Since June 16, 2000

STUDIO KAMADA

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News and updates, May 2007

May 31, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
4·10¹⁵⁴+3 = 4(0)₁₅₃3_<155> = 1327 · 870755550325850941_<18> · C134
C134 = P35 · P40 · P60
P35 = 22208856755600059957457268067062121_<35>
P40 = 1894425688430070080563866230389466204449_<40>
P60 = 822790066767611381874600814825665810874654564700976063637801_<60>

Number: n N=34617270133071285415914354745753361151760004396813244310996447931454777677825544431616161322375402810136808065672456644101628679212529 ( 134 digits) SNFS difficulty: 155 digits. Divisors found: r1=22208856755600059957457268067062121 (pp35) r2=1894425688430070080563866230389466204449 (pp40) r3=822790066767611381874600814825665810874654564700976063637801 (pp60) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 28.57 hours. Scaled time: 38.97 units (timescale=1.364). Factorization parameters were as follows: name: KA_4_0_153_3 n: 34617270133071285415914354745753361151760004396813244310996447931454777677825544431616161322375402810136808065672456644101628679212529 skew: 1.50 deg: 5 c5: 2 c0: 15 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:216721, largePrimes:6921372 encountered Relations: rels:6417283, finalFF:508343 Max relations in full relation-set: 28 Initial matrix: 433602 x 508343 with sparse part having weight 33814808. Pruned matrix : 369514 x 371746 with weight 20585563. Total sieving time: 25.59 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.38 hours. Total square root time: 0.41 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.57 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 31, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
4·10¹⁵⁵+3 = 4(0)₁₅₄3_<156> = 131 · 277 · 1597 · 131311 · 823553 · 667849372139_<12> · C125
C125 = P54 · P72
P54 = 492825456187630481531157139782940959270957733499511907_<54>
P72 = 193927631621634265976915268190761855606404319236001612241209942831445103_<72>

Number: 40003_155 N=95572473521318661498662645987832126295159614647710436217024143597699587551562764245776486857662364971023065753927621965341421 ( 125 digits) SNFS difficulty: 155 digits. Divisors found: r1=492825456187630481531157139782940959270957733499511907 (pp54) r2=193927631621634265976915268190761855606404319236001612241209942831445103 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.81 hours. Scaled time: 16.60 units (timescale=0.932). Factorization parameters were as follows: n: 95572473521318661498662645987832126295159614647710436217024143597699587551562764245776486857662364971023065753927621965341421 m: 10000000000000000000000000000000 c5: 4 c0: 3 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:216936, largePrimes:5532285 encountered Relations: rels:5477183, finalFF:544684 Max relations in full relation-set: 28 Initial matrix: 433819 x 544684 with sparse part having weight 40709982. Pruned matrix : 354442 x 356675 with weight 25742292. Total sieving time: 16.97 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.72 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 17.81 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 31, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs
(2·10¹⁸⁸-17)/3 = (6)₁₈₇1_<188> = 1249 · 4441 · 6752297 · 1389323376967_<13> · 16824073891211_<14> · 1216695017169281822145299803_<28> · C122
C122 = P39 · P41 · P43
P39 = 615078923306073798787696079184152415389_<39>
P41 = 85050733879933863941346674478983397401509_<41>
P43 = 1196434264494666367424967458018651028134987_<43>

Number: 66661_188 N=62588962571313430923171131998101606731573624728012758991844454013795770476577693323728766959320614463002807069297413648987 ( 122 digits) Divisors found: r1=615078923306073798787696079184152415389 (pp39) r2=85050733879933863941346674478983397401509 (pp41) r3=1196434264494666367424967458018651028134987 (pp43) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 159.90 hours. Scaled time: 97.54 units (timescale=0.610). Factorization parameters were as follows: name: 66661_188 n: 62588962571313430923171131998101606731573624728012758991844454013795770476577693323728766959320614463002807069297413648987 skew: 114576.20 # norm 3.31e+17 c5: 13440 c4: 2462590922 c3: -6373329795304895 c2: 17153346731370743370 c1: 5085559537440422841815590 c0: -17067805229319834584176509187 # alpha -6.44 Y1: 476997068339 Y0: -341680091446117488971230 # Murphy_E 2.10e-10 # M 45437465253762539043198554707571244147803654915231204116125873835555610032596555634445435860298252922599408721648658256309 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5380001) Primes: RFBsize:348513, AFBsize:349461, largePrimes:7667930 encountered Relations: rels:7745473, finalFF:782034 Max relations in full relation-set: 0 Initial matrix: 698054 x 782034 with sparse part having weight 82397365. Pruned matrix : 631630 x 635184 with weight 58591835. Total sieving time: 128.25 hours. Total relation processing time: 1.52 hours. Matrix solve time: 29.47 hours. Time per square root: 0.66 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 159.90 hours. --------- CPU info (if available) ----------

May 31, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0
(4·10¹⁷⁰+23)/9 = (4)₁₆₉7_<170> = 193 · C168
C168 = P54 · P114
P54 = 549040020458710771002201900655139572384963724205511693_<54>
P114 = 419426794015259711436313029497443646256396503285623169529962875069579148740583046787001583894004049064540008475803_<114>

Number: n N=230282095567069660333909038572251007484168105929763960852043753598157743235463442717328727691421991940126655152561888313183649971214738054116292458261370178468624064479 ( 168 digits) SNFS difficulty: 170 digits. Divisors found: r1=549040020458710771002201900655139572384963724205511693 (pp54) r2=419426794015259711436313029497443646256396503285623169529962875069579148740583046787001583894004049064540008475803 (pp114) Version: GGNFS-0.77.1-20051202-athlon Total time: 100.59 hours. Scaled time: 130.46 units (timescale=1.297). Factorization parameters were as follows: name: KA_4_169_7 n: 230282095567069660333909038572251007484168105929763960852043753598157743235463442717328727691421991940126655152561888313183649971214738054116292458261370178468624064479 skew: 1.42 deg: 5 c5: 4 c0: 23 m: 10000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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: 48/48 Sieved algebraic special-q in [100000, 4100001) Primes: RFBsize:348513, AFBsize:349036, largePrimes:8203799 encountered Relations: rels:7823329, finalFF:797317 Max relations in full relation-set: 48 Initial matrix: 697613 x 797316 with sparse part having weight 47748724. Pruned matrix : 612060 x 615612 with weight 32155030. Total sieving time: 90.86 hours. Total relation processing time: 0.33 hours. Matrix solve time: 9.30 hours. Total square root time: 0.11 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 100.59 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(89·10¹⁶⁹+1)/9 = 9(8)₁₆₈9_<170> = 3 · 11 · C169
C169 = P31 · P31 · P109
P31 = 1043029760492294778115192930717_<31>
P31 = 2137408286980640850586822612999_<31>
P109 = 1344155050671296329476443457173504996983463628893573178601520913356656425293555294725257688032563620895713451_<109>
4·10¹⁵³-3 = 3(9)₁₅₂7_<154> = 7 · 36598463075809_<14> · C140
C140 = P42 · P98
P42 = 701099996975822570854039960283603801308933_<42>
P98 = 22269944676906901137452796561787706700352178347453639664548712306567745747002959525951900206522943_<98>

Number: n N=15613458145631164347237085705726909851541504966835942770071043310541639583131603539496937230552694437403073893194338315775770015008095349819 ( 140 digits) SNFS difficulty: 153 digits. Divisors found: r1=701099996975822570854039960283603801308933 (pp42) r2=22269944676906901137452796561787706700352178347453639664548712306567745747002959525951900206522943 (pp98) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.25 hours. Scaled time: 27.83 units (timescale=1.446). Factorization parameters were as follows: name: KA_3_9_152_7 n: 15613458145631164347237085705726909851541504966835942770071043310541639583131603539496937230552694437403073893194338315775770015008095349819 skew: 0.47 deg: 5 c5: 125 c0: -3 m: 2000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:216816, AFBsize:216491, largePrimes:6596221 encountered Relations: rels:6125563, finalFF:526499 Max relations in full relation-set: 28 Initial matrix: 433372 x 526499 with sparse part having weight 29888782. Pruned matrix : 349897 x 352127 with weight 15831553. Total sieving time: 16.64 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.14 hours. Total square root time: 0.30 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 19.25 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 30, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8
4·10¹⁴⁸+3 = 4(0)₁₄₇3_<149> = 43 · 433 · 100065703 · 12687175129_<11> · 6739023729247306489_<19> · C108
C108 = P45 · P63
P45 = 653001312242351067783538309652220151840959811_<45>
P63 = 384540790042736112351657990250185253692610846424727214146899269_<63>

Number: 40003_148 N=251105640508617088508594586058925115736503829395097331809337690282772505242310817076184722144502554494278159 ( 108 digits) SNFS difficulty: 148 digits. Divisors found: r1=653001312242351067783538309652220151840959811 (pp45) r2=384540790042736112351657990250185253692610846424727214146899269 (pp63) Version: GGNFS-0.77.1-20060513-k8 Total time: 20.03 hours. Scaled time: 40.12 units (timescale=2.003). Factorization parameters were as follows: name: 40003_148 n: 251105640508617088508594586058925115736503829395097331809337690282772505242310817076184722144502554494278159 m: 200000000000000000000000000000 c5: 125 c0: 3 skew: 1 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, 3150001) Primes: RFBsize:114155, AFBsize:113877, largePrimes:2878785 encountered Relations: rels:2881700, finalFF:275946 Max relations in full relation-set: 28 Initial matrix: 228097 x 275946 with sparse part having weight 29748606. Pruned matrix : 213753 x 214957 with weight 21355785. Total sieving time: 19.28 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.52 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 20.03 hours. --------- CPU info (if available) ----------

May 30, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
4·10¹⁴⁶-3 = 3(9)₁₄₅7_<147> = 83 · 42777895789_<11> · 15924396733100297500381_<23> · C112
C112 = P54 · P59
P54 = 396348820700316782956965255363264113551018768822430003_<54>
P59 = 17849330111541476189358027901066221476707550990700167833117_<59>

