652729740454583309021232849433_<70>
P104 = 11242960046332128968771133199614355501934832225686603228803080298550488784257145880620332675742271558851_<104>

Number: 24449_173 N=81481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481483 ( 173 digits) SNFS difficulty: 174 digits. Divisors found: r1=7247333544342156249361332950765992322106652729740454583309021232849433 (pp70) r2=11242960046332128968771133199614355501934832225686603228803080298550488784257145880620332675742271558851 (pp104) Version: GGNFS-0.77.1-20050930-nocona Total time: 271.39 hours. Scaled time: 273.83 units (timescale=1.009). Factorization parameters were as follows: name: 24449_173 n: 81481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481483 m: 20000000000000000000000000000000000 c5: 1375 c0: 82 skew: 0.57 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, 13400001) Primes: RFBsize:501962, AFBsize:501393, largePrimes:6712203 encountered Relations: rels:7232983, finalFF:1179697 Max relations in full relation-set: 28 Initial matrix: 1003421 x 1179697 with sparse part having weight 85859116. Pruned matrix : 855294 x 860375 with weight 65427418. Total sieving time: 264.22 hours. Total relation processing time: 0.16 hours. Matrix solve time: 6.86 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,174,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 271.39 hours. --------- CPU info (if available) ----------
Jul 21, 2008 (3rd): By Wataru Sakai / GGNFS
6·10¹⁹⁶+1 = 6(0)₁₉₅1_<197> = C197
C197 = P67 · P131
P67 = 4526985911422555852980453461875447673693370404671619628486604463189_<67>
P131 = 13253851718117155717822280766012995701858464863771693748201984239161431357726436028994453405662098135543550990120795749232748691709_<131>

Number: 60001_196 N=60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 ( 197 digits) SNFS difficulty: 196 digits. Divisors found: r1=4526985911422555852980453461875447673693370404671619628486604463189 (pp67) r2=13253851718117155717822280766012995701858464863771693748201984239161431357726436028994453405662098135543550990120795749232748691709 (pp131) Version: GGNFS-0.77.1-20060722-nocona Total time: 2601.57 hours. Scaled time: 5190.14 units (timescale=1.995). Factorization parameters were as follows: n: 60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 m: 1000000000000000000000000000000000000000 c5: 60 c0: 1 skew: 0.44 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, 43700001) Primes: RFBsize:501962, AFBsize:501211, largePrimes:8270429 encountered Relations: rels:9230838, finalFF:1133951 Max relations in full relation-set: 32 Initial matrix: 1003240 x 1133951 with sparse part having weight 191292090. Pruned matrix : 927307 x 932387 with weight 174534450. Total sieving time: 2581.77 hours. Total relation processing time: 0.44 hours. Matrix solve time: 19.00 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 2601.57 hours. --------- CPU info (if available) ----------
Jul 21, 2008 (2nd): By Jo Yeong Uk / GMP-ECM, Msieve
(22·10¹⁶⁶+41)/9 = 2(4)₁₆₅9_<167> = 53 · 83 · 8819 · 530427087249316307_<18> · 50263678452053034167_<20> · C122
C122 = P35 · P36 · P52
P35 = 57372938262772414492411144007923057_<35>
P36 = 225361366817860241485519425537206353_<36>
P52 = 1827849120928944890321391127384847605488278593446721_<52>

Mon Jul 21 12:58:41 2008 Mon Jul 21 12:58:41 2008 Mon Jul 21 12:58:41 2008 Msieve v. 1.34 Mon Jul 21 12:58:41 2008 random seeds: 002e7883 9734cdf0 Mon Jul 21 12:58:41 2008 factoring 104869074768719184432156021238416395118856035807718212846525806858901934786582196946097 (87 digits) Mon Jul 21 12:58:41 2008 no P-1/P+1/ECM available, skipping Mon Jul 21 12:58:41 2008 commencing quadratic sieve (87-digit input) Mon Jul 21 12:58:41 2008 using multiplier of 1 Mon Jul 21 12:58:41 2008 using 32kb Intel Core sieve core Mon Jul 21 12:58:41 2008 sieve interval: 17 blocks of size 32768 Mon Jul 21 12:58:41 2008 processing polynomials in batches of 12 Mon Jul 21 12:58:41 2008 using a sieve bound of 1470841 (55895 primes) Mon Jul 21 12:58:41 2008 using large prime bound of 117667280 (26 bits) Mon Jul 21 12:58:41 2008 using double large prime bound of 336651265440320 (41-49 bits) Mon Jul 21 12:58:41 2008 using trial factoring cutoff of 49 bits Mon Jul 21 12:58:41 2008 polynomial 'A' values have 11 factors Mon Jul 21 13:34:54 2008 56176 relations (15553 full + 40623 combined from 590767 partial), need 55991 Mon Jul 21 13:34:54 2008 begin with 606320 relations Mon Jul 21 13:34:54 2008 reduce to 134589 relations in 9 passes Mon Jul 21 13:34:54 2008 attempting to read 134589 relations Mon Jul 21 13:34:55 2008 recovered 134589 relations Mon Jul 21 13:34:55 2008 recovered 114672 polynomials Mon Jul 21 13:34:55 2008 attempting to build 56176 cycles Mon Jul 21 13:34:55 2008 found 56176 cycles in 5 passes Mon Jul 21 13:34:55 2008 distribution of cycle lengths: Mon Jul 21 13:34:55 2008 length 1 : 15553 Mon Jul 21 13:34:55 2008 length 2 : 11023 Mon Jul 21 13:34:55 2008 length 3 : 10008 Mon Jul 21 13:34:55 2008 length 4 : 7469 Mon Jul 21 13:34:55 2008 length 5 : 5111 Mon Jul 21 13:34:55 2008 length 6 : 3141 Mon Jul 21 13:34:55 2008 length 7 : 1794 Mon Jul 21 13:34:55 2008 length 9+: 2077 Mon Jul 21 13:34:55 2008 largest cycle: 18 relations Mon Jul 21 13:34:55 2008 matrix is 55895 x 56176 (13.3 MB) with weight 3027730 (53.90/col) Mon Jul 21 13:34:55 2008 sparse part has weight 3027730 (53.90/col) Mon Jul 21 13:34:55 2008 filtering completed in 3 passes Mon Jul 21 13:34:55 2008 matrix is 51376 x 51440 (12.2 MB) with weight 2791920 (54.28/col) Mon Jul 21 13:34:55 2008 sparse part has weight 2791920 (54.28/col) Mon Jul 21 13:34:56 2008 saving the first 48 matrix rows for later Mon Jul 21 13:34:56 2008 matrix is 51328 x 51440 (7.6 MB) with weight 2134271 (41.49/col) Mon Jul 21 13:34:56 2008 sparse part has weight 1470468 (28.59/col) Mon Jul 21 13:34:56 2008 matrix includes 64 packed rows Mon Jul 21 13:34:56 2008 using block size 20576 for processor cache size 4096 kB Mon Jul 21 13:34:56 2008 commencing Lanczos iteration Mon Jul 21 13:34:56 2008 memory use: 7.1 MB Mon Jul 21 13:35:05 2008 lanczos halted after 813 iterations (dim = 51328) Mon Jul 21 13:35:05 2008 recovered 17 nontrivial dependencies Mon Jul 21 13:35:05 2008 prp35 factor: 57372938262772414492411144007923057 Mon Jul 21 13:35:05 2008 prp52 factor: 1827849120928944890321391127384847605488278593446721 Mon Jul 21 13:35:05 2008 elapsed time 00:36:24
Jul 21, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(22·10¹⁵⁶+41)/9 = 2(4)₁₅₅9_<157> = 7² · 992111 · C149
C149 = P35 · P115
P35 = 34403366202778334391060150858471779_<35>
P115 = 1461580998276864345860844458718294113767553420340741001484818970216017514257778694796433577617315925915621203003029_<115>
8·10¹⁶⁸-9 = 7(9)₁₆₇1_<169> = 17 · 168837552669242694718423_<24> · C145
C145 = P44 · P102
P44 = 11681215841603794478271720614912632360063687_<44>
P102 = 238607433000818367820061770438598453100921190268658947143978441159074725390668672932146359772318330023_<102>

Number: n N=2787224926293575534663953848834295056925125529822509299870571408485875014665190039863959156312828009389084493476356617788753739536968981764174801 ( 145 digits) SNFS difficulty: 168 digits. Divisors found: Mon Jul 21 11:20:53 2008 prp44 factor: 11681215841603794478271720614912632360063687 Mon Jul 21 11:20:53 2008 prp102 factor: 238607433000818367820061770438598453100921190268658947143978441159074725390668672932146359772318330023 Mon Jul 21 11:20:53 2008 elapsed time 02:05:02 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.83 hours. Scaled time: 79.91 units (timescale=1.823). Factorization parameters were as follows: name: KA_7_9_167_1 n: 2787224926293575534663953848834295056925125529822509299870571408485875014665190039863959156312828009389084493476356617788753739536968981764174801 skew: 0.51 deg: 5 c5: 250 c0: -9 m: 2000000000000000000000000000000000 type: snfs rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2500001) Primes: RFBsize:399993, AFBsize:399254, largePrimes:9743482 encountered Relations: rels:9275445, finalFF:825351 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 43.56 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000 total time: 43.83 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 20, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(22·10¹⁵¹+41)/9 = 2(4)₁₅₀9_<152> = 50777 · C147
C147 = P59 · P89
P59 = 30747866532082367838345848099460820768463553615562170458503_<59>
P89 = 15656624858700526687871150149500413269209603785459994790145094019676577696231079026640879_<89>

Number: n N=481407811498206755902169179834264419805117365036225937815240058381638230782528397590335081718976001820596814393218276866385261918672714899352944137 ( 147 digits) SNFS difficulty: 152 digits. Divisors found: Sun Jul 20 13:39:18 2008 prp59 factor: 30747866532082367838345848099460820768463553615562170458503 Sun Jul 20 13:39:18 2008 prp89 factor: 15656624858700526687871150149500413269209603785459994790145094019676577696231079026640879 Sun Jul 20 13:39:18 2008 elapsed time 01:23:08 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 20.54 hours. Scaled time: 26.78 units (timescale=1.304). Factorization parameters were as follows: name: KA_2_4_150_9 n: 481407811498206755902169179834264419805117365036225937815240058381638230782528397590335081718976001820596814393218276866385261918672714899352944137 skew: 0.71 deg: 5 c5: 220 c0: 41 m: 1000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 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: 50/50 Sieved special-q in [100000, 1100001) Primes: RFBsize:148933, AFBsize:149787, largePrimes:8214123 encountered Relations: rels:7234772, finalFF:302813 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 20.33 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,152,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,50,50,2.5,2.5,100000 total time: 20.54 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(19·10¹⁶⁶+71)/9 = 2(1)₁₆₅9_<167> = 7 · 7253 · 54378083 · 50343939967158130056229_<23> · C132
C132 = P63 · P69
P63 = 301435271504692523257664371180080720857128869883045784752185487_<63>
P69 = 503883585883986267026777603663420832974904119028443835373022979452021_<69>

Number: n N=151888285517697453349404132924871468767777805685695965312726172612353451929406967016381249252832945080495001996679890790773409019227 ( 132 digits) SNFS difficulty: 167 digits. Divisors found: Sun Jul 20 14:20:37 2008 prp63 factor: 301435271504692523257664371180080720857128869883045784752185487 Sun Jul 20 14:20:37 2008 prp69 factor: 503883585883986267026777603663420832974904119028443835373022979452021 Sun Jul 20 14:20:37 2008 elapsed time 02:27:03 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 58.26 hours. Scaled time: 106.55 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_1_165_9 n: 151888285517697453349404132924871468767777805685695965312726172612353451929406967016381249252832945080495001996679890790773409019227 skew: 0.82 deg: 5 c5: 190 c0: 71 m: 1000000000000000000000000000000000 type: snfs rlim: 5200000 alim: 5200000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5200000/5200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 3600000) Primes: RFBsize:361407, AFBsize:361798, largePrimes:10438565 encountered Relations: rels:10034059, finalFF:839198 Max relations in full relation-set: 28 Initial matrix: 723272 x 839198 with sparse part having weight 83825767. Pruned matrix : 631948 x 635628 with weight 56173117. Total sieving time: 57.88 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,50,50,2.5,2.5,100000 total time: 58.26 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(28·10¹⁶⁹+17)/9 = 3(1)₁₆₈3_<170> = 3 · 11 · 19 · 310055033 · C159
C159 = P46 · P113
P46 = 2415206321322037173599420711140338010790023979_<46>
P113 = 66260538169077111369916032292205300925953034481165074616471999679785377784367854169703990146660279900274172153217_<113>

Number: n N=160032870640155162550188298305797990544533418321959766573500508174037736228648792769050260989051569394837206366583950880158878277647558739735213553585491990443 ( 159 digits) SNFS difficulty: 171 digits. Divisors found: Sun Jul 20 15:32:22 2008 prp46 factor: 2415206321322037173599420711140338010790023979 Sun Jul 20 15:32:22 2008 prp113 factor: 66260538169077111369916032292205300925953034481165074616471999679785377784367854169703990146660279900274172153217 Sun Jul 20 15:32:22 2008 elapsed time 03:30:08 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 63.65 hours. Scaled time: 111.13 units (timescale=1.746). Factorization parameters were as follows: name: KA_3_1_168_3 n: 160032870640155162550188298305797990544533418321959766573500508174037736228648792769050260989051569394837206366583950880158878277647558739735213553585491990443 type: snfs skew: 1.43 deg: 5 c5: 14 c0: 85 m: 10000000000000000000000000000000000 rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 qintsize: 100000 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2300001) Primes: RFBsize:425648, AFBsize:425672, largePrimes:10044587 encountered Relations: rels:9775401, finalFF:976677 Max relations in full relation-set: 28 Initial matrix: 851386 x 976677 with sparse part having weight 58701082. Pruned matrix : Total sieving time: 63.27 hours. Total relation processing time: 0.38 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,50,50,2.6,2.6,100000 total time: 63.65 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 20, 2008: By Sinkiti Sibata / GGNFS
(22·10¹⁴¹+41)/9 = 2(4)₁₄₀9_<142> = 29 · 149 · 5449 · 452946459853_<12> · 67357504684949_<14> · C109
C109 = P54 · P56
P54 = 330751162736293369432428637738428342414840410247225443_<54>
P56 = 10288329338218503898012571540672054405004510290431734211_<56>

Number: 24449_141 N=3402876891229689848436598461222854587652833006566211367190450112565004405320662633342669332652310661572730473 ( 109 digits) Divisors found: r1=330751162736293369432428637738428342414840410247225443 (pp54) r2=10288329338218503898012571540672054405004510290431734211 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 22.97 hours. Scaled time: 17.71 units (timescale=0.771). Factorization parameters were as follows: name: 24449_141 n: 3402876891229689848436598461222854587652833006566211367190450112565004405320662633342669332652310661572730473 skew: 30807.09 # norm 3.85e+15 c5: 69120 c4: 2895205464 c3: -280193627009614 c2: -2131733424676079691 c1: 98239689575495530872726 c0: -135859311080054690787186605 # alpha -6.94 Y1: 341702854723 Y0: -547578302901837438032 # Murphy_E 1.13e-09 # M 2624517538539014615930987387730867606025583956109033825991318871842305983421265016580000378459286719069186525 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, 2900001) Primes: RFBsize:230209, AFBsize:230058, largePrimes:7228712 encountered Relations: rels:6973746, finalFF:525266 Max relations in full relation-set: 28 Initial matrix: 460344 x 525266 with sparse part having weight 39329504. Pruned matrix : 407937 x 410302 with weight 26054930. Total sieving time: 20.82 hours. Total relation processing time: 0.28 hours. Matrix solve time: 1.61 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 22.97 hours. --------- CPU info (if available) ----------
(22·10¹⁵⁴+41)/9 = 2(4)₁₅₃9_<155> = 17 · 3610089887_<10> · 616771282165439_<15> · 104974090577393839_<18> · 925466719406338609_<18> · C94
C94 = P45 · P50
P45 = 459905896132990216649786240439121054688244443_<45>
P50 = 14453638434218503727640096477729668894378052287453_<50>

Number: 24449_154 N=6647313536471490523384054516889594848412193076035299505863961930987106914439120763464965873679 ( 94 digits) Divisors found: r1=459905896132990216649786240439121054688244443 (pp45) r2=14453638434218503727640096477729668894378052287453 (pp50) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.02 hours. Scaled time: 6.14 units (timescale=0.765). Factorization parameters were as follows: name: 24449_154 n: 6647313536471490523384054516889594848412193076035299505863961930987106914439120763464965873679 m: 3925432779428596964968 deg: 4 c4: 27996000 c3: -86903748365 c2: 550027718475813193 c1: 229055727357494269 c0: -454436951428866878844665 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.859 # E(F1,F2) = 3.999849e-05 # GGNFS version 0.77.1-20050930-nocona polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1216504368. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1380001) Primes: RFBsize:92938, AFBsize:93133, largePrimes:1934443 encountered Relations: rels:2058820, finalFF:267616 Max relations in full relation-set: 28 Initial matrix: 186148 x 267616 with sparse part having weight 23334623. Pruned matrix : 154321 x 155315 with weight 11475763. Total sieving time: 7.74 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.14 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 8.02 hours. --------- CPU info (if available) ----------
(22·10¹³⁹+41)/9 = 2(4)₁₃₈9_<140> = 1181 · 1423 · 5985013 · 27989977 · 1178781981409_<13> · C107
C107 = P36 · P72
P36 = 316278564394734722828161457146528573_<36>
P72 = 232891954950910687233387848924968216474272090842685731013040356996107539_<72>

Number: 24449_139 N=73658733170957263936885436254788076953910255688365008131780721746620663191907956191768368728974527244211847 ( 107 digits) SNFS difficulty: 141 digits. Divisors found: r1=316278564394734722828161457146528573 (pp36) r2=232891954950910687233387848924968216474272090842685731013040356996107539 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.91 hours. Scaled time: 9.29 units (timescale=0.780). Factorization parameters were as follows: name: 24449_139 n: 73658733170957263936885436254788076953910255688365008131780721746620663191907956191768368728974527244211847 m: 10000000000000000000000000000 c5: 11 c0: 205 skew: 1.8 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, 1950001) Primes: RFBsize:100021, AFBsize:100200, largePrimes:2746564 encountered Relations: rels:2719321, finalFF:249721 Max relations in full relation-set: 28 Initial matrix: 200286 x 249721 with sparse part having weight 24385516. Pruned matrix : 185707 x 186772 with weight 16198328. Total sieving time: 11.48 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.30 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 11.91 hours. --------- CPU info (if available) ----------
Jul 19, 2008 (5th): By Sinkiti Sibata / GGNFS
(22·10¹³⁷+41)/9 = 2(4)₁₃₆9_<138> = 3 · 197 · 4721 · 21532792806979_<14> · 2558904966847610279_<19> · C100
C100 = P45 · P55
P45 = 866628596690676908124381538472636863619623849_<45>
P55 = 1834725747446334136962416765898795700139838509999294251_<55>

Number: 24449_137 N=1590025799821669844965039915392518155073858809059005816989579180428522176731895180810762304088192099 ( 100 digits) SNFS difficulty: 138 digits. Divisors found: r1=866628596690676908124381538472636863619623849 (pp45) r2=1834725747446334136962416765898795700139838509999294251 (pp55) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 15.16 hours. Scaled time: 7.16 units (timescale=0.472). Factorization parameters were as follows: name: 24449_137 n: 1590025799821669844965039915392518155073858809059005816989579180428522176731895180810762304088192099 m: 1000000000000000000000000000 c5: 2200 c0: 41 skew: 0.45 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, 2050001) Primes: RFBsize:78498, AFBsize:63670, largePrimes:1652714 encountered Relations: rels:1677088, finalFF:173641 Max relations in full relation-set: 28 Initial matrix: 142235 x 173641 with sparse part having weight 18526781. Pruned matrix : 134432 x 135207 with weight 12954715. Total sieving time: 14.63 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.37 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 15.16 hours. --------- CPU info (if available) ----------
Jul 19, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
(22·10¹³⁵+41)/9 = 2(4)₁₃₄9_<136> = 19 · 59 · 197217048137_<12> · 3473512671526180949462569_<25> · C97
C97 = P34 · P64
P34 = 2065104407058693668461888789327799_<34>
P64 = 1541413660666489857341708687188271597185167763339609496930078327_<64>

Number: n N=3183180143742841983978949218813441515939722303188901929973696523261819759463827185617358748512273 ( 97 digits) SNFS difficulty: 136 digits. Divisors found: r1=2065104407058693668461888789327799 (pp34) r2=1541413660666489857341708687188271597185167763339609496930078327 (pp64) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 5.54 hours. Scaled time: 7.25 units (timescale=1.309). Factorization parameters were as follows: name: KA_2_4_134_9 n: 3183180143742841983978949218813441515939722303188901929973696523261819759463827185617358748512273 skew: 1.13 deg: 5 c5: 22 c0: 41 m: 1000000000000000000000000000 type: snfs rlim: 950000 alim: 950000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 950000/950000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:74907, AFBsize:74185, largePrimes:7821834 encountered Relations: rels:7065344, finalFF:237913 Max relations in full relation-set: 28 Initial matrix: 149158 x 237913 with sparse part having weight 25256409. Pruned matrix : 129264 x 130073 with weight 11067695. Total sieving time: 4.87 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.42 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,950000,950000,28,28,50,50,2.5,2.5,75000 total time: 5.54 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(65·10¹⁶⁷+43)/9 = 7(2)₁₆₆7_<168> = 11 · 5879 · 31159 · 286831 · 517095792649_<12> · C142
C142 = P49 · P93
P49 = 6350896847958870927475301612070577433786600427541_<49>
P93 = 380503836982596483446568644330742044611360532394516326298199791512990729260726018085652941203_<93>

Number: n N=2416540618929028067669513756315393816139046863325989248996067013124199091486295011457802290992087222445824703172180542641244773807423934871823 ( 142 digits) SNFS difficulty: 168 digits. Divisors found: Sat Jul 19 16:15:17 2008 prp49 factor: 6350896847958870927475301612070577433786600427541 Sat Jul 19 16:15:17 2008 prp93 factor: 380503836982596483446568644330742044611360532394516326298199791512990729260726018085652941203 Sat Jul 19 16:15:17 2008 elapsed time 02:23:29 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 44.76 hours. Scaled time: 82.09 units (timescale=1.834). Factorization parameters were as follows: name: KA_7_2_166_7 n: 2416540618929028067669513756315393816139046863325989248996067013124199091486295011457802290992087222445824703172180542641244773807423934871823 skew: 0.37 deg: 5 c5: 6500 c0: 43 m: 1000000000000000000000000000000000 type: snfs rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2700209) Primes: RFBsize:399993, AFBsize:399914, largePrimes:9845687 encountered Relations: rels:9387478, finalFF:832705 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 44.42 hours. Total relation processing time: 0.34 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000 total time: 44.76 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 19, 2008 (3rd): By Sinkiti Sibata / GGNFS
(22·10¹⁴⁵+41)/9 = 2(4)₁₄₄9_<146> = 107 · 649488379249_<12> · C132
C132 = P36 · P97
P36 = 330656667519370766780036608680693031_<36>
P97 = 1063769965393139226970800550235148159416860116316758164927268244022746113357233560752845829368053_<97>

Number: 24449_145 N=351742631764091784060929143940635209161080432608066070671172188248276741820313159008906507475054840176158667869578115152472811138643 ( 132 digits) SNFS difficulty: 146 digits. Divisors found: r1=330656667519370766780036608680693031 (pp36) r2=1063769965393139226970800550235148159416860116316758164927268244022746113357233560752845829368053 (pp97) Version: GGNFS-0.77.1-20050930-nocona Total time: 22.76 hours. Scaled time: 17.66 units (timescale=0.776). Factorization parameters were as follows: name: 24449_145 n: 351742631764091784060929143940635209161080432608066070671172188248276741820313159008906507475054840176158667869578115152472811138643 m: 100000000000000000000000000000 c5: 22 c0: 41 skew: 1.13 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3250001) Primes: RFBsize:114155, AFBsize:113514, largePrimes:2953981 encountered Relations: rels:2977548, finalFF:281309 Max relations in full relation-set: 28 Initial matrix: 227735 x 281309 with sparse part having weight 31945458. Pruned matrix : 212164 x 213366 with weight 22643648. Total sieving time: 22.10 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.47 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 22.76 hours. --------- CPU info (if available) ----------
Jul 19, 2008 (2nd): By Serge Batalov / Msieve
(4·10²⁰⁷-1)/3 = 1(3)₂₀₇_<208> = 227 · C205
C205 = P100 · P106
P100 = 3999406295062729501331514001724671368377647689512510156551098073080765712556308639257272683646862107_<100>
P106 = 1468646766913267291096484238457962531138809604380942950365724174756132537097046980347507927618050634373797_<106>

Number: 13333_207 N=5873715124816446402349486049926578560939794419970631424375917767988252569750367107195301027900146842878120411160058737151248164464023494860499265785609397944199706314243759177679882525697503671071953010279 ( 205 digits) SNFS difficulty: 207 digits. Divisors found: r1=3999406295062729501331514001724671368377647689512510156551098073080765712556308639257272683646862107 (p100) r2=1468646766913267291096484238457962531138809604380942950365724174756132537097046980347507927618050634373797 (p106) Version: Msieve 1.36 Total time: 25 CPU-days. (timescale=2.952). Factorization parameters were as follows: n: 5873715124816446402349486049926578560939794419970631424375917767988252569750367107195301027900146842878120411160058737151248164464023494860499265785609397944199706314243759177679882525697503671071953010279 Y0: -200000000000000000000000000000000000000000 Y1: 1 c0: -2 c5: 25 skew: 0.65 type: snfs lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 rlim: 20000000 alim: 20000000 Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved rational special-q in [10000000, 22300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 42704260 relations (38902786 unique relations and about 34331443 large ideals) Max relations in full relation-set: Initial matrix: 3899964 x 3900911 (1179.1 MB) with weight 369366720 (94.69/col) sparse part has weight 266186760 (68.24/col) (memory use: 1591.7 MB) Pruned matrix : 3845390 x 3845638 (1123.7 MB) with weight 283186391 (73.64/col) sparse part has weight 256108183 (66.60/col) Total sieving time: 20 CPU-days.. Total relation processing time: 1.00 hours. Matrix solve time: 84:14:53 recovered 48 nontrivial dependencies Time per square root: 01:02:59 (on 1st dependency) Prototype def-par.txt line would be: snfs,207,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,58,58,2.6,2.6,100000 total time: 25 CPU-days. (8 calendar days; the matrix step was on a single CPU) --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS All stages were under 2.0Gb of memory (the C200+'s _can_ be now done on home computers) P.S. Many thanks to JasonP, the greatest.
C205 is the largest snfs-factored composite number in our tables so far and P100 is also the largest snfs-discovered prime factor in our tables so far. In addition, this effort shows that you can factor numbers which have 200 digits or more by your home computers with 2GB memory. Congratulations on the exciting records!!! See also www.mersenneforum.org.
(22·10¹²¹+41)/9 = 2(4)₁₂₀9_<122> = 131041 · 2319738263_<10> · C107
C107 = P35 · P73
P35 = 25062368393601465451556297653785029_<35>
P73 = 3208572650535973954961225795597759882808586084195449958716499723851512507_<73>

Number: 24449_121 N=80414429785366873756397237324162557271658995122046202935508783138144456898631522252449895246859675082857703 ( 107 digits) SNFS difficulty: 122 digits. Divisors found: r1=25062368393601465451556297653785029 r2=3208572650535973954961225795597759882808586084195449958716499723851512507 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: n: 80414429785366873756397237324162557271658995122046202935508783138144456898631522252449895246859675082857703 Y1: 1 Y0: -1000000000000000000000000 c5: 220 c0: 41 skew: 0.71 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 102792 x 103019 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.10 hours.
Jul 19, 2008: By Robert Backstrom / GGNFS, GMP-ECM
(22·10¹¹⁴+41)/9 = 2(4)₁₁₃9_<115> = 7² · 23 · 53 · C110
C110 = P38 · P73
P38 = 36786423298913986934702187003334911349_<38>
P73 = 1112481561942967290761054206790315374836962739575611381377759806988761071_<73>

Number: n N=40924217649870995704817338474903223526216611884020767180265598172547662762124264526702121920685145811127294779 ( 110 digits) SNFS difficulty: 116 digits. Divisors found: r1=36786423298913986934702187003334911349 (pp38) r2=1112481561942967290761054206790315374836962739575611381377759806988761071 (pp73) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 1.32 hours. Scaled time: 1.73 units (timescale=1.308). Factorization parameters were as follows: name: KA_2_4_113_9 n: 40924217649870995704817338474903223526216611884020767180265598172547662762124264526702121920685145811127294779 skew: 1.80 deg: 5 c5: 11 c0: 205 m: 100000000000000000000000 type: snfs rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:41538, AFBsize:41594, largePrimes:3882954 encountered Relations: rels:3287386, finalFF:111057 Max relations in full relation-set: 28 Initial matrix: 83197 x 111057 with sparse part having weight 8625133. Pruned matrix : 74572 x 75051 with weight 4207667. Total sieving time: 1.16 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.06 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,500000,500000,28,28,50,50,2.5,2.5,50000 total time: 1.32 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(22·10¹³¹+41)/9 = 2(4)₁₃₀9_<132> = 3² · 4787 · 6966823 · 1281492591809_<13> · 19736198501419_<14> · C95
C95 = P32 · P63
P32 = 38341155108220418699692555245493_<32>
P63 = 839836335247171403374568311996768228503199306945428622409955187_<63>
Jul 18, 2008 (8th): By Jo Yeong Uk / GMP-ECM
8·10¹⁶⁷+3 = 8(0)₁₆₆3_<168> = 251467910385709_<15> · 126974570731714215575127079_<27> · C128
C128 = P45 · P83
P45 = 837436146854618446845679601742976105039316057_<45>
P83 = 29918440904777602878053870979485087624956432150490430623595618437356372457311766689_<83>

GMP-ECM 6.2 [powered by GMP 4.2.2] [ECM] Input number is 25054783871194560239401225829811852453817515096204346029171349857158592954195626273041212563779604664854740343106865830915425273 (128 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=127447873 Step 1 took 6030ms Step 2 took 2946ms ********** Factor found in step 2: 837436146854618446845679601742976105039316057 Found probable prime factor of 45 digits: 837436146854618446845679601742976105039316057 Probable prime cofactor 29918440904777602878053870979485087624956432150490430623595618437356372457311766689 has 83 digits
Jul 18, 2008 (7th): By Robert Backstrom / GGNFS, Msieve
5·10¹⁶⁸-1 = 4(9)₁₆₈_<169> = 71 · 461 · 1609 · 14951 · 80777981 · C149
C149 = P41 · P45 · P64
P41 = 22639721157902129095414403005942496800349_<41>
P45 = 457434303099638694586122437203847366912844131_<45>
P64 = 7590871641081854629092704253048698545019692817001067700599918729_<64>

Number: n N=78612471559442958193948932412621943215928354030608716743603360935146350691540877706643356686115717423275593902051381288373526750237641857883878895151 ( 149 digits) SNFS difficulty: 169 digits. Divisors found: Fri Jul 18 13:57:52 2008 prp41 factor: 22639721157902129095414403005942496800349 Fri Jul 18 13:57:52 2008 prp45 factor: 457434303099638694586122437203847366912844131 Fri Jul 18 13:57:52 2008 prp64 factor: 7590871641081854629092704253048698545019692817001067700599918729 Fri Jul 18 13:57:52 2008 elapsed time 03:10:45 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 55.74 hours. Scaled time: 36.51 units (timescale=0.655). Factorization parameters were as follows: name: KA_4_9_168 n: 78612471559442958193948932412621943215928354030608716743603360935146350691540877706643356686115717423275593902051381288373526750237641857883878895151 skew: 0.91 deg: 5 c5: 8 c0: -5 m: 5000000000000000000000000000000000 type: snfs rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2402509) Primes: RFBsize:399993, AFBsize:399814, largePrimes:9619479 encountered Relations: rels:9166302, finalFF:834416 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 55.38 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000 total time: 55.74 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 18, 2008 (6th): By Sinkiti Sibata / Msieve, GGNFS
(22·10¹³⁶+41)/9 = 2(4)₁₃₅9_<137> = 23 · 61 · 178844202666818707982925019_<27> · 8717675454678942130350489919_<28> · C80
C80 = P36 · P44
P36 = 531452776093609479259543855857961849_<36>
P44 = 21027239274346636115400378553683570984303247_<44>

