News and updates, July 2008

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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-0.77.1-200