Number: n N=7074560940000117910361767328829998654766660683366389419564365970920304578753086742163420558422550942946917809351 ( 112 digits) SNFS difficulty: 146 digits. Divisors found: r1=396348820700316782956965255363264113551018768822430003 (pp54) r2=17849330111541476189358027901066221476707550990700167833117 (pp59) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 9.64 hours. Scaled time: 12.58 units (timescale=1.305). Factorization parameters were as follows: name: KA_3_9_145_7 n: 7074560940000117910361767328829998654766660683366389419564365970920304578753086742163420558422550942946917809351 skew: 0.60 deg: 5 c5: 40 c0: -3 m: 100000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:183072, AFBsize:182506, largePrimes:6452273 encountered Relations: rels:5881816, finalFF:435332 Max relations in full relation-set: 28 Initial matrix: 365644 x 435332 with sparse part having weight 25318441. Pruned matrix : 305134 x 307026 with weight 14058892. Total sieving time: 7.61 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.77 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 9.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

4·10¹⁵²+3 = 4(0)₁₅₁3_<153> = 13 · 31 · 1051 · C147
C147 = P67 · P81
P67 = 2801114324800249062766187692606357600549569364661409619095961178167_<67>
P81 = 337148626424781873328036805457958920928175121942812922349685550558244211164690453_<81>

Number: n N=944391847065184286264056682398660852360861568682077567624358698911352298295608814009108659364943702441016826701735083921020509829938638139736939651 ( 147 digits) SNFS difficulty: 152 digits. Divisors found: r1=2801114324800249062766187692606357600549569364661409619095961178167 (pp67) r2=337148626424781873328036805457958920928175121942812922349685550558244211164690453 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 17.49 hours. Scaled time: 25.34 units (timescale=1.449). Factorization parameters were as follows: name: KA_4_0_151_3 n: 944391847065184286264056682398660852360861568682077567624358698911352298295608814009108659364943702441016826701735083921020509829938638139736939651 skew: 0.75 deg: 5 c5: 25 c0: 6 m: 2000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:216816, AFBsize:215956, largePrimes:6769972 encountered Relations: rels:6408744, finalFF:619286 Max relations in full relation-set: 28 Initial matrix: 432836 x 619286 with sparse part having weight 33677825. Pruned matrix : 266552 x 268780 with weight 14872464. Total sieving time: 15.76 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.48 hours. Total square root time: 0.09 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 17.49 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

4·10¹⁵¹+3 = 4(0)₁₅₀3_<152> = 87523 · 4494503443_<10> · C138
C138 = P43 · P95
P43 = 1297415475912073088053509540386798385058609_<43>
P95 = 78374900853242505310466623601273918272208107442148395944232718006339250364736934925355798428203_<95>

Number: n N=101684809290071168164673608485184602435969068234105883657731058672297789123043221176110896404625443994231824114694450958074636842233549627 ( 138 digits) SNFS difficulty: 151 digits. Divisors found: r1=1297415475912073088053509540386798385058609 (pp43) r2=78374900853242505310466623601273918272208107442148395944232718006339250364736934925355798428203 (pp95) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 16.66 hours. Scaled time: 22.81 units (timescale=1.369). Factorization parameters were as follows: name: KA_4_0_150_3 n: 101684809290071168164673608485184602435969068234105883657731058672297789123043221176110896404625443994231824114694450958074636842233549627 skew: 0.60 deg: 5 c5: 40 c0: 3 m: 1000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:216816, AFBsize:215821, largePrimes:6287333 encountered Relations: rels:5832658, finalFF:518542 Max relations in full relation-set: 28 Initial matrix: 432703 x 518542 with sparse part having weight 27684554. Pruned matrix : 351235 x 353462 with weight 14649647. Total sieving time: 14.75 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.66 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 16.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 30, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
4·10¹⁵³+3 = 4(0)₁₅₂3_<154> = 163 · 647531 · 11061581 · 4124679348155700834063553597_<28> · C111
C111 = P52 · P60
P52 = 3535740861654872658270519573725613482190542128854473_<52>
P60 = 234922167135062332183441254151884253123634863112124506309891_<60>

Number: 40003_153 N=830623905647955297761358148882626558774270445628540572480336272874132992508238565769278537971704421868179492443 ( 111 digits) SNFS difficulty: 153 digits. Divisors found: r1=3535740861654872658270519573725613482190542128854473 (pp52) r2=234922167135062332183441254151884253123634863112124506309891 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.10 hours. Scaled time: 15.97 units (timescale=0.934). Factorization parameters were as follows: n: 830623905647955297761358148882626558774270445628540572480336272874132992508238565769278537971704421868179492443 m: 2000000000000000000000000000000 c5: 125 c0: 3 skew: 1 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, 2200001) Primes: RFBsize:176302, AFBsize:175868, largePrimes:5638026 encountered Relations: rels:5620624, finalFF:535694 Max relations in full relation-set: 28 Initial matrix: 352235 x 535694 with sparse part having weight 48622419. Pruned matrix : 279893 x 281718 with weight 25069298. Total sieving time: 16.52 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.46 hours. Time per square root: 0.03 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: 17.10 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 29, 2007 (8th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs
4·10¹⁵²-3 = 3(9)₁₅₁7_<153> = 21200771 · 25893612998221_<14> · 14503289669621063451952205056921_<32> · C101
C101 = P45 · P57
P45 = 230079279032884613931774793453258451457362123_<45>
P57 = 218359280476393118332391848988420792397153683310217125049_<57>

Number: 39997_152 N=50239945822147965823364715757449975132547131611251114455272136849140078848825124186413611002367119027 ( 101 digits) Divisors found: r1=230079279032884613931774793453258451457362123 (pp45) r2=218359280476393118332391848988420792397153683310217125049 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.32 hours. Scaled time: 4.04 units (timescale=0.935). Factorization parameters were as follows: name: 39997_152 n: 50239945822147965823364715757449975132547131611251114455272136849140078848825124186413611002367119027 skew: 2745.59 # norm 4.18e+13 c5: 253440 c4: -2237299026 c3: -1907163396717 c2: 18351442515410243 c1: 16149480465216217123 c0: -4732032708429412165896 # alpha -5.26 Y1: 20037749981 Y0: -11466639011392083421 # Murphy_E 3.20e-09 # M 9786743912553846833483490233928381167753400889953592353099544647107720629570548238023689159496745801 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [750000, 1300001) Primes: RFBsize:114155, AFBsize:114153, largePrimes:3944606 encountered Relations: rels:3941658, finalFF:355357 Max relations in full relation-set: 28 Initial matrix: 228389 x 355357 with sparse part having weight 29022648. Pruned matrix : 163717 x 164922 with weight 11611115. Polynomial selection time: 0.28 hours. Total sieving time: 3.83 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000 total time: 4.32 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 29, 2007 (7th)

By Max Voznyy / GGNFS-0.77.1-20060513-pentium4
2·10¹⁵⁵-3 = 1(9)₁₅₄7_<156> = 7 · 67 · 71 · 343866401642039_<15> · 141423577541870006652967_<24> · C114
C114 = P46 · P69
P46 = 1176075110392218874344361392155876226533549449_<46>
P69 = 105015204394259862679542119957655122688478278199700532417643933576919_<69>

May 29, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
4·10¹⁴⁵-3 = 3(9)₁₄₄7_<146> = 29 · 37 · 636458547278605123477_<21> · C122
C122 = P47 · P76
P47 = 22032652827179182252311595341228758697101383067_<47>
P76 = 2658418526818926672086758087119698387445371990728081899202841400303836244571_<76>

Number: 39997_145 N=58572012470742541478080301062763303277153080662009129442516557774603576611369036613001881755526790043397812934327370079257 ( 122 digits) SNFS difficulty: 145 digits. Divisors found: r1=22032652827179182252311595341228758697101383067 (pp47) r2=2658418526818926672086758087119698387445371990728081899202841400303836244571 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.31 hours. Scaled time: 8.69 units (timescale=0.933). Factorization parameters were as follows: n: 58572012470742541478080301062763303277153080662009129442516557774603576611369036613001881755526790043397812934327370079257 m: 100000000000000000000000000000 c5: 4 c0: -3 skew: 1 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, 1350001) Primes: RFBsize:114155, AFBsize:113917, largePrimes:2689998 encountered Relations: rels:2699548, finalFF:315804 Max relations in full relation-set: 28 Initial matrix: 228139 x 315804 with sparse part having weight 21287815. Pruned matrix : 191614 x 192818 with weight 10724400. Total sieving time: 9.13 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.12 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000 total time: 9.31 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 29, 2007 (5th)

By suberi / GMP-ECM 6.1.2 B1=3000000
2·10¹⁷³+3 = 2(0)₁₇₂3_<174> = 31 · 3164590541963_<13> · C160
C160 = P43 · C118
P43 = 1377280097548571230432695973091803101076339_<43>
C118 = [1480227622542794165404399819785920618847153787232185974759390499635827513314206276438905310385107334421379192165686509_<118>]

May 29, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
4·10¹⁴⁴-3 = 3(9)₁₄₃7_<145> = 359 · 9311 · 8600737381_<10> · C129
C129 = P37 · P44 · P49
P37 = 1127069158597835253730690599540227387_<37>
P44 = 25704964961697827080699390888797399431064217_<44>
P49 = 4802484227003858903586540234824184542371863661547_<49>

Number: n N=139134082728901552207477531234965837137139548962918480744051676763860644141313152952523265954505770179676760121611692870007824513 ( 129 digits) SNFS difficulty: 145 digits. Divisors found: r1=1127069158597835253730690599540227387 (pp37) r2=25704964961697827080699390888797399431064217 (pp44) r3=4802484227003858903586540234824184542371863661547 (pp49) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 10.39 hours. Scaled time: 14.13 units (timescale=1.361). Factorization parameters were as follows: name: KA_3_9_143_7 n: 139134082728901552207477531234965837137139548962918480744051676763860644141313152952523265954505770179676760121611692870007824513 skew: 1.50 deg: 5 c5: 2 c0: -15 m: 100000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:183072, AFBsize:182991, largePrimes:6720704 encountered Relations: rels:6184111, finalFF:468239 Max relations in full relation-set: 28 Initial matrix: 366128 x 468238 with sparse part having weight 29402590. Pruned matrix : 281075 x 282969 with weight 14990558. Total sieving time: 8.64 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.31 hours. Total square root time: 0.25 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 10.39 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

4·10¹⁴⁵+3 = 4(0)₁₄₄3_<146> = 15679 · 8391654179_<10> · 1630535804362988309_<19> · C114
C114 = P45 · P69
P45 = 646714525652426822605941812765336474593578059_<45>
P69 = 288304285235034063465342910556093561504177705697017827218911974846793_<69>