Fri Jul 18 13:45:18 2008 Msieve v. 1.36 Fri Jul 18 13:45:18 2008 random seeds: 46217630 d69eac1b Fri Jul 18 13:45:18 2008 factoring 11174984685936094268528804965283109768871202961445260752328824538012748772823703 (80 digits) Fri Jul 18 13:45:19 2008 no P-1/P+1/ECM available, skipping Fri Jul 18 13:45:19 2008 commencing quadratic sieve (80-digit input) Fri Jul 18 13:45:19 2008 using multiplier of 1 Fri Jul 18 13:45:19 2008 using 64kb Pentium 4 sieve core Fri Jul 18 13:45:19 2008 sieve interval: 6 blocks of size 65536 Fri Jul 18 13:45:19 2008 processing polynomials in batches of 17 Fri Jul 18 13:45:19 2008 using a sieve bound of 1186657 (45938 primes) Fri Jul 18 13:45:19 2008 using large prime bound of 118665700 (26 bits) Fri Jul 18 13:45:19 2008 using trial factoring cutoff of 27 bits Fri Jul 18 13:45:19 2008 polynomial 'A' values have 10 factors Fri Jul 18 14:00:45 2008 46148 relations (23831 full + 22317 combined from 251282 partial), need 46034 Fri Jul 18 14:00:46 2008 begin with 275113 relations Fri Jul 18 14:00:46 2008 reduce to 65721 relations in 2 passes Fri Jul 18 14:00:46 2008 attempting to read 65721 relations Fri Jul 18 14:00:48 2008 recovered 65721 relations Fri Jul 18 14:00:48 2008 recovered 53985 polynomials Fri Jul 18 14:00:48 2008 attempting to build 46148 cycles Fri Jul 18 14:00:48 2008 found 46148 cycles in 1 passes Fri Jul 18 14:00:48 2008 distribution of cycle lengths: Fri Jul 18 14:00:48 2008 length 1 : 23831 Fri Jul 18 14:00:48 2008 length 2 : 22317 Fri Jul 18 14:00:48 2008 largest cycle: 2 relations Fri Jul 18 14:00:48 2008 matrix is 45938 x 46148 (6.0 MB) with weight 1395149 (30.23/col) Fri Jul 18 14:00:48 2008 sparse part has weight 1395149 (30.23/col) Fri Jul 18 14:00:48 2008 filtering completed in 3 passes Fri Jul 18 14:00:48 2008 matrix is 32312 x 32375 (4.7 MB) with weight 1091791 (33.72/col) Fri Jul 18 14:00:48 2008 sparse part has weight 1091791 (33.72/col) Fri Jul 18 14:00:48 2008 saving the first 48 matrix rows for later Fri Jul 18 14:00:48 2008 matrix is 32264 x 32375 (2.8 MB) with weight 793320 (24.50/col) Fri Jul 18 14:00:48 2008 sparse part has weight 546231 (16.87/col) Fri Jul 18 14:00:48 2008 matrix includes 64 packed rows Fri Jul 18 14:00:48 2008 using block size 12950 for processor cache size 512 kB Fri Jul 18 14:00:49 2008 commencing Lanczos iteration Fri Jul 18 14:00:49 2008 memory use: 3.4 MB Fri Jul 18 14:00:57 2008 lanczos halted after 512 iterations (dim = 32262) Fri Jul 18 14:00:57 2008 recovered 16 nontrivial dependencies Fri Jul 18 14:00:57 2008 prp36 factor: 531452776093609479259543855857961849 Fri Jul 18 14:00:57 2008 prp44 factor: 21027239274346636115400378553683570984303247 Fri Jul 18 14:00:57 2008 elapsed time 00:15:39
(22·10¹¹⁹+41)/9 = 2(4)₁₁₈9_<120> = 3 · 607 · 19426872662255651093434709_<26> · C91
C91 = P41 · P51
P41 = 47566566335345876577853460008460440738421_<41>
P51 = 145266519005140854768685462486158749326268729347421_<51>

Fri Jul 18 14:36:07 2008 Msieve v. 1.36 Fri Jul 18 14:36:07 2008 random seeds: 02092aa2 9098e17e Fri Jul 18 14:36:07 2008 factoring 6909829512562814960843460860887417512953556989063562541544742552648533771432775918691962241 (91 digits) Fri Jul 18 14:36:08 2008 no P-1/P+1/ECM available, skipping Fri Jul 18 14:36:08 2008 commencing quadratic sieve (91-digit input) Fri Jul 18 14:36:08 2008 using multiplier of 1 Fri Jul 18 14:36:08 2008 using 64kb Pentium 4 sieve core Fri Jul 18 14:36:08 2008 sieve interval: 18 blocks of size 65536 Fri Jul 18 14:36:08 2008 processing polynomials in batches of 6 Fri Jul 18 14:36:08 2008 using a sieve bound of 1719241 (64706 primes) Fri Jul 18 14:36:08 2008 using large prime bound of 165047136 (27 bits) Fri Jul 18 14:36:08 2008 using double large prime bound of 619005322436736 (42-50 bits) Fri Jul 18 14:36:08 2008 using trial factoring cutoff of 50 bits Fri Jul 18 14:36:08 2008 polynomial 'A' values have 12 factors Fri Jul 18 17:27:51 2008 65119 relations (16691 full + 48428 combined from 768023 partial), need 64802 Fri Jul 18 17:27:53 2008 begin with 784714 relations Fri Jul 18 17:27:54 2008 reduce to 163266 relations in 10 passes Fri Jul 18 17:27:54 2008 attempting to read 163266 relations Fri Jul 18 17:27:59 2008 recovered 163266 relations Fri Jul 18 17:27:59 2008 recovered 143283 polynomials Fri Jul 18 17:27:59 2008 attempting to build 65119 cycles Fri Jul 18 17:27:59 2008 found 65119 cycles in 5 passes Fri Jul 18 17:27:59 2008 distribution of cycle lengths: Fri Jul 18 17:27:59 2008 length 1 : 16691 Fri Jul 18 17:27:59 2008 length 2 : 12043 Fri Jul 18 17:27:59 2008 length 3 : 11400 Fri Jul 18 17:27:59 2008 length 4 : 8911 Fri Jul 18 17:27:59 2008 length 5 : 6291 Fri Jul 18 17:27:59 2008 length 6 : 3993 Fri Jul 18 17:27:59 2008 length 7 : 2570 Fri Jul 18 17:27:59 2008 length 9+: 3220 Fri Jul 18 17:27:59 2008 largest cycle: 19 relations Fri Jul 18 17:27:59 2008 matrix is 64706 x 65119 (16.1 MB) with weight 3956681 (60.76/col) Fri Jul 18 17:27:59 2008 sparse part has weight 3956681 (60.76/col) Fri Jul 18 17:28:01 2008 filtering completed in 3 passes Fri Jul 18 17:28:01 2008 matrix is 60964 x 61028 (15.1 MB) with weight 3719537 (60.95/col) Fri Jul 18 17:28:01 2008 sparse part has weight 3719537 (60.95/col) Fri Jul 18 17:28:01 2008 saving the first 48 matrix rows for later Fri Jul 18 17:28:01 2008 matrix is 60916 x 61028 (9.7 MB) with weight 2948615 (48.32/col) Fri Jul 18 17:28:01 2008 sparse part has weight 2173245 (35.61/col) Fri Jul 18 17:28:01 2008 matrix includes 64 packed rows Fri Jul 18 17:28:01 2008 using block size 21845 for processor cache size 512 kB Fri Jul 18 17:28:02 2008 commencing Lanczos iteration Fri Jul 18 17:28:02 2008 memory use: 9.4 MB Fri Jul 18 17:28:40 2008 lanczos halted after 965 iterations (dim = 60913) Fri Jul 18 17:28:40 2008 recovered 15 nontrivial dependencies Fri Jul 18 17:28:42 2008 prp41 factor: 47566566335345876577853460008460440738421 Fri Jul 18 17:28:42 2008 prp51 factor: 145266519005140854768685462486158749326268729347421 Fri Jul 18 17:28:42 2008 elapsed time 02:52:35
(22·10¹²²+41)/9 = 2(4)₁₂₁9_<123> = 3³ · 17 · 397 · 509 · 226522559 · 20019177865109_<14> · C93
C93 = P37 · P57
P37 = 2479394702744903130958322262280605137_<37>
P57 = 234399040945537669940119153419177139386619105466093573281_<57>

Fri Jul 18 17:41:27 2008 Msieve v. 1.36 Fri Jul 18 17:41:27 2008 random seeds: f13eb197 24f0b957 Fri Jul 18 17:41:27 2008 factoring 581167740448851748884915075302866508210009792004549285245839702179434977036441317607334544497 (93 digits) Fri Jul 18 17:41:28 2008 no P-1/P+1/ECM available, skipping Fri Jul 18 17:41:28 2008 commencing quadratic sieve (93-digit input) Fri Jul 18 17:41:29 2008 using multiplier of 17 Fri Jul 18 17:41:29 2008 using 64kb Pentium 4 sieve core Fri Jul 18 17:41:29 2008 sieve interval: 18 blocks of size 65536 Fri Jul 18 17:41:29 2008 processing polynomials in batches of 6 Fri Jul 18 17:41:29 2008 using a sieve bound of 1956901 (72801 primes) Fri Jul 18 17:41:29 2008 using large prime bound of 244612625 (27 bits) Fri Jul 18 17:41:29 2008 using double large prime bound of 1256787622996125 (42-51 bits) Fri Jul 18 17:41:29 2008 using trial factoring cutoff of 51 bits Fri Jul 18 17:41:29 2008 polynomial 'A' values have 12 factors Fri Jul 18 21:47:43 2008 73312 relations (18883 full + 54429 combined from 988028 partial), need 72897 Fri Jul 18 21:47:46 2008 begin with 1006911 relations Fri Jul 18 21:47:47 2008 reduce to 185758 relations in 11 passes Fri Jul 18 21:47:47 2008 attempting to read 185758 relations Fri Jul 18 21:47:53 2008 recovered 185758 relations Fri Jul 18 21:47:53 2008 recovered 166149 polynomials Fri Jul 18 21:47:54 2008 attempting to build 73312 cycles Fri Jul 18 21:47:54 2008 found 73312 cycles in 5 passes Fri Jul 18 21:47:54 2008 distribution of cycle lengths: Fri Jul 18 21:47:54 2008 length 1 : 18883 Fri Jul 18 21:47:54 2008 length 2 : 13309 Fri Jul 18 21:47:54 2008 length 3 : 12540 Fri Jul 18 21:47:54 2008 length 4 : 9829 Fri Jul 18 21:47:54 2008 length 5 : 7230 Fri Jul 18 21:47:54 2008 length 6 : 4642 Fri Jul 18 21:47:54 2008 length 7 : 3012 Fri Jul 18 21:47:54 2008 length 9+: 3867 Fri Jul 18 21:47:54 2008 largest cycle: 18 relations Fri Jul 18 21:47:54 2008 matrix is 72801 x 73312 (18.6 MB) with weight 4575927 (62.42/col) Fri Jul 18 21:47:54 2008 sparse part has weight 4575927 (62.42/col) Fri Jul 18 21:47:56 2008 filtering completed in 3 passes Fri Jul 18 21:47:56 2008 matrix is 68635 x 68698 (17.4 MB) with weight 4293577 (62.50/col) Fri Jul 18 21:47:56 2008 sparse part has weight 4293577 (62.50/col) Fri Jul 18 21:47:56 2008 saving the first 48 matrix rows for later Fri Jul 18 21:47:56 2008 matrix is 68587 x 68698 (10.7 MB) with weight 3329385 (48.46/col) Fri Jul 18 21:47:56 2008 sparse part has weight 2391376 (34.81/col) Fri Jul 18 21:47:56 2008 matrix includes 64 packed rows Fri Jul 18 21:47:56 2008 using block size 21845 for processor cache size 512 kB Fri Jul 18 21:47:57 2008 commencing Lanczos iteration Fri Jul 18 21:47:57 2008 memory use: 10.6 MB Fri Jul 18 21:48:46 2008 lanczos halted after 1086 iterations (dim = 68583) Fri Jul 18 21:48:46 2008 recovered 14 nontrivial dependencies Fri Jul 18 21:48:50 2008 prp37 factor: 2479394702744903130958322262280605137 Fri Jul 18 21:48:50 2008 prp57 factor: 234399040945537669940119153419177139386619105466093573281 Fri Jul 18 21:48:50 2008 elapsed time 04:07:23
(22·10¹³⁸+41)/9 = 2(4)₁₃₇9_<139> = 7 · 17 · 31 · 193 · 373 · 673 · 937 · 41161 · C120
C120 = P36 · P84
P36 = 610651208920497670366733893531787309_<36>
P84 = 580726416089174434252413269353020068317056403185036791065062056709332599816085902681_<84>

Number: 24449_138 N=354621288036922317129460378447709402989326839295547924604905462758134623744329528219757499403532898824792484232564875429 ( 120 digits) SNFS difficulty: 139 digits. Divisors found: r1=610651208920497670366733893531787309 (pp36) r2=580726416089174434252413269353020068317056403185036791065062056709332599816085902681 (pp84) Version: GGNFS-0.77.1-20050930-nocona Total time: 13.03 hours. Scaled time: 10.18 units (timescale=0.781). Factorization parameters were as follows: name: 24449_138 n: 354621288036922317129460378447709402989326839295547924604905462758134623744329528219757499403532898824792484232564875429 m: 2000000000000000000000000000 c5: 1375 c0: 82 skew: 0.57 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, 2125001) Primes: RFBsize:78498, AFBsize:64075, largePrimes:1684247 encountered Relations: rels:1730964, finalFF:191244 Max relations in full relation-set: 28 Initial matrix: 142639 x 191244 with sparse part having weight 20674544. Pruned matrix : 131077 x 131854 with weight 12803762. Total sieving time: 12.77 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.13 hours. Time per square root: 0.04 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: 13.03 hours. --------- CPU info (if available) ----------
Jul 18, 2008 (5th): By Serge Batalov / GMP-ECM, Msieve
(22·10¹³⁰+41)/9 = 2(4)₁₂₉9_<131> = 623007889151_<12> · 391864797803729335146086239_<27> · C93
C93 = P34 · P59
P34 = 2404106623587392833380957646953757_<34>
P59 = 41648239554086215738636228680214783731775995314642888620213_<59>
(22·10¹⁴⁰+41)/9 = 2(4)₁₃₉9_<141> = 3² · 53 · 385157668968708457_<18> · C121
C121 = P33 · P88
P33 = 636996487870315120894764412495687_<33>
P88 = 2088748759088354916772576445771665562338190776869101189675739705777594695442923658592843_<88>
(22·10¹¹²+41)/9 = 2(4)₁₁₁9_<113> = 6389 · 882751 · C103
C103 = P49 · P55
P49 = 3337089450937904685056902869759131185338950859791_<49>
P55 = 1298796820924815062861063233533242770022606282492927501_<55>

Number: 24449_112 N=4334201170019887212757136278967289763497618984157758520106755541166969075712698056910874692340579012291 ( 103 digits) SNFS difficulty: 113 digits. Divisors found: r1=3337089450937904685056902869759131185338950859791 r2=1298796820924815062861063233533242770022606282492927501 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.300). Factorization parameters were as follows: n: 4334201170019887212757136278967289763497618984157758520106755541166969075712698056910874692340579012291 Y1: 1 Y0: -10000000000000000000000 c5: 2200 c0: 41 skew: 0.45 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 85491 x 85712 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.90 hours.
(22·10¹⁹⁶+41)/9 = 2(4)₁₉₅9_<197> = 61 · 29927 · 14045039 · 175281864497_<12> · 78685402711417120250969_<23> · 121595069518936332737259113161_<30> · 164769187376264668609706570911_<30> · C91
C91 = P34 · P57
P34 = 5803154930334451126145780382617113_<34>
P57 = 594534302111706146898488870469731843809863616765324450427_<57>

Thu Jul 17 23:11:07 2008 Msieve v. 1.36 Thu Jul 17 23:11:07 2008 random seeds: 1f8931f2 b1016748 Thu Jul 17 23:11:07 2008 factoring 3450174666552499603958825634868719551155941132530381444028934776059628299672087790690357251 (91 digits) Thu Jul 17 23:11:08 2008 no P-1/P+1/ECM available, skipping Thu Jul 17 23:11:08 2008 commencing quadratic sieve (91-digit input) Thu Jul 17 23:11:08 2008 using multiplier of 11 Thu Jul 17 23:11:08 2008 using 64kb Opteron sieve core Thu Jul 17 23:11:08 2008 sieve interval: 18 blocks of size 65536 Thu Jul 17 23:11:08 2008 processing polynomials in batches of 6 Thu Jul 17 23:11:08 2008 using a sieve bound of 1684919 (63529 primes) Thu Jul 17 23:11:08 2008 using large prime bound of 155012548 (27 bits) Thu Jul 17 23:11:08 2008 using double large prime bound of 552917357712160 (42-49 bits) Thu Jul 17 23:11:08 2008 using trial factoring cutoff of 49 bits Thu Jul 17 23:11:08 2008 polynomial 'A' values have 12 factors Fri Jul 18 00:45:24 2008 64103 relations (17260 full + 46843 combined from 724321 partial), need 63625 Fri Jul 18 00:45:24 2008 begin with 741581 relations Fri Jul 18 00:45:25 2008 reduce to 156628 relations in 10 passes Fri Jul 18 00:45:25 2008 attempting to read 156628 relations Fri Jul 18 00:45:26 2008 recovered 156628 relations Fri Jul 18 00:45:26 2008 recovered 134292 polynomials Fri Jul 18 00:45:26 2008 attempting to build 64103 cycles Fri Jul 18 00:45:26 2008 found 64103 cycles in 5 passes Fri Jul 18 00:45:26 2008 distribution of cycle lengths: Fri Jul 18 00:45:26 2008 length 1 : 17260 Fri Jul 18 00:45:26 2008 length 2 : 12150 Fri Jul 18 00:45:26 2008 length 3 : 11287 Fri Jul 18 00:45:26 2008 length 4 : 8555 Fri Jul 18 00:45:26 2008 length 5 : 6019 Fri Jul 18 00:45:26 2008 length 6 : 3774 Fri Jul 18 00:45:26 2008 length 7 : 2313 Fri Jul 18 00:45:26 2008 length 9+: 2745 Fri Jul 18 00:45:26 2008 largest cycle: 17 relations Fri Jul 18 00:45:27 2008 matrix is 63529 x 64103 (16.6 MB) with weight 3834011 (59.81/col) Fri Jul 18 00:45:27 2008 sparse part has weight 3834011 (59.81/col) Fri Jul 18 00:45:28 2008 filtering completed in 3 passes Fri Jul 18 00:45:28 2008 matrix is 59293 x 59357 (15.4 MB) with weight 3550633 (59.82/col) Fri Jul 18 00:45:28 2008 sparse part has weight 3550633 (59.82/col) Fri Jul 18 00:45:28 2008 saving the first 48 matrix rows for later Fri Jul 18 00:45:28 2008 matrix is 59245 x 59357 (9.8 MB) with weight 2743225 (46.22/col) Fri Jul 18 00:45:28 2008 sparse part has weight 1973750 (33.25/col) Fri Jul 18 00:45:28 2008 matrix includes 64 packed rows Fri Jul 18 00:45:28 2008 using block size 23742 for processor cache size 1024 kB Fri Jul 18 00:45:28 2008 commencing Lanczos iteration Fri Jul 18 00:45:28 2008 memory use: 8.8 MB Fri Jul 18 00:45:55 2008 lanczos halted after 939 iterations (dim = 59240) Fri Jul 18 00:45:56 2008 recovered 14 nontrivial dependencies Fri Jul 18 00:45:56 2008 prp34 factor: 5803154930334451126145780382617113 Fri Jul 18 00:45:56 2008 prp57 factor: 594534302111706146898488870469731843809863616765324450427 Fri Jul 18 00:45:56 2008 elapsed time 01:34:49
Jul 18, 2008 (4th): Factorizations of 244...449 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.
Jul 18, 2008 (3rd): By Serge Batalov / GMP-ECM
(73·10¹⁹¹-1)/9 = 8(1)₁₉₁_<192> = 7² · 2957 · 28391329 · 81902647 · 1197538717_<10> · 4210320749_<10> · C153
C153 = P27 · C127
P27 = 281150019363827276479091879_<27>
C127 = [1698268766936150674397664693080209666761726866084951569803456920236110045824863664598013300791554963893047144133640896867139147_<127>]
Jul 18, 2008 (2nd): By suberi / GMP-ECM
(10¹⁷⁸+53)/9 = (1)₁₇₇7_<178> = 17 · 19 · 31 · 29774267 · 17227909875533589273161569_<26> · C141
C141 = P52 · P89
P52 = 4616319830731803277321116745402333657467824322700921_<52>
P89 = 46862312350682118639301501622052895505443364470908072445277360687050905418909375922185723_<89>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1762451977 Step 1 took 88941ms Step 2 took 29294ms ********** Factor found in step 2: 4616319830731803277321116745402333657467824322700921 Found probable prime factor of 52 digits: 4616319830731803277321116745402333657467824322700921 Probable prime cofactor 46862312350682118639301501622052895505443364470908072445277360687050905418909375922185723 has 89 digits
Jul 18, 2008: By Serge Batalov / GMP-ECM, Msieve
(43·10¹⁹⁴-7)/9 = 4(7)₁₉₄_<195> = 3 · 89 · 107 · 38917751 · 109329978532264895118221121359_<30> · 27984220393915439255871446690087_<32> · C123
C123 = P39 · P42 · P43
P39 = 150253016357827367252162610270549921517_<39>
P42 = 750043144488989115802079916490146682858549_<42>
P43 = 1246296144452316719852297075309650379237447_<43>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1189677086 Step 1 took 21161ms Step 2 took 17730ms ********** Factor found in step 2: 150253016357827367252162610270549921517 Found probable prime factor of 39 digits: 150253016357827367252162610270549921517 Thu Jul 17 12:15:31 2008 Msieve v. 1.36 Thu Jul 17 12:15:31 2008 random seeds: c40b47a0 78880a05 Thu Jul 17 12:15:31 2008 factoring 934775879149519040345063733991838603284029386859630642611343691487753360644784884403 (84 digits) Thu Jul 17 12:15:32 2008 no P-1/P+1/ECM available, skipping Thu Jul 17 12:15:32 2008 commencing quadratic sieve (84-digit input) Thu Jul 17 12:15:32 2008 using multiplier of 2 Thu Jul 17 12:15:32 2008 using 64kb Opteron sieve core Thu Jul 17 12:15:32 2008 sieve interval: 6 blocks of size 65536 Thu Jul 17 12:15:32 2008 processing polynomials in batches of 17 Thu Jul 17 12:15:32 2008 using a sieve bound of 1409171 (53729 primes) Thu Jul 17 12:15:32 2008 using large prime bound of 119779535 (26 bits) Thu Jul 17 12:15:32 2008 using trial factoring cutoff of 27 bits Thu Jul 17 12:15:32 2008 polynomial 'A' values have 11 factors Thu Jul 17 12:52:32 2008 53862 relations (26979 full + 26883 combined from 284871 partial), need 53825 Thu Jul 17 12:52:32 2008 begin with 311850 relations Thu Jul 17 12:52:32 2008 reduce to 77390 relations in 2 passes Thu Jul 17 12:52:32 2008 attempting to read 77390 relations Thu Jul 17 12:52:32 2008 recovered 77390 relations Thu Jul 17 12:52:32 2008 recovered 72319 polynomials Thu Jul 17 12:52:33 2008 attempting to build 53862 cycles Thu Jul 17 12:52:33 2008 found 53862 cycles in 1 passes Thu Jul 17 12:52:33 2008 distribution of cycle lengths: Thu Jul 17 12:52:33 2008 length 1 : 26979 Thu Jul 17 12:52:33 2008 length 2 : 26883 Thu Jul 17 12:52:33 2008 largest cycle: 2 relations Thu Jul 17 12:52:33 2008 matrix is 53729 x 53862 (8.4 MB) with weight 1758571 (32.65/col) Thu Jul 17 12:52:33 2008 sparse part has weight 1758571 (32.65/col) Thu Jul 17 12:52:33 2008 filtering completed in 3 passes Thu Jul 17 12:52:33 2008 matrix is 39922 x 39986 (6.7 MB) with weight 1436413 (35.92/col) Thu Jul 17 12:52:33 2008 sparse part has weight 1436413 (35.92/col) Thu Jul 17 12:52:33 2008 saving the first 48 matrix rows for later Thu Jul 17 12:52:33 2008 matrix is 39874 x 39986 (4.4 MB) with weight 1075978 (26.91/col) Thu Jul 17 12:52:33 2008 sparse part has weight 761119 (19.03/col) Thu Jul 17 12:52:33 2008 matrix includes 64 packed rows Thu Jul 17 12:52:33 2008 using block size 15994 for processor cache size 1024 kB Thu Jul 17 12:52:34 2008 commencing Lanczos iteration Thu Jul 17 12:52:34 2008 memory use: 4.4 MB Thu Jul 17 12:52:40 2008 lanczos halted after 632 iterations (dim = 39872) Thu Jul 17 12:52:41 2008 recovered 17 nontrivial dependencies Thu Jul 17 12:52:41 2008 prp42 factor: 750043144488989115802079916490146682858549 Thu Jul 17 12:52:41 2008 prp43 factor: 1246296144452316719852297075309650379237447 Thu Jul 17 12:52:41 2008 elapsed time 00:37:10
Jul 17, 2008 (5th): By Wataru Sakai / GGNFS
6·10¹⁸³-1 = 5(9)₁₈₃_<184> = 7 · 2837 · C180
C180 = P63 · P118
P63 = 112649776609562047883105198303449664536396037482590034913768341_<63>
P118 = 2682029434148964127373780620479656968569866368989364416202844775610580864046145940166851280210227212021563042712498321_<118>

Number: 59999_183 N=302130016617150913943300266881514678483307316581902412004632660254796314013797270758849891736744045520922503650737700790573543481544891484969031673296742031320811722644644745455461 ( 180 digits) SNFS difficulty: 184 digits. Divisors found: r1=112649776609562047883105198303449664536396037482590034913768341 (pp63) r2=2682029434148964127373780620479656968569866368989364416202844775610580864046145940166851280210227212021563042712498321 (pp118) Version: GGNFS-0.77.1-20060722-nocona Total time: 571.11 hours. Scaled time: 1149.08 units (timescale=2.012). Factorization parameters were as follows: n: 302130016617150913943300266881514678483307316581902412004632660254796314013797270758849891736744045520922503650737700790573543481544891484969031673296742031320811722644644745455461 m: 2000000000000000000000000000000000000 c5: 375 c0: -2 skew: 0.35 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10800001) Primes: RFBsize:501962, AFBsize:501426, largePrimes:6705920 encountered Relations: rels:7228998, finalFF:1191175 Max relations in full relation-set: 32 Initial matrix: 1003454 x 1191175 with sparse part having weight 89284613. Pruned matrix : 846750 x 851831 with weight 68965118. Total sieving time: 563.95 hours. Total relation processing time: 0.12 hours. Matrix solve time: 6.82 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 571.11 hours. --------- CPU info (if available) ----------
(2·10¹⁷⁸+1)/3 = (6)₁₇₇7_<178> = 59 · C177
C177 = P81 · P96
P81 = 185421820977433014232739114726348871301256180810891425507564250791297781333322283_<81>
P96 = 609390791692408139110213498907677209688513214774525388871591629305745057845486938328656711665011_<96>

Number: 66667_178 N=112994350282485875706214689265536723163841807909604519774011299435028248587570621468926553672316384180790960451977401129943502824858757062146892655367231638418079096045197740113 ( 177 digits) SNFS difficulty: 178 digits. Divisors found: r1=185421820977433014232739114726348871301256180810891425507564250791297781333322283 (pp81) r2=609390791692408139110213498907677209688513214774525388871591629305745057845486938328656711665011 (pp96) Version: GGNFS-0.77.1-20060722-nocona Total time: 257.83 hours. Scaled time: 519.01 units (timescale=2.013). Factorization parameters were as follows: n: 112994350282485875706214689265536723163841807909604519774011299435028248587570621468926553672316384180790960451977401129943502824858757062146892655367231638418079096045197740113 m: 200000000000000000000000000000000000 c5: 125 c0: 2 skew: 0.44 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, ) Primes: RFBsize:501962, AFBsize:501581, largePrimes:6581325 encountered Relations: rels:7061543, finalFF:1142735 Max relations in full relation-set: 32 Initial matrix: 1003608 x 1142735 with sparse part having weight 81062804. Pruned matrix : 887061 x 892143 with weight 62469237. Total sieving time: 255.54 hours. Total relation processing time: 0.11 hours. Matrix solve time: 1.98 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,178,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 257.83 hours. --------- CPU info (if available) ----------
(79·10¹⁷⁸-7)/9 = 8(7)₁₇₈_<179> = 3 · C179
C179 = P44 · P136
P44 = 19971896401363047141199475475638205189325457_<44>
P136 = 1465021581889557857924256214667419479705503658147178481828370509373285421613856871941147734400057046089676390097180025635682843605088587_<136>

Number: 87777_178 N=29259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259 ( 179 digits) SNFS difficulty: 179 digits. Divisors found: r1=19971896401363047141199475475638205189325457 (pp44) r2=1465021581889557857924256214667419479705503658147178481828370509373285421613856871941147734400057046089676390097180025635682843605088587 (pp136) Version: GGNFS-0.77.1-20060722-nocona Total time: 563.40 hours. Scaled time: 1127.37 units (timescale=2.001). Factorization parameters were as follows: n: 29259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259 m: 100000000000000000000000000000000000 c5: 79000 c0: -7 skew: 0.15 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 25400001) Primes: RFBsize:501962, AFBsize:502131, largePrimes:7373002 encountered Relations: rels:8019550, finalFF:1174666 Max relations in full relation-set: 32 Initial matrix: 1004160 x 1174666 with sparse part having weight 144974941. Pruned matrix : 879802 x 884886 with weight 124736252. Total sieving time: 550.51 hours. Total relation processing time: 0.18 hours. Matrix solve time: 11.93 hours. Time per square root: 0.78 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: 563.40 hours. --------- CPU info (if available) ----------
Jul 17, 2008 (4th): By matsui / GGNFS
10¹⁷⁴+7 = 1(0)₁₇₃7_<175> = 29 · 71 · 487 · 11125843 · C161
C161 = P62 · P100
P62 = 11284673357060483641065406171245055689125329700802610659045727_<62>
P100 = 7943150153899727308211547689503218266715542847275764169224019083630803802075842027404310615659484239_<100>

N=89635854912843133047377276427170795358631018925432063304303551079726674670973827431931933014153835794202245565283120853861244899792595963890869576186164736796753 ( 161 digits) SNFS difficulty: 175 digits. Divisors found: r1=11284673357060483641065406171245055689125329700802610659045727 (pp62) r2=7943150153899727308211547689503218266715542847275764169224019083630803802075842027404310615659484239 (pp100) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 154.34 hours. Scaled time: 221.02 units (timescale=1.432). Factorization parameters were as follows: n: 89635854912843133047377276427170795358631018925432063304303551079726674670973827431931933014153835794202245565283120853861244899792595963890869576186164736796753 m: 100000000000000000000000000000000000 c5: 1 c0: 70 skew: 2.34 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, 11200001) Primes: RFBsize:501962, AFBsize:503466, largePrimes:6481592 encountered Relations: rels:6948668, finalFF:1144792 Max relations in full relation-set: 28 Initial matrix: 1005492 x 1144792 with sparse part having weight 69603650. Pruned matrix : 885359 x 890450 with weight 52443459. Total sieving time: 148.66 hours. Total relation processing time: 0.12 hours. Matrix solve time: 5.17 hours. Time per square root: 0.39 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: 154.34 hours.
Jul 17, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(5·10¹⁶⁸+13)/9 = (5)₁₆₇7_<168> = 2193410005059955014607_<22> · C147
C147 = P66 · P82
P66 = 211201992164536130541235848631497798541612474874808458918779453283_<66>
P82 = 1199249826735630800334398062812385809281436836301713944282871073656817271907107897_<82>