Number: n N=186450569069337016472379512674172687327990157379633781153481333472695354444304795726582573723536382949298211314787 ( 114 digits) SNFS difficulty: 145 digits. Divisors found: r1=646714525652426822605941812765336474593578059 (pp45) r2=288304285235034063465342910556093561504177705697017827218911974846793 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.95 hours. Scaled time: 11.52 units (timescale=1.449). Factorization parameters were as follows: name: KA_4_0_144_3 n: 186450569069337016472379512674172687327990157379633781153481333472695354444304795726582573723536382949298211314787 skew: 0.94 deg: 5 c5: 4 c0: 3 m: 100000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:183072, AFBsize:182816, largePrimes:6481222 encountered Relations: rels:5947081, finalFF:465397 Max relations in full relation-set: 28 Initial matrix: 365955 x 465397 with sparse part having weight 26481654. Pruned matrix : 278114 x 280007 with weight 12854649. Total sieving time: 6.13 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.30 hours. Total square root time: 0.37 hours, sqrts: 9. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 7.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 29, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8
4·10¹⁴⁶+3 = 4(0)₁₄₅3_<147> = 13 · 41023 · 2958721 · 248105437 · 1101807494113_<13> · 7014417751034503_<16> · C99
C99 = P41 · P58
P41 = 41503832743290556850451533494303423483207_<41>
P58 = 3185395578251891000053013244421171035550838420033010094357_<58>

Number: 40003_146 N=132206125300983790896326376581325564446111856146621668386739588502853251960027942344108792674962899 ( 99 digits) SNFS difficulty: 146 digits. Divisors found: r1=41503832743290556850451533494303423483207 (pp41) r2=3185395578251891000053013244421171035550838420033010094357 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 14.41 hours. Scaled time: 28.87 units (timescale=2.003). Factorization parameters were as follows: name: 40003_146 n: 132206125300983790896326376581325564446111856146621668386739588502853251960027942344108792674962899 m: 100000000000000000000000000000 c5: 40 c0: 3 skew: 1 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 2450001) Primes: RFBsize:114155, AFBsize:113697, largePrimes:2764799 encountered Relations: rels:2738945, finalFF:275539 Max relations in full relation-set: 28 Initial matrix: 227918 x 275539 with sparse part having weight 25625759. Pruned matrix : 211958 x 213161 with weight 17651075. Total sieving time: 13.81 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.41 hours. Time per square root: 0.09 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: 14.41 hours. --------- CPU info (if available) ----------

May 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
(5·10¹⁷⁴+1)/3 = 1(6)₁₇₃7_<175> = C175
C175 = P38 · P137
P38 = 38957826032363776525856717580374065723_<38>
P137 = 42781305745400219407473710733596304514150377883882257718360293742320702825809015275337663456972351386349942222557906259254671065933070929_<137>

Number: 16667_174 N=1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667 ( 175 digits) SNFS difficulty: 175 digits. Divisors found: r1=38957826032363776525856717580374065723 (pp38) r2=42781305745400219407473710733596304514150377883882257718360293742320702825809015275337663456972351386349942222557906259254671065933070929 (pp137) Version: GGNFS-0.77.1-20050930-nocona Total time: 137.22 hours. Scaled time: 127.48 units (timescale=0.929). Factorization parameters were as follows: n: 1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667 m: 100000000000000000000000000000000000 c5: 1 c0: 2 skew: 1.15 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 49/49 Sieved algebraic special-q in [4500000, 6600001) Primes: RFBsize:602489, AFBsize:602700, largePrimes:10034680 encountered Relations: rels:10282311, finalFF:1497466 Max relations in full relation-set: 28 Initial matrix: 1205253 x 1497466 with sparse part having weight 66712191. Pruned matrix : 923325 x 929415 with weight 36490841. Total sieving time: 132.24 hours. Total relation processing time: 0.17 hours. Matrix solve time: 4.73 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,49,49,2.6,2.6,100000 total time: 137.22 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 29, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
4·10¹⁴¹-3 = 3(9)₁₄₀7_<142> = 7 · 52313 · C137
C137 = P62 · P75
P62 = 72534046490829353664593295091274835834185520668502881701648559_<62>
P75 = 150594953495731883967116548567354812204313653884473343476632001562146074013_<75>

Number: n N=10923261358143700964797059458042387715700276631593894989226933485530774923468900109505695115390602172090521066874936849895273231728797267 ( 137 digits) SNFS difficulty: 141 digits. Divisors found: r1=72534046490829353664593295091274835834185520668502881701648559 (pp62) r2=150594953495731883967116548567354812204313653884473343476632001562146074013 (pp75) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 7.74 hours. Scaled time: 10.58 units (timescale=1.366). Factorization parameters were as follows: name: KA_3_9_140_7 n: 10923261358143700964797059458042387715700276631593894989226933485530774923468900109505695115390602172090521066874936849895273231728797267 skew: 0.60 deg: 5 c5: 40 c0: -3 m: 10000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:183072, AFBsize:182506, largePrimes:5965783 encountered Relations: rels:5451650, finalFF:451267 Max relations in full relation-set: 28 Initial matrix: 365644 x 451267 with sparse part having weight 21857445. Pruned matrix : 283591 x 285483 with weight 10333770. Total sieving time: 6.72 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.83 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 7.74 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

4·10¹⁴²+3 = 4(0)₁₄₁3_<143> = 19 · 397523109523_<12> · 1792722597263327053_<19> · C112
C112 = P51 · P61
P51 = 361944429343387970109181659326070203309043443208301_<51>
P61 = 8161857721768944819535587526816743204330570033059102272751923_<61>

Number: n N=2954138935487585358037504212441582467115017534237517833386470674579036800877959937028708758566992431307387312823 ( 112 digits) SNFS difficulty: 142 digits. Divisors found: r1=361944429343387970109181659326070203309043443208301 (pp51) r2=8161857721768944819535587526816743204330570033059102272751923 (pp61) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.94 hours. Scaled time: 10.04 units (timescale=1.447). Factorization parameters were as follows: name: KA_4_0_141_3 n: 2954138935487585358037504212441582467115017534237517833386470674579036800877959937028708758566992431307387312823 skew: 0.75 deg: 5 c5: 25 c0: 6 m: 20000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:183072, AFBsize:182381, largePrimes:6642527 encountered Relations: rels:6258535, finalFF:588785 Max relations in full relation-set: 28 Initial matrix: 365517 x 588785 with sparse part having weight 31133532. Pruned matrix : 183587 x 185478 with weight 13613993. Total sieving time: 5.76 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.93 hours. Total square root time: 0.10 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 6.94 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 28, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(7·10¹⁶⁰-61)/9 = (7)₁₅₉1_<160> = 1087 · C157
C157 = P60 · P98
P60 = 133767292172935551579599522862258137018645605013343066361981_<60>
P98 = 53490425264281855146460077769801026058944569491640678743898434821351499978338309471009601998689593_<98>

Number: n N=7155269344781764284984156189307983236226106511295103751405499335582132270264744965756925278544413779004395379740365940917918838802003475416538893999795563733 ( 157 digits) SNFS difficulty: 160 digits. Divisors found: r1=133767292172935551579599522862258137018645605013343066361981 (pp60) r2=53490425264281855146460077769801026058944569491640678743898434821351499978338309471009601998689593 (pp98) Version: GGNFS-0.77.1-20051202-athlon Total time: 34.44 hours. Scaled time: 49.48 units (timescale=1.437). Factorization parameters were as follows: name: KA_7_159_1 n: 7155269344781764284984156189307983236226106511295103751405499335582132270264744965756925278544413779004395379740365940917918838802003475416538893999795563733 skew: 1.54 deg: 5 c5: 7 c0: -61 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:250150, AFBsize:250502, largePrimes:7175624 encountered Relations: rels:6724740, finalFF:585888 Max relations in full relation-set: 28 Initial matrix: 500717 x 585888 with sparse part having weight 36048352. Pruned matrix : 426488 x 429055 with weight 21797147. Total sieving time: 30.15 hours. Total relation processing time: 0.20 hours. Matrix solve time: 4.01 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 34.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 28, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
4·10¹³⁸+3 = 4(0)₁₃₇3_<139> = 7 · 1033 · C135
C135 = P48 · P87
P48 = 930729119481891694801482963283168394796716926087_<48>
P87 = 594344609294641138185135993021839496344619029158623927721993187831394871362972952598299_<87>

Number: 40003_138 N=553173834877610289033328723551376019914258055593970405199834047849536716913290001382934587194025722583321808878440049785645138984926013 ( 135 digits) SNFS difficulty: 138 digits. Divisors found: r1=930729119481891694801482963283168394796716926087 (pp48) r2=594344609294641138185135993021839496344619029158623927721993187831394871362972952598299 (pp87) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.68 hours. Scaled time: 4.37 units (timescale=0.934). Factorization parameters were as follows: n: 553173834877610289033328723551376019914258055593970405199834047849536716913290001382934587194025722583321808878440049785645138984926013 m: 2000000000000000000000000000 c5: 125 c0: 3 skew: 1 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [700000, 1550001) Primes: RFBsize:107126, AFBsize:107023, largePrimes:1652918 encountered Relations: rels:1714233, finalFF:241604 Max relations in full relation-set: 28 Initial matrix: 214214 x 241604 with sparse part having weight 12448402. Pruned matrix : 201680 x 202815 with weight 8746891. Total sieving time: 4.51 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000 total time: 4.68 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³⁸-3 = 3(9)₁₃₇7_<139> = 167 · 61953817 · C129
C129 = P57 · P73
P57 = 234806247524789276541047560136279747605593670548390630143_<57>
P73 = 1646515424474759157709862360552930904493428048558253258347121490936014861_<73>

Number: 39997_138 N=386612108312603782474518587555742467131354168827475971306232718709990983848984480161415704893794803065494070892108722517002555123 ( 129 digits) SNFS difficulty: 138 digits. Divisors found: r1=234806247524789276541047560136279747605593670548390630143 (pp57) r2=1646515424474759157709862360552930904493428048558253258347121490936014861 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.94 hours. Scaled time: 4.61 units (timescale=0.934). Factorization parameters were as follows: n: 386612108312603782474518587555742467131354168827475971306232718709990983848984480161415704893794803065494070892108722517002555123 m: 2000000000000000000000000000 c5: 125 c0: -3 skew: 1 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [700000, 1600001) Primes: RFBsize:107126, AFBsize:107023, largePrimes:1685915 encountered Relations: rels:1768512, finalFF:259015 Max relations in full relation-set: 28 Initial matrix: 214214 x 259015 with sparse part having weight 14204838. Pruned matrix : 192969 x 194104 with weight 8814070. Total sieving time: 4.78 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000 total time: 4.94 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³⁹+3 = 4(0)₁₃₈3_<140> = 730085207 · 4622218820599_<13> · 1090080139886653_<16> · C104
C104 = P40 · P64
P40 = 2443464119454710007355153216679458364521_<40>
P64 = 4450118210277028673112750346091921480847013205495714394729918167_<64>