Number: n N=253283952509540008450507359677177401846286089874624769147262785793068091845083311740268079983995444677484848230048759659916753262836974367351875851 ( 147 digits) SNFS difficulty: 169 digits. Divisors found: Thu Jul 17 22:16:48 2008 prp66 factor: 211201992164536130541235848631497798541612474874808458918779453283 Thu Jul 17 22:16:48 2008 prp82 factor: 1199249826735630800334398062812385809281436836301713944282871073656817271907107897 Thu Jul 17 22:16:48 2008 elapsed time 02:04:27 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 42.01 hours. Scaled time: 76.83 units (timescale=1.829). Factorization parameters were as follows: name: KA_5_167_7 n: 253283952509540008450507359677177401846286089874624769147262785793068091845083311740268079983995444677484848230048759659916753262836974367351875851 skew: 1.52 deg: 5 c5: 8 c0: 65 m: 5000000000000000000000000000000000 type: snfs rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2700001) Primes: RFBsize:399993, AFBsize:399999, largePrimes:9791480 encountered Relations: rels:9307871, finalFF:813987 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 41.76 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,169,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,50,50,2.5,2.5,100000 total time: 42.01 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 17, 2008 (2nd): By Robert Backstrom / GMP-ECM
(4·10¹⁶⁹+11)/3 = 1(3)₁₆₈7_<170> = 3398633569951_<13> · C157
C157 = P30 · P128
P30 = 243693271397142150776644064113_<30>
P128 = 16098701792205555493787516689184765943671906327794613923990682608079019066384014799429979843106295062079900053829846688958148599_<128>
Jul 17, 2008: By Serge Batalov / GMP-ECM, Msieve
9·10¹⁹⁹-7 = 8(9)₁₉₈3_<200> = 31 · 743 · 6841 · 12697 · 316339 · 413089877 · 107105780766623_<15> · 13919023264892149_<17> · 19620579832179617602901623499857_<32> · C113
C113 = P37 · P76
P37 = 6427503805579223317744356595461437807_<37>
P76 = 1831041340434809452833718361805463604259680227651236173580827772015915361667_<76>

Number: 89993_199 N=11769025183817619952672417054651487669578574210254607906854183871505045045861473013946425938221361597450232344269 ( 113 digits) Divisors found: r1=6427503805579223317744356595461437807 r2=1831041340434809452833718361805463604259680227651236173580827772015915361667 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: name: 89993_199 n: 11769025183817619952672417054651487669578574210254607906854183871505045045861473013946425938221361597450232344269 skew: 53840.95 # norm 3.64e+15 c5: 8880 c4: -1129742670 c3: -155660144868577 c2: 2381642608767554524 c1: 137513208798163850234032 c0: -2172126232263059673608813344 # alpha -6.03 Y1: 231688360871 Y0: -4211784220495418937693 # Murphy_E 7.67e-10 # M 7420350881970755408277194183514819226857195980988978384894736154280999709633602187020363784915146259202193086546 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3650001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 7928000 relations Max relations in full relation-set: Initial matrix: Pruned matrix : 463893 x 464136 Total sieving time: 11.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.75 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 12.00 hours.
(22·10¹⁸³-13)/9 = 2(4)₁₈₂3_<184> = 7 · 74821 · 3777824523836434735369063990067_<31> · C148
C148 = P30 · P54 · P64
P30 = 233948542471655416966539695957_<30>
P54 = 728025222965584731793931788563408594665953022055106061_<54>
P64 = 7253541024316580869418663127314988483163280924756047872134021891_<64>

#-- first, by ECM -- Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=369411570 Step 1 took 18298ms Step 2 took 14326ms ********** Factor found in step 2: 233948542471655416966539695957 Found probable prime factor of 30 digits: 233948542471655416966539695957 Composite cofactor 5280760821518094650260482230697796599116648705786845313167148884685871265840183994032230085997595905486342212500781351 has 118 digits #--then by Msieve (gnfs,118) Number: 24443_183 N=5280760821518094650260482230697796599116648705786845313167148884685871265840183994032230085997595905486342212500781351 ( 118 digits) Divisors found: r1=728025222965584731793931788563408594665953022055106061 r2=7253541024316580869418663127314988483163280924756047872134021891 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: name: 24443_183 n: 5280760821518094650260482230697796599116648705786845313167148884685871265840183994032230085997595905486342212500781351 skew: 37599.46 # norm 2.85e+16 c5: 114720 c4: -19508028470 c3: -143899311857623 c2: 42457844710427220106 c1: 763166056347895704407064 c0: -45130489940034694521668160 # alpha -6.40 Y1: 7577882143777 Y0: -34089038769616882470619 # Murphy_E 3.93e-10 # M 2727036486374593181091379991914029708867927407917977652616807660464128792055469928307341336543407724973003349846889828 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3950001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 8162000 relations Max relations in full relation-set: Initial matrix: Pruned matrix : 569973 x 570212 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000 total time: 27.00 hours.
(4·10¹⁹⁸-13)/9 = (4)₁₉₇3_<198> = 523 · 82737301 · 22861189383523_<14> · C174
C174 = P30 · C145
P30 = 109004345405742704229513258503_<30>
C145 = [4121656653229606688891632821619209502441186611362878540444545066393408185585679257868260089902556418333145433375944552756831904252394732003086489_<145>]
(43·10¹⁹⁴-7)/9 = 4(7)₁₉₄_<195> = 3 · 89 · 107 · 38917751 · 109329978532264895118221121359_<30> · C154
C154 = P32 · C123
P32 = 27984220393915439255871446690087_<32>
C123 = [140452895460755142568169629971827239108134551763753952081688857640992802509386073644380889037709828929708318820579567399351_<123>]
(34·10¹⁹³-43)/9 = 3(7)₁₉₂3_<194> = 3³ · 11 · 19² · 79 · 661 · 33889871 · 206690543 · 93566161264769_<14> · C155
C155 = P30 · C125
P30 = 219952497998232711504934775239_<30>
C125 = [46806479030908156153665353632537735280964258077511172703126540334606775972905563382609259392230247331755789931137661196139137_<125>]
10¹⁹¹-3 = (9)₁₉₀7_<191> = 113 · 2454455881_<10> · 13778267355178489115141197_<26> · C155
C155 = P40 · P115
P40 = 4177672914958740985247164938293269252349_<40>
P115 = 6263791373890807735811613899906525630519387461611911965595048014000039506928204827175275652877326155130619692271533_<115>
Jul 16, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(22·10¹⁶⁸+23)/9 = 2(4)₁₆₇7_<169> = 4543813 · 1878087349_<10> · C153
C153 = P36 · P47 · P72
P36 = 157077838092449523332749097610339671_<36>
P47 = 12314963809991883286233006440538730997310281149_<47>
P72 = 148079820454272076138749463653539263120184911826609262340495505792576389_<72>

Number: n N=1823597629884456456024969058909706258632372020265790999907676961582423394895913928332215564831650488011286590649190961 ( 118 digits) Divisors found: Wed Jul 16 03:18:19 2008 prp47 factor: 12314963809991883286233006440538730997310281149 Wed Jul 16 03:18:19 2008 prp72 factor: 148079820454272076138749463653539263120184911826609262340495505792576389 Wed Jul 16 03:18:19 2008 elapsed time 04:29:31 (Msieve 1.36, Dep=6) Version: GGNFS-0.77.1-20051202-athlon Total time: 51.39 hours. Scaled time: 90.04 units (timescale=1.752). Factorization parameters were as follows: name: KA_2_4_167_7 n: 1823597629884456456024969058909706258632372020265790999907676961582423394895913928332215564831650488011286590649190961 skew: 48983.94 # norm 6.46e+15 c5: 50040 c4: 3600602710 c3: -376262433842969 c2: -8229887425109787560 c1: 404072477709485347899232 c0: 2578150019307161193042749712 # alpha -5.44 Y1: 2056468829983 Y0: -32532837847316073020785 # Murphy_E 3.87e-10 # M 74352331651996214033401096617626779374954279297543952462796538594023349857190087022767517996283017661881645908058429 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 2300000) Primes: RFBsize:315948, AFBsize:315738, largePrimes:9457688 encountered Relations: rels:8737174, finalFF:664621 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 51.02 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,50,50,2.5,2.5,60000 total time: 51.39 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(83·10¹⁶⁸+61)/9 = 9(2)₁₆₇9_<169> = 5381 · 36173552095222639_<17> · C149
C149 = P39 · P111
P39 = 106355916117472562674540821070957317439_<39>
P111 = 445471353245345900119817406448596918723980474959155182424548921066868827075147451237495128565791226177408521729_<111>
2·10¹⁶⁸-7 = 1(9)₁₆₇3_<169> = 8002843 · 679331923056720559092781_<24> · C138
C138 = P55 · P84
P55 = 1743135735135318112931632042583008770405177795897939247_<55>
P84 = 211043737325077621766641712794419286115201489247799793695341755432378145694998105193_<84>

Number: n N=367877880207854154431115542622985059730951001687730951844231434351077499649003285665322749166951767834677806526397408965900679678429209671 ( 138 digits) SNFS difficulty: 168 digits. Divisors found: Wed Jul 16 17:57:06 2008 prp55 factor: 1743135735135318112931632042583008770405177795897939247 Wed Jul 16 17:57:06 2008 prp84 factor: 211043737325077621766641712794419286115201489247799793695341755432378145694998105193 Wed Jul 16 17:57:06 2008 elapsed time 02:13:52 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 53.77 hours. Scaled time: 98.35 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_9_167_3 n: 367877880207854154431115542622985059730951001687730951844231434351077499649003285665322749166951767834677806526397408965900679678429209671 skew: 0.65 deg: 5 c5: 125 c0: -14 m: 2000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 3400000) Primes: RFBsize:380800, AFBsize:381052, largePrimes:10127809 encountered Relations: rels:9638577, finalFF:794819 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 53.49 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,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,50,50,2.5,2.5,100000 total time: 53.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 15, 2008 (4th): By suberi / GMP-ECM
(4·10²¹³-1)/3 = 1(3)₂₁₃_<214> = 31 · 43 · 42929 · 1647001 · 55070453 · 109103879 · 315971342878788876787_<21> · C163
C163 = P34 · C130
P34 = 2472176201488989163470538770710003_<34>
C130 = [3014241151258482250646629430943474307709267290595380818070266010335607748326473373305206926053831950374530423789611599608439806667_<130>]
Jul 15, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(22·10¹⁵⁶+23)/9 = 2(4)₁₅₅7_<157> = 4547 · 10601 · 817603 · 2219635954465259223327708947_<28> · C116
C116 = P54 · P63
P54 = 140350244666350609226894618859195516341027638500563633_<54>
P63 = 199099872181567014671579008715002480094143366187033872354713317_<63>

Number: n N=27943715773722063936691722152698523908458765196954280032157968841627837312957044871581762548438985303588808631000661 ( 116 digits) Divisors found: Tue Jul 15 16:08:22 2008 prp54 factor: 140350244666350609226894618859195516341027638500563633 Tue Jul 15 16:08:22 2008 prp63 factor: 199099872181567014671579008715002480094143366187033872354713317 Tue Jul 15 16:08:22 2008 elapsed time 01:31:56 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 42.90 hours. Scaled time: 56.33 units (timescale=1.313). Factorization parameters were as follows: name: n n: 27943715773722063936691722152698523908458765196954280032157968841627837312957044871581762548438985303588808631000661 skew: 47568.43 # norm 1.44e+16 c5: 44160 c4: 4908212444 c3: -559428385396405 c2: -8122621523859034918 c1: 191177662074665609611144 c0: -1057339503448102257405097600 # alpha -6.06 Y1: 3013035451613 Y0: -14462687652541172636637 # Murphy_E 4.75e-10 # M 13749798645903224652008884833430320114302017669267970026189959974505191987149920357678449950213629431261078728068770 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 1799990) Primes: RFBsize:315948, AFBsize:315778, largePrimes:9341040 encountered Relations: rels:8769691, finalFF:762080 Max relations in full relation-set: 28 Initial matrix: 631808 x 762080 with sparse part having weight 45124286. Pruned matrix : Total sieving time: 42.50 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,50,50,2.5,2.5,60000 total time: 42.90 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(22·10¹⁶¹+23)/9 = 2(4)₁₆₀7_<162> = 7² · 73795848330403_<14> · 107546926227583_<15> · C132
C132 = P52 · P81
P52 = 1502437621398893305826089711439184886680078009309919_<52>
P81 = 418367277957308925333921233455513317862150641697102827631297773846327424699635013_<81>

Number: n N=628570737965308867894616758650083694072525682923772825126976449775573725741245698307743195957424393590240832150518669803215300593947 ( 132 digits) SNFS difficulty: 162 digits. Divisors found: Tue Jul 15 18:20:17 2008 prp52 factor: 1502437621398893305826089711439184886680078009309919 Tue Jul 15 18:20:17 2008 prp81 factor: 418367277957308925333921233455513317862150641697102827631297773846327424699635013 Tue Jul 15 18:20:17 2008 elapsed time 01:38:49 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 47.99 hours. Scaled time: 69.73 units (timescale=1.453). Factorization parameters were as follows: name: KA_2_4_160_7 n: 628570737965308867894616758650083694072525682923772825126976449775573725741245698307743195957424393590240832150518669803215300593947 skew: 0.64 deg: 5 c5: 220 c0: 23 m: 100000000000000000000000000000000 type: snfs rlim: 4400000 alim: 4400000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2300001) Primes: RFBsize:309335, AFBsize:309159, largePrimes:7452388 encountered Relations: rels:6986017, finalFF:643203 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 47.75 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,162,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,48,48,2.5,2.5,100000 total time: 47.99 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Jul 15, 2008 (2nd): By Jo Yeong Uk / GGNFS
(13·10¹⁹¹+41)/9 = 1(4)₁₉₀9_<192> = C192
C192 = P51 · P141
P51 = 497657554076973302518779613306102473057258401585609_<51>
P141 = 290248672528143811855534364536737651221044179346938023837658334270944573019672423163353331467770581052482338681134129509473272799800519044761_<141>

Number: 14449_191 N=144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 ( 192 digits) SNFS difficulty: 192 digits. Divisors found: r1=497657554076973302518779613306102473057258401585609 (pp51) r2=290248672528143811855534364536737651221044179346938023837658334270944573019672423163353331467770581052482338681134129509473272799800519044761 (pp141) Version: GGNFS-0.77.1-20050930-nocona Total time: 592.51 hours. Scaled time: 1409.59 units (timescale=2.379). Factorization parameters were as follows: n: 144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 m: 100000000000000000000000000000000000000 c5: 130 c0: 41 skew: 0.79 type: snfs Factor base limits: 16000000/16000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved algebraic special-q in [8000000, 18100001) Primes: RFBsize:1031130, AFBsize:1029654, largePrimes:14861895 encountered Relations: rels:16051847, finalFF:2329705 Max relations in full relation-set: 28 Initial matrix: 2060851 x 2329705 with sparse part having weight 193127240. Pruned matrix : 1827746 x 1838114 with weight 151862872. Total sieving time: 552.20 hours. Total relation processing time: 0.44 hours. Matrix solve time: 39.65 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,192,5,0,0,0,0,0,0,0,0,16000000,16000000,28,28,52,52,2.6,2.6,100000 total time: 592.51 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: 8047052k/8912896k available (2459k kernel code, 339236k reserved, 1247k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.23 BogoMIPS (lpj=2672116) Calibrating delay using timer specific routine.. 5589.60 BogoMIPS (lpj=2794804)
Jul 15, 2008: By Serge Batalov / Msieve
(22·10¹⁷⁶+23)/9 = 2(4)₁₇₅7_<177> = 13 · 1109 · 2083 · 12637 · 2201791629722900115084517_<25> · 98202646709372914952284004731_<29> · C112
C112 = P33 · P80
P33 = 263918040926244833932442223532777_<33>
P80 = 11287649866483430593118539466784682520308464734220950406084876622638519492533399_<80>

Number: 24447_176 N=2979014439423696070680381230689894498227059660077707317426808607490416509659199184543278457103523964979443719023 ( 112 digits) Divisors found: r1=263918040926244833932442223532777 r2=11287649866483430593118539466784682520308464734220950406084876622638519492533399 Version: Msieve 1.36 Factorization parameters were as follows: name: 24447_176 n: 2979014439423696070680381230689894498227059660077707317426808607490416509659199184543278457103523964979443719023 skew: 43254.19 # norm 3.04e+15 c5: 3840 c4: 2706565576 c3: 2492910207212 c2: -5833440226913678650 c1: -98011231431123673328307 c0: -232632515522583734331555306 # alpha -6.06 Y1: 643298896207 Y0: -3783884480249237801755 # Murphy_E 8.01e-10 # M 1300968512421426024764568100635526414813480594650460600267126043707504036536817791911229599377015845824674248517 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3250001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 430899 x 431147 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 15.00 hours.
Jul 14, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
(7·10¹⁶⁷-61)/9 = (7)₁₆₆1_<167> = 114807751 · 3626102422772747707_<19> · C141
C141 = P57 · P84
P57 = 823035057767144134239967477480765928602729472785254183529_<57>
P84 = 227000032497982054005520830210122515119411890431796815636671279518904326397745213007_<84>

Number: n N=186828984860120255606519839560874657226518689870717896574431922306201449144447043355099889582452640081134312356077616468363781250379975961703 ( 141 digits) SNFS difficulty: 167 digits. Divisors found: Mon Jul 14 15:50:30 2008 prp57 factor: 823035057767144134239967477480765928602729472785254183529 Mon Jul 14 15:50:30 2008 prp84 factor: 227000032497982054005520830210122515119411890431796815636671279518904326397745213007 Mon Jul 14 15:50:30 2008 elapsed time 01:51:25 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 69.67 hours. Scaled time: 126.80 units (timescale=1.820). Factorization parameters were as follows: name: KA_7_166_1 n: 186828984860120255606519839560874657226518689870717896574431922306201449144447043355099889582452640081134312356077616468363781250379975961703 skew: 0.61 deg: 5 c5: 700 c0: -61 m: 1000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4300001) Primes: RFBsize:380800, AFBsize:380053, largePrimes:8163761 encountered Relations: rels:7710086, finalFF:765959 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 69.35 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,167,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 69.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 14, 2008 (3rd): By matsui / GGNFS
4·10¹⁷⁴+1 = 4(0)₁₇₃1_<175> = 21669802129_<11> · C165
C165 = P47 · P118
P47 = 90895849637269554525310385291775885388075787009_<47>
P118 = 2030771183197325350577624750920707697746469994254856700264575730266390155389375430973873995208761043763694185654787441_<118>

N=184588672115604069528972854978670396146283150031988000899756623707562973659121407660916256260292684834971895741761989764036760485363820924070607603839279154684153969 ( 165 digits) SNFS difficulty: 175 digits. Divisors found: r1=90895849637269554525310385291775885388075787009 (pp47) r2=2030771183197325350577624750920707697746469994254856700264575730266390155389375430973873995208761043763694185654787441 (pp118) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 105.95 hours. Scaled time: 151.40 units (timescale=1.429). Factorization parameters were as follows: n: 184588672115604069528972854978670396146283150031988000899756623707562973659121407660916256260292684834971895741761989764036760485363820924070607603839279154684153969 m: 100000000000000000000000000000000000 c5: 2 c0: 5 skew: 1.2 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, 10400001) Primes: RFBsize:501962, AFBsize:501861, largePrimes:6413242 encountered Relations: rels:6884769, finalFF:1153553 Max relations in full relation-set: 28 Initial matrix: 1003888 x 1153553 with sparse part having weight 68214227. Pruned matrix : 873507 x 878590 with weight 50441029. Total sieving time: 101.00 hours. Total relation processing time: 0.12 hours. Matrix solve time: 4.44 hours. Time per square root: 0.39 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: 105.95 hours.
Jul 14, 2008 (2nd): By Sinkiti Sibata / GGNFS
(22·10¹⁵¹+23)/9 = 2(4)₁₅₀7_<152> = 3 · 97 · 8834843 · 18558168955073395708146667411_<29> · C114
C114 = P53 · P61
P53 = 70985983835086576997852624750687510213827313422930409_<53>
P61 = 7217397353726318978026298518599642790594988964775374257181581_<61>

Number: 24447_151 N=512334051883013116583423649922513914567713078285125905872387242449953931012240050043094620958754046039730239596629 ( 114 digits) Divisors found: r1=70985983835086576997852624750687510213827313422930409 (pp53) r2=7217397353726318978026298518599642790594988964775374257181581 (pp61) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 59.21 hours. Scaled time: 28.00 units (timescale=0.473). Factorization parameters were as follows: name: 24447_151 n: 512334051883013116583423649922513914567713078285125905872387242449953931012240050043094620958754046039730239596629 skew: 58934.48 # norm 1.67e+16 c5: 39240 c4: 2548362158 c3: -848790397397041 c2: -7561237389283676814 c1: 1098028132791631657707704 c0: -101853278834969772710102272 # alpha -6.65 Y1: 698620596401 Y0: -6655248136878522324179 # Murphy_E 5.69e-10 # M 411099533570434247334050740846394508864406295354105061320770663934783270735188517730048665882061695384371932235740 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2950001) Primes: RFBsize:250150, AFBsize:249615, largePrimes:7495265 encountered Relations: rels:7340500, finalFF:563249 Max relations in full relation-set: 28 Initial matrix: 499845 x 563249 with sparse part having weight 48058090. Pruned matrix : 449089 x 451652 with weight 33803649. Total sieving time: 50.37 hours. Total relation processing time: 0.55 hours. Matrix solve time: 7.94 hours. Time per square root: 0.35 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 59.21 hours. --------- CPU info (if available) ----------
Jul 14, 2008: By Serge Batalov / GMP-ECM, Msieve
(2·10¹⁹²+1)/3 = (6)₁₉₁7_<192> = 22441 · 437977 · 48109987 · 1526524747081880791478251001_<28> · C147
C147 = P38 · P45 · P66
P38 = 11948477248990278755249447965289499937_<38>
P45 = 166390757028721578564820877464821642636142609_<45>
P66 = 464552052602373136402651573347040115738820665732325211913648101361_<66>

# first, by ECM Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3529291452 Step 1 took 5972ms Step 2 took 5538ms ********** Factor found in step 2: 11948477248990278755249447965289499937 Found probable prime factor of 38 digits: 11948477248990278755249447965289499937 Composite cofactor 77297167711755354438769313097704800502672814513221504344872692101599293570057314899883042225028440669682990849 has 110 digits # then by Msieve/gnfs,110 Number: 66667_192 N=77297167711755354438769313097704800502672814513221504344872692101599293570057314899883042225028440669682990849 ( 110 digits) Divisors found: r1=166390757028721578564820877464821642636142609 r2=464552052602373136402651573347040115738820665732325211913648101361 Factorization parameters were as follows: name: 66667_192 n: 77297167711755354438769313097704800502672814513221504344872692101599293570057314899883042225028440669682990849 skew: 10017.40 # norm 6.40e+14 c5: 74880 c4: 2885407200 c3: 17695074766288 c2: -253585168675014076 c1: 568043165283630402721 c0: -813150504652600490326365 # alpha -5.61 Y1: 345585391877 Y0: -1006371663273310375634 # Murphy_E 1.14e-09 # M 31155127991704449356442579169587931086327302371789743816853144263449870130460753713703574862673252103015339066 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, 2900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 369426 x 369674 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 11.00 hours.
5·10¹⁹⁹-3 = 4(9)₁₉₈7_<200> = 219619 · 3639959 · 4744042763965047965693_<22> · C167
C167 = P31 · P136
P31 = 8093176768651631185069802113901_<31>
P136 = 1629055878393401770330660883294105510464026569183051106513390639156296434054875594593755637398223572917720059576936252313923440973374849_<136>
(8·10¹⁷⁴-71)/9 = (8)₁₇₃1_<174> = 7 · 53 · 12101 · C168
C168 = P28 · C141
P28 = 1939607078801257064760060301_<28>
C141 = [102079502915150872449364582616265150010758333661353575581993053425424847966829582828720569749338022010525015105109233120216741718055475742411_<141>]
(2·10¹⁸⁸+7)/9 = (2)₁₈₇3_<188> = 113 · 587 · 2659 · 1864630093819_<13> · C167
C167 = P33 · P135
P33 = 112654204167499843146979520977037_<33>
P135 = 599808355233464006448212960910397629581245269600833415238862953159561681692737075144423658619895686481443976435337829801517842607704129_<135>
(19·10¹⁹⁵+17)/9 = 2(1)₁₉₄3_<196> = 59 · 1267577 · 158612774241033861923_<21> · C168
C168 = P39 · P129
P39 = 282503324001414019100503379652927974071_<39>
P129 = 629974551490611084435937066618096229596276276489387128835727689298806791822488193421449041113663483875019510871892831411163366727_<129>
(32·10¹⁹⁵-23)/9 = 3(5)₁₉₄3_<196> = 11 · 17 · 1019 · 11597 · 67829 · 244979073043_<12> · C170
C170 = P33 · C138
P33 = 103006187361337566011944121049239_<33>
C138 = [940022626361736428027252898323336782308056104327236273583195401942375080676203948933037333853780425271367083459258236281339248935045206101_<138>]
Jul 13, 2008 (4th): By Sinkiti Sibata / GGNFS
(22·10¹⁵⁴+23)/9 = 2(4)₁₅₃7_<155> = 3² · 1613 · 6144493 · 85808033 · 26756289861065329_<17> · C120
C120 = P58 · P62
P58 = 1798409594124660216759258210120687655281031358400703839301_<58>
P62 = 66370454423809885762078346386195882275783383739027815254557491_<62>

Number: 24447_154 N=119361262002193195821448307853344484885855650684642416843797966406457642714370053703754405333884430590534099281529753791 ( 120 digits) Divisors found: r1=1798409594124660216759258210120687655281031358400703839301 (pp58) r2=66370454423809885762078346386195882275783383739027815254557491 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 70.89 hours. Scaled time: 55.58 units (timescale=0.784). Factorization parameters were as follows: name: 24447_154 n: 119361262002193195821448307853344484885855650684642416843797966406457642714370053703754405333884430590534099281529753791 skew: 60960.40 # norm 1.84e+16 c5: 47940 c4: 5307530782 c3: -625612329042056 c2: -16268669865623770227 c1: 204342567025062309743036 c0: 8794015424991234094426300580 # alpha -5.74 Y1: 5404961881777 Y0: -75723797960330337216429 # Murphy_E 3.09e-10 # M 75322734279060307587904586726507012317372125376889169597155511412590324434436033530464569542901548305306847769101384234 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4350001) Primes: RFBsize:315948, AFBsize:316629, largePrimes:7720056 encountered Relations: rels:7821817, finalFF:759929 Max relations in full relation-set: 28 Initial matrix: 632662 x 759929 with sparse part having weight 66754450. Pruned matrix : 529324 x 532551 with weight 43939785. Total sieving time: 66.31 hours. Total relation processing time: 0.50 hours. Matrix solve time: 3.68 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 70.89 hours. --------- CPU info (if available) ----------
Jul 13, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
4·10¹⁶⁸+7 = 4(0)₁₆₇7_<169> = 11² · 2618693672249983639196789_<25> · C143
C143 = P63 · P80
P63 = 434600913422969283935715734532476163912699428553621729133663787_<63>
P80 = 29046866416543146278620690212890391220410722501413452500320961183706650069675369_<80>

Number: n N=12623794676704621965362748212067023827563490650371887005640338255443815536512266154311383935241401663051630078521097059654813799889624681162403 ( 143 digits) SNFS difficulty: 168 digits. Divisors found: Sun Jul 13 16:29:05 2008 prp63 factor: 434600913422969283935715734532476163912699428553621729133663787 Sun Jul 13 16:29:05 2008 prp80 factor: 29046866416543146278620690212890391220410722501413452500320961183706650069675369 Sun Jul 13 16:29:05 2008 elapsed time 01:05:28 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 47.09 hours. Scaled time: 86.36 units (timescale=1.834). Factorization parameters were as follows: name: KA_4_0_167_7 n: 12623794676704621965362748212067023827563490650371887005640338255443815536512266154311383935241401663051630078521097059654813799889624681162403 skew: 0.56 deg: 5 c5: 125 c0: 7 m: 2000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2900000) Primes: RFBsize:380800, AFBsize:380502, largePrimes:7959970 encountered Relations: rels:7657643, finalFF:861422 Max relations in full relation-set: 28 Initial matrix: 761367 x 861422 with sparse part having weight 40728051. Pruned matrix : Total sieving time: 46.84 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,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 47.09 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 13, 2008 (2nd): By Serge Batalov / GMP-ECM
7·10¹⁸³+9 = 7(0)₁₈₂9_<184> = 79 · 69172788077_<11> · C172
C172 = P30 · C142
P30 = 133818982259225767835521221337_<30>
C142 = [9572336242243985044301236538042107107618534026530064456879616370843986823511954236728268510314492217680175701229960850902545463856024173108379_<142>]
9·10¹⁹⁹-7 = 8(9)₁₉₈3_<200> = 31 · 743 · 6841 · 12697 · 316339 · 413089877 · 107105780766623_<15> · 13919023264892149_<17> · C144
C144 = P32 · C113
P32 = 19620579832179617602901623499857_<32>
C113 = [11769025183817619952672417054651487669578574210254607906854183871505045045861473013946425938221361597450232344269_<113>]
6·10¹⁹⁴+1 = 6(0)₁₉₃1_<195> = 153817 · 33881245227068299278185531_<26> · C165
C165 = P33 · C132
P33 = 901361069267656452128353133474957_<33>
C132 = [127728776954149061732629779151943546510736581677373866290113899810994265965188567884730521444012921154476658141238516044262272295959_<132>]
Jul 13, 2008: By Robert Backstrom / GGNFS, Msieve
(19·10¹⁶³+71)/9 = 2(1)₁₆₂9_<164> = 53 · 62755516806818389237490084489_<29> · C133
C133 = P67 · P67
P67 = 1702357182418622530789291597341299637631432288875092672261013494321_<67>
P67 = 3728486921641779431391217242278242452352917616981245286538949510667_<67>

Number: n N=6347216490610783077441171781434338047436822507152466738398464557918916343716774041846421465798549105708434295220219648071786733422107 ( 133 digits) SNFS difficulty: 164 digits. Divisors found: Sun Jul 13 04:05:21 2008 prp67 factor: 1702357182418622530789291597341299637631432288875092672261013494321 Sun Jul 13 04:05:21 2008 prp67 factor: 3728486921641779431391217242278242452352917616981245286538949510667 Sun Jul 13 04:05:21 2008 elapsed time 02:59:59 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 86.99 hours. Scaled time: 113.78 units (timescale=1.308). Factorization parameters were as follows: name: KA_2_1_162_9 n: 6347216490610783077441171781434338047436822507152466738398464557918916343716774041846421465798549105708434295220219648071786733422107 skew: 0.33 deg: 5 c5: 19000 c0: 71 m: 100000000000000000000000000000000 type: snfs rlim: 4600000 alim: 4600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5700001) Primes: RFBsize:322441, AFBsize:322667, largePrimes:8115761 encountered Relations: rels:7560077, finalFF:650072 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 86.72 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,48,48,2.5,2.5,100000 total time: 86.99 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 12, 2008 (2nd): By Serge Batalov / GMP-ECM, pol51, Msieve
(17·10¹⁹⁸-53)/9 = 1(8)₁₉₇3_<199> = 7603 · 30803 · 43261 · 102559 · 1042469 · 2250737867569_<13> · 1941823279749679397_<19> · C144
C144 = P36 · P38 · P71
P36 = 532909957499658687338853693037114127_<36>
P38 = 12127492055545606309658842712355349019_<38>
P71 = 61735571024736893980769353536098228900774070762653834895799357457201053_<71>

# by ECM -- Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=323913398 Step 1 took 6878ms Step 2 took 5269ms ********** Factor found in step 2: 12127492055545606309658842712355349019 Found probable prime factor of 38 digits: 12127492055545606309658842712355349019 Composite cofactor 32899500531009698487939962220216476251136087124144340859751512031161508952739461583756806371723685945575731 has 107 digits # # then by GNFS/Msieve # Number: 18883_198 N=32899500531009698487939962220216476251136087124144340859751512031161508952739461583756806371723685945575731 ( 107 digits) Divisors found: r1=532909957499658687338853693037114127 r2=61735571024736893980769353536098228900774070762653834895799357457201053 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: name: 18883_198 n: 32899500531009698487939962220216476251136087124144340859751512031161508952739461583756806371723685945575731 skew: 44376.14 # norm 8.55e+14 c5: 8100 c4: -489452472 c3: -48951202463129 c2: 862613667364327251 c1: 36219942136802215898001 c0: -363404921018249872201819607 # alpha -5.93 Y1: 88261732339 Y0: -332462181768746779864 # Murphy_E 1.37e-09 # M 18483838965041290916740587464894868353558034896369087202581405858735878552821000366540532693858814885993829 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 310515 x 310763 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 6.00 hours.
(22·10¹⁷⁸+23)/9 = 2(4)₁₇₇7_<179> = 3 · 9511 · 7058628672138574632984994873_<28> · C147
C147 = P30 · P50 · P67
P30 = 407818136912747014681334981443_<30>
P50 = 75160945043175857866901963484673054341461063508311_<50>
P67 = 3959621107875479961537988501024588458702472685250586541345053347871_<67>

# by ECM -- # Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=430382 Step 1 took 20824ms Step 2 took 15058ms ********** Factor found in step 2: 407818136912747014681334981443 Found probable prime factor of 30 digits: 407818136912747014681334981443 Composite cofactor 297608864480828054398175478834481222993428795506090706648602298717700679595827000206738339572148229407385859182655881 has 117 digits # # then by GNFS/Msieve # Number: 24447_178 N=297608864480828054398175478834481222993428795506090706648602298717700679595827000206738339572148229407385859182655881 ( 117 digits) Divisors found: r1=75160945043175857866901963484673054341461063508311 r2=3959621107875479961537988501024588458702472685250586541345053347871 Factorization parameters were as follows: name: 24447_178 n: 297608864480828054398175478834481222993428795506090706648602298717700679595827000206738339572148229407385859182655881 skew: 56866.92 # norm 3.03e+16 c5: 11760 c4: 58587242 c3: -948018741867885 c2: 5359060334242097837 c1: 500754803694110056951611 c0: -3720239981301914611368153205 # alpha -6.05 Y1: 3414751932097 Y0: -30244587069795188032038 # Murphy_E 4.18e-10 # M 109539901323225467029707024396066592108219284886924732442320854580487753105415174514190809144234342576834319914949849 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3850001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 570807 x 571055 Total sieving time: 15.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 01:14:42 Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.5,2.5,100000 total time: 17.00 hours.
Jul 12, 2008: By Serge Batalov / GMP-ECM
(2·10¹⁸⁰+7)/9 = (2)₁₇₉3_<180> = 71 · 3581374329011_<13> · C165
C165 = P42 · P124
P42 = 282287262952400056073198405956934109921109_<42>
P124 = 3095908655365249055568580267803159689569266960813853471093469310442231639214617495399521734305189014030222056875561596808087_<124>
6·10¹⁸⁹+7 = 6(0)₁₈₈7_<190> = 6209183697097282695749827_<25> · C165
C165 = P29 · C137
P29 = 84650755361806968467920668269_<29>
C137 = [11415262534024941376215177642404391202003957780146884337777704466878931859742980790987063731573828128798768767273676353885360988327570689_<137>]
(4·10¹⁷⁴+41)/9 = (4)₁₇₃9_<174> = 401 · 1531 · 2333 · C165
C165 = P32 · C134
P32 = 11103172231868232665208082632227_<32>
C134 = [27947058444735539012965143631675640717984624676970856746909322865014587987121750699821648616857592608427104241739512228516510591633269_<134>]
(8·10¹⁹⁸-17)/9 = (8)₁₉₇7_<198> = 29 · 2551 · 26987713 · 24810652678294736989_<20> · C167
C167 = P30 · C138
P30 = 122763886401873301220354203087_<30>
C138 = [146171976769747747349388334776423064471607044898176691920488992333574187962280014690489994846698316344610133907207472343085837277045010167_<138>]
(4·10¹⁹¹-7)/3 = 1(3)₁₉₀1_<192> = 11 · 8111 · 22485379500775341739_<20> · C167
C167 = P32 · P136
P32 = 17187029396452962451764372549233_<32>
P136 = 3866968269055691419473815558756213198307575801275502239579209994484850503385131935406232395834688131221430324342382120842650685242448053_<136>
(14·10¹⁹⁶-41)/9 = 1(5)₁₉₅1_<197> = 43 · 12991941439670998826484083573_<29> · C167
C167 = P32 · C135
P32 = 31549870079323557671928299889097_<32>
C135 = [882562440577446030345916906651940795515837407245481246517202735480841275954656517617252892526279545364367486770393761420751543094322497_<135>]
(4·10¹⁹⁹-13)/9 = (4)₁₉₈3_<199> = 3 · 97 · 107 · 175859 · 682417 · 130656152593_<12> · C172
C172 = P32 · P141
P32 = 21660553494232995120193600442447_<32>
P141 = 420268522590178138077849423985006098086889585395357247913022086632798078770561566068346842586303068386567989060067693212646894386791399439703_<141>
(7·10¹⁹²-61)/9 = (7)₁₉₁1_<192> = 3 · 313 · 761 · 9139826512344133_<16> · 358804313245062117504457_<24> · C147
C147 = P31 · P117
P31 = 2736444955335091738175869222951_<31>
P117 = 121289430700501471603498088503911465819708333729664041167291526413944869019180851149006200154305108790796966792303979_<117>
(17·10¹⁹⁷-53)/9 = 1(8)₁₉₆3_<198> = 3 · 19 · 619 · 8581 · 20073649757649413_<17> · 5797970114799596368404037_<25> · C148
C148 = P31 · P118
P31 = 2604864000866961077367688444027_<31>
P118 = 2057859104406529255404097678068784747468733410880713070871039782861735411913581127133206348898129767928452882855107983_<118>
(5·10¹⁹⁷+31)/9 = (5)₁₉₆9_<197> = 7² · 43891 · 162829 · 81609246936439853_<17> · 42761497358777840501_<20> · C149
C149 = P27 · P122
P27 = 950049141625022318627404183_<27>
P122 = 47850429337345006784444707647769333495962030245726338067483271465533087330815675138269874797856518257348618342044284285431_<122>
Jul 11, 2008 (6th): By Sinkiti Sibata / GGNFS
5·10¹⁸⁰-7 = 4(9)₁₇₉3_<181> = 109 · 1488967 · 8420351363_<10> · 25030322608453531_<17> · 10767890436875898837091171_<26> · C122
C122 = P51 · P71
P51 = 139863195581166062045796944539175077355000899883699_<51>
P71 = 97057186527914640161646341782139678769623110723336236535802668798096963_<71>

Number: 49993_180 N=13574728261911441147955700905150374565535532034665629960565878514238403995814790116946394699688601479367104968379225106137 ( 122 digits) Divisors found: r1=139863195581166062045796944539175077355000899883699 (pp51) r2=97057186527914640161646341782139678769623110723336236535802668798096963 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 85.86 hours. Scaled time: 67.31 units (timescale=0.784). Factorization parameters were as follows: name: 49993_180 n: 13574728261911441147955700905150374565535532034665629960565878514238403995814790116946394699688601479367104968379225106137 skew: 77051.65 # norm 4.21e+16 c5: 34020 c4: -13370552037 c3: -806276712066080 c2: 43437997914285937766 c1: 379528431266404362894308 c0: 12554215439813951821136969239 # alpha -6.11 Y1: 2279412482303 Y0: -209025725432362513645620 # Murphy_E 2.48e-10 # M 12408996827428119508990999514464920706883057660258542158125313393200473585265399403708299436417097179742052149520854139575 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, 4960001) Primes: RFBsize:348513, AFBsize:348568, largePrimes:7707588 encountered Relations: rels:7855683, finalFF:809185 Max relations in full relation-set: 28 Initial matrix: 697159 x 809185 with sparse part having weight 68458102. Pruned matrix : 604522 x 608071 with weight 46617823. Total sieving time: 80.23 hours. Total relation processing time: 0.62 hours. Matrix solve time: 4.58 hours. Time per square root: 0.43 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 85.86 hours. --------- CPU info (if available) ----------
Jul 11, 2008 (5th): By Robert Backstrom / GGNFS, Msieve
(61·10¹⁶⁶-7)/9 = 6(7)₁₆₆_<167> = 67 · 367 · 18457172593_<11> · 59403451729_<11> · C142
C142 = P51 · P91
P51 = 571362150201701442101639602427041315624408776223453_<51>
P91 = 4400055322869183148068430795279616992237472574915031133555720308758263448099841707032943673_<91>

Number: n N=2514025070280978156173856658318084509079462260303472446853628761692169926867747112435428341002721935384211845341853088789294874496506610562869 ( 142 digits) SNFS difficulty: 167 digits. Divisors found: Fri Jul 11 20:01:05 2008 prp51 factor: 571362150201701442101639602427041315624408776223453 Fri Jul 11 20:01:05 2008 prp91 factor: 4400055322869183148068430795279616992237472574915031133555720308758263448099841707032943673 Fri Jul 11 20:01:05 2008 elapsed time 03:52:37 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 95.20 hours. Scaled time: 166.51 units (timescale=1.749). Factorization parameters were as follows: name: KA_6_7_166 n: 2514025070280978156173856658318084509079462260303472446853628761692169926867747112435428341002721935384211845341853088789294874496506610562869 type: snfs skew: 0.41 deg: 5 c5: 610 c0: -7 m: 1000000000000000000000000000000000 rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4000001) Primes: RFBsize:380800, AFBsize:381368, largePrimes:8083118 encountered Relations: rels:7642312, finalFF:764250 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 94.85 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.6,2.6,100000 total time: 95.20 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 11, 2008 (4th): By Serge Batalov / GMP-ECM
(22·10¹⁷²-13)/9 = 2(4)₁₇₁3_<173> = 832582043 · 21430900157_<11> · C154
C154 = P32 · P123
P32 = 10657958831905102704921058981771_<32>
P123 = 128540113827202101407963240722095256356240982179406016084691632863292226740107335226351658112576118368825069138632503298783_<123>
(4·10²⁴⁵-1)/3 = 1(3)₂₄₅_<246> = 293 · 4428013 · 436570924477_<12> · 197820650760877883_<18> · 1940832977077439598289_<22> · C186
C186 = P30 · C157
P30 = 245134337177055685486188936209_<30>
C157 = [2501171562988825851415370384081321419214621935721077851805784023208701598634345508830113823065528926160766234175487084012080520263262356598377156307842064507_<157>]
(22·10²⁰⁴+23)/9 = 2(4)₂₀₃7_<205> = 720023 · 50715854861597509_<17> · 1888715261066607592247_<22> · C161
C161 = P33 · P129
P33 = 192419819014657626660048413404243_<33>
P129 = 184193270944572775718293604852340692637144385757769845962737152831321614464484501568395567703368265474703829715890241313565646801_<129>
(22·10¹⁸²+23)/9 = 2(4)₁₈₁7_<183> = 13² · 17 · 19 · 3673990757_<10> · C169
C169 = P35 · C134
P35 = 44982980583091433538219963671317681_<35>
C134 = [27095967114785546061369574234256681325758554891730009334878063346192359766250427904748769055763410666798187604335850455402484330235193_<134>]
(4·10²³¹-1)/3 = 1(3)₂₃₁_<232> = 2917 · 51824844853_<11> · C217
C217 = P32 · C186
P32 = 23692560197239551081270833387477_<32>
C186 = [372265083945976876768738111732476398995298007157226123029218145214349213362722613653536404844918572502440528633936829558008893550996679328683843376684364405105826229589913544277836064729_<186>]
(22·10¹⁸⁸+23)/9 = 2(4)₁₈₇7_<189> = 13 · C188
C188 = P34 · P154
P34 = 6189273399288534095811470799393323_<34>
P154 = 3038065632321280803476378108253243566314611187787592040202073700106715272161599074003370726703208829303229285374974719559646659679887499093314088198875153_<154>
(34·10¹⁸¹-43)/9 = 3(7)₁₈₀3_<182> = 3 · 11 · 29 · 163 · 5200627 · C170
C170 = P39 · C132
P39 = 213915155316488930742987770646789353867_<39>
C132 = [217690564118948162947524692462895493375283510041319060406784879841316278978454648395634663748148125534702826272476735696747049821067_<132>]
(22·10¹⁹³-13)/9 = 2(4)₁₉₂3_<194> = 5657 · C190
C190 = P38 · C152
P38 = 56324686381350084101805638381550307243_<38>
C152 = [76717635739151528363645309382391042558552748328658787346390836596385290572482473167190784819468980117146226312447151202964037959418539144514394956959993_<152>]
(11·10¹⁹⁰+7)/9 = 1(2)₁₈₉3_<191> = 31 · 4241 · 6376025173745417_<16> · C170
C170 = P31 · C139
P31 = 1863228909427870138828633619159_<31>
C139 = [7825353626582025776538354806681030279556975533141499321701053340837219702251845795735815749187118825483332759959817834394476302231364380271_<139>]
(22·10¹⁹⁰-31)/9 = 2(4)₁₈₉1_<191> = 3 · 107 · 30301683840760864991_<20> · C169
C169 = P31 · C139
P31 = 2490251637797916931309772842307_<31>
C139 = [1009171883154106743508535605718677600660412608929316157145576041105042869396199255493030596518470433121808888282588221824147334028807874733_<139>]
(67·10¹⁸⁵+23)/9 = 7(4)₁₈₄7_<186> = 3 · 11 · 25733 · 632743 · 1531297 · C168
C168 = P32 · P137
P32 = 34750107879239961728047681359629_<32>
P137 = 26036643415171346432359099267987911251355957717634424727606538886386969243082299006926238395178631918394732555045442482566554127640653897_<137>
Jul 11, 2008 (3rd): By Sinkiti Sibata / GGNFS
(22·10¹⁴⁷+23)/9 = 2(4)₁₄₆7_<148> = 65203 · 128552809986493_<15> · C129
C129 = P61 · P69
P61 = 1719658046526775063872329620833713151617719446440944978655437_<61>
P69 = 169585580715031070644678516951803468114192521983834826364569163297389_<69>

Number: 24447_147 N=291629208451519068887102421369332315645823720830469690559715370792266303503783111885851927973996158741963183104053718746592753993 ( 129 digits) SNFS difficulty: 148 digits. Divisors found: r1=1719658046526775063872329620833713151617719446440944978655437 (pp61) r2=169585580715031070644678516951803468114192521983834826364569163297389 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 26.74 hours. Scaled time: 27.04 units (timescale=1.011). Factorization parameters were as follows: name: 24447_147 n: 291629208451519068887102421369332315645823720830469690559715370792266303503783111885851927973996158741963183104053718746592753993 m: 100000000000000000000000000000 c5: 2200 c0: 23 skew: 0.4 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 4450001) Primes: RFBsize:114155, AFBsize:113693, largePrimes:3180001 encountered Relations: rels:3315913, finalFF:304892 Max relations in full relation-set: 28 Initial matrix: 227915 x 304892 with sparse part having weight 39345363. Pruned matrix : 209004 x 210207 with weight 26695627. Total sieving time: 26.30 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.33 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 26.74 hours. --------- CPU info (if available) ----------
Jul 11, 2008 (2nd): By Serge Batalov / GMP-ECM, pol51, Msieve
(22·10¹⁶⁵+23)/9 = 2(4)₁₆₄7_<166> = 3630210973012969_<16> · 184423336707533618359111_<24> · C127
C127 = P33 · P41 · P54
P33 = 519065104826878486825033434428939_<33>
P41 = 13564038936664591900573721755613575846723_<41>
P54 = 518586933045876452658110256298142053169804574677366689_<54>

Number: 24447_165 N=7034133351879741953545824637111591729772173449090960338984032566235543003595723345747130010147 ( 94 digits) Divisors found: r1=13564038936664591900573721755613575846723 r2=518586933045876452658110256298142053169804574677366689 Version: Msieve 1.36 Factorization parameters were as follows: name: 24447_165 n: 7034133351879741953545824637111591729772173449090960338984032566235543003595723345747130010147 skew: 3323.02 # norm 2.17e+13 c5: 12480 c4: 132852514 c3: 2026591728383 c2: -2797070364676835 c1: -152907382291947879 c0: 2428472541599586000585 # alpha -6.27 Y1: 21826676509 Y0: -891613348784733154 # Murphy_E 7.04e-09 # M 985921677842606424635089187194602414969543492765505871351915733770294116031045157405970754230 type: gnfs rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 900001) Relations: 1827435 relations Pruned matrix : 113960 x 114182 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,93,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 1.70 hours.
(22·10¹⁶⁰+23)/9 = 2(4)₁₅₉7_<161> = 3 · 59 · 1185889 · 111246536441_<12> · C142
C142 = P38 · P104
P38 = 18275254618976078978614739674353667489_<38>
P104 = 57281308395505724725642726213432671439294032138257996320630107178666862119375122137370004294231648428551_<104>
(22·10¹⁵⁸+23)/9 = 2(4)₁₅₇7_<159> = 13 · 103 · 100591 · 14065771 · 77006431 · C136
C136 = P38 · P98
P38 = 41970499708599475548745693906469796007_<38>
P98 = 39921402516784417137477507774986630829373202203626798195388657530740030186361497142025588004796529_<98>
(22·10¹⁶⁴+23)/9 = 2(4)₁₆₃7_<165> = 13 · 19 · 157 · 877 · 370824437303_<12> · 3897947297568115721_<19> · C127
C127 = P40 · P88
P40 = 1995019063063025398231422514593900200743_<40>
P88 = 2492485343226881663435258057593521762659123549921057652169671101365172576804392184453401_<88>
(4·10²⁰³-1)/3 = 1(3)₂₀₃_<204> = 1296951005067479_<16> · 3007224097573595988541199_<25> · C164
C164 = P35 · C130
P35 = 22202898588664747899239883251976133_<35>
C130 = [1539712722915429936027828705221199253961258103511550016874758536693107690174955859182188496690238915491251386488264294882125167481_<130>]
Jul 11, 2008: By Sinkiti Sibata / GGNFS
(22·10¹⁴⁶+23)/9 = 2(4)₁₄₅7_<147> = 13 · 19 · 691 · 827 · 225508344619_<12> · C127
C127 = P45 · P82
P45 = 877528400546131797964133967369485080367167411_<45>
P82 = 8751366321326903185967256414898843569806199348466925509478330018011501491730031177_<82>

Number: 24447_146 N=7679572490547282653445779566837844449760348140477557883118528874893256621861959423600369133825523183623545437777492618208372747 ( 127 digits) SNFS difficulty: 147 digits. Divisors found: r1=877528400546131797964133967369485080367167411 (pp45) r2=8751366321326903185967256414898843569806199348466925509478330018011501491730031177 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 22.11 hours. Scaled time: 22.36 units (timescale=1.011). Factorization parameters were as follows: name: 24447_146 n: 7679572490547282653445779566837844449760348140477557883118528874893256621861959423600369133825523183623545437777492618208372747 m: 100000000000000000000000000000 c5: 220 c0: 23 skew: 0.64 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3650001) Primes: RFBsize:114155, AFBsize:113843, largePrimes:3064283 encountered Relations: rels:3144276, finalFF:305371 Max relations in full relation-set: 28 Initial matrix: 228065 x 305371 with sparse part having weight 37448122. Pruned matrix : 207710 x 208914 with weight 24673037. Total sieving time: 21.70 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.30 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 22.11 hours. --------- CPU info (if available) ----------
(22·10¹⁶³+23)/9 = 2(4)₁₆₂7_<164> = 3³ · 443567 · 2488363 · 18057001737479_<14> · 73151581097461_<14> · 9341132069122380143_<19> · C104
C104 = P45 · P60
P45 = 249102491687358608662848197534804232352965847_<45>
P60 = 266868000887712185768043059435968943896537652150789168406059_<60>

Number: 24447_163 N=66477483972753334552687859983056965286835579716750839563958970783526092476680414187738718186558254866973 ( 104 digits) Divisors found: r1=249102491687358608662848197534804232352965847 (pp45) r2=266868000887712185768043059435968943896537652150789168406059 (pp60) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 13.82 hours. Scaled time: 6.54 units (timescale=0.473). Factorization parameters were as follows: name: 24447_163 n: 66477483972753334552687859983056965286835579716750839563958970783526092476680414187738718186558254866973 skew: 17881.90 # norm 4.12e+14 c5: 26280 c4: -214869564 c3: -22555996750888 c2: -53134620097994881 c1: -558143968031074428782 c0: 7374303972577595376526720 # alpha -6.71 Y1: 12172641437 Y0: -75964372797368143719 # Murphy_E 2.22e-09 # M 29165913441586357822458021902992880104855066735453999372086240476381350149477004246431504334222637972910 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: RFBsize:169511, AFBsize:169933, largePrimes:4303283 encountered Relations: rels:4293785, finalFF:413693 Max relations in full relation-set: 28 Initial matrix: 339528 x 413693 with sparse part having weight 29409280. Pruned matrix : 277889 x 279650 with weight 15942175. Polynomial selection time: 0.78 hours. Total sieving time: 10.85 hours. Total relation processing time: 0.32 hours. Matrix solve time: 1.68 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 13.82 hours. --------- CPU info (if available) ----------
Jul 10, 2008 (8th): By Tyler Cadigan / GGNFS, Msieve
6·10¹⁹⁹+1 = 6(0)₁₉₈1_<200> = 100827365033_<12> · 21583541164043_<14> · 10056670285225909_<17> · 2683916005958404450397_<22> · C139
C139 = P60 · P79
P60 = 479403087032713635428088886452712241517044136079900092034489_<60>
P79 = 2130718979593492245520692728000484684740606068588764504461505725233767054216707_<79>

Number: 60001_199 N=1021473256416313751511313085195015415741101216728868678354738007603336860446052672596356366452772363939729027082207007676223269169924007723 ( 139 digits) Divisors found: r1=479403087032713635428088886452712241517044136079900092034489 r2=2130718979593492245520692728000484684740606068588764504461505725233767054216707 Version: Total time: 729.05 hours. Scaled time: 1862.01 units (timescale=2.554). Factorization parameters were as follows: name: 60001_199 n: 1021473256416313751511313085195015415741101216728868678354738007603336860446052672596356366452772363939729027082207007676223269169924007723 skew: 280338.19 # norm 1.04e+019 c5: 252300 c4: 245677573930 c3: -164464139065339148 c2: -14892083660147997638066 c1: 2698421714535061042480987013 c0: 224570424633670708149720645350596 # alpha -5.52 Y1: 7549711331871863 Y0: -332246204352086047653102315 # Murphy_E 2.43e-011 # M 763279243787741847951479506369752047463195655372871890327270343578515699232362167261281075751089072705232087075956662908098373259288311939 type: gnfs rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 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, 1 ) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1293519 x 1293747 Total sieving time: 729.05 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,138,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5, total time: 729.05 hours. --------- CPU info (if available) ----------
Jul 10, 2008 (7th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(22·10¹⁶³-13)/9 = 2(4)₁₆₂3_<164> = 2713 · 56432111231_<11> · 141768691238978391619_<21> · C130
C130 = P65 · P65
P65 = 27792384200043657245658680170611919922816011461860744469047783927_<65>
P65 = 40522659874175581080586722921710792443780673884463536926755858537_<65>

Number: n N=1126221332030780515366787389894956177448864285682143722873412986001818217724292991301588775644224073995875067988739088144154334799 ( 130 digits) SNFS difficulty: 164 digits. Divisors found: Thu Jul 10 11:46:24 2008 prp65 factor: 27792384200043657245658680170611919922816011461860744469047783927 Thu Jul 10 11:46:24 2008 prp65 factor: 40522659874175581080586722921710792443780673884463536926755858537 Thu Jul 10 11:46:24 2008 elapsed time 01:44:02 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 53.83 hours. Scaled time: 78.10 units (timescale=1.451). Factorization parameters were as follows: name: KA_2_4_162_3 n: 1126221332030780515366787389894956177448864285682143722873412986001818217724292991301588775644224073995875067988739088144154334799 skew: 0.45 deg: 5 c5: 1375 c0: -26 m: 200000000000000000000000000000000 type: snfs rlim: 4600000 alim: 4600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2600001) Primes: RFBsize:322441, AFBsize:322367, largePrimes:7552829 encountered Relations: rels:7113306, finalFF:680302 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 53.58 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,164,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,48,48,2.5,2.5,100000 total time: 53.83 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(22·10¹⁶⁹-1)/3 = 7(3)₁₆₉_<170> = 17 · 73 · 3727 · C164
C164 = P44 · P46 · P75
P44 = 55182912468944908194699383336535592987483933_<44>
P46 = 1869960505794526294457703325188424521177501593_<46>
P75 = 153650224634059109499407293340558535698949481554589881535242993884968124551_<75>

Number: n N=15855146230932655194315267042822804110893487217617143045345502013927881137716286716104453991644770349377516148646608321169913764580338422330791537185975315987659219 ( 164 digits) SNFS difficulty: 171 digits. Divisors found: Thu Jul 10 15:53:51 2008 prp44 factor: 55182912468944908194699383336535592987483933 Thu Jul 10 15:53:51 2008 prp46 factor: 1869960505794526294457703325188424521177501593 Thu Jul 10 15:53:51 2008 prp75 factor: 153650224634059109499407293340558535698949481554589881535242993884968124551 Thu Jul 10 15:53:51 2008 elapsed time 01:29:24 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 58.25 hours. Scaled time: 106.53 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_3_169 n: 15855146230932655194315267042822804110893487217617143045345502013927881137716286716104453991644770349377516148646608321169913764580338422330791537185975315987659219 skew: 0.85 deg: 5 c5: 11 c0: -5 m: 10000000000000000000000000000000000 type: snfs rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3600001) Primes: RFBsize:425648, AFBsize:425618, largePrimes:8091283 encountered Relations: rels:7744929, finalFF:876648 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 57.97 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,48,48,2.5,2.5,100000 total time: 58.25 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(65·10¹⁸⁷+43)/9 = 7(2)₁₈₆7_<188> = 7 · 11 · 17 · 73 · 367 · 227627 · 12114132883_<11> · 31708861836795119_<17> · 1408778549650698007_<19> · C131
C131 = P40 · P91
P40 = 3377652857328732875380257962975302947377_<40>
P91 = 4949801375445568906672988898650230437891483199484561725621942929232193814285739846837010593_<91>
Jul 10, 2008 (6th): By Sinkiti Sibata / GGNFS
(22·10¹⁴³+23)/9 = 2(4)₁₄₂7_<144> = 7 · 47 · 22277 · 7533054917_<10> · C127
C127 = P35 · P93
P35 = 24899585554378077503177286185969857_<35>
P93 = 177813330540874967071390044687145423961622216372486528405096995740758978152899220369615973311_<93>

Number: 24447_143 N=4427478236511424556653540737563208231598857083891635006455103628275009139523403268427254684269587423295577407426383647562486527 ( 127 digits) SNFS difficulty: 144 digits. Divisors found: r1=24899585554378077503177286185969857 (pp35) r2=177813330540874967071390044687145423961622216372486528405096995740758978152899220369615973311 (pp93) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.00 hours. Scaled time: 16.98 units (timescale=0.999). Factorization parameters were as follows: name: 24447_143 n: 4427478236511424556653540737563208231598857083891635006455103628275009139523403268427254684269587423295577407426383647562486527 m: 20000000000000000000000000000 c5: 1375 c0: 46 skew: 0.51 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:99749, largePrimes:3058574 encountered Relations: rels:3168065, finalFF:285821 Max relations in full relation-set: 28 Initial matrix: 199836 x 285821 with sparse part having weight 36330475. Pruned matrix : 180305 x 181368 with weight 22450673. Total sieving time: 16.66 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.23 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 17.00 hours. --------- CPU info (if available) ----------
(22·10¹¹⁷+23)/9 = 2(4)₁₁₆7_<118> = 911 · 954962039576383_<15> · C100
C100 = P45 · P56
P45 = 153350347540615171531355729586920964045930299_<45>
P56 = 18322761197418823300515221966963200845626965065189219581_<56>

Number: 24447_117 N=2809801797527874745136340628744054936820227528609256621780222174244995101695208495794891430931984719 ( 100 digits) SNFS difficulty: 118 digits. Divisors found: r1=153350347540615171531355729586920964045930299 (pp45) r2=18322761197418823300515221966963200845626965065189219581 (pp56) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 2.93 hours. Scaled time: 1.39 units (timescale=0.473). Factorization parameters were as follows: name: 24447_117 n: 2809801797527874745136340628744054936820227528609256621780222174244995101695208495794891430931984719 m: 100000000000000000000000 c5: 2200 c0: 23 skew: 0.4 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, 600001) Primes: RFBsize:49098, AFBsize:63764, largePrimes:2268593 encountered Relations: rels:2519915, finalFF:366680 Max relations in full relation-set: 28 Initial matrix: 112929 x 366680 with sparse part having weight 33794001. Pruned matrix : 73925 x 74553 with weight 6172791. Total sieving time: 2.74 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.07 hours. Time per square root: 0.03 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: 2.93 hours. --------- CPU info (if available) ----------
(22·10¹⁴⁴+23)/9 = 2(4)₁₄₃7_<145> = 29 · 281 · 6690491558713094261_<19> · C122
C122 = P35 · P88
P35 = 24491557737939074393638448434527023_<35>
P88 = 1830633552595663753669826211681350715915526535694694172275334022433701837826737468955001_<88>

Number: 24447_144 N=44835067350405226132220665937906722622652243693041125936761642925899229679585266289557561143910490252449797666019505492023 ( 122 digits) SNFS difficulty: 146 digits. Divisors found: r1=24491557737939074393638448434527023 (pp35) r2=1830633552595663753669826211681350715915526535694694172275334022433701837826737468955001 (pp88) Version: GGNFS-0.77.1-20050930-nocona Total time: 13.14 hours. Scaled time: 13.21 units (timescale=1.005). Factorization parameters were as follows: name: 24447_144 n: 44835067350405226132220665937906722622652243693041125936761642925899229679585266289557561143910490252449797666019505492023 m: 100000000000000000000000000000 c5: 11 c0: 115 skew: 1.6 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 2450001) Primes: RFBsize:114155, AFBsize:113898, largePrimes:2942200 encountered Relations: rels:3014645, finalFF:358154 Max relations in full relation-set: 28 Initial matrix: 228118 x 358154 with sparse part having weight 35742933. Pruned matrix : 190894 x 192098 with weight 18442775. Total sieving time: 12.84 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.21 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 13.14 hours. --------- CPU info (if available) ----------
(22·10¹⁴⁵+23)/9 = 2(4)₁₄₄7_<146> = 3² · 43 · 10671352823_<11> · C133
C133 = P47 · P87
P47 = 26172017367152437248707175326456702997166050893_<47>
P87 = 226158298190510848206744669030862864131241436076272580498188671436573372939791504234879_<87>

Number: 24447_145 N=5919018907967689542617280706178958723228668739763380195197924256951909716923374279609506382494224904358851019371435845744377939696947 ( 133 digits) SNFS difficulty: 146 digits. Divisors found: r1=26172017367152437248707175326456702997166050893 (pp47) r2=226158298190510848206744669030862864131241436076272580498188671436573372939791504234879 (pp87) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.40 hours. Scaled time: 15.57 units (timescale=1.011). Factorization parameters were as follows: name: 24447_145 n: 5919018907967689542617280706178958723228668739763380195197924256951909716923374279609506382494224904358851019371435845744377939696947 m: 100000000000000000000000000000 c5: 22 c0: 23 skew: 1.01 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 2850001) Primes: RFBsize:114155, AFBsize:114118, largePrimes:3011437 encountered Relations: rels:3111828, finalFF:366744 Max relations in full relation-set: 28 Initial matrix: 228339 x 366744 with sparse part having weight 39789463. Pruned matrix : 191140 x 192345 with weight 21006123. Total sieving time: 15.07 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.23 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 15.40 hours. --------- CPU info (if available) ----------
Jul 10, 2008 (5th): By Serge Batalov / Msieve
(22·10¹³¹+23)/9 = 2(4)₁₃₀7_<132> = 7 · 233 · 674318596793_<12> · 127599449770529340523_<21> · C97
C97 = P40 · P58
P40 = 1485468538436582264497629280992342831383_<40>
P58 = 1172597093940178493433708438105100250038657021267386646301_<58>

Number: 24447_131 N=1741856091310300700715755929448806029623162241556917825463352044460114273431692604987339103664283 ( 97 digits) SNFS difficulty: 132 digits. Divisors found: r1=1485468538436582264497629280992342831383 r2=1172597093940178493433708438105100250038657021267386646301 Version: Msieve 1.36 Factorization parameters were as follows: n: 1741856091310300700715755929448806029623162241556917825463352044460114273431692604987339103664283 Y1: 1 Y0: -100000000000000000000000000 c5: 220 c0: 23 skew: 0.64 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [400000, 1100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 120923 x 121140 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 2.00 hours --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 2.00 hours
(22·10¹³⁸+23)/9 = 2(4)₁₃₇7_<139> = 2799078671_<10> · C129
C129 = P60 · P70
P60 = 155810637693047503621475661225318370708471397541118401055253_<60>
P70 = 5604901198936834141789322417044567348370536055675412409260801606914669_<70>