Number: 40003_139 N=10873704174143929896811554488954462461135888027735618494324499305001323585745628849144582691257986153007 ( 104 digits) SNFS difficulty: 140 digits. Divisors found: r1=2443464119454710007355153216679458364521 (pp40) r2=4450118210277028673112750346091921480847013205495714394729918167 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.54 hours. Scaled time: 7.97 units (timescale=0.934). Factorization parameters were as follows: n: 10873704174143929896811554488954462461135888027735618494324499305001323585745628849144582691257986153007 m: 10000000000000000000000000000 c5: 2 c0: 15 skew: 1.5 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [700000, 1250001) Primes: RFBsize:107126, AFBsize:107113, largePrimes:1679573 encountered Relations: rels:1762335, finalFF:255346 Max relations in full relation-set: 28 Initial matrix: 214304 x 255346 with sparse part having weight 13522951. Pruned matrix : 192825 x 193960 with weight 8429277. Total sieving time: 8.39 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000 total time: 8.54 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 28, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(14·10¹⁵⁹-41)/9 = 1(5)₁₅₈1_<160> = 3² · 11 · 5783 · 6871 · C150
C150 = P34 · P116
P34 = 6031459152120337884517237707176687_<34>
P116 = 65562393470958923411536676667369852579711360794342128936197039393056889008855481635744308817305722437678656721468939_<116>

Number: n N=395436898135329884560761905239269729221109523772888194939726864412661303745861547763429730960634179030786440951749566920750332476783936500229055425093 ( 150 digits) SNFS difficulty: 160 digits. Divisors found: r1=6031459152120337884517237707176687 (pp34) r2=65562393470958923411536676667369852579711360794342128936197039393056889008855481635744308817305722437678656721468939 (pp116) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 38.14 hours. Scaled time: 52.13 units (timescale=1.367). Factorization parameters were as follows: name: KA_1_5_158_1 n: 395436898135329884560761905239269729221109523772888194939726864412661303745861547763429730960634179030786440951749566920750332476783936500229055425093 skew: 1.96 deg: 5 c5: 7 c0: -205 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:250150, AFBsize:250442, largePrimes:7155416 encountered Relations: rels:6677810, finalFF:563496 Max relations in full relation-set: 28 Initial matrix: 500657 x 563496 with sparse part having weight 34543217. Pruned matrix : 444914 x 447481 with weight 22819760. Total sieving time: 33.89 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.39 hours. Total square root time: 0.64 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 38.14 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 27, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve 1.21
4·10¹²⁷-3 = 3(9)₁₂₆7_<128> = 37 · 1663 · 18719 · 5365901 · C112
C112 = P48 · P64
P48 = 705022162775505898789224106446296802990040895033_<48>
P64 = 9179899962009583566770141001685302094407984058465806768333958181_<64>

Number: 39997_127 N=6472032925278781041797362499390546042050955598537907195224264982188752618866909381403194723929818401764832614973 ( 112 digits) SNFS difficulty: 127 digits. Divisors found: r1=705022162775505898789224106446296802990040895033 (pp48) r2=9179899962009583566770141001685302094407984058465806768333958181 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.86 hours. Scaled time: 1.74 units (timescale=0.934). Factorization parameters were as follows: n: 6472032925278781041797362499390546042050955598537907195224264982188752618866909381403194723929818401764832614973 m: 20000000000000000000000000 c5: 25 c0: -6 skew: 1 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 850001) Primes: RFBsize:78498, AFBsize:78301, largePrimes:1560655 encountered Relations: rels:1638252, finalFF:247040 Max relations in full relation-set: 28 Initial matrix: 156863 x 247040 with sparse part having weight 11693537. Pruned matrix : 113199 x 114047 with weight 4653390. Total sieving time: 1.80 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.86 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁷+3 = 4(0)₁₂₆3_<128> = 17 · 43² · 59 · 11285195303_<11> · C112
C112 = P54 · P58
P54 = 521293731281094645703485420673506602610925860757394203_<54>
P58 = 3666321666068084664903157915264085011548958113765261075461_<58>

Number: 40003_127 N=1911230501381351344749672587619391998018934950167832705841037082931427635475944060798992580228159562795706952583 ( 112 digits) SNFS difficulty: 127 digits. Divisors found: r1=521293731281094645703485420673506602610925860757394203 (pp54) r2=3666321666068084664903157915264085011548958113765261075461 (pp58) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.62 hours. Scaled time: 1.51 units (timescale=0.931). Factorization parameters were as follows: n: 1911230501381351344749672587619391998018934950167832705841037082931427635475944060798992580228159562795706952583 m: 20000000000000000000000000 c5: 25 c0: 6 skew: 1 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 800001) Primes: RFBsize:78498, AFBsize:78301, largePrimes:1453042 encountered Relations: rels:1464297, finalFF:189090 Max relations in full relation-set: 28 Initial matrix: 156863 x 189090 with sparse part having weight 8244070. Pruned matrix : 135788 x 136636 with weight 4723501. Total sieving time: 1.55 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.62 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³¹+3 = 4(0)₁₃₀3_<132> = 29 · 199 · 122709869 · C120
C120 = P47 · P74
P47 = 17745113024976168939376435372018500870859981957_<47>
P74 = 31831027271271917917211409577687106292138046864406391959013403689139371721_<74>

Number: 40003_131 N=564845176629818951808827035744745452246841772623803650887282390890456141189641461532135200682772613833908993808376037997 ( 120 digits) SNFS difficulty: 132 digits. Divisors found: r1=17745113024976168939376435372018500870859981957 (pp47) r2=31831027271271917917211409577687106292138046864406391959013403689139371721 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.30 hours. Scaled time: 2.15 units (timescale=0.935). Factorization parameters were as follows: n: 564845176629818951808827035744745452246841772623803650887282390890456141189641461532135200682772613833908993808376037997 m: 200000000000000000000000000 c5: 5 c0: 12 skew: 1.19 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 950001) Primes: RFBsize:78498, AFBsize:78441, largePrimes:1508956 encountered Relations: rels:1522496, finalFF:190629 Max relations in full relation-set: 28 Initial matrix: 157005 x 190629 with sparse part having weight 9748353. Pruned matrix : 142097 x 142946 with weight 5737145. Total sieving time: 2.22 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.30 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³²+3 = 4(0)₁₃₁3_<133> = 7 · 367699 · 75669648215166599173_<20> · C107
C107 = P49 · P59
P49 = 1112013696695243458462948812197952325199534586937_<49>
P59 = 18468756317073684462309916330756661620043623970152551745171_<59>

Number: 40003_132 N=20537509985512737778662764382555381457009554393279769385933028106871931241847355158296348401924213969431227 ( 107 digits) SNFS difficulty: 132 digits. Divisors found: r1=1112013696695243458462948812197952325199534586937 (pp49) r2=18468756317073684462309916330756661620043623970152551745171 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.52 hours. Scaled time: 2.35 units (timescale=0.934). Factorization parameters were as follows: n: 20537509985512737778662764382555381457009554393279769385933028106871931241847355158296348401924213969431227 m: 200000000000000000000000000 c5: 25 c0: 6 skew: 1 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 1000001) Primes: RFBsize:78498, AFBsize:78301, largePrimes:1515396 encountered Relations: rels:1524246, finalFF:186816 Max relations in full relation-set: 28 Initial matrix: 156863 x 186816 with sparse part having weight 9456577. Pruned matrix : 145417 x 146265 with weight 5828837. Total sieving time: 2.43 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.52 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³³-3 = 3(9)₁₃₂7_<134> = 19 · 37 · 607 · 275521 · 267823455452010358133437_<24> · C100
C100 = P41 · P59
P41 = 19092348197612899949161309484911390214209_<41>
P59 = 66535483009793897303525410667693774065268754524280636711649_<59>

Number: 39997_133 N=1270318609119342242678692386755510163774768851318400499046674123124105513718087324363376691475620641 ( 100 digits) SNFS difficulty: 133 digits. Divisors found: r1=19092348197612899949161309484911390214209 (pp41) r2=66535483009793897303525410667693774065268754524280636711649 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.94 hours. Scaled time: 2.75 units (timescale=0.934). Factorization parameters were as follows: n: 1270318609119342242678692386755510163774768851318400499046674123124105513718087324363376691475620641 m: 200000000000000000000000000 c5: 125 c0: -3 skew: 1 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [700000, 1200001) Primes: RFBsize:107126, AFBsize:107023, largePrimes:1614997 encountered Relations: rels:1684678, finalFF:247912 Max relations in full relation-set: 28 Initial matrix: 214214 x 247912 with sparse part having weight 10516119. Pruned matrix : 188686 x 189821 with weight 6629000. Total sieving time: 2.82 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.08 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000 total time: 2.94 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³⁶-3 = 3(9)₁₃₅7_<137> = 23 · 37 · 2293 · C131
C131 = P35 · P97
P35 = 15081196794111057038592942294865571_<35>
P97 = 1359222545014331678259321655350929515123649897436325733988274979310778665003786733637386489826449_<97>

Number: 39997_136 N=20498702688353610820855175128104080113029846623581810066195435656365897743246574282430100705001632209201560156261610593319575287379 ( 131 digits) SNFS difficulty: 137 digits. Divisors found: r1=15081196794111057038592942294865571 (pp35) r2=1359222545014331678259321655350929515123649897436325733988274979310778665003786733637386489826449 (pp97) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.84 hours. Scaled time: 3.58 units (timescale=0.932). Factorization parameters were as follows: n: 20498702688353610820855175128104080113029846623581810066195435656365897743246574282430100705001632209201560156261610593319575287379 m: 2000000000000000000000000000 c5: 5 c0: -12 skew: 1.19 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [700000, 1400001) Primes: RFBsize:107126, AFBsize:106758, largePrimes:1667272 encountered Relations: rels:1757157, finalFF:266622 Max relations in full relation-set: 28 Initial matrix: 213950 x 266622 with sparse part having weight 12122124. Pruned matrix : 185668 x 186801 with weight 7034894. Total sieving time: 3.71 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000 total time: 3.84 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹⁵¹-3 = 3(9)₁₅₀7_<152> = 17² · 19 · 37 · 813601 · 94455601 · 97616772977_<11> · 196347596050337_<15> · 5853974215361273_<16> · C92
C92 = P43 · P50
P43 = 1910611134746116246492096414368671609087657_<43>
P50 = 11950731510953569288974090598473301504132412787619_<50>