Number: 24447_138 N=873303230012874634363731481002180250775968434523662748614629575891775442150280471500346924134182166559206525583376303911125206257 ( 129 digits) SNFS difficulty: 139 digits. Divisors found: r1=155810637693047503621475661225318370708471397541118401055253 r2=5604901198936834141789322417044567348370536055675412409260801606914669 Version: Factorization parameters were as follows: n: 873303230012874634363731481002180250775968434523662748614629575891775442150280471500346924134182166559206525583376303911125206257 Y1: 1 Y0: -2000000000000000000000000000 c5: 1375 c0: 46 skew: 0.51 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 2600001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 174196 x 174436 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 5.80 hours
(22·10¹³²+23)/9 = 2(4)₁₃₁7_<133> = 2687 · 778785229 · 31870902618307355072948857_<26> · C95
C95 = P46 · P50
P46 = 1066310319098017272671211681952031856865065671_<46>
P50 = 34372951380569981263498111038130737929995501699787_<50>

Number: 24447_132 N=36652232754956210070888323715313598937737298897994870862991340173992678559983082119579881712077 ( 95 digits) SNFS difficulty: 133 digits. Divisors found: r1=1066310319098017272671211681952031856865065671 r2=34372951380569981263498111038130737929995501699787 Version: Msieve 1.36 Factorization parameters were as follows: n: 36652232754956210070888323715313598937737298897994870862991340173992678559983082119579881712077 Y1: 1 Y0: -100000000000000000000000000 c5: 2200 c0: 23 skew: 0.4 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [400000, 1250001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 1458934 unique relations Pruned matrix : 130812 x 131059 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: 2.50 hours.
(22·10¹³⁷+23)/9 = 2(4)₁₃₆7_<138> = 7 · 1741 · 6477307 · 56495077137950327_<17> · C110
C110 = P37 · P73
P37 = 5838733377978851433090143474291042027_<37>
P73 = 9387709216450097303503200248806037900230421287622289557752517186938865827_<73>

Number: 24447_137 N=54812331144846873200817559961946909008650132404608284127492823677164804029605122171898283048704688433371111329 ( 110 digits) SNFS difficulty: 138 digits. Divisors found: r1=5838733377978851433090143474291042027 r2=9387709216450097303503200248806037900230421287622289557752517186938865827 Version: Factorization parameters were as follows: n: 54812331144846873200817559961946909008650132404608284127492823677164804029605122171898283048704688433371111329 Y1: 1 Y0: -1000000000000000000000000000 c5: 2200 c0: 23 skew: 0.4 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 1925001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 157294 x 157519 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 4.00 hours.
Jul 10, 2008 (4th): By Robert Backstrom / GMP-ECM, GGNFS
(22·10¹³⁹+23)/9 = 2(4)₁₃₈7_<140> = 3 · 4349 · C136
C136 = P36 · P41 · P60
P36 = 384822306832803106175504740480258261_<36>
P41 = 29820580306445179468434784370467918075513_<41>
P60 = 163265032757307485732791583648752186409635917475529565664157_<60>

Number: n N=4868658020573690727126546481856282776892240686260398313613025995290300464136292012462195107123487541 ( 100 digits) SNFS difficulty: 141 digits. Divisors found: r1=29820580306445179468434784370467918075513 (pp41) r2=163265032757307485732791583648752186409635917475529565664157 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.87 hours. Scaled time: 7.06 units (timescale=1.823). Factorization parameters were as follows: name: KA_2_4_138_7 n: 4868658020573690727126546481856282776892240686260398313613025995290300464136292012462195107123487541 skew: 1.60 deg: 5 c5: 11 c0: 115 m: 10000000000000000000000000000 type: snfs rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 760001) Primes: RFBsize:92938, AFBsize:92505, largePrimes:6164160 encountered Relations: rels:5408624, finalFF:225942 Max relations in full relation-set: 48 Initial matrix: 185508 x 225942 with sparse part having weight 26325682. Pruned matrix : 171948 x 172939 with weight 15531984. Total sieving time: 3.49 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.23 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,100000 total time: 3.87 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 10, 2008 (3rd): By Sinkiti Sibata / GGNFS
(22·10¹⁷⁴-13)/9 = 2(4)₁₇₃3_<175> = 811 · 3379049371_<10> · C162
C162 = P47 · P57 · P60
P47 = 11072656343693520216315180207406030758141993043_<47>
P57 = 287966682004537921225496398852946852204100412458502336373_<57>
P60 = 279750400108181033972244071591541983136545321330179478911277_<60>

Number: 24443_174 N=891999847055895139743115124913569524755749316127777265347092103819927701303676855809664819338719798539911436166731483759915450801415537254910271854080136443820803 ( 162 digits) SNFS difficulty: 176 digits. Divisors found: r1=11072656343693520216315180207406030758141993043 (pp47) r2=287966682004537921225496398852946852204100412458502336373 (pp57) r3=279750400108181033972244071591541983136545321330179478911277 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 252.40 hours. Scaled time: 255.17 units (timescale=1.011). Factorization parameters were as follows: name: 24443_174 n: 891999847055895139743115124913569524755749316127777265347092103819927701303676855809664819338719798539911436166731483759915450801415537254910271854080136443820803 m: 100000000000000000000000000000000000 c5: 11 c0: -65 skew: 1.43 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 12600001) Primes: RFBsize:501962, AFBsize:502347, largePrimes:6616943 encountered Relations: rels:7110143, finalFF:1158815 Max relations in full relation-set: 28 Initial matrix: 1004374 x 1158815 with sparse part having weight 81668155. Pruned matrix : 874715 x 879800 with weight 62188821. Total sieving time: 245.38 hours. Total relation processing time: 0.15 hours. Matrix solve time: 6.72 hours. Time per square root: 0.14 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: 252.40 hours. --------- CPU info (if available) ----------
Jul 10, 2008 (2nd): By Serge Batalov / Msieve
(22·10¹²⁸+23)/9 = 2(4)₁₂₇7_<129> = 13 · 19 · 8194776089_<10> · 3934292331971_<13> · C104
C104 = P33 · P34 · P38
P33 = 668426865130797987405649315345219_<33>
P34 = 1388343975982515290269796897309261_<34>
P38 = 33077183561244911430284006767620500381_<38>

Number: 24447_128 N=30695838422148846501555786734418298265899042615875233041634129014791334814237998087446452640996474073579 ( 104 digits) SNFS difficulty: 129 digits. Divisors found: r1=668426865130797987405649315345219 r2=1388343975982515290269796897309261 r3=33077183561244911430284006767620500381 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 30695838422148846501555786734418298265899042615875233041634129014791334814237998087446452640996474073579 Y1: 1 Y0: -20000000000000000000000000 c5: 1375 c0: 46 skew: 0.51 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [400000, 1000001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 118754 x 118983 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 2.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 2.00 hours.
(22·10¹⁸⁴+23)/9 = 2(4)₁₈₃7_<185> = 3 · 8741 · 883727969 · 428463058069_<12> · 103877743860680497_<18> · 218460649344400193524021_<24> · 144099946999744771890872989_<27> · C93
C93 = P38 · P56
P38 = 14478093885479986710222592427921863391_<38>
P56 = 51998985992916577835802224283132907761310866802294639523_<56>

Wed Jul 9 04:10:59 2008 Msieve v. 1.36 Wed Jul 9 04:10:59 2008 random seeds: c8d737d3 84691ec3 Wed Jul 9 04:10:59 2008 factoring 752846201155204981101305409504528957770644176142445561475056010325809486586027355292795402493 (93 digits) Wed Jul 9 04:11:00 2008 no P-1/P+1/ECM available, skipping Wed Jul 9 04:11:00 2008 commencing quadratic sieve (93-digit input) Wed Jul 9 04:11:00 2008 using multiplier of 13 Wed Jul 9 04:11:00 2008 using 64kb Opteron sieve core Wed Jul 9 04:11:00 2008 sieve interval: 18 blocks of size 65536 Wed Jul 9 04:11:00 2008 processing polynomials in batches of 6 Wed Jul 9 04:11:00 2008 using a sieve bound of 1946657 (72941 primes) Wed Jul 9 04:11:00 2008 using large prime bound of 243332125 (27 bits) Wed Jul 9 04:11:00 2008 using double large prime bound of 1244970127754625 (42-51 bits) Wed Jul 9 04:11:00 2008 using trial factoring cutoff of 51 bits Wed Jul 9 04:11:00 2008 polynomial 'A' values have 12 factors Wed Jul 9 04:11:00 2008 restarting with 1770 full and 95871 partial relations Wed Jul 9 06:13:59 2008 73176 relations (18297 full + 54879 combined from 994629 partial), need 73037 Wed Jul 9 06:13:59 2008 begin with 1012926 relations Wed Jul 9 06:14:00 2008 reduce to 187728 relations in 10 passes Wed Jul 9 06:14:00 2008 attempting to read 187728 relations Wed Jul 9 06:14:02 2008 recovered 187728 relations Wed Jul 9 06:14:02 2008 recovered 170584 polynomials Wed Jul 9 06:14:02 2008 attempting to build 73176 cycles Wed Jul 9 06:14:02 2008 found 73176 cycles in 5 passes Wed Jul 9 06:14:02 2008 distribution of cycle lengths: Wed Jul 9 06:14:02 2008 length 1 : 18297 Wed Jul 9 06:14:02 2008 length 2 : 13020 Wed Jul 9 06:14:02 2008 length 3 : 12504 Wed Jul 9 06:14:02 2008 length 4 : 10068 Wed Jul 9 06:14:02 2008 length 5 : 7265 Wed Jul 9 06:14:02 2008 length 6 : 4859 Wed Jul 9 06:14:02 2008 length 7 : 2997 Wed Jul 9 06:14:02 2008 length 9+: 4166 Wed Jul 9 06:14:02 2008 largest cycle: 21 relations Wed Jul 9 06:14:02 2008 matrix is 72941 x 73176 (20.1 MB) with weight 4680697 (63.96/col) Wed Jul 9 06:14:03 2008 sparse part has weight 4680697 (63.96/col) Wed Jul 9 06:14:03 2008 filtering completed in 3 passes Wed Jul 9 06:14:03 2008 matrix is 69245 x 69309 (19.1 MB) with weight 4458851 (64.33/col) Wed Jul 9 06:14:03 2008 sparse part has weight 4458851 (64.33/col) Wed Jul 9 06:14:04 2008 saving the first 48 matrix rows for later Wed Jul 9 06:14:04 2008 matrix is 69197 x 69309 (12.5 MB) with weight 3534404 (50.99/col) Wed Jul 9 06:14:04 2008 sparse part has weight 2592435 (37.40/col) Wed Jul 9 06:14:04 2008 matrix includes 64 packed rows Wed Jul 9 06:14:04 2008 using block size 27723 for processor cache size 1024 kB Wed Jul 9 06:14:04 2008 commencing Lanczos iteration Wed Jul 9 06:14:04 2008 memory use: 11.0 MB Wed Jul 9 06:14:34 2008 lanczos halted after 1095 iterations (dim = 69196) Wed Jul 9 06:14:34 2008 recovered 17 nontrivial dependencies Wed Jul 9 06:14:34 2008 prp38 factor: 14478093885479986710222592427921863391 Wed Jul 9 06:14:34 2008 prp56 factor: 51998985992916577835802224283132907761310866802294639523 Wed Jul 9 06:14:34 2008 elapsed time 02:03:35 total time: 2.5 hours
(19·10¹⁶⁴+71)/9 = 2(1)₁₆₃9_<165> = 3 · 1547632204735021741335968620259_<31> · C134
C134 = P58 · P76
P58 = 6742027040094211846211453572461118212957579443337461963393_<58>
P76 = 6744217820260450083366667566814032486869788470472656779231418088265090202679_<76>

Number: 21119_164 N=45469698908481199516727249124846049133783177271867124530465321077300054016404482853634631520144827560167514096151705840653303648529847 ( 134 digits) SNFS difficulty: 166 digits. Divisors found: r1=6742027040094211846211453572461118212957579443337461963393 r2=6744217820260450083366667566814032486869788470472656779231418088265090202679 Version: Total time: 28.00 hours. Scaled time: 82.656 units (timescale=2.952). Factorization parameters were as follows: n: 45469698908481199516727249124846049133783177271867124530465321077300054016404482853634631520144827560167514096151705840653303648529847 Y0: -1000000000000000000000000000000000 Y1: 1 c5: 19 c0: 710 skew: 2.06 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 4600001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 10573189 relations Max relations in full relation-set: 9708274 relations and about 9462589 large ideals Initial matrix: 866332 x 866551 (261.2 MB) with weight 83061728 (95.85/col) Pruned matrix : 860767 x 861015 (249.7 MB) with weight 63635070 (73.91/col) Total sieving time: 25.00 hours. Matrix solve time: 02:44:00. Time per square root: 00:09:52. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.5,2.5,100000 total time: 28.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Total time: 28.00 hours.
(22·10¹⁰⁹+23)/9 = 2(4)₁₀₈7_<110> = 3³ · C108
C108 = P48 · P61
P48 = 113608441459662824962269148437092967080552227087_<48>
P61 = 7969036302290367567268621003851406845020368538649090611909603_<61>

Number: 24447_109 N=905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016461 ( 108 digits) SNFS difficulty: 111 digits. Divisors found: r1=113608441459662824962269148437092967080552227087 r2=7969036302290367567268621003851406845020368538649090611909603 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016461 Y1: 1 Y0: -10000000000000000000000 c5: 11 c0: 115 skew: 1.6 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 350001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 72091 x 72333 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 1.00 hours.
(22·10¹³⁶+23)/9 = 2(4)₁₃₅7_<137> = 3⁴ · 17597 · 474430838713204111_<18> · C113
C113 = P57 · P57
P57 = 160942727758616147304759991172660468836593226620551349083_<57>
P57 = 224601291731175620982413630782755053499706451971227086767_<57>

# NICE SPLIT :-) P57 . P57 Number: 24447_136 N=36147944549324121969604965835519947229596904347641869546100384519388695605927646880868433968210753734213746884661 ( 113 digits) SNFS difficulty: 137 digits. Divisors found: r1=160942727758616147304759991172660468836593226620551349083 r2=224601291731175620982413630782755053499706451971227086767 Factorization parameters were as follows: n: 36147944549324121969604965835519947229596904347641869546100384519388695605927646880868433968210753734213746884661 Y1: 1 Y0: -1000000000000000000000000000 c5: 220 c0: 23 skew: 0.64 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 1925001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 156383 x 156621 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 4 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 4 hours.
Jul 10, 2008: Factorizations of 133...33 were extended to n=250. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.
Factorizations of 244...447 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.
Jul 9, 2008 (5th): By matsui / GGNFS
(10¹⁷⁵-7)/3 = (3)₁₇₄1_<175> = 23 · 3323 · C170
C170 = P45 · P53 · P74
P45 = 235780448596050115929700871470352538873891461_<45>
P53 = 10421228205712331802636719386399164355520595269666467_<53>
P74 = 17749816682347588484905538626867074536389885930396621086863262194900258897_<74>

N=43613462603636490511891210578881489138067138564332038013494005329565130164379140553105932739317972671804332561375045248967451272858906087130975589544980744656260494489439 ( 170 digits) SNFS difficulty: 175 digits. Divisors found: r1=235780448596050115929700871470352538873891461 (pp45) r2=10421228205712331802636719386399164355520595269666467 (pp53) r3=17749816682347588484905538626867074536389885930396621086863262194900258897 (pp74) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 110.75 hours. Scaled time: 314.20 units (timescale=2.837). Factorization parameters were as follows: n: 43613462603636490511891210578881489138067138564332038013494005329565130164379140553105932739317972671804332561375045248967451272858906087130975589544980744656260494489439 m: 100000000000000000000000000000000000 c5: 1 c0: -7 skew: 1.48 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, 9800001) Primes: RFBsize:501962, AFBsize:501141, largePrimes:6403058 encountered Relations: rels:6902001, finalFF:1178713 Max relations in full relation-set: 28 Initial matrix: 1003169 x 1178713 with sparse part having weight 65422220. Pruned matrix : 846847 x 851926 with weight 46933518. Total sieving time: 106.18 hours. Total relation processing time: 0.11 hours. Matrix solve time: 4.29 hours. Time per square root: 0.18 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: 110.75 hours.
Jul 9, 2008 (4th): By Sinkiti Sibata / Msieve
(22·10¹²⁶+23)/9 = 2(4)₁₂₅7_<127> = 499 · 1103 · 87797 · 448607 · 6732252439515400559819_<22> · C89
C89 = P31 · P58
P31 = 5244805083985130173131426609173_<31>
P58 = 3193512685867020820044526963651820924786832284035313015287_<58>

Wed Jul 9 16:54:55 2008 Msieve v. 1.36 Wed Jul 9 16:54:55 2008 random seeds: dd38a79e ee65a53f Wed Jul 9 16:54:55 2008 factoring 16749351570606358764161948724391155809899067723886709775698749787610441965641844723427651 (89 digits) Wed Jul 9 16:54:57 2008 no P-1/P+1/ECM available, skipping Wed Jul 9 16:54:57 2008 commencing quadratic sieve (89-digit input) Wed Jul 9 16:54:57 2008 using multiplier of 3 Wed Jul 9 16:54:57 2008 using 64kb Pentium 4 sieve core Wed Jul 9 16:54:57 2008 sieve interval: 15 blocks of size 65536 Wed Jul 9 16:54:57 2008 processing polynomials in batches of 7 Wed Jul 9 16:54:57 2008 using a sieve bound of 1546823 (58602 primes) Wed Jul 9 16:54:57 2008 using large prime bound of 123745840 (26 bits) Wed Jul 9 16:54:57 2008 using double large prime bound of 368599753674560 (42-49 bits) Wed Jul 9 16:54:57 2008 using trial factoring cutoff of 49 bits Wed Jul 9 16:54:57 2008 polynomial 'A' values have 11 factors Wed Jul 9 18:34:09 2008 58806 relations (15836 full + 42970 combined from 622685 partial), need 58698 Wed Jul 9 18:34:11 2008 begin with 638521 relations Wed Jul 9 18:34:12 2008 reduce to 142912 relations in 11 passes Wed Jul 9 18:34:12 2008 attempting to read 142912 relations Wed Jul 9 18:34:16 2008 recovered 142912 relations Wed Jul 9 18:34:16 2008 recovered 120166 polynomials Wed Jul 9 18:34:16 2008 attempting to build 58806 cycles Wed Jul 9 18:34:16 2008 found 58806 cycles in 5 passes Wed Jul 9 18:34:16 2008 distribution of cycle lengths: Wed Jul 9 18:34:16 2008 length 1 : 15836 Wed Jul 9 18:34:16 2008 length 2 : 11406 Wed Jul 9 18:34:16 2008 length 3 : 10376 Wed Jul 9 18:34:16 2008 length 4 : 7683 Wed Jul 9 18:34:16 2008 length 5 : 5523 Wed Jul 9 18:34:16 2008 length 6 : 3494 Wed Jul 9 18:34:16 2008 length 7 : 2010 Wed Jul 9 18:34:16 2008 length 9+: 2478 Wed Jul 9 18:34:16 2008 largest cycle: 17 relations Wed Jul 9 18:34:16 2008 matrix is 58602 x 58806 (14.4 MB) with weight 3527793 (59.99/col) Wed Jul 9 18:34:16 2008 sparse part has weight 3527793 (59.99/col) Wed Jul 9 18:34:17 2008 filtering completed in 3 passes Wed Jul 9 18:34:17 2008 matrix is 54483 x 54547 (13.4 MB) with weight 3301942 (60.53/col) Wed Jul 9 18:34:17 2008 sparse part has weight 3301942 (60.53/col) Wed Jul 9 18:34:18 2008 saving the first 48 matrix rows for later Wed Jul 9 18:34:18 2008 matrix is 54435 x 54547 (9.6 MB) with weight 2709907 (49.68/col) Wed Jul 9 18:34:18 2008 sparse part has weight 2194112 (40.22/col) Wed Jul 9 18:34:18 2008 matrix includes 64 packed rows Wed Jul 9 18:34:18 2008 using block size 21818 for processor cache size 512 kB Wed Jul 9 18:34:18 2008 commencing Lanczos iteration Wed Jul 9 18:34:18 2008 memory use: 8.8 MB Wed Jul 9 18:34:52 2008 lanczos halted after 863 iterations (dim = 54432) Wed Jul 9 18:34:52 2008 recovered 16 nontrivial dependencies Wed Jul 9 18:34:53 2008 prp31 factor: 5244805083985130173131426609173 Wed Jul 9 18:34:53 2008 prp58 factor: 3193512685867020820044526963651820924786832284035313015287 Wed Jul 9 18:34:53 2008 elapsed time 01:39:58
(22·10¹¹⁴+23)/9 = 2(4)₁₁₃7_<115> = 83 · 163 · 78191 · 3416683 · 33319373 · C92
C92 = P31 · P61
P31 = 4616751856764010560641603977181_<31>
P61 = 4396627454638834962965514259782807864624263415930800244963587_<61>

Wed Jul 9 18:46:02 2008 Msieve v. 1.36 Wed Jul 9 18:46:02 2008 random seeds: 3e553e05 eee29778 Wed Jul 9 18:46:02 2008 factoring 20298137964703466931499613781729059356375064174379028443684191792924037555723406483723908247 (92 digits) Wed Jul 9 18:46:04 2008 no P-1/P+1/ECM available, skipping Wed Jul 9 18:46:04 2008 commencing quadratic sieve (92-digit input) Wed Jul 9 18:46:04 2008 using multiplier of 7 Wed Jul 9 18:46:04 2008 using 64kb Pentium 4 sieve core Wed Jul 9 18:46:04 2008 sieve interval: 18 blocks of size 65536 Wed Jul 9 18:46:04 2008 processing polynomials in batches of 6 Wed Jul 9 18:46:04 2008 using a sieve bound of 1785001 (67059 primes) Wed Jul 9 18:46:04 2008 using large prime bound of 187425105 (27 bits) Wed Jul 9 18:46:04 2008 using double large prime bound of 778197657514830 (42-50 bits) Wed Jul 9 18:46:04 2008 using trial factoring cutoff of 50 bits Wed Jul 9 18:46:04 2008 polynomial 'A' values have 12 factors Wed Jul 9 22:25:10 2008 67378 relations (16844 full + 50534 combined from 837582 partial), need 67155 Wed Jul 9 22:25:13 2008 begin with 854426 relations Wed Jul 9 22:25:14 2008 reduce to 171242 relations in 11 passes Wed Jul 9 22:25:14 2008 attempting to read 171242 relations Wed Jul 9 22:25:19 2008 recovered 171242 relations Wed Jul 9 22:25:19 2008 recovered 153667 polynomials Wed Jul 9 22:25:20 2008 attempting to build 67378 cycles Wed Jul 9 22:25:20 2008 found 67378 cycles in 5 passes Wed Jul 9 22:25:20 2008 distribution of cycle lengths: Wed Jul 9 22:25:20 2008 length 1 : 16844 Wed Jul 9 22:25:20 2008 length 2 : 12110 Wed Jul 9 22:25:20 2008 length 3 : 11636 Wed Jul 9 22:25:20 2008 length 4 : 9235 Wed Jul 9 22:25:20 2008 length 5 : 6751 Wed Jul 9 22:25:20 2008 length 6 : 4363 Wed Jul 9 22:25:20 2008 length 7 : 2761 Wed Jul 9 22:25:20 2008 length 9+: 3678 Wed Jul 9 22:25:20 2008 largest cycle: 19 relations Wed Jul 9 22:25:20 2008 matrix is 67059 x 67378 (16.6 MB) with weight 4070504 (60.41/col) Wed Jul 9 22:25:20 2008 sparse part has weight 4070504 (60.41/col) Wed Jul 9 22:25:21 2008 filtering completed in 3 passes Wed Jul 9 22:25:21 2008 matrix is 63591 x 63654 (15.7 MB) with weight 3858318 (60.61/col) Wed Jul 9 22:25:21 2008 sparse part has weight 3858318 (60.61/col) Wed Jul 9 22:25:22 2008 saving the first 48 matrix rows for later Wed Jul 9 22:25:22 2008 matrix is 63543 x 63654 (9.1 MB) with weight 2921246 (45.89/col) Wed Jul 9 22:25:22 2008 sparse part has weight 1996484 (31.36/col) Wed Jul 9 22:25:22 2008 matrix includes 64 packed rows Wed Jul 9 22:25:22 2008 using block size 21845 for processor cache size 512 kB Wed Jul 9 22:25:23 2008 commencing Lanczos iteration Wed Jul 9 22:25:23 2008 memory use: 9.4 MB Wed Jul 9 22:26:02 2008 lanczos halted after 1007 iterations (dim = 63543) Wed Jul 9 22:26:02 2008 recovered 18 nontrivial dependencies Wed Jul 9 22:26:03 2008 prp31 factor: 4616751856764010560641603977181 Wed Jul 9 22:26:03 2008 prp61 factor: 4396627454638834962965514259782807864624263415930800244963587 Wed Jul 9 22:26:03 2008 elapsed time 03:40:01
Jul 9, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(34·10¹⁶⁷-7)/9 = 3(7)₁₆₇_<168> = 19² · 61 · 3391 · 319591 · 713117 · C149
C149 = P53 · P97
P53 = 17765799744251399391751532208792506707077198483134659_<53>
P97 = 1249486269597586121075036778169187427046511143878302586983277601012099857469072501275389410982659_<97>

Number: n N=22198122848862430580991565540343634709543895530381938659399213758074630177988467525888585175990283070868339958702115301444012179905280476799810878281 ( 149 digits) SNFS difficulty: 168 digits. Divisors found: Wed Jul 09 19:19:54 2008 prp53 factor: 17765799744251399391751532208792506707077198483134659 Wed Jul 09 19:19:54 2008 prp97 factor: 1249486269597586121075036778169187427046511143878302586983277601012099857469072501275389410982659 Wed Jul 09 19:19:54 2008 elapsed time 02:04:09 Version: GGNFS-0.77.1-20051202-athlon Total time: 64.20 hours. Scaled time: 117.41 units (timescale=1.829). Factorization parameters were as follows: name: KA_3_7_167 n: 22198122848862430580991565540343634709543895530381938659399213758074630177988467525888585175990283070868339958702115301444012179905280476799810878281 skew: 0.29 deg: 5 c5: 3400 c0: -7 m: 1000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4000153) Primes: RFBsize:380800, AFBsize:380992, largePrimes:8099098 encountered Relations: rels:7674418, finalFF:781427 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 63.88 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 64.20 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(22·10¹²⁹+23)/9 = 2(4)₁₂₈7_<130> = 767747 · 9294347693_<10> · C114
C114 = P36 · P79
P36 = 145463583266265491036564533866890587_<36>
P79 = 2354988803953860722933036576440462288212379685460602193096133727602333545086411_<79>
Jul 9, 2008 (2nd): By Serge Batalov / Msieve
(22·10¹⁰⁸+23)/9 = 2(4)₁₀₇7_<109> = 443 · 7529 · C102
C102 = P39 · P63
P39 = 769844223455726196788224292250471499171_<39>
P63 = 951998562560586340256760402450547611450431456341933895606371031_<63>

Number: 24447_108 N=732890594125422165802971758094268585680723608201618735455244819937609023722102811025193014233434915301 ( 102 digits) SNFS difficulty: 109 digits. Divisors found: r1=769844223455726196788224292250471499171 r2=951998562560586340256760402450547611450431456341933895606371031 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.915). Factorization parameters were as follows: n: 732890594125422165802971758094268585680723608201618735455244819937609023722102811025193014233434915301 Y1: 1 Y0: -2000000000000000000000 c5: 1375 c0: 46 skew: 0.51 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 73387 x 73623 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,109,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Total: 42 minutes
(22·10¹⁰²+23)/9 = 2(4)₁₀₁7_<103> = 17 · 59 · 277 · C97
C97 = P47 · P51
P47 = 10618264544595981314549183771879838048526138753_<47>
P51 = 828601906275618561461709775254426181373901654948329_<51>

Number: 24447_102 N=8798314242991042916177260436900289904454306554864088040731395864552351769400982771700942099493737 ( 97 digits) SNFS difficulty: 103 digits. Divisors found: r1=10618264544595981314549183771879838048526138753 r2=828601906275618561461709775254426181373901654948329 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.943). Factorization parameters were as follows: #res: 4678 n: 8798314242991042916177260436900289904454306554864088040731395864552351769400982771700942099493737 Y1: 1 Y0: -100000000000000000000 c5: 2200 c0: 23 skew: 0.4 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [225000, 285001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 47340 x 47577 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 22 min
(22·10¹⁰⁷+23)/9 = 2(4)₁₀₆7_<108> = 7 · 1087 · C104
C104 = P42 · P62
P42 = 381591330607017206412657428815125306888619_<42>
P62 = 84188755147859735744695342070485785175230396419321883226185157_<62>

Number: 24447_107 N=32125699099020166177479884931586863509586600662957608679779792935266716315474365152378031862852470028183 ( 104 digits) SNFS difficulty: 108 digits. Divisors found: r1=381591330607017206412657428815125306888619 r2=84188755147859735744695342070485785175230396419321883226185157 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.947). Factorization parameters were as follows: n: 32125699099020166177479884931586863509586600662957608679779792935266716315474365152378031862852470028183 Y1: 1 Y0: -1000000000000000000000 c5: 2200 c0: 23 skew: 0.4 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 61013 x 61240 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,108,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 41 min
(22·10¹²⁴+23)/9 = 2(4)₁₂₃7_<125> = 3 · 43 · 103 · C121
C121 = P47 · P74
P47 = 31127363639203918155230106265371550433065849027_<47>
P74 = 59103186631439869309748970750979721507029739430928737715066147860616020803_<74>

Number: 24447_124 N=1839726382512564494953296037062124214980390189240945619360611458150405994163049931846499920557269846048351354289489308681 ( 121 digits) SNFS difficulty: 126 digits. Divisors found: r1=31127363639203918155230106265371550433065849027 r2=59103186631439869309748970750979721507029739430928737715066147860616020803 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.945). Factorization parameters were as follows: n: 1839726382512564494953296037062124214980390189240945619360611458150405994163049931846499920557269846048351354289489308681 Y1: 1 Y0: -10000000000000000000000000 c5: 11 c0: 115 skew: 1.6 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 111567 x 111791 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 49min. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 49min.
(22·10¹²⁷+23)/9 = 2(4)₁₂₆7_<128> = 3² · C127
C127 = P40 · P88
P40 = 1055851411540761761126901338111649728911_<40>
P88 = 2572378417103811115329524052621719508567986338053396769025584246379410302932317285466153_<88>

N=2716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049383 ( 127 digits) SNFS difficulty: 128 digits. Divisors found: r1=1055851411540761761126901338111649728911 r2=2572378417103811115329524052621719508567986338053396769025584246379410302932317285466153 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.821). Factorization parameters were as follows: n: 2716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049383 Y1: 1 Y0: -10000000000000000000000000 c5: 2200 c0: 23 skew: 0.4 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [400000, 900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 110989 x 111235 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 1.50 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 1.50 hours.
(22·10¹²³+23)/9 = 2(4)₁₂₂7_<124> = 22142383 · 4261412657_<10> · C107
C107 = P38 · P69
P38 = 26763002716631911281029424155030335139_<38>
P69 = 967982226653429397489275031441447420090456022581392764391905774301483_<69>

Number: 24447_123 N=25906110961577137444577994220052608180999890138710163516987992524436446672531714607299587564660203114711137 ( 107 digits) SNFS difficulty: 124 digits. Divisors found: r1=26763002716631911281029424155030335139 r2=967982226653429397489275031441447420090456022581392764391905774301483 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=1.624). Factorization parameters were as follows: n: 25906110961577137444577994220052608180999890138710163516987992524436446672531714607299587564660203114711137 Y1: 1 Y0: -2000000000000000000000000 c5: 1375 c0: 46 skew: 0.51 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 600001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 109891 x 110122 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.20 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 1.20 hours.
(22·10¹⁵²+23)/9 = 2(4)₁₅₁7_<153> = 13 · 150329 · 769837 · 87625711531_<11> · 769556122625057200022794067_<27> · C103
C103 = P35 · P69
P35 = 10813062888571622922756770354132923_<35>
P69 = 222830526301659720606359045665497825172567913566370741154408463204093_<69>