Sun May 27 21:42:43 2007 Sun May 27 21:42:43 2007 Sun May 27 21:42:43 2007 Msieve v. 1.21 Sun May 27 21:42:43 2007 random seeds: 82914263 85d6b2cd Sun May 27 21:42:43 2007 factoring 22833200693189167378341858058780999507653626440332814574305576940890044459677406916695318683 (92 digits) Sun May 27 21:42:43 2007 commencing quadratic sieve (92-digit input) Sun May 27 21:42:43 2007 using multiplier of 3 Sun May 27 21:42:43 2007 using 32kb Intel Core sieve core Sun May 27 21:42:43 2007 sieve interval: 36 blocks of size 32768 Sun May 27 21:42:43 2007 processing polynomials in batches of 6 Sun May 27 21:42:43 2007 using a sieve bound of 1787717 (67004 primes) Sun May 27 21:42:43 2007 using large prime bound of 187710285 (27 bits) Sun May 27 21:42:43 2007 using double large prime bound of 780330238063215 (42-50 bits) Sun May 27 21:42:43 2007 using trial factoring cutoff of 50 bits Sun May 27 21:42:43 2007 polynomial 'A' values have 12 factors Sun May 27 23:02:34 2007 67494 relations (17641 full + 49853 combined from 828022 partial), need 67100 Sun May 27 23:02:35 2007 begin with 845663 relations Sun May 27 23:02:35 2007 reduce to 168237 relations in 10 passes Sun May 27 23:02:35 2007 attempting to read 168237 relations Sun May 27 23:02:36 2007 recovered 168237 relations Sun May 27 23:02:36 2007 recovered 147912 polynomials Sun May 27 23:02:36 2007 attempting to build 67494 cycles Sun May 27 23:02:36 2007 found 67493 cycles in 5 passes Sun May 27 23:02:37 2007 distribution of cycle lengths: Sun May 27 23:02:37 2007 length 1 : 17641 Sun May 27 23:02:37 2007 length 2 : 12653 Sun May 27 23:02:37 2007 length 3 : 11612 Sun May 27 23:02:37 2007 length 4 : 9122 Sun May 27 23:02:37 2007 length 5 : 6485 Sun May 27 23:02:37 2007 length 6 : 4245 Sun May 27 23:02:37 2007 length 7 : 2509 Sun May 27 23:02:37 2007 length 9+: 3226 Sun May 27 23:02:37 2007 largest cycle: 19 relations Sun May 27 23:02:37 2007 matrix is 67004 x 67493 with weight 4127294 (avg 61.15/col) Sun May 27 23:02:37 2007 filtering completed in 4 passes Sun May 27 23:02:37 2007 matrix is 65382 x 65446 with weight 3919902 (avg 59.90/col) Sun May 27 23:02:38 2007 saving the first 48 matrix rows for later Sun May 27 23:02:38 2007 matrix is 65334 x 65446 with weight 3070899 (avg 46.92/col) Sun May 27 23:02:38 2007 matrix includes 32 packed rows Sun May 27 23:02:38 2007 using block size 26178 for processor cache size 4096 kB Sun May 27 23:02:58 2007 lanczos halted after 1034 iterations Sun May 27 23:02:58 2007 recovered 18 nontrivial dependencies Sun May 27 23:02:59 2007 prp43 factor: 1910611134746116246492096414368671609087657 Sun May 27 23:02:59 2007 prp50 factor: 11950731510953569288974090598473301504132412787619 Sun May 27 23:02:59 2007 elapsed time 01:20:16

May 27, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000, Msieve v. 1.21
4·10¹⁴⁸-3 = 3(9)₁₄₇7_<149> = 37 · 157 · 373 · 2389 · 2917 · 201743 · 343164397202925323_<18> · C113
C113 = P32 · P34 · P47
P32 = 64183606304071153348418983401419_<32>
P34 = 6908604692602464799988145292045693_<34>
P47 = 86294287414556460254625701135729827536592888259_<47>

Sat May 19 13:39:49 2007 Sat May 19 13:39:49 2007 Sat May 19 13:39:49 2007 Msieve v. 1.21 Sat May 19 13:39:49 2007 random seeds: ab5a05f8 8d5d6b6c Sat May 19 13:39:49 2007 factoring 13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791 (107 digits) Sat May 19 13:39:49 2007 commencing quadratic sieve (106-digit input) Sat May 19 13:39:50 2007 using multiplier of 11 Sat May 19 13:39:50 2007 using 64kb Pentium 4 sieve core Sat May 19 13:39:50 2007 sieve interval: 21 blocks of size 65536 Sat May 19 13:39:50 2007 processing polynomials in batches of 5 Sat May 19 13:39:50 2007 using a sieve bound of 4662979 (163333 primes) Sat May 19 13:39:50 2007 using large prime bound of 699446850 (29 bits) Sat May 19 13:39:50 2007 using double large prime bound of 8328340221930300 (45-53 bits) Sat May 19 13:39:50 2007 using trial factoring cutoff of 53 bits Sat May 19 13:39:50 2007 polynomial 'A' values have 14 factors Sat May 19 13:42:08 2007 18 relations (18 full + 0 combined from 995 partial), need 163429 Sat May 19 13:42:08 2007 c107 factor: 13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791 Sat May 19 13:42:08 2007 elapsed time 00:02:19 Sun May 27 16:46:55 2007 Sun May 27 16:46:55 2007 Sun May 27 16:46:55 2007 Msieve v. 1.21 Sun May 27 16:46:55 2007 random seeds: 8d7ccf94 2a377ae6 Sun May 27 16:46:55 2007 factoring 79 (2 digits) Sun May 27 16:46:55 2007 p2 factor: 79 Sun May 27 16:46:55 2007 elapsed time 00:00:00 Sun May 27 16:47:44 2007 Sun May 27 16:47:44 2007 Sun May 27 16:47:44 2007 Msieve v. 1.21 Sun May 27 16:47:44 2007 random seeds: 48e51ae0 131d458c Sun May 27 16:47:44 2007 factoring 5538678569706254011261695426721774138491854232285156975782913679145001209039521 (79 digits) Sun May 27 16:47:45 2007 commencing quadratic sieve (79-digit input) Sun May 27 16:47:45 2007 using multiplier of 1 Sun May 27 16:47:45 2007 using 64kb Pentium 4 sieve core Sun May 27 16:47:45 2007 sieve interval: 6 blocks of size 65536 Sun May 27 16:47:45 2007 processing polynomials in batches of 17 Sun May 27 16:47:45 2007 using a sieve bound of 1168879 (45267 primes) Sun May 27 16:47:45 2007 using large prime bound of 116887900 (26 bits) Sun May 27 16:47:45 2007 using trial factoring cutoff of 27 bits Sun May 27 16:47:45 2007 polynomial 'A' values have 10 factors Sun May 27 16:59:38 2007 45549 relations (24447 full + 21102 combined from 238802 partial), need 45363 Sun May 27 16:59:38 2007 begin with 263249 relations Sun May 27 16:59:39 2007 reduce to 64059 relations in 2 passes Sun May 27 16:59:39 2007 attempting to read 64059 relations Sun May 27 16:59:40 2007 recovered 64059 relations Sun May 27 16:59:40 2007 recovered 47555 polynomials Sun May 27 16:59:40 2007 attempting to build 45549 cycles Sun May 27 16:59:40 2007 found 45549 cycles in 1 passes Sun May 27 16:59:40 2007 distribution of cycle lengths: Sun May 27 16:59:40 2007 length 1 : 24447 Sun May 27 16:59:40 2007 length 2 : 21102 Sun May 27 16:59:40 2007 largest cycle: 2 relations Sun May 27 16:59:40 2007 matrix is 45267 x 45549 with weight 1349433 (avg 29.63/col) Sun May 27 16:59:40 2007 filtering completed in 4 passes Sun May 27 16:59:40 2007 matrix is 37509 x 37573 with weight 1083366 (avg 28.83/col) Sun May 27 16:59:41 2007 saving the first 48 matrix rows for later Sun May 27 16:59:41 2007 matrix is 37461 x 37573 with weight 738243 (avg 19.65/col) Sun May 27 16:59:41 2007 matrix includes 32 packed rows Sun May 27 17:00:24 2007 lanczos halted after 593 iterations Sun May 27 17:00:25 2007 recovered 12 nontrivial dependencies Sun May 27 17:00:25 2007 prp32 factor: 64183606304071153348418983401419 Sun May 27 17:00:25 2007 prp47 factor: 86294287414556460254625701135729827536592888259 Sun May 27 17:00:25 2007 elapsed time 00:12:41

May 27, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(7·10¹⁶⁰-43)/9 = (7)₁₅₉3_<160> = 3² · 67 · C158
C158 = P49 · P109
P49 = 7569214186545777793665631319644598306342954210369_<49>
P109 = 1704069972394272056243610341411329237778860200857566090684279076415414313907033462129726700942953362876790039_<109>

Number: n N=12898470609913395983047724341256679565137276580062649714391007923346231803943246729316381057674590012898470609913395983047724341256679565137276580062649714391 ( 158 digits) SNFS difficulty: 160 digits. Divisors found: r1=7569214186545777793665631319644598306342954210369 (pp49) r2=1704069972394272056243610341411329237778860200857566090684279076415414313907033462129726700942953362876790039 (pp109) Version: GGNFS-0.77.1-20051202-athlon Total time: 41.13 hours. Scaled time: 59.28 units (timescale=1.441). Factorization parameters were as follows: name: KA_7_159_3 n: 12898470609913395983047724341256679565137276580062649714391007923346231803943246729316381057674590012898470609913395983047724341256679565137276580062649714391 skew: 1.44 deg: 5 c5: 7 c0: -43 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1900001) Primes: RFBsize:250150, AFBsize:250336, largePrimes:7244344 encountered Relations: rels:6806415, finalFF:586324 Max relations in full relation-set: 28 Initial matrix: 500553 x 586324 with sparse part having weight 39447333. Pruned matrix : 427427 x 429993 with weight 24457695. Total sieving time: 36.21 hours. Total relation processing time: 0.27 hours. Matrix solve time: 4.58 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 41.13 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 26, 2007 (6th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
2·10¹⁶⁰+3 = 2(0)₁₅₉3_<161> = 269741 · C155
C155 = P60 · P96
P60 = 300244161062830630302818080353294695395582491459143920704439_<60>
P96 = 246949676822489123478546797860086337445136656832298441810501694114885422418729064737492466489097_<96>

Number: n N=74145198542305396658275901698295772611505110457809528399464671666524555036127247989738304521744933102494615204955865070567692712639161269514089441353001583 ( 155 digits) SNFS difficulty: 160 digits. Divisors found: r1=300244161062830630302818080353294695395582491459143920704439 (pp60) r2=246949676822489123478546797860086337445136656832298441810501694114885422418729064737492466489097 (pp96) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 32.43 hours. Scaled time: 44.17 units (timescale=1.362). Factorization parameters were as follows: name: KA_2_0_159_3 n: 74145198542305396658275901698295772611505110457809528399464671666524555036127247989738304521744933102494615204955865070567692712639161269514089441353001583 skew: 1.08 deg: 5 c5: 2 c0: 3 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:250150, AFBsize:250246, largePrimes:6994412 encountered Relations: rels:6520555, finalFF:565351 Max relations in full relation-set: 28 Initial matrix: 500461 x 565351 with sparse part having weight 33244971. Pruned matrix : 440405 x 442971 with weight 21278744. Total sieving time: 28.78 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.24 hours. Total square root time: 0.22 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 32.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 26, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
4·10¹²²+3 = 4(0)₁₂₁3_<123> = 13 · 31 · 751 · C118
C118 = P36 · P82
P36 = 140302808583575220937569935644682059_<36>
P82 = 9419950992110895877545261702594558645655155927342812397620420321479963685240471389_<82>

Number: 40003_122 N=1321645580912794520457421535553918183530313593455211083319841534694848555936997155157887085209794715400144720191109951 ( 118 digits) SNFS difficulty: 122 digits. Divisors found: r1=140302808583575220937569935644682059 (pp36) r2=9419950992110895877545261702594558645655155927342812397620420321479963685240471389 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.17 hours. Scaled time: 1.08 units (timescale=0.927). Factorization parameters were as follows: n: 1321645580912794520457421535553918183530313593455211083319841534694848555936997155157887085209794715400144720191109951 m: 2000000000000000000000000 c5: 25 c0: 6 skew: 1 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 480001) Primes: RFBsize:49098, AFBsize:49121, largePrimes:2076587 encountered Relations: rels:2174816, finalFF:224976 Max relations in full relation-set: 28 Initial matrix: 98283 x 224976 with sparse part having weight 21075220. Pruned matrix : 75996 x 76551 with weight 4950199. Total sieving time: 1.11 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 1.17 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁵-3 = 3(9)₁₂₄7_<126> = 13 · 347 · 1919134447_<10> · 3973122502709_<13> · C101
C101 = P44 · P57
P44 = 14176781570225689422590837043552305747546179_<44>
P57 = 820298957620154295413668754748555247326186604713123112531_<57>

Number: 39997_125 N=11629199144464747273873992857836226276685046458776844818521404624591944271991616740778007884136069049 ( 101 digits) SNFS difficulty: 125 digits. Divisors found: r1=14176781570225689422590837043552305747546179 (pp44) r2=820298957620154295413668754748555247326186604713123112531 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.38 hours. Scaled time: 1.29 units (timescale=0.935). Factorization parameters were as follows: n: 11629199144464747273873992857836226276685046458776844818521404624591944271991616740778007884136069049 m: 10000000000000000000000000 c5: 4 c0: -3 skew: 1 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 750001) Primes: RFBsize:78498, AFBsize:78486, largePrimes:1470046 encountered Relations: rels:1503361, finalFF:207858 Max relations in full relation-set: 28 Initial matrix: 157051 x 207858 with sparse part having weight 9056955. Pruned matrix : 123990 x 124839 with weight 4351782. Total sieving time: 1.32 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.38 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 26, 2007 (4th)

By suberi / GMP-ECM 6.1.2 B1=1000000
4·10¹⁵⁴-3 = 3(9)₁₅₃7_<155> = 37 · 853 · C151
C151 = P32 · P119
P32 = 13650357197160249109048459378477_<32>
P119 = 92846432266895293000127005136899584386269985976279393784014840396257054232599914470996487908411988310488572830000344201_<119>
4·10¹³⁵+3 = 4(0)₁₃₄3_<136> = 11328523 · C129
C129 = P30 · P100
P30 = 167209353214438072108071764699_<30>
P100 = 2111670406352169953615950969505952926778362473341224768552933956228839776053527035084886239827494539_<100>

May 26, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
3·10¹⁷⁰-1 = 2(9)_170<171> = 13 · 5783 · C166
C166 = P54 · P113
P54 = 173013747441272949252140271307882198468644836377812061_<54>
P113 = 23064502808650629916626080541133445738284945384523360813873885767965239712427790623664167124028559969692067948321_<113>

Number: n N=3990476063794410673193311962117080567711728009151491772968515143856662099788504768618896234320754466007794729911278415514970936032668697375596908711209247263198499581 ( 166 digits) SNFS difficulty: 170 digits. Divisors found: r1=173013747441272949252140271307882198468644836377812061 (pp54) r2=23064502808650629916626080541133445738284945384523360813873885767965239712427790623664167124028559969692067948321 (pp113) Version: GGNFS-0.77.1-20051202-athlon Total time: 83.81 hours. Scaled time: 110.71 units (timescale=1.321). Factorization parameters were as follows: name: KA_2_9_170 n: 3990476063794410673193311962117080567711728009151491772968515143856662099788504768618896234320754466007794729911278415514970936032668697375596908711209247263198499581 skew: 0.80 deg: 5 c5: 3 c0: -1 m: 10000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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: 48/48 Sieved algebraic special-q in [100000, 3300001) Primes: RFBsize:348513, AFBsize:348501, largePrimes:7962339 encountered Relations: rels:7605195, finalFF:792642 Max relations in full relation-set: 48 Initial matrix: 697079 x 792642 with sparse part having weight 44278165. Pruned matrix : 611079 x 614628 with weight 28486101. Total sieving time: 74.99 hours. Total relation processing time: 0.34 hours. Matrix solve time: 8.38 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 83.81 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 26, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
4·10¹¹⁹-3 = 3(9)₁₁₈7_<120> = 13 · 17 · 85819 · 2138429 · C106
C106 = P44 · P63
P44 = 25985319399001881232057951389966634997820353_<44>
P63 = 379543338404314085166151446656730517304702047891649789900943119_<63>

Number: 39997_119 N=9862554874199558511652521413589225413570302672368196255395589043914114001064063424236049653226344033501007 ( 106 digits) SNFS difficulty: 120 digits. Divisors found: r1=25985319399001881232057951389966634997820353 (pp44) r2=379543338404314085166151446656730517304702047891649789900943119 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.95 hours. Scaled time: 0.89 units (timescale=0.934). Factorization parameters were as follows: n: 9862554874199558511652521413589225413570302672368196255395589043914114001064063424236049653226344033501007 m: 1000000000000000000000000 c5: 2 c0: -15 skew: 1.5 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 450001) Primes: RFBsize:49098, AFBsize:49146, largePrimes:1924432 encountered Relations: rels:1892891, finalFF:125989 Max relations in full relation-set: 28 Initial matrix: 98309 x 125989 with sparse part having weight 10775752. Pruned matrix : 90888 x 91443 with weight 6048950. Total sieving time: 0.89 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.95 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁰-3 = 3(9)₁₁₉7_<121> = 311 · 2251511 · 9660397 · C105
C105 = P35 · P71
P35 = 14957350687977701210646823592952109_<35>
P71 = 39534466142745973691646463023061454844518637076105956734312901955956709_<71>

Number: 39997_120 N=591330874359032625073270746495953718723219748632694947903328381586309125199738351352363557080262714249281 ( 105 digits) SNFS difficulty: 120 digits. Divisors found: r1=14957350687977701210646823592952109 (pp35) r2=39534466142745973691646463023061454844518637076105956734312901955956709 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.00 hours. Scaled time: 0.94 units (timescale=0.934). Factorization parameters were as follows: n: 591330874359032625073270746495953718723219748632694947903328381586309125199738351352363557080262714249281 m: 1000000000000000000000000 c5: 4 c0: -3 skew: 1 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 450001) Primes: RFBsize:49098, AFBsize:49031, largePrimes:2089674 encountered Relations: rels:2224684, finalFF:262044 Max relations in full relation-set: 28 Initial matrix: 98196 x 262044 with sparse part having weight 24274221. Pruned matrix : 70560 x 71114 with weight 4834916. Total sieving time: 0.95 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 1.00 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁰+3 = 4(0)₁₁₉3_<121> = 7 · C120
C120 = P43 · P78
P43 = 5612274364620889506308759859628576707925837_<43>
P78 = 101817647232428482152474928700295254049026878546996061124502636639930949090617_<78>

Number: 40003_120 N=571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 ( 120 digits) SNFS difficulty: 120 digits. Divisors found: r1=5612274364620889506308759859628576707925837 (pp43) r2=101817647232428482152474928700295254049026878546996061124502636639930949090617 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.81 hours. Scaled time: 0.76 units (timescale=0.927). Factorization parameters were as follows: n: 571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 m: 1000000000000000000000000 c5: 4 c0: 3 skew: 1 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 420001) Primes: RFBsize:49098, AFBsize:49031, largePrimes:1870291 encountered Relations: rels:1811935, finalFF:113613 Max relations in full relation-set: 28 Initial matrix: 98196 x 113613 with sparse part having weight 9031756. Pruned matrix : 93407 x 93961 with weight 6170340. Total sieving time: 0.75 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.81 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²¹+3 = 4(0)₁₂₀3_<122> = 6961 · 170977595876812450723_<21> · C98
C98 = P41 · P57
P41 = 34585230048100307623332840382749782681057_<41>
P57 = 971758800986673748132478129675100273134597913849135461393_<57>