Number: 24447_152 N=2409480494393359654417053972732335004481060547935443629191110013513357239972483882405770870013399653839 ( 103 digits) Divisors found: r1=10813062888571622922756770354132923 r2=222830526301659720606359045665497825172567913566370741154408463204093 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: name: 24447_152 n: 2409480494393359654417053972732335004481060547935443629191110013513357239972483882405770870013399653839 skew: 19561.08 # norm 8.91e+13 c5: 420 c4: -82996087 c3: -4257878742953 c2: 33361211199951301 c1: 145479990723098945878 c0: -843488700671868424525899 # alpha -4.74 Y1: 24707240459 Y0: -89482799835749821772 # Murphy_E 2.44e-09 # M 2165897549338724270610609111043907709624331788247989596227418375996497476424002657125822225638182266954 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 250649 x 250883 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 4.20 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) total time: 4.20 hours.
Jul 9, 2008: Factorizations of 244...447 were extended to n=200. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors are probably greater than 10³⁰.
Jul 8, 2008: By Robert Backstrom / GMP-ECM
(37·10¹⁸¹-1)/9 = 4(1)₁₈₁_<182> = 17 · 41 · 4127 · 24499 · 167471 · 245443424673836171_<18> · 246875141547236483_<18> · C131
C131 = P43 · P88
P43 = 9694281830014265153818506928082037151687589_<43>
P88 = 5930066875553988652313184804417901312203848627507573517688576121033537218672808937502993_<88>
Jul 7, 2008 (4th): By Robert Backstrom / GGNFS
(22·10¹⁷³-31)/9 = 2(4)₁₇₂1_<174> = 29 · C172
C172 = P62 · P111
P62 = 53929390053448635802755667268850142007562273054280940188884371_<62>
P111 = 156299167589182500831339219188302177128441788079387540549837743824293003742698300050396169986960092098989076799_<111>

Number: n N=8429118773946360153256704980842911877394636015325670498084291187739463601532567049808429118773946360153256704980842911877394636015325670498084291187739463601532567049808429 ( 172 digits) SNFS difficulty: 174 digits. Divisors found: Mon Jul 07 22:10:46 2008 prp62 factor: 53929390053448635802755667268850142007562273054280940188884371 Mon Jul 07 22:10:46 2008 prp111 factor: 156299167589182500831339219188302177128441788079387540549837743824293003742698300050396169986960092098989076799 Mon Jul 07 22:10:46 2008 elapsed time 03:58:11 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 195.03 hours. Scaled time: 255.49 units (timescale=1.310). Factorization parameters were as follows: name: KA_2_4_172_1 n: 8429118773946360153256704980842911877394636015325670498084291187739463601532567049808429118773946360153256704980842911877394636015325670498084291187739463601532567049808429 skew: 0.54 deg: 5 c5: 1375 c0: -62 m: 20000000000000000000000000000000000 type: snfs rlim: 7000000 alim: 7000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 7100173) Primes: RFBsize:476648, AFBsize:475941, largePrimes:9026408 encountered Relations: rels:8609903, finalFF:954855 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 194.26 hours. Total relation processing time: 0.77 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,174,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,48,48,2.5,2.5,100000 total time: 195.03 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 7, 2008 (3rd): By Serge Batalov / GMP-ECM
(64·10²¹⁵+53)/9 = 7(1)₂₁₄7_<216> = 3 · 11 · 3079 · C211
C211 = P45 · P47 · P120
P45 = 125676554603285221667793460094390282916482437_<45>
P47 = 81213719868582797366318791991053471705206424789_<47>
P120 = 685693711441738179761734159616977676586319021004974435893926620849586278615885854977785958434104586204829762960643199667_<120>

# I have now already sieved 38 MILLION relations (30-bit LPs!), with 320 CPU-hours on Opteron (on 8 CPUs) # # ...in parallel I ran a lot of ECMs, full 1M, 3M, then 11M... # ...and when I cracked off the P47 I was disappointed, but GNFS was still unfeasible # ...and another day later, I checked the B1=43000000 ECM processes (far from complete) # and the number was cracked completely. # # What a pity! # # P.S. Maybe you could leave this story in a text box # (you usually don't for ECMs, but this may be a lesson how to avoid # trivial painful factorizations by two months of GGNFS) # Nobody likes an ECM miss! # The P45 and P47 are not really a miss (for home computing), but nobody wants a 30-39-digit factor, that's for sure. # # --Serge C211 = P45 . P47 . P120 GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 6998642919396410789720305796954059376923943341611415661431900470549382533793056690101185067083085920370753108655024861585433199593641295492545898521864744664354927427353539727687178158110278928726476631640645931 (211 digits) Run 3861 out of 4600: Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=1048397889 Step 1 took 122874ms Step 2 took 55826ms ********** Factor found in step 2: 81213719868582797366318791991053471705206424789 Found probable prime factor of 47 digits: 81213719868582797366318791991053471705206424789 Composite cofactor 86175623167136908906028312775085985010301678182392368154328956428185102943358698524469334462125149952396328912164009032468557009157053703824006666253050812289748479 has 164 digits GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Run 33 out of 1000: Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1801021090 Step 1 took 361683ms Step 2 took 92881ms ********** Factor found in step 2: 125676554603285221667793460094390282916482437 Found probable prime factor of 45 digits: 125676554603285221667793460094390282916482437 Probable prime cofactor 685693711441738179761734159616977676586319021004974435893926620849586278615885854977785958434104586204829762960643199667 has 120 digits all three factors prime by APRT-CLE.
Jul 7, 2008 (2nd): By Sinkiti Sibata / GGNFS
(22·10¹⁶⁹-13)/9 = 2(4)₁₆₈3_<170> = 6603123233761858889_<19> · C151
C151 = P35 · P117
P35 = 34538325050649741960582584869569799_<35>
P117 = 107183885461665753591363007370745581050786551598708387085447555024370036792587759492946489199946634658942041297437413_<117>

Number: 24443_169 N=3701951876266622979874422342651354796993731339689201245901440527900042776675366699392640951666692911201609719346004277223504578989840161477542437489987 ( 151 digits) SNFS difficulty: 171 digits. Divisors found: r1=34538325050649741960582584869569799 (pp35) r2=107183885461665753591363007370745581050786551598708387085447555024370036792587759492946489199946634658942041297437413 (pp117) Version: GGNFS-0.77.1-20050930-nocona Total time: 141.04 hours. Scaled time: 142.17 units (timescale=1.008). Factorization parameters were as follows: name: 24443_169 n: 3701951876266622979874422342651354796993731339689201245901440527900042776675366699392640951666692911201609719346004277223504578989840161477542437489987 m: 10000000000000000000000000000000000 c5: 11 c0: -65 skew: 1.43 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, 8300001) Primes: RFBsize:412849, AFBsize:413107, largePrimes:6158208 encountered Relations: rels:6424609, finalFF:926523 Max relations in full relation-set: 28 Initial matrix: 826021 x 926523 with sparse part having weight 64258799. Pruned matrix : 747047 x 751241 with weight 49325952. Total sieving time: 136.65 hours. Total relation processing time: 0.11 hours. Matrix solve time: 4.17 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 141.04 hours. --------- CPU info (if available) ----------
Jul 7, 2008: By Robert Backstrom / GGNFS, Msieve
3·10¹⁶⁸+7 = 3(0)₁₆₇7_<169> = 31² · 220442934797851_<15> · C152
C152 = P59 · P93
P59 = 68134668790873592384459578322644469894232860523283147276193_<59>
P93 = 207842105702935771469899396383940505601339931626765063877009064283675813950588095504388659109_<93>

Number: n N=14161253032867268200456854209951828454345061458914538796845639216326800017761514121711220530384697406593320683898998558239446506333949451311352948292037 ( 152 digits) SNFS difficulty: 168 digits. Divisors found: Mon Jul 07 06:38:48 2008 prp59 factor: 68134668790873592384459578322644469894232860523283147276193 Mon Jul 07 06:38:48 2008 prp93 factor: 207842105702935771469899396383940505601339931626765063877009064283675813950588095504388659109 Mon Jul 07 06:38:48 2008 elapsed time 01:31:51 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 52.57 hours. Scaled time: 96.15 units (timescale=1.829). Factorization parameters were as follows: name: KA_3_0_167_7 n: 14161253032867268200456854209951828454345061458914538796845639216326800017761514121711220530384697406593320683898998558239446506333949451311352948292037 skew: 0.30 deg: 5 c5: 3000 c0: 7 m: 1000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3200129) Primes: RFBsize:380800, AFBsize:380817, largePrimes:7815275 encountered Relations: rels:7399067, finalFF:765549 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 52.37 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,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 52.57 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(19·10¹⁶⁹+17)/9 = 2(1)₁₆₈3_<170> = 202343 · C165
C165 = P41 · P45 · P79
P41 = 11854813632301944696197779784107475828959_<41>
P45 = 989586227294571474744567542974907856207448937_<45>
P79 = 8893537356585734852905220128099726473408062960442837007302516244982560116409577_<79>

Number: n N=104333291050894328497210731832142011886307463619255971845386848623926259426375565802182981922335396386883218649081565021330666794063106265653425673787139219597965391 ( 165 digits) SNFS difficulty: 171 digits. Divisors found: Mon Jul 07 08:20:12 2008 prp41 factor: 11854813632301944696197779784107475828959 Mon Jul 07 08:20:12 2008 prp45 factor: 989586227294571474744567542974907856207448937 Mon Jul 07 08:20:12 2008 prp79 factor: 8893537356585734852905220128099726473408062960442837007302516244982560116409577 Mon Jul 07 08:20:12 2008 elapsed time 03:35:37 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 131.75 hours. Scaled time: 190.77 units (timescale=1.448). Factorization parameters were as follows: name: KA_2_1_168_3 n: 104333291050894328497210731832142011886307463619255971845386848623926259426375565802182981922335396386883218649081565021330666794063106265653425673787139219597965391 skew: 1.55 deg: 5 c5: 19 c0: 170 m: 10000000000000000000000000000000000 type: snfs rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5900189) Primes: RFBsize:425648, AFBsize:427217, largePrimes:8696525 encountered Relations: rels:8265355, finalFF:868827 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 131.37 hours. Total relation processing time: 0.38 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,48,48,2.5,2.5,100000 total time: 131.75 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Jul 6, 2008 (3rd): By matsui / GGNFS
7·10¹⁷⁵-9 = 6(9)₁₇₄1_<176> = 1301 · 700849 · C167
C167 = P58 · P110
P58 = 2998263129687771495713319147093796698599357538666071288999_<58>
P110 = 25605103830539641054955333281714615256570243024259263526043334000070733816061239428491153704128112278858660541_<110>

N=76770838746934130507392324931250151067188852114401986823165103555542800872777834759409606762117612554266824567026809163243163420541346739870235062843495421078448688459 ( 167 digits) SNFS difficulty: 175 digits. Divisors found: r1=2998263129687771495713319147093796698599357538666071288999 (pp58) r2=25605103830539641054955333281714615256570243024259263526043334000070733816061239428491153704128112278858660541 (pp110) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 120.77 hours. Scaled time: 343.95 units (timescale=2.848). Factorization parameters were as follows: n: 76770838746934130507392324931250151067188852114401986823165103555542800872777834759409606762117612554266824567026809163243163420541346739870235062843495421078448688459 m: 100000000000000000000000000000000000 c5: 7 c0: -9 skew: 1.05 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, 12000001) Primes: RFBsize:501962, AFBsize:502356, largePrimes:6549781 encountered Relations: rels:7030593, finalFF:1152542 Max relations in full relation-set: 28 Initial matrix: 1004384 x 1152542 with sparse part having weight 76779199. Pruned matrix : 878852 x 883937 with weight 58230885. Total sieving time: 112.93 hours. Total relation processing time: 0.11 hours. Matrix solve time: 7.52 hours. Time per square root: 0.22 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: 120.77 hours.
Jul 6, 2008 (2nd): By Wataru Sakai / GGNFS
(8·10¹⁷⁵-71)/9 = (8)₁₇₄1_<175> = 31 · C174
C174 = P76 · P98
P76 = 5771423368902638327030970168234828127947353990816013247148660980653867079991_<76>
P98 = 49682432378721834064763150900527183566952281275682356497289727057025185041987238713931398215237961_<98>

Number: 88881_175 N=286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351 ( 174 digits) SNFS difficulty: 175 digits. Divisors found: r1=5771423368902638327030970168234828127947353990816013247148660980653867079991 (pp76) r2=49682432378721834064763150900527183566952281275682356497289727057025185041987238713931398215237961 (pp98) Version: GGNFS-0.77.1-20060722-nocona Total time: 201.98 hours. Scaled time: 406.99 units (timescale=2.015). Factorization parameters were as follows: n: 286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351254480286738351 m: 100000000000000000000000000000000000 c5: 8 c0: -71 skew: 1.55 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, 10200001) Primes: RFBsize:501962, AFBsize:501892, largePrimes:6609281 encountered Relations: rels:7255516, finalFF:1306535 Max relations in full relation-set: 32 Initial matrix: 1003919 x 1306535 with sparse part having weight 79027919. Pruned matrix : 736827 x 741910 with weight 57352113. Total sieving time: 197.68 hours. Total relation processing time: 0.10 hours. Matrix solve time: 4.02 hours. Time per square root: 0.18 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: 201.98 hours. --------- CPU info (if available) ----------
Jul 6, 2008: By Robert Backstrom / GGNFS, Msieve
(14·10¹⁶⁸-41)/9 = 1(5)₁₆₇1_<169> = 3³ · 37656643141339_<14> · C154
C154 = P38 · P116
P38 = 16981226766391967119183913630606464339_<38>
P116 = 90097159217599722569381430542429490640646635539748578844942039627166323665820109863974364446625831381931678300595853_<116>

Number: n N=1529960291681783151114531193400230721051917068342751517577310648254554333940389934727118286669463974028994922153019732058807777461380973311907897295786167 ( 154 digits) SNFS difficulty: 169 digits. Divisors found: Sun Jul 06 09:20:10 2008 prp38 factor: 16981226766391967119183913630606464339 Sun Jul 06 09:20:10 2008 prp116 factor: 90097159217599722569381430542429490640646635539748578844942039627166323665820109863974364446625831381931678300595853 Sun Jul 06 09:20:10 2008 elapsed time 02:40:33 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 81.62 hours. Scaled time: 142.92 units (timescale=1.751). Factorization parameters were as follows: name: KA_1_5_167_1 n: 1529960291681783151114531193400230721051917068342751517577310648254554333940389934727118286669463974028994922153019732058807777461380973311907897295786167 type: snfs skew: 0.62 deg: 5 c5: 875 c0: -82 m: 2000000000000000000000000000000000 rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3800113) Primes: RFBsize:399993, AFBsize:400415, largePrimes:8020626 encountered Relations: rels:7627568, finalFF:810616 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 81.31 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,48,48,2.6,2.6,100000 total time: 81.62 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 5, 2008 (4th): By suberi / GMP-ECM
2·10¹⁷⁵+3 = 2(0)₁₇₄3_<176> = 1607 · 9041761 · 65731411 · 1081691158291_<13> · C146
C146 = P41 · P105
P41 = 76852616085817677774513791387885482895603_<41>
P105 = 251898861882089203262483987189502786622824705946228241740108420753071099837412827838656218659332309040463_<105>
2·10¹⁷⁶+3 = 2(0)₁₇₅3_<177> = 7 · 1307 · 17785019238356023897_<20> · C154
C154 = P37 · P117
P37 = 3214888775730183633684484492940316319_<37>
P117 = 382327974808924344375250235945475131233497457127498460037175594820337444676213458154174274593752449576287105681456329_<117>
Jul 5, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(67·10¹⁶⁷+23)/9 = 7(4)₁₆₆7_<168> = 3 · 11 · 590725541875506926873_<21> · C146
C146 = P45 · P101
P45 = 757066989154644615491448690405189133528186327_<45>
P101 = 50442696473007939117602260588880692523791409579601037039522012224179074179617065626216315357828500929_<101>

Number: n N=38188500343661731641278628082568518596787475525445421725857796402998819571882558221901996369633874551499717256707212411143098580436331158604597783 ( 146 digits) SNFS difficulty: 168 digits. Divisors found: Sat Jul 5 16:35:21 2008 prp45 factor: 757066989154644615491448690405189133528186327 Sat Jul 5 16:35:21 2008 prp101 factor: 50442696473007939117602260588880692523791409579601037039522012224179074179617065626216315357828500929 Sat Jul 5 16:35:21 2008 elapsed time 01:28:07 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 72.21 hours. Scaled time: 60.44 units (timescale=0.837). Factorization parameters were as follows: name: KA_7_4_166_7 n: 38188500343661731641278628082568518596787475525445421725857796402998819571882558221901996369633874551499717256707212411143098580436331158604597783 type: snfs deg: 5 c5: 6700 c0: 23 skew: 0.32 m: 1000000000000000000000000000000000 rlim: 5800000 alim: 5800000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3700187) Primes: RFBsize:399993, AFBsize:399534, largePrimes:5669956 encountered Relations: rels:5827169, finalFF:820255 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 72.01 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,168,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,48,48,2.5,2.5,100000 total time: 72.21 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).
Jul 5, 2008 (2nd): By Sinkiti Sibata / GGNFS, Msieve
(22·10¹⁶⁴-13)/9 = 2(4)₁₆₃3_<165> = 3⁴ · 29 · 3416647763_<10> · 21835992391633997_<17> · C136
C136 = P54 · P82
P54 = 188977149108201979911706385119937160520580933260307287_<54>
P82 = 7380991743316560115806233653476384595263723304504052365842469875363867165673435351_<82>

Number: 24443_164 N=1394838777243141255510981001163768886819125792240408935920463319142421907920649440350855154985034708459237944672082108063593967188702737 ( 136 digits) SNFS difficulty: 166 digits. Divisors found: r1=188977149108201979911706385119937160520580933260307287 (pp54) r2=7380991743316560115806233653476384595263723304504052365842469875363867165673435351 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 83.57 hours. Scaled time: 84.33 units (timescale=1.009). Factorization parameters were as follows: name: 24443_164 n: 1394838777243141255510981001163768886819125792240408935920463319142421907920649440350855154985034708459237944672082108063593967188702737 m: 1000000000000000000000000000000000 c5: 11 c0: -65 skew: 1.43 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, 5400001) Primes: RFBsize:348513, AFBsize:348832, largePrimes:5983032 encountered Relations: rels:6212091, finalFF:859947 Max relations in full relation-set: 28 Initial matrix: 697410 x 859947 with sparse part having weight 56628198. Pruned matrix : 568712 x 572263 with weight 39516683. Total sieving time: 80.89 hours. Total relation processing time: 0.10 hours. Matrix solve time: 2.48 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 83.57 hours. --------- CPU info (if available) ----------
(22·10¹⁶¹-13)/9 = 2(4)₁₆₀3_<162> = 3 · 1777 · 33815254328427941_<17> · 4435250828334077701_<19> · C123
C123 = P51 · P72
P51 = 918751243450106267060747603778791899353350478837103_<51>
P72 = 332768880114005275926756609421497514018998126560607437380875803735204911_<72>

Number: 24443_161 N=305731822386241687388365973109241630242229346029252053757510744441829217228259242418405758238321559754128107663948694612833 ( 123 digits) SNFS difficulty: 162 digits. Divisors found: r1=918751243450106267060747603778791899353350478837103 (pp51) r2=332768880114005275926756609421497514018998126560607437380875803735204911 (pp72) Version: GGNFS-0.77.1-20060513-k8 Total time: 73.49 hours. Scaled time: 146.68 units (timescale=1.996). Factorization parameters were as follows: name: 24443_161 n: 305731822386241687388365973109241630242229346029252053757510744441829217228259242418405758238321559754128107663948694612833 m: 100000000000000000000000000000000 c5: 220 c0: -13 skew: 0.57 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, 4550001) Primes: RFBsize:315948, AFBsize:316452, largePrimes:5901718 encountered Relations: rels:6110503, finalFF:826721 Max relations in full relation-set: 28 Initial matrix: 632467 x 826721 with sparse part having weight 51666016. Pruned matrix : 479579 x 482805 with weight 35391694. Total sieving time: 70.08 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.99 hours. Time per square root: 0.20 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: 73.49 hours. --------- CPU info (if available) ----------
(22·10¹⁵⁵-13)/9 = 2(4)₁₅₄3_<156> = 3² · 23 · 143981 · 218747941 · 249745250462299_<15> · 292725366458429872841_<21> · C105
C105 = P45 · P61
P45 = 482708719167218258004205150027333793774609359_<45>
P61 = 1062473059782581072690917238909162188127886673467946816631449_<61>

Wed Jul 2 12:30:04 2008 Msieve v. 1.36 Wed Jul 2 12:30:04 2008 random seeds: df1e72e0 8972023e Wed Jul 2 12:30:04 2008 factoring 512865009837325022345519467664391330612010588131901538421543902669711759984610894342811574933034249131191 (105 digits) Wed Jul 2 12:30:05 2008 no P-1/P+1/ECM available, skipping Wed Jul 2 12:30:05 2008 commencing quadratic sieve (105-digit input) Wed Jul 2 12:30:06 2008 using multiplier of 7 Wed Jul 2 12:30:06 2008 using 64kb Pentium 4 sieve core Wed Jul 2 12:30:06 2008 sieve interval: 18 blocks of size 65536 Wed Jul 2 12:30:06 2008 processing polynomials in batches of 6 Wed Jul 2 12:30:06 2008 using a sieve bound of 3948821 (140000 primes) Wed Jul 2 12:30:06 2008 using large prime bound of 592323150 (29 bits) Wed Jul 2 12:30:06 2008 using double large prime bound of 6174554804868150 (44-53 bits) Wed Jul 2 12:30:06 2008 using trial factoring cutoff of 53 bits Wed Jul 2 12:30:06 2008 polynomial 'A' values have 14 factors Sat Jul 5 13:38:29 2008 140161 relations (33632 full + 106529 combined from 2089225 partial), need 140096 Sat Jul 5 13:38:38 2008 begin with 2122857 relations Sat Jul 5 13:38:40 2008 reduce to 368943 relations in 10 passes Sat Jul 5 13:38:40 2008 attempting to read 368943 relations Sat Jul 5 13:38:55 2008 recovered 368943 relations Sat Jul 5 13:38:55 2008 recovered 361714 polynomials Sat Jul 5 13:38:55 2008 attempting to build 140161 cycles Sat Jul 5 13:38:56 2008 found 140160 cycles in 5 passes Sat Jul 5 13:38:56 2008 distribution of cycle lengths: Sat Jul 5 13:38:56 2008 length 1 : 33632 Sat Jul 5 13:38:56 2008 length 2 : 23929 Sat Jul 5 13:38:56 2008 length 3 : 23141 Sat Jul 5 13:38:56 2008 length 4 : 19244 Sat Jul 5 13:38:56 2008 length 5 : 14585 Sat Jul 5 13:38:56 2008 length 6 : 10068 Sat Jul 5 13:38:56 2008 length 7 : 6438 Sat Jul 5 13:38:56 2008 length 9+: 9123 Sat Jul 5 13:38:56 2008 largest cycle: 19 relations Sat Jul 5 13:38:56 2008 matrix is 140000 x 140160 (39.1 MB) with weight 9682174 (69.08/col) Sat Jul 5 13:38:56 2008 sparse part has weight 9682174 (69.08/col) Sat Jul 5 13:39:00 2008 filtering completed in 3 passes Sat Jul 5 13:39:00 2008 matrix is 134452 x 134516 (37.7 MB) with weight 9352275 (69.53/col) Sat Jul 5 13:39:00 2008 sparse part has weight 9352275 (69.53/col) Sat Jul 5 13:39:01 2008 saving the first 48 matrix rows for later Sat Jul 5 13:39:01 2008 matrix is 134404 x 134516 (22.0 MB) with weight 7251326 (53.91/col) Sat Jul 5 13:39:01 2008 sparse part has weight 4967697 (36.93/col) Sat Jul 5 13:39:01 2008 matrix includes 64 packed rows Sat Jul 5 13:39:01 2008 using block size 21845 for processor cache size 512 kB Sat Jul 5 13:39:03 2008 commencing Lanczos iteration Sat Jul 5 13:39:03 2008 memory use: 22.2 MB Sat Jul 5 13:42:22 2008 lanczos halted after 2127 iterations (dim = 134403) Sat Jul 5 13:42:23 2008 recovered 17 nontrivial dependencies Sat Jul 5 13:42:25 2008 prp45 factor: 482708719167218258004205150027333793774609359 Sat Jul 5 13:42:25 2008 prp61 factor: 1062473059782581072690917238909162188127886673467946816631449 Sat Jul 5 13:42:25 2008 elapsed time 73:12:21
Jul 5, 2008: By Robert Backstrom / GGNFS, Msieve
(4·10¹⁶⁸+41)/9 = (4)₁₆₇9_<168> = 4597 · 130447182347_<12> · C153
C153 = P72 · P82
P72 = 663251634063362739752196199073426751298383313952477786487187756107043583_<72>
P82 = 1117454752021047188523688656180078402295445713630605513644151002858054731527619817_<82>

Number: n N=741153690269829344816607101538581813580363824537014619808453740497332331010205538207186533049730298407091798388514224200756023662978131538180140673484311 ( 153 digits) SNFS difficulty: 168 digits. Divisors found: Sat Jul 05 01:16:13 2008 prp72 factor: 663251634063362739752196199073426751298383313952477786487187756107043583 Sat Jul 05 01:16:13 2008 prp82 factor: 1117454752021047188523688656180078402295445713630605513644151002858054731527619817 Sat Jul 05 01:16:13 2008 elapsed time 01:38:25 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 59.64 hours. Scaled time: 109.07 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_167_9 n: 741153690269829344816607101538581813580363824537014619808453740497332331010205538207186533049730298407091798388514224200756023662978131538180140673484311 skew: 0.80 deg: 5 c5: 125 c0: 41 m: 2000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3600221) Primes: RFBsize:380800, AFBsize:381398, largePrimes:8025714 encountered Relations: rels:7629445, finalFF:796763 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 59.44 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,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 59.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 4, 2008 (8th): By Wataru Sakai / GGNFS
(10¹⁷⁴+17)/9 = (1)₁₇₃3_<174> = 377876511031_<12> · C162
C162 = P64 · P98
P64 = 7316041903847007779820595674552294686019937425938604329901433463_<64>
P98 = 40191240367144016302815181110516174673310246906156873550846174801629866981184855893817082957652921_<98>

Number: 11113_174 N=294040798693613020978721557691027645861505411458095217132747791724995390273507246425889611518903150754520207364042759151086227684121488178193073709170363929095423 ( 162 digits) SNFS difficulty: 175 digits. Divisors found: r1=7316041903847007779820595674552294686019937425938604329901433463 (pp64) r2=40191240367144016302815181110516174673310246906156873550846174801629866981184855893817082957652921 (pp98) Version: GGNFS-0.77.1-20060722-nocona Total time: 194.34 hours. Scaled time: 352.33 units (timescale=1.813). Factorization parameters were as follows: n: 294040798693613020978721557691027645861505411458095217132747791724995390273507246425889611518903150754520207364042759151086227684121488178193073709170363929095423 m: 100000000000000000000000000000000000 c5: 1 c0: 170 skew: 2.79 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:502431, largePrimes:6427815 encountered Relations: rels:6885252, finalFF:1141474 Max relations in full relation-set: 32 Initial matrix: 1004457 x 1141474 with sparse part having weight 68636874. Pruned matrix : 885866 x 890952 with weight 51307737. Total sieving time: 187.27 hours. Total relation processing time: 0.10 hours. Matrix solve time: 6.75 hours. Time per square root: 0.22 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: 194.34 hours. --------- CPU info (if available) ----------
(10¹⁶⁹+71)/9 = (1)₁₆₈9_<169> = 3 · 59 · 97 · 2029033 · 6513786343_<10> · C148
C148 = P41 · P107
P41 = 58256274272138916126619839433275911718637_<41>
P107 = 84051828163356372247625226617883687184833701501969291495680461061656160491744043801648027577705796315595717_<107>

Number: 11119_169 N=4896546354559178996140354102442220159529990569466487676403385572974008116436611422680942354556609657246123689866555093038830658609501137723946277729 ( 148 digits) SNFS difficulty: 170 digits. Divisors found: r1=58256274272138916126619839433275911718637 (pp41) r2=84051828163356372247625226617883687184833701501969291495680461061656160491744043801648027577705796315595717 (pp107) Version: GGNFS-0.77.1-20060722-nocona Total time: 168.68 hours. Scaled time: 339.73 units (timescale=2.014). Factorization parameters were as follows: n: 4896546354559178996140354102442220159529990569466487676403385572974008116436611422680942354556609657246123689866555093038830658609501137723946277729 m: 10000000000000000000000000000000000 c5: 1 c0: 710 skew: 3.72 type: snfsFactor 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, 8700001) Primes: RFBsize:412849, AFBsize:413722, largePrimes:6522753 encountered Relations: rels:7031474, finalFF:1142419 Max relations in full relation-set: 32 Initial matrix: 826635 x 1142419 with sparse part having weight 87304407. Pruned matrix : 574125 x 578322 with weight 74347583. Total sieving time: 165.14 hours. Total relation processing time: 0.10 hours. Matrix solve time: 3.27 hours. Time per square root: 0.17 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: 168.68 hours. --------- CPU info (if available) ----------
Jul 4, 2008 (7th): By Serge Batalov / GMP-ECM
(64·10²⁴⁹+53)/9 = 7(1)₂₄₈7_<250> = 11 · 8171 · 944916181322280177394519_<24> · C221
C221 = P40 · C182
P40 = 1115409808826481487721767396696401745727_<40>
C182 = [75065749185647424301639973766450991088912379509114416801234054773803073644854905012027429069765331464723207178998756891472876524389458263589608376114581569780896727097603078911963789_<182>]
Jul 4, 2008 (6th): By suberi / GMP-ECM
5·10¹⁸⁸+3 = 5(0)₁₈₇3_<189> = 17 · 353 · 694042304507_<12> · C174
C174 = P45 · P129
P45 = 534714061843976765275098162965857648543309727_<45>
P129 = 224511622860875644540507133498734394246496745568262356156954776102962010083439706705021118582845752441312785525001232938868447927_<129>
Jul 4, 2008 (5th): By Serge Batalov / Msieve
6·10²⁰⁰+1 = 6(0)₁₉₉1_<201> = 29 · C200
C200 = P84 · P116
P84 = 367530286683762818311653969900003494345257271270268514080948164981978980653079960969_<84>
P116 = 56293742099725151227484967667076511849333661046901547637197489587498221199711228253147257513850471263698402737741901_<116>

Number: 60001_200 N=20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 ( 200 digits) SNFS difficulty: 200 digits. Divisors found: r1=367530286683762818311653969900003494345257271270268514080948164981978980653079960969 (p84) r2=56293742099725151227484967667076511849333661046901547637197489587498221199711228253147257513850471263698402737741901 (p116) Version: Msieve v. 1.36 Total time: 13 CPU-days. (1 CPU) Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 Y1: 10000000000000000000000000000000000000000 Y0: -1 c0: 6 c5: 1 skew: 1 type: snfs lpbr: 29 lpba: 29 mfbr: 57 mfba: 57 rlambda: 2.5 alambda: 2.5 rlim: 15000000 alim: 15000000 Factor base limits: 15000000/15000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 57/57 Sieved rational special-q in [7500000, 13600001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3079496 x 3079744 Total sieving time: 12.5 days. Matrix solve time: 53:07:51 hours. Time per square root: 00:40:47 hours. (1st dependency!) Prototype def-par.txt line would be: snfs,200,5,0,0,0,0,0,0,0,0,15000000,15000000,29,29,57,57,2.5,2.5,100000 total time: 13 CPU-days. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Fri Jun 20 21:33:29 2008 Msieve v. 1.36 Fri Jun 20 21:33:29 2008 random seeds: 009edf2b 6d52626c Fri Jun 20 21:33:29 2008 factoring 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 (200 digits) Fri Jun 20 21:33:31 2008 no P-1/P+1/ECM available, skipping Fri Jun 20 21:33:31 2008 commencing number field sieve (200-digit input) Fri Jun 20 21:33:31 2008 R0: -1 Fri Jun 20 21:33:31 2008 R1: 10000000000000000000000000000000000000000 Fri Jun 20 21:33:31 2008 A0: 6 Fri Jun 20 21:33:31 2008 A1: 0 Fri Jun 20 21:33:31 2008 A2: 0 Fri Jun 20 21:33:31 2008 A3: 0 Fri Jun 20 21:33:31 2008 A4: 0 Fri Jun 20 21:33:31 2008 A5: 1 Fri Jun 20 21:33:31 2008 size score = 1.681569e-13, Murphy alpha = 0.815479, combined = 1.281333e-13 Fri Jun 20 21:33:31 2008 generating factor base Fri Jun 20 21:33:38 2008 factor base complete: Fri Jun 20 21:33:38 2008 970704 rational roots (max prime = 14999981) Fri Jun 20 21:33:38 2008 969545 algebraic roots (max prime = 14999977) ... ...sieving... ... Tue Jul 1 15:27:06 2008 filtering wants 125832 more relations Tue Jul 1 15:27:06 2008 elapsed time 00:33:10 -> makeJobFile(): Adjusted to q0=13599901, q1=13600000. -> client 1 q0: 13599901 Tue Jul 1 16:23:17 2008 Tue Jul 1 16:23:17 2008 Tue Jul 1 16:23:17 2008 Msieve v. 1.36 Tue Jul 1 16:23:17 2008 random seeds: 73293338 5ae60b30 Tue Jul 1 16:23:17 2008 factoring 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 (200 digits) Tue Jul 1 16:23:19 2008 no P-1/P+1/ECM available, skipping Tue Jul 1 16:23:19 2008 commencing number field sieve (200-digit input) Tue Jul 1 16:23:19 2008 R0: -1 Tue Jul 1 16:23:19 2008 R1: 10000000000000000000000000000000000000000 Tue Jul 1 16:23:19 2008 A0: 6 Tue Jul 1 16:23:19 2008 A1: 0 Tue Jul 1 16:23:19 2008 A2: 0 Tue Jul 1 16:23:19 2008 A3: 0 Tue Jul 1 16:23:19 2008 A4: 0 Tue Jul 1 16:23:19 2008 A5: 1 Tue Jul 1 16:23:19 2008 size score = 1.681569e-13, Murphy alpha = 0.815479, combined = 1.281333e-13 Tue Jul 1 16:23:27 2008 restarting with 38716423 relations Tue Jul 1 16:23:27 2008 Tue Jul 1 16:23:27 2008 commencing relation filtering Tue Jul 1 16:23:27 2008 commencing duplicate removal, pass 1 Tue Jul 1 16:23:28 2008 error -9 reading relation 1 Tue Jul 1 16:24:34 2008 error -9 reading relation 8560327 Tue Jul 1 16:28:26 2008 found 4666296 hash collisions in 38716421 relations Tue Jul 1 16:28:26 2008 commencing duplicate removal, pass 2 Tue Jul 1 16:28:52 2008 found 2885930 duplicates and 35830491 unique relations Tue Jul 1 16:28:52 2008 memory use: 153.2 MB Tue Jul 1 16:28:58 2008 ignoring smallest 955332 rational and 954318 algebraic ideals Tue Jul 1 16:28:58 2008 filtering rational ideals above 14745600 Tue Jul 1 16:28:58 2008 filtering algebraic ideals above 14745600 Tue Jul 1 16:28:58 2008 need 2864475 more relations than ideals Tue Jul 1 16:28:58 2008 commencing singleton removal, pass 1 Tue Jul 1 16:33:56 2008 relations with 0 large ideals: 349980 Tue Jul 1 16:33:56 2008 relations with 1 large ideals: 2681713 Tue Jul 1 16:33:56 2008 relations with 2 large ideals: 9046027 Tue Jul 1 16:33:56 2008 relations with 3 large ideals: 14378910 Tue Jul 1 16:33:56 2008 relations with 4 large ideals: 9313993 Tue Jul 1 16:33:56 2008 relations with 5 large ideals: 59754 Tue Jul 1 16:33:56 2008 relations with 6 large ideals: 114 Tue Jul 1 16:33:56 2008 relations with 7+ large ideals: 0 Tue Jul 1 16:33:56 2008 35830491 relations and about 33000174 large ideals Tue Jul 1 16:33:56 2008 commencing singleton removal, pass 2 Tue Jul 1 16:38:54 2008 found 12137340 singletons Tue Jul 1 16:38:54 2008 current dataset: 23693151 relations and about 18987468 large ideals Tue Jul 1 16:38:54 2008 commencing singleton removal, pass 3 Tue Jul 1 16:42:10 2008 found 2831933 singletons Tue Jul 1 16:42:10 2008 current dataset: 20861218 relations and about 16012294 large ideals Tue Jul 1 16:42:10 2008 commencing singleton removal, pass 4 Tue Jul 1 16:45:07 2008 found 760992 singletons Tue Jul 1 16:45:07 2008 current dataset: 20100226 relations and about 15239442 large ideals Tue Jul 1 16:45:07 2008 commencing singleton removal, pass 5 Tue Jul 1 16:47:59 2008 found 209746 singletons Tue Jul 1 16:47:59 2008 current dataset: 19890480 relations and about 15028746 large ideals Tue Jul 1 16:47:59 2008 commencing singleton removal, final pass Tue Jul 1 16:51:43 2008 memory use: 352.2 MB Tue Jul 1 16:51:44 2008 commencing in-memory singleton removal Tue Jul 1 16:51:47 2008 begin with 19890480 relations and 18306064 unique ideals Tue Jul 1 16:52:34 2008 reduce to 12514527 relations and 10463483 ideals in 21 passes Tue Jul 1 16:52:34 2008 max relations containing the same ideal: 21 Tue Jul 1 16:52:37 2008 filtering rational ideals above 720000 Tue Jul 1 16:52:37 2008 filtering algebraic ideals above 720000 Tue Jul 1 16:52:37 2008 need 116191 more relations than ideals Tue Jul 1 16:52:37 2008 commencing singleton removal, final pass Tue Jul 1 16:55:59 2008 keeping 11195651 ideals with weight <= 20, new excess is 1177388 Tue Jul 1 16:56:11 2008 memory use: 355.6 MB Tue Jul 1 16:56:11 2008 commencing in-memory singleton removal Tue Jul 1 16:56:13 2008 begin with 12514528 relations and 11195651 unique ideals Tue Jul 1 16:56:34 2008 reduce to 12511886 relations and 11193004 ideals in 9 passes Tue Jul 1 16:56:34 2008 max relations containing the same ideal: 20 Tue Jul 1 16:56:47 2008 removing 287933 relations and 276056 ideals in 11878 cliques Tue Jul 1 16:56:48 2008 commencing in-memory singleton removal Tue Jul 1 16:56:50 2008 begin with 12223953 relations and 11193004 unique ideals Tue Jul 1 16:57:13 2008 reduce to 12217820 relations and 10910803 ideals in 9 passes Tue Jul 1 16:57:13 2008 max relations containing the same ideal: 20 Tue Jul 1 16:57:25 2008 removing 208850 relations and 196972 ideals in 11878 cliques Tue Jul 1 16:57:25 2008 commencing in-memory singleton removal Tue Jul 1 16:57:29 2008 begin with 12008970 relations and 10910803 unique ideals Tue Jul 1 16:57:59 2008 reduce to 12005805 relations and 10710657 ideals in 11 passes Tue Jul 1 16:57:59 2008 max relations containing the same ideal: 20 Tue Jul 1 16:58:02 2008 relations with 0 large ideals: 113697 Tue Jul 1 16:58:02 2008 relations with 1 large ideals: 770261 Tue Jul 1 16:58:02 2008 relations with 2 large ideals: 2472911 Tue Jul 1 16:58:02 2008 relations with 3 large ideals: 4030039 Tue Jul 1 16:58:02 2008 relations with 4 large ideals: 3306042 Tue Jul 1 16:58:02 2008 relations with 5 large ideals: 1129408 Tue Jul 1 16:58:02 2008 relations with 6 large ideals: 171106 Tue Jul 1 16:58:02 2008 relations with 7+ large ideals: 12341 Tue Jul 1 16:58:02 2008 commencing 2-way merge Tue Jul 1 16:58:15 2008 reduce to 6550256 relation sets and 5255140 unique ideals Tue Jul 1 16:58:15 2008 ignored 33 oversize relation sets Tue Jul 1 16:58:15 2008 commencing full merge Tue Jul 1 16:59:48 2008 memory use: 454.1 MB Tue Jul 1 16:59:49 2008 found 3213687 cycles, need 3125340 Tue Jul 1 16:59:50 2008 weight of 3125340 cycles is about 219015996 (70.08/cycle) Tue Jul 1 16:59:50 2008 distribution of cycle lengths: Tue Jul 1 16:59:50 2008 1 relations: 425540 Tue Jul 1 16:59:50 2008 2 relations: 415093 Tue Jul 1 16:59:50 2008 3 relations: 401689 Tue Jul 1 16:59:50 2008 4 relations: 351498 Tue Jul 1 16:59:50 2008 5 relations: 288577 Tue Jul 1 16:59:50 2008 6 relations: 247431 Tue Jul 1 16:59:50 2008 7 relations: 201519 Tue Jul 1 16:59:50 2008 8 relations: 161059 Tue Jul 1 16:59:50 2008 9 relations: 129940 Tue Jul 1 16:59:50 2008 10+ relations: 502994 Tue Jul 1 16:59:50 2008 heaviest cycle: 22 relations Tue Jul 1 16:59:51 2008 commencing cycle optimization Tue Jul 1 17:00:03 2008 start with 17192621 relations Tue Jul 1 17:00:44 2008 pruned 170374 relations Tue Jul 1 17:00:44 2008 memory use: 619.4 MB Tue Jul 1 17:00:45 2008 distribution of cycle lengths: Tue Jul 1 17:00:45 2008 1 relations: 425540 Tue Jul 1 17:00:45 2008 2 relations: 418823 Tue Jul 1 17:00:45 2008 3 relations: 408212 Tue Jul 1 17:00:45 2008 4 relations: 354004 Tue Jul 1 17:00:45 2008 5 relations: 291359 Tue Jul 1 17:00:45 2008 6 relations: 247776 Tue Jul 1 17:00:45 2008 7 relations: 201337 Tue Jul 1 17:00:45 2008 8 relations: 160104 Tue Jul 1 17:00:45 2008 9 relations: 128766 Tue Jul 1 17:00:45 2008 10+ relations: 489419 Tue Jul 1 17:00:45 2008 heaviest cycle: 22 relations Tue Jul 1 17:00:55 2008 elapsed time 00:37:38 Tue Jul 1 17:00:57 2008 Tue Jul 1 17:00:57 2008 Tue Jul 1 17:00:57 2008 Msieve v. 1.36 Tue Jul 1 17:00:57 2008 random seeds: 325f3526 08946e45 Tue Jul 1 17:00:57 2008 factoring 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 (200 digits) Tue Jul 1 17:01:03 2008 no P-1/P+1/ECM available, skipping Tue Jul 1 17:01:03 2008 commencing number field sieve (200-digit input) Tue Jul 1 17:01:03 2008 R0: -1 Tue Jul 1 17:01:03 2008 R1: 10000000000000000000000000000000000000000 Tue Jul 1 17:01:03 2008 A0: 6 Tue Jul 1 17:01:03 2008 A1: 0 Tue Jul 1 17:01:03 2008 A2: 0 Tue Jul 1 17:01:03 2008 A3: 0 Tue Jul 1 17:01:03 2008 A4: 0 Tue Jul 1 17:01:03 2008 A5: 1 Tue Jul 1 17:01:03 2008 size score = 1.681569e-13, Murphy alpha = 0.815479, combined = 1.281333e-13 Tue Jul 1 17:01:03 2008 Tue Jul 1 17:01:03 2008 commencing linear algebra Tue Jul 1 17:01:08 2008 read 3125340 cycles Tue Jul 1 17:01:28 2008 cycles contain 10751011 unique relations Tue Jul 1 17:02:59 2008 read 10751011 relations Tue Jul 1 17:03:27 2008 using 32 quadratic characters above 536868974 Tue Jul 1 17:05:31 2008 building initial matrix Tue Jul 1 17:08:07 2008 memory use: 1308.9 MB Tue Jul 1 17:08:10 2008 read 3125340 cycles Tue Jul 1 17:08:13 2008 matrix is 3124507 x 3125340 (946.8 MB) with weight 299306570 (95.77/col) Tue Jul 1 17:08:13 2008 sparse part has weight 213814726 (68.41/col) Tue Jul 1 17:10:18 2008 filtering completed in 3 passes Tue Jul 1 17:10:19 2008 matrix is 3079544 x 3079744 (939.5 MB) with weight 296593355 (96.30/col) Tue Jul 1 17:10:19 2008 sparse part has weight 212416998 (68.97/col) Tue Jul 1 17:10:58 2008 read 3079744 cycles Tue Jul 1 17:11:01 2008 matrix is 3079544 x 3079744 (939.5 MB) with weight 296593355 (96.30/col) Tue Jul 1 17:11:01 2008 sparse part has weight 212416998 (68.97/col) Tue Jul 1 17:11:01 2008 saving the first 48 matrix rows for later Tue Jul 1 17:11:03 2008 matrix is 3079496 x 3079744 (901.2 MB) with weight 229186974 (74.42/col) Tue Jul 1 17:11:03 2008 sparse part has weight 205451830 (66.71/col) Tue Jul 1 17:11:03 2008 matrix includes 64 packed rows Tue Jul 1 17:11:03 2008 using block size 43690 for processor cache size 1024 kB Tue Jul 1 17:11:22 2008 commencing Lanczos iteration Tue Jul 1 17:11:22 2008 memory use: 866.0 MB Thu Jul 3 22:08:36 2008 lanczos halted after 48705 iterations (dim = 3079494) Thu Jul 3 22:08:48 2008 recovered 46 nontrivial dependencies Thu Jul 3 22:08:48 2008 elapsed time 53:07:51 Thu Jul 3 22:08:48 2008 Thu Jul 3 22:08:48 2008 Thu Jul 3 22:08:48 2008 Msieve v. 1.36 Thu Jul 3 22:08:48 2008 random seeds: 93ca7f7c 9d776727 Thu Jul 3 22:08:48 2008 factoring 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069 (200 digits) Thu Jul 3 22:08:50 2008 no P-1/P+1/ECM available, skipping Thu Jul 3 22:08:50 2008 commencing number field sieve (200-digit input) Thu Jul 3 22:08:50 2008 R0: -1 Thu Jul 3 22:08:50 2008 R1: 10000000000000000000000000000000000000000 Thu Jul 3 22:08:50 2008 A0: 6 Thu Jul 3 22:08:50 2008 A1: 0 Thu Jul 3 22:08:50 2008 A2: 0 Thu Jul 3 22:08:50 2008 A3: 0 Thu Jul 3 22:08:50 2008 A4: 0 Thu Jul 3 22:08:50 2008 A5: 1 Thu Jul 3 22:08:50 2008 size score = 1.681569e-13, Murphy alpha = 0.815479, combined = 1.281333e-13 Thu Jul 3 22:08:50 2008 Thu Jul 3 22:08:50 2008 commencing square root phase Thu Jul 3 22:08:50 2008 reading relations for dependency 1 Thu Jul 3 22:08:50 2008 read 1538490 cycles Thu Jul 3 22:08:57 2008 cycles contain 6386580 unique relations Thu Jul 3 22:09:54 2008 read 6386580 relations Thu Jul 3 22:10:51 2008 multiplying 8458902 relations Thu Jul 3 22:25:40 2008 multiply complete, coefficients have about 201.64 million bits Thu Jul 3 22:25:44 2008 initial square root is modulo 17227841 Thu Jul 3 22:49:35 2008 prp84 factor: 367530286683762818311653969900003494345257271270268514080948164981978980653079960969 Thu Jul 3 22:49:35 2008 prp116 factor: 56293742099725151227484967667076511849333661046901547637197489587498221199711228253147257513850471263698402737741901 Thu Jul 3 22:49:35 2008 elapsed time 00:40:47 total time: 13 CPU-days.
C200 is the second largest snfs-factored number in our tables so far and P84 is so big as our expectations. Congratulations!
Jul 4, 2008 (4th): By Robert Backstrom / GMP-ECM
(4·10¹⁷³+41)/9 = (4)₁₇₂9_<173> = 17 · 151 · C170
C170 = P40 · P130
P40 = 3690261951417434928982708714910132460751_<40>
P130 = 4691745193852098076874265382218613551734230024345277073373087798519293567157971656250985794207394773191162000531186646913618048697_<130>
Jul 4, 2008 (3rd): By Sinkiti Sibata / GGNFS
(22·10¹⁸⁶-13)/9 = 2(4)₁₈₅3_<187> = 31 · 16879 · 1543033 · 5960683 · 189223412921_<12> · 13731509942096227_<17> · 46081468145707033413173827_<26> · C115
C115 = P56 · P59
P56 = 43959204954398191758967014257475577232360237024190677731_<56>
P59 = 96500868268959376515840611142404886048601428365351772525347_<59>

Number: 24443_186 N=4242101446512566279037752919245875197556434359228304425000793653490947024758992103027621559431224282849289305947657 ( 115 digits) Divisors found: r1=43959204954398191758967014257475577232360237024190677731 (pp56) r2=96500868268959376515840611142404886048601428365351772525347 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 40.02 hours. Scaled time: 40.34 units (timescale=1.008). Factorization parameters were as follows: name: 24443_186 n: 4242101446512566279037752919245875197556434359228304425000793653490947024758992103027621559431224282849289305947657 skew: 41072.16 # norm 1.73e+16 c5: 28980 c4: -5531699547 c3: 372309325381604 c2: 23901648869437194434 c1: -212452296877258001651416 c0: 402545251072873544415047961 # alpha -6.80 Y1: 1980335979017 Y0: -10791941343671477762770 # Murphy_E 5.63e-10 # M 2831575661041463818221452258434492024696583287593071787784957834298756538742697938919050064827202075377543747090696 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3050001) Primes: RFBsize:250150, AFBsize:250878, largePrimes:7937801 encountered Relations: rels:8210451, finalFF:866897 Max relations in full relation-set: 28 Initial matrix: 501111 x 866897 with sparse part having weight 84364678. Pruned matrix : 288555 x 291124 with weight 56212619. Total sieving time: 38.67 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.94 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 40.02 hours. --------- CPU info (if available) ----------
Jul 4, 2008 (2nd): By Robert Backstrom / GMP-ECM
(22·10¹⁶⁸-13)/9 = 2(4)₁₆₇3_<169> = 61 · 1181 · 2753 · C161
C161 = P36 · P125
P36 = 272806960740898694897744916795109789_<36>
P125 = 45179225343192939814830264722714360700948905264435948248866595060194010598980819143752130662346477005769664390040536535097919_<125>
Jul 4, 2008: By Serge Batalov / GMP-ECM, pol51, Msieve
(22·10¹⁶⁰-13)/9 = 2(4)₁₅₉3_<161> = 83 · 343823 · 855737224949_<12> · C142
C142 = P33 · P48 · P61
P33 = 735790587500551731348419488073351_<33>
P48 = 587239052741479910497804853780708830854156297691_<48>
P61 = 2316634778346193718074128370167758320496447356746829997837303_<61>

# memo: # 1. started as SNFS (complexity=160) + ECM in parallel # ==> ECM found P33, reduced to C109 # 2. Restarted as GNFS-109 and finished in under 8 hours Run 618 out of 950: Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2528959712 Step 1 took 5168ms Step 2 took 2516ms ********** Factor found in step 2: 735790587500551731348419488073351 Found probable prime factor of 33 digits: 735790587500551731348419488073351 Composite cofactor ... has 109 digits ________________________________ Number: 24443_160_1 N=1360418412783987074914444113841721330588031373907259564665334948457960743026634867009277756438778267452567373 ( 109 digits) Divisors found: r1=587239052741479910497804853780708830854156297691 r2=2316634778346193718074128370167758320496447356746829997837303 Version: Total time: 7.00 hours. Scaled time: 21.00 units (timescale=2.952). Factorization parameters were as follows: name: 24443_160_1 n: 1360418412783987074914444113841721330588031373907259564665334948457960743026634867009277756438778267452567373 skew: 41860.23 # norm 1.64e+15 c5: 3420 c4: 1690161444 c3: -41999216776651 c2: -2882404502481927453 c1: 13452908855870193561711 c0: -31177496575363663531230471 # alpha -6.60 Y1: 24432329119 Y0: -831625922016089307142 # Murphy_E 1.22e-09 # M 698164231928883033395764254761249812600819043440596205752521820506521365412989261638914584739305378444049168 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1600000, 2800001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 383287 x 383535 Total sieving time: 6.20 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.51 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,26,26,49,49,2.6,2.6,100000 total time: 7.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)
Jul 3, 2008 (4th): By Sinkiti Sibata / GGNFS
(22·10¹⁵⁹-13)/9 = 2(4)₁₅₈3_<160> = 7³ · 241 · 174319009 · C147
C147 = P53 · P94
P53 = 35979740872329018517519746209133239737925977264625179_<53>
P94 = 4714832073781596621362448799071690079103424956069158006846652811186139395908205559836553336951_<94>

Number: 24443_159 N=169638436271207498618321778981267682748389403467968388237789976659448429627083605891836793599367968896683372273498374419202359611720013660705689229 ( 147 digits) SNFS difficulty: 161 digits. Divisors found: r1=35979740872329018517519746209133239737925977264625179 (pp53) r2=4714832073781596621362448799071690079103424956069158006846652811186139395908205559836553336951 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 44.04 hours. Scaled time: 43.82 units (timescale=0.995). Factorization parameters were as follows: name: 24443_159 n: 169638436271207498618321778981267682748389403467968388237789976659448429627083605891836793599367968896683372273498374419202359611720013660705689229 m: 100000000000000000000000000000000 c5: 11 c0: -65 skew: 1.43 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3700001) Primes: RFBsize:283146, AFBsize:283393, largePrimes:5721164 encountered Relations: rels:5780761, finalFF:678838 Max relations in full relation-set: 28 Initial matrix: 566604 x 678838 with sparse part having weight 44595218. Pruned matrix : 483941 x 486838 with weight 30357189. Total sieving time: 42.29 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.58 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 44.04 hours. --------- CPU info (if available) ----------
(22·10¹⁵⁷-13)/9 = 2(4)₁₅₆3_<158> = 1901 · 45646637540051_<14> · C141
C141 = P69 · P72
P69 = 941115575237730669914918455345091326630972261040701955276054024800787_<69>
P72 = 299327281814835613590373614390897333859536305210099996132872751678060239_<72>

Number: 24443_157 N=281701567009515337244234737436856874873686680115008093807195786046964542930044212193347083470278961240801256470701268719003298688370560608093 ( 141 digits) SNFS difficulty: 158 digits. Divisors found: r1=941115575237730669914918455345091326630972261040701955276054024800787 (pp69) r2=299327281814835613590373614390897333859536305210099996132872751678060239 (pp72) Version: GGNFS-0.77.1-20060513-k8 Total time: 59.57 hours. Scaled time: 118.90 units (timescale=1.996). Factorization parameters were as follows: name: 24443_157 n: 281701567009515337244234737436856874873686680115008093807195786046964542930044212193347083470278961240801256470701268719003298688370560608093 m: 10000000000000000000000000000000 c5: 2200 c0: -13 skew: 0.36 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, 3900001) Primes: RFBsize:283146, AFBsize:283003, largePrimes:5890953 encountered Relations: rels:6046569, finalFF:756840 Max relations in full relation-set: 28 Initial matrix: 566216 x 756840 with sparse part having weight 51799263. Pruned matrix : 427261 x 430156 with weight 36328521. Total sieving time: 56.77 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.41 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 59.57 hours. --------- CPU info (if available) ----------
Jul 3, 2008 (3rd): By Sinkiti Sibata / GGNFS
(22·10¹⁵⁶-13)/9 = 2(4)₁₅₅3_<157> = 31 · 69610967 · C148
C148 = P68 · P80
P68 = 58736020814238558891405825208486913134774314421667326208192258974379_<68>
P80 = 19285739207270759069175268490680623206978396054095595843811679209703382453696521_<80>

Number: 24443_156 N=1132767579496231949385886206437540984692756560598462115818360616266781568801922447745841285021267505089852851103858318504307705517077245584780435459 ( 148 digits) SNFS difficulty: 157 digits. Divisors found: r1=58736020814238558891405825208486913134774314421667326208192258974379 (pp68) r2=19285739207270759069175268490680623206978396054095595843811679209703382453696521 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 32.99 hours. Scaled time: 33.28 units (timescale=1.009). Factorization parameters were as follows: name: 24443_156 n: 1132767579496231949385886206437540984692756560598462115818360616266781568801922447745841285021267505089852851103858318504307705517077245584780435459 m: 10000000000000000000000000000000 c5: 220 c0: -13 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, 2800001) Primes: RFBsize:216816, AFBsize:216882, largePrimes:5615042 encountered Relations: rels:5551495, finalFF:527766 Max relations in full relation-set: 28 Initial matrix: 433765 x 527766 with sparse part having weight 43035221. Pruned matrix : 385213 x 387445 with weight 28597768. Total sieving time: 31.80 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.02 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 32.99 hours. --------- CPU info (if available) ----------
Jul 3, 2008 (2nd): By matsui / GGNFS
3·10¹⁹¹+1 = 3(0)₁₉₀1_<192> = 13 · 43 · 41981 · 90059 · 222941 · 1235130679_<10> · 8247897299_<10> · 94927819198801891456854631_<26> · C129
C129 = P61 · P69
P61 = 3509579947593832172401267969183483650808143002961993244596581_<61>
P69 = 187600851274178017217228137473536104234402691756912413319983272561371_<69>

N=658400185783387989190276926287923699496691827000194736855165613840550040610396624987732594211308692726270672023640418105459272551 ( 129 digits) Divisors found: r1=3509579947593832172401267969183483650808143002961993244596581 (pp61) r2=187600851274178017217228137473536104234402691756912413319983272561371 (pp69) Version: GGNFS-0.77.1-20060513-prescott Total time: 321.19 hours. Scaled time: 462.20 units (timescale=1.439). Factorization parameters were as follows: name: 8000 n: 658400185783387989190276926287923699496691827000194736855165613840550040610396624987732594211308692726270672023640418105459272551 skew: 72736.40 # norm 1.83e+18 c5: 786240 c4: -747480222072 c3: 20219639540097418 c2: 3368292628923275673139 c1: -8265186657456836050216142 c0: -2406243418535148656504477194428 # alpha -7.19 Y1: 82320578815277 Y0: -3842277531817596663468793 # Murphy_E 9.16e-11 # M 557761899041843066496540040677737346243348996541460686464442362588014926906968250733206482629057103019058836980746328716567488758 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, 10680001) Primes: RFBsize:374362, AFBsize:375087, largePrimes:9623028 encountered Relations: rels:10716441, finalFF:852775 Max relations in full relation-set: 28 Initial matrix: 749534 x 852775 with sparse part having weight 120954160. Pruned matrix : 674473 x 678284 with weight 101198922. Total sieving time: 308.26 hours. Total relation processing time: 0.80 hours. Matrix solve time: 11.52 hours. Time per square root: 0.62 hours. Prototype def-par.txt line would be: gnfs,128,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000 total time: 321.19 hours.
Jul 3, 2008: By Serge Batalov / pol51, Msieve
(22·10¹⁷¹-13)/9 = 2(4)₁₇₀3_<172> = 7 · 31 · 827 · 5246447 · 479536609 · 4338158526930879037_<19> · 242847323361115062389_<21> · C112
C112 = P38 · P75
P38 = 17489659331233420841041848831787915121_<38>
P75 = 293837879123436495340659649946267814150481624381132301381989520081108118583_<75>

Number: 24443_171 N=5139124404481049086395651731906800311483837611273017081671461373903727665577251446454615728185746159540406793543 ( 112 digits) Divisors found: r1=17489659331233420841041848831787915121 r2=293837879123436495340659649946267814150481624381132301381989520081108118583 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.925). Factorization parameters were as follows: name: 24443_171 n: 5139124404481049086395651731906800311483837611273017081671461373903727665577251446454615728185746159540406793543 skew: 23580.22 # norm 7.24e+15 c5: 148800 c4: -4636284728 c3: -470193859049548 c2: 438239297947085878 c1: 79112332684214555643067 c0: -394126047946406209907151014 # alpha -6.39 Y1: 86199672119 Y0: -2030754175241905544721 # Murphy_E 7.70e-10 # M 2640026109499838171364872472237626803511669852765746996736091001649567901109710655658807811642173908560437128601 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3550001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 445649 x 445892 Total sieving time: 11.00 hours. Total relation processing time: 0.80 hours. Matrix solve time: 1.00 hours. Time per square root: 0.79 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Tue Jul 1 20:09:33 2008 Msieve v. 1.36 Tue Jul 1 20:09:33 2008 random seeds: 702b4d8c a9e2f611 Tue Jul 1 20:09:33 2008 factoring 5139124404481049086395651731906800311483837611273017081671461373903727665577251446454615728185746159540406793543 (112 digits) Tue Jul 1 20:09:33 2008 no P-1/P+1/ECM available, skipping Tue Jul 1 20:09:33 2008 commencing number field sieve (112-digit input) Tue Jul 1 20:09:33 2008 R0: -2030754175241905544721 Tue Jul 1 20:09:33 2008 R1: 86199672119 Tue Jul 1 20:09:33 2008 A0: -394126047946406209907151014 Tue Jul 1 20:09:33 2008 A1: 79112332684214555643067 Tue Jul 1 20:09:33 2008 A2: 438239297947085878 Tue Jul 1 20:09:33 2008 A3: -470193859049548 Tue Jul 1 20:09:33 2008 A4: -4636284728 Tue Jul 1 20:09:33 2008 A5: 148800 Tue Jul 1 20:09:33 2008 size score = 1.249103e-11, Murphy alpha = -6.388435, combined = 1.050556e-10 Tue Jul 1 20:09:33 2008 generating factor base Tue Jul 1 20:09:35 2008 factor base complete: Tue Jul 1 20:09:35 2008 250150 rational roots (max prime = 3499999) Tue Jul 1 20:09:35 2008 250613 algebraic roots (max prime = 3499999) Tue Jul 1 20:09:36 2008 a range: [-4000000, 4000000] Tue Jul 1 20:09:36 2008 b range: [1, 300] Tue Jul 1 20:09:36 2008 number of hash buckets: 54 Tue Jul 1 20:09:36 2008 sieve block size: 65536 Tue Jul 1 20:09:36 2008 Tue Jul 1 20:09:36 2008 maximum RFB prime: 3499999 Tue Jul 1 20:09:36 2008 RFB entries: 250150 Tue Jul 1 20:09:36 2008 medium RFB entries: 6542 Tue Jul 1 20:09:36 2008 resieved RFB entries: 6374 Tue Jul 1 20:09:36 2008 small RFB prime powers: 26 ...... Wed Jul 2 07:37:03 2008 read 222881 cycles Wed Jul 2 07:37:04 2008 cycles contain 942396 unique relations Wed Jul 2 07:37:13 2008 read 942396 relations Wed Jul 2 07:37:19 2008 multiplying 1389020 relations Wed Jul 2 07:40:48 2008 multiply complete, coefficients have about 62.98 million bits Wed Jul 2 07:40:51 2008 initial square root is modulo 1099946581 Wed Jul 2 07:48:08 2008 reading relations for dependency 2 Wed Jul 2 07:48:08 2008 read 223005 cycles Wed Jul 2 07:48:09 2008 cycles contain 943124 unique relations Wed Jul 2 07:48:18 2008 read 943124 relations Wed Jul 2 07:48:24 2008 multiplying 1390606 relations Wed Jul 2 07:51:51 2008 multiply complete, coefficients have about 63.05 million bits Wed Jul 2 07:51:54 2008 initial square root is modulo 1127141789 Wed Jul 2 08:00:03 2008 reading relations for dependency 3 Wed Jul 2 08:00:03 2008 read 222905 cycles Wed Jul 2 08:00:04 2008 cycles contain 944334 unique relations Wed Jul 2 08:00:13 2008 read 944334 relations Wed Jul 2 08:00:19 2008 multiplying 1393096 relations Wed Jul 2 08:04:08 2008 multiply complete, coefficients have about 63.16 million bits Wed Jul 2 08:04:11 2008 initial square root is modulo 1169218081 Wed Jul 2 08:12:57 2008 reading relations for dependency 4 Wed Jul 2 08:12:57 2008 read 222408 cycles Wed Jul 2 08:12:58 2008 cycles contain 941642 unique relations Wed Jul 2 08:13:07 2008 read 941642 relations Wed Jul 2 08:13:14 2008 multiplying 1387418 relations Wed Jul 2 08:16:55 2008 multiply complete, coefficients have about 62.90 million bits Wed Jul 2 08:16:58 2008 initial square root is modulo 1073482523 Wed Jul 2 08:24:19 2008 prp38 factor: 17489659331233420841041848831787915121 Wed Jul 2 08:24:19 2008 prp75 factor: 293837879123436495340659649946267814150481624381132301381989520081108118583 Wed Jul 2 08:24:19 2008 elapsed time 00:47:17 Total time: 13hrs.
Jul 2, 2008 (6th): By suberi / GMP-ECM
10¹⁸⁶+7 = 1(0)₁₈₅7_<187> = 23 · 1674321589150079_<16> · 5169259926503910472517_<22> · C148
C148 = P44 · P105
P44 = 10519579813202962164191587968549958338845129_<44>
P105 = 477536446524351969730209842702002079292017485236107832937025486800606023755171179378285725378006234337547_<105>
Jul 2, 2008 (5th): By Jo Yeong Uk / GMP-ECM
(22·10¹⁶⁶-13)/9 = 2(4)₁₆₅3_<167> = 204748963 · 1560730573355017_<16> · 52343527673168281003_<20> · C124
C124 = P35 · P89
P35 = 92451731827226267738142652673971531_<35>
P89 = 15807110284823092936676892186474766682999520995799709781771826467335821057469454232049481_<89>
Jul 2, 2008 (4th): By Sinkiti Sibata / GGNFS
(22·10¹⁵⁴-13)/9 = 2(4)₁₅₃3_<155> = 3463 · 15581 · C147
C147 = P49 · P99
P49 = 2146985142350986093864164662530779984526223381689_<49>
P99 = 211010133979284123150461874857456724663907315722703385915179202631648184177974032185559336543961529_<99>