Number: 40003_121 N=33608501683390235777263910364754662400497207736229051883674130597789461249450276268990816255932401 ( 98 digits) SNFS difficulty: 122 digits. Divisors found: r1=34585230048100307623332840382749782681057 (pp41) r2=971758800986673748132478129675100273134597913849135461393 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.97 hours. Scaled time: 0.91 units (timescale=0.929). Factorization parameters were as follows: n: 33608501683390235777263910364754662400497207736229051883674130597789461249450276268990816255932401 m: 2000000000000000000000000 c5: 5 c0: 12 skew: 1.19 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 450001) Primes: RFBsize:49098, AFBsize:49316, largePrimes:1946453 encountered Relations: rels:1937498, finalFF:144532 Max relations in full relation-set: 28 Initial matrix: 98480 x 144532 with sparse part having weight 12447254. Pruned matrix : 87105 x 87661 with weight 5405410. Total sieving time: 0.92 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.97 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²²-3 = 3(9)₁₂₁7_<123> = 31391 · 2684288903_<10> · 58006487029_<11> · C98
C98 = P48 · P51
P48 = 344007467969662880678387556467819763326309749859_<48>
P51 = 237892718439068787805376755582318249071248333701499_<51>

Number: 39997_122 N=81836871718643986185728151933388840266271776853244320350768896586357955470594077763743698263338641 ( 98 digits) SNFS difficulty: 122 digits. Divisors found: r1=344007467969662880678387556467819763326309749859 (pp48) r2=237892718439068787805376755582318249071248333701499 (pp51) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.16 hours. Scaled time: 1.08 units (timescale=0.932). Factorization parameters were as follows: n: 81836871718643986185728151933388840266271776853244320350768896586357955470594077763743698263338641 m: 2000000000000000000000000 c5: 25 c0: -6 skew: 1 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 480001) Primes: RFBsize:49098, AFBsize:49121, largePrimes:2037427 encountered Relations: rels:2086785, finalFF:182743 Max relations in full relation-set: 28 Initial matrix: 98283 x 182743 with sparse part having weight 16947217. Pruned matrix : 82061 x 82616 with weight 5173414. Total sieving time: 1.10 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 1.16 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 26, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
4·10¹¹³+3 = 4(0)₁₁₂3_<114> = 151 · 2521 · 9341 · 9946673530747_<13> · C92
C92 = P39 · P53
P39 = 213150967517384807318120724304052423803_<39>
P53 = 53058095146024700376361296298594029717899946692445353_<53>

Number: 40003_113 N=11309384315004623424899180326922060659645124717317858332549892278146483153678074568773937459 ( 92 digits) SNFS difficulty: 113 digits. Divisors found: r1=213150967517384807318120724304052423803 (pp39) r2=53058095146024700376361296298594029717899946692445353 (pp53) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.67 hours. Scaled time: 0.63 units (timescale=0.935). Factorization parameters were as follows: n: 11309384315004623424899180326922060659645124717317858332549892278146483153678074568773937459 m: 20000000000000000000000 c5: 125 c0: 3 skew: 1 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 300001) Primes: RFBsize:30757, AFBsize:30524, largePrimes:966239 encountered Relations: rels:870153, finalFF:70742 Max relations in full relation-set: 28 Initial matrix: 61346 x 70742 with sparse part having weight 3221294. Pruned matrix : 57493 x 57863 with weight 2097058. Total sieving time: 0.65 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.67 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 25, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, GMP-ECM 6.1.2
4·10¹¹⁸+3 = 4(0)₁₁₇3_<119> = C119
C119 = P39 · P81
P39 = 211621276763532507670415744223334748617_<39>
P81 = 189016910831212661627315911618686407924531685546937547055501093534558399895914859_<81>

Number: 40003_118 N=40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 119 digits) SNFS difficulty: 118 digits. Divisors found: r1=211621276763532507670415744223334748617 (pp39) r2=189016910831212661627315911618686407924531685546937547055501093534558399895914859 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.96 hours. Scaled time: 0.90 units (timescale=0.935). Factorization parameters were as follows: n: 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 m: 200000000000000000000000 c5: 125 c0: 3 skew: 1 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 420001) Primes: RFBsize:49098, AFBsize:48756, largePrimes:1908722 encountered Relations: rels:1884500, finalFF:138422 Max relations in full relation-set: 28 Initial matrix: 97919 x 138422 with sparse part having weight 11276802. Pruned matrix : 86646 x 87199 with weight 5081607. Total sieving time: 0.90 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.96 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁹+3 = 4(0)₁₂₈3_<130> = C130
C130 = P52 · P79
P52 = 2125328766779684187720000305302944444700439100557051_<52>
P79 = 1882061760289836591422460816044047312356413460440607394774696364308476485811353_<79>

Number: 40003_129 N=4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 130 digits) SNFS difficulty: 130 digits. Divisors found: r1=2125328766779684187720000305302944444700439100557051 (pp52) r2=1882061760289836591422460816044047312356413460440607394774696364308476485811353 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.58 hours. Scaled time: 2.37 units (timescale=0.920). Factorization parameters were as follows: n: 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 m: 100000000000000000000000000 c5: 2 c0: 15 skew: 1.5 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 1000001) Primes: RFBsize:78498, AFBsize:78671, largePrimes:1535768 encountered Relations: rels:1549847, finalFF:192091 Max relations in full relation-set: 28 Initial matrix: 157234 x 192091 with sparse part having weight 9975542. Pruned matrix : 143749 x 144599 with weight 5929322. Total sieving time: 2.49 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.58 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹⁷⁴-3 = 3(9)₁₇₃7_<175> = C175
C175 = P32 · C143
P32 = 60245455742914874964935791279271_<32>
C143 = [66395049231085237918736844489235035302968882127983995400674751551693234252075026857441283507447362557455506331177428848643832758876913437458107_<143>]
4·10¹⁰⁹+3 = 4(0)₁₀₈3_<110> = 157 · 659 · 3015622139_<10> · C96
C96 = P46 · P50
P46 = 8789691551616868774948328182836667117193493269_<46>
P50 = 14585602253855018384156891160085996096225659769091_<50>

Number: 40003_109 N=128202944905953414864392618133593516660075229232730226022631615760351226868770194151050202748479 ( 96 digits) SNFS difficulty: 110 digits. Divisors found: r1=8789691551616868774948328182836667117193493269 (pp46) r2=14585602253855018384156891160085996096225659769091 (pp50) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.62 hours. Scaled time: 0.58 units (timescale=0.931). Factorization parameters were as follows: n: 128202944905953414864392618133593516660075229232730226022631615760351226868770194151050202748479 m: 10000000000000000000000 c5: 2 c0: 15 skew: 1.5 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 300001) Primes: RFBsize:30757, AFBsize:30809, largePrimes:1049595 encountered Relations: rels:976872, finalFF:96164 Max relations in full relation-set: 28 Initial matrix: 61631 x 96164 with sparse part having weight 4380179. Pruned matrix : 51415 x 51787 with weight 1652064. Total sieving time: 0.59 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.62 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹⁷⁹+3 = 4(0)₁₇₈3_<180> = C180
C180 = P37 · C143
P37 = 9679838127597185553923930374350132743_<37>
C143 = [41323005067574566304410175051619336014247547874804676702862982021554231126531999977945569827460087540832516415965598056089191661607896947926821_<143>]
4·10¹¹³-3 = 3(9)₁₁₂7_<114> = 13 · C113
C113 = P31 · P83
P31 = 1702356884234854309940250225619_<31>
P83 = 18074488994744710410784707596626357056720051107053667811146452741104552488586191851_<83>

Number: 39997_113 N=30769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769 ( 113 digits) SNFS difficulty: 113 digits. Divisors found: r1=1702356884234854309940250225619 (pp31) r2=18074488994744710410784707596626357056720051107053667811146452741104552488586191851 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.68 hours. Scaled time: 0.63 units (timescale=0.932). Factorization parameters were as follows: n: 30769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769 m: 20000000000000000000000 c5: 125 c0: -3 skew: 1 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 300001) Primes: RFBsize:30757, AFBsize:30524, largePrimes:971787 encountered Relations: rels:878648, finalFF:73299 Max relations in full relation-set: 28 Initial matrix: 61346 x 73299 with sparse part having weight 3338199. Pruned matrix : 56856 x 57226 with weight 1991611. Total sieving time: 0.65 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.68 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 25, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(2·10¹⁷⁰+43)/9 = (2)₁₆₉7_<170> = 3 · 31 · C168
C168 = P72 · P96
P72 = 822727558550038088856535467720496024936606976987042056653456323459910599_<72>
P96 = 290434693188738543956075989104111212671965096094614253375494043532658467524800249969328397926361_<96>

Number: n N=238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400239 ( 168 digits) SNFS difficulty: 170 digits. Divisors found: r1=822727558550038088856535467720496024936606976987042056653456323459910599 (pp72) r2=290434693188738543956075989104111212671965096094614253375494043532658467524800249969328397926361 (pp96) Version: GGNFS-0.77.1-20051202-athlon Total time: 101.07 hours. Scaled time: 120.88 units (timescale=1.196). Factorization parameters were as follows: name: KA_2_169_7 n: 238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400239 type: snfs skew: 1.85 deg: 5 c5: 2 c0: 43 m: 10000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3500001) Primes: RFBsize:348513, AFBsize:348531, largePrimes:8123742 encountered Relations: rels:7797506, finalFF:823183 Max relations in full relation-set: 28 Initial matrix: 697109 x 823183 with sparse part having weight 47249027. Pruned matrix : 584171 x 587720 with weight 29395354. Total sieving time: 92.50 hours. Total relation processing time: 0.38 hours. Matrix solve time: 8.04 hours. Total square root time: 0.15 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000 total time: 101.07 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

May 25, 2007 (2nd)

The factor tables of 399...997 and 400...003 were extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 25, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
2·10¹⁵⁷-3 = 1(9)₁₅₆7_<158> = 43 · 179 · 2733863182530927049217_<22> · C132
C132 = P42 · P91
P42 = 496078180985187011253921599029146472448633_<42>
P91 = 1915938687245105985797755896058272648806048756431283226141003881366035015771171783110925141_<91>