Number: 24443_154 N=453035622539013970891682854298717155295753628948673158226457545176192318250968172647477185573936425721132888801189429376654675287366209803099042481 ( 147 digits) SNFS difficulty: 156 digits. Divisors found: r1=2146985142350986093864164662530779984526223381689 (pp49) r2=211010133979284123150461874857456724663907315722703385915179202631648184177974032185559336543961529 (pp99) Version: GGNFS-0.77.1-20050930-nocona Total time: 33.25 hours. Scaled time: 33.45 units (timescale=1.006). Factorization parameters were as follows: name: 24443_154 n: 453035622539013970891682854298717155295753628948673158226457545176192318250968172647477185573936425721132888801189429376654675287366209803099042481 m: 10000000000000000000000000000000 c5: 11 c0: -65 skew: 1.43 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:217057, largePrimes:5707407 encountered Relations: rels:5715253, finalFF:588373 Max relations in full relation-set: 28 Initial matrix: 433938 x 588373 with sparse part having weight 48008079. Pruned matrix : 348032 x 350265 with weight 29877041. Total sieving time: 32.22 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.88 hours. Time per square root: 0.07 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: 33.25 hours. --------- CPU info (if available) ----------
Jul 2, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(22·10¹⁴⁷-13)/9 = 2(4)₁₄₆3_<148> = 7 · C147
C147 = P40 · P108
P40 = 2021712041728844821895966127264309751829_<40>
P108 = 172728035446496740787707614044367729343826209385361445373501288263149880818963169788976312580236715350305881_<108>

Number: n N=349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349 ( 147 digits) SNFS difficulty: 148 digits. Divisors found: r1=2021712041728844821895966127264309751829 (pp40) r2=172728035446496740787707614044367729343826209385361445373501288263149880818963169788976312580236715350305881 (pp108) Version: GGNFS-0.77.1-20051202-athlon Total time: 10.68 hours. Scaled time: 19.54 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_4_146_3 n: 349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349 skew: 0.36 deg: 5 c5: 2200 c0: -13 m: 100000000000000000000000000000 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, 2050001) Primes: RFBsize:114155, AFBsize:114288, largePrimes:7233951 encountered Relations: rels:6609013, finalFF:269764 Max relations in full relation-set: 48 Initial matrix: 228510 x 269764 with sparse part having weight 44600679. Pruned matrix : 220578 x 221784 with weight 32514856. Total sieving time: 9.77 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.67 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 10.68 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(22·10¹⁴⁹-13)/9 = 2(4)₁₄₈3_<150> = 3 · 17 · C148
C148 = P59 · P89
P59 = 69002924247755090799484487397373660603707328555480983703141_<59>
P89 = 69461234791017154769799796429709791557515126520850419394325840918738250512555886792605573_<89>

Number: n N=4793028322440087145969498910675381263616557734204793028322440087145969498910675381263616557734204793028322440087145969498910675381263616557734204793 ( 148 digits) SNFS difficulty: 151 digits. Divisors found: r1=69002924247755090799484487397373660603707328555480983703141 (pp59) r2=69461234791017154769799796429709791557515126520850419394325840918738250512555886792605573 (pp89) Version: GGNFS-0.77.1-20051202-athlon Total time: 11.78 hours. Scaled time: 21.54 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_4_148_3 n: 4793028322440087145969498910675381263616557734204793028322440087145969498910675381263616557734204793028322440087145969498910675381263616557734204793 skew: 1.43 deg: 5 c5: 11 c0: -65 m: 1000000000000000000000000000000 type: snfs rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:135072, AFBsize:135314, largePrimes:6328487 encountered Relations: rels:5664046, finalFF:311042 Max relations in full relation-set: 48 Initial matrix: 270451 x 311042 with sparse part having weight 32188544. Pruned matrix : 249681 x 251097 with weight 20817556. Total sieving time: 10.90 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.49 hours. Total square root time: 0.26 hours, sqrts: 7. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000 total time: 11.78 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
4·10¹⁶⁸-3 = 3(9)₁₆₇7_<169> = 349 · 241074611 · C158
C158 = P77 · P82
P77 = 21544306803353103509843977179159206218824143080472857184693633917823174539019_<77>
P82 = 2206736938256127773273970339311752643567289428173222443185875220281755576364296817_<82>

Number: n N=47542617632082091100384231437845636303263529996343334801020808732923113197004353274453935504867471617106807111737038599279044427284432373996054873344064002523 ( 158 digits) SNFS difficulty: 168 digits. Divisors found: Wed Jul 2 15:47:50 2008 prp77 factor: 21544306803353103509843977179159206218824143080472857184693633917823174539019 Wed Jul 2 15:47:50 2008 prp82 factor: 2206736938256127773273970339311752643567289428173222443185875220281755576364296817 Wed Jul 2 15:47:50 2008 elapsed time 01:07:16 Version: GGNFS-0.77.1-20050930-k8 Total time: 57.18 hours. Scaled time: 47.92 units (timescale=0.838). Factorization parameters were as follows: name: KA_3_9_167_7 n: 47542617632082091100384231437845636303263529996343334801020808732923113197004353274453935504867471617106807111737038599279044427284432373996054873344064002523 type: snfs deg: 5 c5: 125 c0: -3 skew: 0.47 m: 2000000000000000000000000000000000 rlim: 5500000 alim: 5500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3200111) Primes: RFBsize:380800, AFBsize:379892, largePrimes:5594103 encountered Relations: rels:5729847, finalFF:793042 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 57.00 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,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.5,2.5,100000 total time: 57.18 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).
Jul 2, 2008 (2nd): By Sinkiti Sibata / GGNFS, Msieve
(22·10¹³⁷-13)/9 = 2(4)₁₃₆3_<138> = 3³ · C136
C136 = P62 · P75
P62 = 58473762489790941516005057792881835042331950647437243978542293_<62>
P75 = 154830090572117720754725648814565048360015424986244247352985425052957023613_<75>

Number: 24443_137 N=9053497942386831275720164609053497942386831275720164609053497942386831275720164609053497942386831275720164609053497942386831275720164609 ( 136 digits) SNFS difficulty: 138 digits. Divisors found: r1=58473762489790941516005057792881835042331950647437243978542293 (pp62) r2=154830090572117720754725648814565048360015424986244247352985425052957023613 (pp75) Version: GGNFS-0.77.1-20060513-k8 Total time: 12.92 hours. Scaled time: 25.85 units (timescale=2.000). Factorization parameters were as follows: name: 24443_137 n: 9053497942386831275720164609053497942386831275720164609053497942386831275720164609053497942386831275720164609053497942386831275720164609 m: 1000000000000000000000000000 c5: 2200 c0: -13 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, 2125001) Primes: RFBsize:78498, AFBsize:64029, largePrimes:1671959 encountered Relations: rels:1698646, finalFF:166229 Max relations in full relation-set: 28 Initial matrix: 142594 x 166229 with sparse part having weight 18916119. Pruned matrix : 136939 x 137715 with weight 14393055. Total sieving time: 12.59 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.19 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 12.92 hours. --------- CPU info (if available) ----------
(22·10¹³²-13)/9 = 2(4)₁₃₁3_<133> = 42227 · C128
C128 = P53 · P76
P53 = 42883627663814341521903001082675283462854504182949003_<53>
P76 = 1349890144337203998734326849512015502391489910957629428484329332974286483403_<76>

Number: 24443_132 N=57888186336809255794739016374462889725636309575495404467389216483397931286722818207413371644787563512549895669700533886954897209 ( 128 digits) SNFS difficulty: 133 digits. Divisors found: r1=42883627663814341521903001082675283462854504182949003 (pp53) r2=1349890144337203998734326849512015502391489910957629428484329332974286483403 (pp76) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.09 hours. Scaled time: 14.15 units (timescale=1.997). Factorization parameters were as follows: name: 24443_132 n: 57888186336809255794739016374462889725636309575495404467389216483397931286722818207413371644787563512549895669700533886954897209 m: 100000000000000000000000000 c5: 2200 c0: -13 skew: 0.36 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1350001) Primes: RFBsize:63951, AFBsize:64029, largePrimes:1557327 encountered Relations: rels:1558691, finalFF:156948 Max relations in full relation-set: 28 Initial matrix: 128047 x 156948 with sparse part having weight 15590982. Pruned matrix : 121238 x 121942 with weight 10526521. Total sieving time: 6.87 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.10 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 7.09 hours. --------- CPU info (if available) ----------
(22·10¹⁴⁰-13)/9 = 2(4)₁₃₉3_<141> = 3 · 79392461 · C133
C133 = P41 · P92
P41 = 30903737715270715377221878457373280830821_<41>
P92 = 33209982218207158692180677111290215531825231303595299136370285580176392535478664638944361001_<92>

Number: 24443_140 N=1026312580000278382622267893691839096428582576392001269257561892198825798856159421503277011169630847965293347960097640523846231211821 ( 133 digits) SNFS difficulty: 141 digits. Divisors found: r1=30903737715270715377221878457373280830821 (pp41) r2=33209982218207158692180677111290215531825231303595299136370285580176392535478664638944361001 (pp92) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.16 hours. Scaled time: 10.22 units (timescale=1.006). Factorization parameters were as follows: name: 24443_140 n: 1026312580000278382622267893691839096428582576392001269257561892198825798856159421503277011169630847965293347960097640523846231211821 m: 10000000000000000000000000000 c5: 22 c0: -13 skew: 0.9 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, 1950001) Primes: RFBsize:100021, AFBsize:100234, largePrimes:2776498 encountered Relations: rels:2775252, finalFF:272961 Max relations in full relation-set: 28 Initial matrix: 200321 x 272961 with sparse part having weight 27976184. Pruned matrix : 179707 x 180772 with weight 16440918. Total sieving time: 9.91 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.17 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 10.16 hours. --------- CPU info (if available) ----------
(22·10¹¹²-13)/9 = 2(4)₁₁₁3_<113> = 3259 · 13950581137_<11> · C99
C99 = P32 · P68
P32 = 13701829988800447487541383114549_<32>
P68 = 39239633019081925818391162394055049075239789099796401438595560894829_<68>

Tue Jul 1 20:15:56 2008 Msieve v. 1.36 Tue Jul 1 20:15:56 2008 random seeds: 85f03703 ba89e7ee Tue Jul 1 20:15:56 2008 factoring 537654780450380973069393496111123321611416061591593186743289377877472784652282513278331113448767121 (99 digits) Tue Jul 1 20:15:58 2008 no P-1/P+1/ECM available, skipping Tue Jul 1 20:15:58 2008 commencing quadratic sieve (99-digit input) Tue Jul 1 20:15:58 2008 using multiplier of 1 Tue Jul 1 20:15:58 2008 using 64kb Pentium 4 sieve core Tue Jul 1 20:15:58 2008 sieve interval: 18 blocks of size 65536 Tue Jul 1 20:15:58 2008 processing polynomials in batches of 6 Tue Jul 1 20:15:58 2008 using a sieve bound of 2608889 (95294 primes) Tue Jul 1 20:15:58 2008 using large prime bound of 391333350 (28 bits) Tue Jul 1 20:15:58 2008 using double large prime bound of 2928089178039000 (43-52 bits) Tue Jul 1 20:15:58 2008 using trial factoring cutoff of 52 bits Tue Jul 1 20:15:58 2008 polynomial 'A' values have 13 factors Wed Jul 2 11:21:29 2008 95448 relations (22485 full + 72963 combined from 1440354 partial), need 95390 Wed Jul 2 11:21:34 2008 begin with 1462839 relations Wed Jul 2 11:21:36 2008 reduce to 252560 relations in 11 passes Wed Jul 2 11:21:36 2008 attempting to read 252560 relations Wed Jul 2 11:21:45 2008 recovered 252560 relations Wed Jul 2 11:21:45 2008 recovered 242733 polynomials Wed Jul 2 11:21:45 2008 attempting to build 95448 cycles Wed Jul 2 11:21:45 2008 found 95448 cycles in 5 passes Wed Jul 2 11:21:45 2008 distribution of cycle lengths: Wed Jul 2 11:21:45 2008 length 1 : 22485 Wed Jul 2 11:21:45 2008 length 2 : 16133 Wed Jul 2 11:21:45 2008 length 3 : 16027 Wed Jul 2 11:21:45 2008 length 4 : 13262 Wed Jul 2 11:21:45 2008 length 5 : 10160 Wed Jul 2 11:21:45 2008 length 6 : 6709 Wed Jul 2 11:21:45 2008 length 7 : 4445 Wed Jul 2 11:21:45 2008 length 9+: 6227 Wed Jul 2 11:21:45 2008 largest cycle: 20 relations Wed Jul 2 11:21:46 2008 matrix is 95294 x 95448 (25.3 MB) with weight 6255327 (65.54/col) Wed Jul 2 11:21:46 2008 sparse part has weight 6255327 (65.54/col) Wed Jul 2 11:21:48 2008 filtering completed in 3 passes Wed Jul 2 11:21:48 2008 matrix is 91505 x 91569 (24.4 MB) with weight 6039314 (65.95/col) Wed Jul 2 11:21:48 2008 sparse part has weight 6039314 (65.95/col) Wed Jul 2 11:21:48 2008 saving the first 48 matrix rows for later Wed Jul 2 11:21:49 2008 matrix is 91457 x 91569 (14.3 MB) with weight 4638240 (50.65/col) Wed Jul 2 11:21:49 2008 sparse part has weight 3191337 (34.85/col) Wed Jul 2 11:21:49 2008 matrix includes 64 packed rows Wed Jul 2 11:21:49 2008 using block size 21845 for processor cache size 512 kB Wed Jul 2 11:21:49 2008 commencing Lanczos iteration Wed Jul 2 11:21:49 2008 memory use: 14.5 MB Wed Jul 2 11:23:17 2008 lanczos halted after 1447 iterations (dim = 91455) Wed Jul 2 11:23:17 2008 recovered 15 nontrivial dependencies Wed Jul 2 11:23:19 2008 prp32 factor: 13701829988800447487541383114549 Wed Jul 2 11:23:19 2008 prp68 factor: 39239633019081925818391162394055049075239789099796401438595560894829 Wed Jul 2 11:23:19 2008 elapsed time 15:07:23
(22·10¹³⁹-13)/9 = 2(4)₁₃₈3_<140> = 149 · 168851 · C132
C132 = P36 · P97
P36 = 153134131586673253525316680340706127_<36>
P97 = 6344804807107506932431402272201079387020389960080550065808574943830533716609237345358028267464891_<97>

Number: 24443_139 N=971606174223357976843188915513989536799608138864038956885201254815241556023578249678947093000919656158644315431926796046363121087157 ( 132 digits) SNFS difficulty: 141 digits. Divisors found: r1=153134131586673253525316680340706127 (pp36) r2=6344804807107506932431402272201079387020389960080550065808574943830533716609237345358028267464891 (pp97) Version: GGNFS-0.77.1-20060513-k8 Total time: 10.28 hours. Scaled time: 20.44 units (timescale=1.989). Factorization parameters were as follows: name: 24443_139 n: 971606174223357976843188915513989536799608138864038956885201254815241556023578249678947093000919656158644315431926796046363121087157 m: 10000000000000000000000000000 c5: 11 c0: -65 skew: 1.43 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, 1750001) Primes: RFBsize:100021, AFBsize:100099, largePrimes:2766896 encountered Relations: rels:2782205, finalFF:298407 Max relations in full relation-set: 28 Initial matrix: 200185 x 298407 with sparse part having weight 27881999. Pruned matrix : 171496 x 172560 with weight 14209059. Total sieving time: 9.82 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.30 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 10.28 hours. --------- CPU info (if available) ----------
Jul 2, 2008: By Serge Batalov / GMP-ECM, pol51, Msieve
(22·10¹⁹⁰-13)/9 = 2(4)₁₈₉3_<191> = 37579 · 197712115002913632677_<21> · 4324556297448073545291529_<25> · 5173627017798433092541301317_<28> · C114
C114 = P44 · P70
P44 = 23032466315154297903558471524435237785670147_<44>
P70 = 6384465648362112581210497692982220217680658290277639789815364462792251_<70>
(68·10¹⁷⁹+13)/9 = 7(5)₁₇₈7_<180> = 11 · 9857 · 33493 · 30812581 · 6965459779_<10> · 2442025749808860916183882823027_<31> · C123
C123 = P44 · P79
P44 = 57629319515256167066500951939735023830699563_<44>
P79 = 6888161396207106342594867165412911745264595604363393849592578966611969346616013_<79>
(22·10¹⁹⁵-13)/9 = 2(4)₁₉₄3_<196> = 7 · 26837687 · 95955997 · 466934099 · 34189412940043_<14> · 387163017726257_<15> · 28293299911166088280426132237163_<32> · C111
C111 = P31 · P40 · P41
P31 = 4432786487726332261901992580177_<31>
P40 = 2282361128060960866345069318662723827857_<40>
P41 = 76644156088849870258058669364338740667237_<41>

Number: 24443_195 N=775425755799446841939053048525302354064197837605938152294567158088550638083405933820635565662056629872055556293 ( 111 digits) Divisors found: r1=4432786487726332261901992580177 r2=2282361128060960866345069318662723827857 r3=76644156088849870258058669364338740667237 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.844). Factorization parameters were as follows: name: 24443_195 n: 775425755799446841939053048525302354064197837605938152294567158088550638083405933820635565662056629872055556293 skew: 38578.42 # norm 4.25e+14 c5: 5940 c4: -241464251 c3: -28961153603108 c2: 292489093069413502 c1: 20420682911241094723856 c0: 133575367865294507252877085 # alpha -4.46 Y1: 309827997097 Y0: -2649422183486934259056 # Murphy_E 8.30e-10 # M 627846271663089527779179125876741566414536726272675783926772171413507244872142141742899588517629762116642887585 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, 2500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 432467 x 432707 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Calibrating delay using timer specific routine.. 5600.62 BogoMIPS (lpj=11201256) Calibrating delay using timer specific routine.. 5600.69 BogoMIPS (lpj=11201386) Calibrating delay using timer specific routine.. 5600.70 BogoMIPS (lpj=11201415) Calibrating delay using timer specific routine.. 5600.65 BogoMIPS (lpj=11201310) Calibrating delay using timer specific routine.. 5600.66 BogoMIPS (lpj=11201320) Calibrating delay using timer specific routine.. 5600.75 BogoMIPS (lpj=11201501) Calibrating delay using timer specific routine.. 5600.56 BogoMIPS (lpj=11201124) saving the first 48 matrix rows for later matrix is 432467 x 432707 (127.7 MB) with weight 34239845 (79.13/col) sparse part has weight 29137637 (67.34/col) matrix includes 64 packed rows using block size 43690 for processor cache size 1024 kB commencing Lanczos iteration memory use: 117.7 MB linear algebra completed 431051 out of 432707 dimensions (99.6%) lanczos halted after 6840 iterations (dim = 432466) recovered 44 nontrivial dependencies elapsed time 00:40:04 =>nice -n 19 "/depts/BioInf/Batalov/MERSE/ggbin/msieve" -s 24443_195.dat -l ggnfs.log -i 24443_195.ini -v -nf 24443_195.fb -t 1 -nc3 Msieve v. 1.36 Tue Jul 1 17:52:34 2008 random seeds: 6a729032 ef40d2b8 factoring 775425755799446841939053048525302354064197837605938152294567158088550638083405933820635565662056629872055556293 (111 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (111-digit input) R0: -2649422183486934259056 R1: 309827997097 A0: 133575367865294507252877085 A1: 20420682911241094723856 A2: 292489093069413502 A3: -28961153603108 A4: -241464251 A5: 5940 size score = 2.646882e-11, Murphy alpha = -4.459988, combined = 1.170534e-10 commencing square root phase reading relations for dependency 1 read 216070 cycles cycles contain 940344 unique relations read 940344 relations multiplying 1324484 relations multiply complete, coefficients have about 54.75 million bits initial square root is modulo 72519241 reading relations for dependency 2 read 216114 cycles cycles contain 940777 unique relations read 940777 relations multiplying 1325292 relations multiply complete, coefficients have about 54.78 million bits initial square root is modulo 73261117 prp31 factor: 4432786487726332261901992580177 prp40 factor: 2282361128060960866345069318662723827857 prp41 factor: 76644156088849870258058669364338740667237 elapsed time 00:20:08 -> Computing time scale for this machine... sumName = g111-24443_195.txt -> Factorization summary written to g111-24443_195.txt. Tue Jul 1 03:08:15 2008 Msieve v. 1.36 Tue Jul 1 03:08:15 2008 random seeds: 2448e225 c3c7c117 Tue Jul 1 03:08:15 2008 factoring 775425755799446841939053048525302354064197837605938152294567158088550638083405933820635565662056629872055556293 (111 digits) Tue Jul 1 03:08:16 2008 no P-1/P+1/ECM available, skipping Tue Jul 1 03:08:16 2008 commencing number field sieve (111-digit input) Tue Jul 1 03:08:16 2008 R0: -2649422183486934259056 Tue Jul 1 03:08:16 2008 R1: 309827997097 Tue Jul 1 03:08:16 2008 A0: 133575367865294507252877085 .... Tue Jul 1 18:02:16 2008 read 216114 cycles Tue Jul 1 18:02:17 2008 cycles contain 940777 unique relations Tue Jul 1 18:02:27 2008 read 940777 relations Tue Jul 1 18:02:33 2008 multiplying 1325292 relations Tue Jul 1 18:05:57 2008 multiply complete, coefficients have about 54.78 million bits Tue Jul 1 18:05:59 2008 initial square root is modulo 73261117 Tue Jul 1 18:12:42 2008 prp31 factor: 4432786487726332261901992580177 Tue Jul 1 18:12:42 2008 prp40 factor: 2282361128060960866345069318662723827857 Tue Jul 1 18:12:42 2008 prp41 factor: 76644156088849870258058669364338740667237 Tue Jul 1 18:12:42 2008 elapsed time 00:20:08 Total time: 15hr 04mn
Jul 1, 2008 (7th): By Robert Backstrom / GGNFS, Msieve
(22·10¹¹⁴-13)/9 = 2(4)₁₁₃3_<115> = C115
C115 = P44 · P71
P44 = 33598656294760900291371699381269381784370549_<44>
P71 = 72754232282366932679878294542235391018639436852035736262753056974819407_<71>

Number: n N=2444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 ( 115 digits) SNFS difficulty: 116 digits. Divisors found: Tue Jul 01 23:04:53 2008 prp44 factor: 33598656294760900291371699381269381784370549 Tue Jul 01 23:04:53 2008 prp71 factor: 72754232282366932679878294542235391018639436852035736262753056974819407 Tue Jul 01 23:04:53 2008 elapsed time 00:04:17 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.76 hours. Scaled time: 1.38 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_4_113_3 n: 2444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 skew: 1.43 deg: 5 c5: 11 c0: -65 m: 100000000000000000000000 type: snfs rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 180347) Primes: RFBsize:41538, AFBsize:41593, largePrimes:3591138 encountered Relations: rels:2958004, finalFF:89757 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 0.71 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,50000 total time: 0.76 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(22·10¹¹⁶-13)/9 = 2(4)₁₁₅3_<117> = 3 · 19 · 105879019 · 137400189118849_<15> · C93
C93 = P41 · P52
P41 = 52216810517743850150033554179233611101121_<41>
P52 = 5645439212850785908811753527171750497376343817221849_<52>

Number: n N=294786829666870480000441341655921667461151477270136085258399731059313122304735247508029592729 ( 93 digits) SNFS difficulty: 117 digits. Divisors found: r1=52216810517743850150033554179233611101121 (pp41) r2=5645439212850785908811753527171750497376343817221849 (pp52) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.87 hours. Scaled time: 1.58 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_4_115_3 n: 294786829666870480000441341655921667461151477270136085258399731059313122304735247508029592729 skew: 0.57 deg: 5 c5: 220 c0: -13 m: 100000000000000000000000 type: snfs rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:41538, AFBsize:41738, largePrimes:3695260 encountered Relations: rels:3062905, finalFF:93831 Max relations in full relation-set: 48 Initial matrix: 83343 x 93831 with sparse part having weight 8682819. Pruned matrix : 80055 x 80535 with weight 5877569. Total sieving time: 0.77 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Total square root time: 0.02 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,50000 total time: 0.87 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 1, 2008 (6th): By Sinkiti Sibata / GGNFS
(22·10¹²⁹-13)/9 = 2(4)₁₂₈3_<130> = 7 · 241 · 39293 · 13299361 · 2695989282557_<13> · C103
C103 = P39 · P64
P39 = 250682305473299306497685825723691855583_<39>
P64 = 4102771067678316053775037080369167598169783113856398411976486603_<64>

Number: 24443_129 N=1028492110074749967929747272840552481537648574781359688266748220360933344058801859376100555290010254549 ( 103 digits) SNFS difficulty: 131 digits. Divisors found: r1=250682305473299306497685825723691855583 (pp39) r2=4102771067678316053775037080369167598169783113856398411976486603 (pp64) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.48 hours. Scaled time: 8.96 units (timescale=2.000). Factorization parameters were as follows: name: 24443_129 n: 1028492110074749967929747272840552481537648574781359688266748220360933344058801859376100555290010254549 m: 100000000000000000000000000 c5: 11 c0: -65 skew: 1.43 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:63789, largePrimes:1469819 encountered Relations: rels:1461589, finalFF:164980 Max relations in full relation-set: 28 Initial matrix: 127805 x 164980 with sparse part having weight 11368937. Pruned matrix : 116430 x 117133 with weight 6330418. Total sieving time: 4.32 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.48 hours. --------- CPU info (if available) ----------
(22·10¹¹⁷-13)/9 = 2(4)₁₁₆3_<118> = 7² · 17 · 233 · 1621 · C109
C109 = P52 · P58
P52 = 4229313234714843164288246278132448514515779114889059_<52>
P58 = 1837072866508690204598997309979916246707045110648608172733_<58>

Number: 24443_117 N=7769556587460737839239858142009053023060286573645996521722787955598485746053241569530231076455526632003828247 ( 109 digits) SNFS difficulty: 118 digits. Divisors found: r1=4229313234714843164288246278132448514515779114889059 (pp52) r2=1837072866508690204598997309979916246707045110648608172733 (pp58) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.31 hours. Scaled time: 1.56 units (timescale=0.677). Factorization parameters were as follows: name: 24443_117 n: 7769556587460737839239858142009053023060286573645996521722787955598485746053241569530231076455526632003828247 m: 100000000000000000000000 c5: 2200 c0: -13 skew: 0.36 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64029, largePrimes:1982637 encountered Relations: rels:1949806, finalFF:139200 Max relations in full relation-set: 28 Initial matrix: 113194 x 139200 with sparse part having weight 11012584. Pruned matrix : 103684 x 104313 with weight 6438928. Total sieving time: 2.02 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.18 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: 2.31 hours. --------- CPU info (if available) ----------
Jul 1, 2008 (5th): By Robert Backstrom / GMP-ECM
(22·10¹²¹-13)/9 = 2(4)₁₂₀3_<122> = 10139 · 21610123627320666846739365871_<29> · C90
C90 = P33 · P58
P33 = 106291118910715568757506518867309_<33>
P58 = 1049616908171780243294136059455718184430708493672261067883_<58>
Jul 1, 2008 (4th): By Serge Batalov / PRIMO 3.0.6
4·10²²⁴⁵+3 = 4(0)₂₂₄₄3_<2246> is prime.
Jul 1, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(22·10¹⁶⁴-31)/9 = 2(4)₁₆₃1_<165> = 2083 · 73135006949_<11> · C151
C151 = P71 · P80
P71 = 51845043108470586834361561919780616245850625521525516787582746406578547_<71>
P80 = 30949836173738031868495545589299632987292537377947824460601813620688132316642509_<80>

Number: n N=1604595590627550625150237684729477444026023270824767911255148304083581825227614724819356366988897922998432503475970715695690680776482715993969227654423 ( 151 digits) SNFS difficulty: 166 digits. Divisors found: Tue Jul 01 12:05:17 2008 prp71 factor: 51845043108470586834361561919780616245850625521525516787582746406578547 Tue Jul 01 12:05:17 2008 prp80 factor: 30949836173738031868495545589299632987292537377947824460601813620688132316642509 Tue Jul 01 12:05:17 2008 elapsed time 02:20:11 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 58.82 hours. Scaled time: 103.57 units (timescale=1.761). Factorization parameters were as follows: name: KA_2_4_163_1 n: 1604595590627550625150237684729477444026023270824767911255148304083581825227614724819356366988897922998432503475970715695690680776482715993969227654423 type: snfs skew: 1.70 deg: 5 c5: 11 c0: -155 m: 1000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2600267) Primes: RFBsize:348513, AFBsize:348353, largePrimes:7679016 encountered Relations: rels:7285979, finalFF:745129 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 58.55 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,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 58.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
6·10¹⁶⁸+7 = 6(0)₁₆₇7_<169> = 13 · 162683 · 1905773 · C157
C157 = P32 · P34 · P91
P32 = 92496541056236438247583376263031_<32>
P34 = 1737404675144043985388097795414143_<34>
P91 = 9263350086582064127298447027451667014374897979566099083674205980098110320670551785060577237_<91>
(17·10¹⁶⁹-53)/9 = 1(8)₁₆₈3_<170> = 13³ · 1153 · C163
C163 = P34 · P130
P34 = 1899184819671361163387290225408063_<34>
P130 = 3926266888112567544073047887536313671079408556962007900627998803362902182734040273650475604473730549935716930277198186398648831001_<130>
7·10¹⁷³+9 = 7(0)₁₇₂9_<174> = 727 · C171
C171 = P50 · P57 · P65
P50 = 46703390984381129306990060832824441396119105760387_<50>
P57 = 803575513133626214041688443279256687479553115056384050651_<57>
P65 = 25655974804389045502754045805223424190216260512796697773191686191_<65>

Number: n N=962861072902338376891334250343878954607977991746905089408528198074277854195323246217331499312242090784044016506189821182943603851444291609353507565337001375515818431911967 ( 171 digits) SNFS difficulty: 173 digits. Divisors found: Tue Jul 01 15:01:54 2008 prp50 factor: 46703390984381129306990060832824441396119105760387 Tue Jul 01 15:01:54 2008 prp57 factor: 803575513133626214041688443279256687479553115056384050651 Tue Jul 01 15:01:54 2008 prp65 factor: 25655974804389045502754045805223424190216260512796697773191686191 Tue Jul 01 15:01:54 2008 elapsed time 03:00:18 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 143.54 hours. Scaled time: 262.54 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_0_172_9 n: 962861072902338376891334250343878954607977991746905089408528198074277854195323246217331499312242090784044016506189821182943603851444291609353507565337001375515818431911967 skew: 0.26 deg: 5 c5: 7000 c0: 9 m: 10000000000000000000000000000000000 type: snfs rlim: 7200000 alim: 7200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 8200537) Primes: RFBsize:489319, AFBsize:488763, largePrimes:9369787 encountered Relations: rels:8949267, finalFF:985202 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 142.94 hours. Total relation processing time: 0.61 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,48,48,2.5,2.5,100000 total time: 143.54 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jul 1, 2008 (2nd): Factorizations of 11...11 (Repunit) was extended to n=100000 and Factorizations of 100...001 was extended to n=50000.
Jul 1, 2008: The factor table of 244...443 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.

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