Number: n N=950455378847699300374424598634237722308057180347692882733859893445386580027802421982455311802165614024833261186121222088656230782253 ( 132 digits) SNFS difficulty: 157 digits. Divisors found: r1=496078180985187011253921599029146472448633 (pp42) r2=1915938687245105985797755896058272648806048756431283226141003881366035015771171783110925141 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 33.62 hours. Scaled time: 48.78 units (timescale=1.451). Factorization parameters were as follows: name: KA_1_9_156_7 n: 950455378847699300374424598634237722308057180347692882733859893445386580027802421982455311802165614024833261186121222088656230782253 skew: 0.43 deg: 5 c5: 200 c0: -3 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:183072, AFBsize:183041, largePrimes:7276973 encountered Relations: rels:6812530, finalFF:487659 Max relations in full relation-set: 28 Initial matrix: 366178 x 487659 with sparse part having weight 43287182. Pruned matrix : 296199 x 298093 with weight 25524280. Total sieving time: 30.36 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.00 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 33.62 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(22·10¹⁶⁰-1)/3 = 7(3)_160<161> = 13 · 263 · C158
C158 = P62 · P96
P62 = 23426441886445012154981750965676224184494269863736197144797481_<62>
P96 = 915579361128915270723247955082996638837387785389087322699384546746236173167534267878078270621047_<96>

Number: n N=21448766695914984888368918787169737740079945403139319489129375060933996295213025251048064736277664034318026713463975821390270059471580384127912645022911182607 ( 158 digits) SNFS difficulty: 161 digits. Divisors found: r1=23426441886445012154981750965676224184494269863736197144797481 (pp62) r2=915579361128915270723247955082996638837387785389087322699384546746236173167534267878078270621047 (pp96) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 40.17 hours. Scaled time: 54.87 units (timescale=1.366). Factorization parameters were as follows: name: KA_7_3_160 n: 21448766695914984888368918787169737740079945403139319489129375060933996295213025251048064736277664034318026713463975821390270059471580384127912645022911182607 skew: 0.54 deg: 5 c5: 22 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:315948, AFBsize:316347, largePrimes:7309058 encountered Relations: rels:6944667, finalFF:720963 Max relations in full relation-set: 28 Initial matrix: 632361 x 720963 with sparse part having weight 35299802. Pruned matrix : 543577 x 546802 with weight 21194774. Total sieving time: 35.03 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.43 hours. Total square root time: 0.49 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 40.17 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 23, 2007 (6th)

By Robert Backstrom / GMP-ECM 5.0 B1=1358500
2·10¹⁵⁶+3 = 2(0)₁₅₅3_<157> = 97 · 125353 · 97436968800347339_<17> · C133
C133 = P38 · P95
P38 = 43135946585687043827750397163601212657_<38>
P95 = 39134557867852232577558454632800142255822036800416522850859882961102818904957125240913476934321_<95>

May 23, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹⁵³-3 = 1(9)₁₅₂7_<154> = 8990693 · 921385311825262730764919_<24> · C123
C123 = P44 · P80
P44 = 18536972846671778888746448349596139528250921_<44>
P80 = 13024370107576147632519746158741250510023486439810098022457117528012765562134071_<80>

Number: 19997_153 N=241432395029142644418795685506626823600720952779925262840558341180193330344056600225360186277355101442030529906274731229391 ( 123 digits) SNFS difficulty: 153 digits. Divisors found: r1=18536972846671778888746448349596139528250921 (pp44) r2=13024370107576147632519746158741250510023486439810098022457117528012765562134071 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.54 hours. Scaled time: 14.53 units (timescale=0.935). Factorization parameters were as follows: n: 241432395029142644418795685506626823600720952779925262840558341180193330344056600225360186277355101442030529906274731229391 m: 2000000000000000000000000000000 c5: 125 c0: -6 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:175758, largePrimes:5489347 encountered Relations: rels:5372513, finalFF:457707 Max relations in full relation-set: 28 Initial matrix: 352125 x 457707 with sparse part having weight 40251711. Pruned matrix : 304309 x 306133 with weight 23581787. Total sieving time: 14.88 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.54 hours. Time per square root: 0.04 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: 15.54 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 23, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(35·10¹⁵⁸-53)/9 = 3(8)₁₅₇3_<159> = 27127 · 48923440453_<11> · C144
C144 = P44 · P100
P44 = 42538481348207485813121172033846526577279483_<44>
P100 = 6888502111425675766578155516284879416746833257639594662538596972928631754995038097561460112280873171_<100>

Number: n N=293026418583968992746656536950228061925053866003057901150847188822375646935590181201198901295151639664429222267982877800737159427578360943450593 ( 144 digits) SNFS difficulty: 160 digits. Divisors found: r1=42538481348207485813121172033846526577279483 (pp44) r2=6888502111425675766578155516284879416746833257639594662538596972928631754995038097561460112280873171 (pp100) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 44.00 hours. Scaled time: 56.27 units (timescale=1.279). Factorization parameters were as follows: name: KA_3_8_157_3 n: 293026418583968992746656536950228061925053866003057901150847188822375646935590181201198901295151639664429222267982877800737159427578360943450593 skew: 1.36 deg: 5 c5: 56 c0: -265 m: 50000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:315948, AFBsize:315361, largePrimes:7625944 encountered Relations: rels:7354460, finalFF:807928 Max relations in full relation-set: 28 Initial matrix: 631375 x 807928 with sparse part having weight 42602060. Pruned matrix : 465064 x 468284 with weight 20824091. Total sieving time: 40.25 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.27 hours. Total square root time: 0.24 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 44.00 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 23, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
9·10¹⁸⁴+1 = 9(0)₁₈₃1_<185> = 29 · 53 · 433 · 17907001038501948144357766109_<29> · 56385136584339210524733082811161_<32> · C120
C120 = P59 · P61
P59 = 13545949246627659985095780182634249171497673616306498864681_<59>
P61 = 9887438744319177885322438170306294338262729295517657911743749_<61>

Number: 90001_184 N=133934743409687504113918170515371822798346958185976385775707154210049376559761047550202532079443200522363980365498629069 ( 120 digits) Divisors found: r1=13545949246627659985095780182634249171497673616306498864681 (pp59) r2=9887438744319177885322438170306294338262729295517657911743749 (pp61) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 104.60 hours. Scaled time: 70.50 units (timescale=0.674). Factorization parameters were as follows: name: 90001_184 n: 133934743409687504113918170515371822798346958185976385775707154210049376559761047550202532079443200522363980365498629069 skew: 107220.47 # norm 2.15e+16 c5: 12600 c4: 3067381107 c3: -574230821471740 c2: -9105185955287273434 c1: 2636139457254556317179812 c0: 17112993314701970007764391495 # alpha -6.21 Y1: 12502178138059 Y0: -101228296750123928750236 # Murphy_E 3.30e-10 # M 38349749078379278951104040809096706378944396920633763085781647089002458673724715501130568777671997717738236889041282710 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4170001) Primes: RFBsize:315948, AFBsize:316633, largePrimes:7605542 encountered Relations: rels:7609290, finalFF:710379 Max relations in full relation-set: 0 Initial matrix: 632661 x 710379 with sparse part having weight 60425268. Pruned matrix : 569194 x 572421 with weight 42554618. Total sieving time: 83.95 hours. Total relation processing time: 1.24 hours. Matrix solve time: 18.90 hours. Time per square root: 0.51 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 104.60 hours. --------- CPU info (if available) ----------

May 23, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹⁵²+3 = 2(0)₁₅₁3_<153> = 7 · 59 · 9437 · 1077079 · 3473719 · C134
C134 = P39 · P95
P39 = 764892666772199274490037661811796227973_<39>
P95 = 17930947920257063532703516829435538148362253000748922501535367754063948223945638948206096726431_<95>

Number: 20003_152 N=13715250572478845705802125321480208820321833385402835338596419671437335621017472336038044329692466760525852970011068555409269090654363 ( 134 digits) SNFS difficulty: 152 digits. Divisors found: r1=764892666772199274490037661811796227973 (pp39) r2=17930947920257063532703516829435538148362253000748922501535367754063948223945638948206096726431 (pp95) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.03 hours. Scaled time: 15.86 units (timescale=0.931). Factorization parameters were as follows: n: 13715250572478845705802125321480208820321833385402835338596419671437335621017472336038044329692466760525852970011068555409269090654363 m: 2000000000000000000000000000000 c5: 25 c0: 12 skew: 1 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, 2200001) Primes: RFBsize:176302, AFBsize:176368, largePrimes:5425155 encountered Relations: rels:5251337, finalFF:405163 Max relations in full relation-set: 28 Initial matrix: 352734 x 405163 with sparse part having weight 35624313. Pruned matrix : 330434 x 332261 with weight 25625210. Total sieving time: 16.28 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.64 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 17.03 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 23, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
2·10¹⁵¹-3 = 1(9)₁₅₀7_<152> = 109 · 5351699092147_<13> · 41659474526382217853629_<23> · C114
C114 = P51 · P64
P51 = 232357967917576122963811199234684498812206335392391_<51>
P64 = 3541933914244940727356281485918685455317930382157304642870395201_<64>

Number: n N=822996566812300756270915694973657445507528537129099442009025996149706730952409519399555793857628590326355578315591 ( 114 digits) SNFS difficulty: 151 digits. Divisors found: r1=232357967917576122963811199234684498812206335392391 (pp51) r2=3541933914244940727356281485918685455317930382157304642870395201 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.36 hours. Scaled time: 28.14 units (timescale=1.454). Factorization parameters were as follows: name: KA_1_9_150_7 n: 822996566812300756270915694973657445507528537129099442009025996149706730952409519399555793857628590326355578315591 skew: 0.68 deg: 5 c5: 20 c0: -3 m: 1000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:183072, AFBsize:182801, largePrimes:6608095 encountered Relations: rels:6045586, finalFF:420551 Max relations in full relation-set: 28 Initial matrix: 365939 x 420551 with sparse part having weight 29835712. Pruned matrix : 321725 x 323618 with weight 19335173. Total sieving time: 16.77 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.32 hours. Total square root time: 0.11 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 19.36 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 22, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
5·10¹⁶⁹-1 = 4(9)_169<170> = 7² · 17 · C167
C167 = P38 · P64 · P66
P38 = 51971109847877751141565924226072367623_<38>
P64 = 6247449254103117689987713647000874500741834590985633042232135777_<64>
P66 = 184867374942010724757709190165050993402607186564005758034404013993_<66>

Number: n N=60024009603841536614645858343337334933973589435774309723889555822328931572629051620648259303721488595438175270108043217286914765906362545018007202881152460984393757503 ( 167 digits) SNFS difficulty: 170 digits. Divisors found: r1=51971109847877751141565924226072367623 (pp38) r2=6247449254103117689987713647000874500741834590985633042232135777 (pp64) r3=184867374942010724757709190165050993402607186564005758034404013993 (pp66) Version: GGNFS-0.77.1-20051202-athlon Total time: 80.00 hours. Scaled time: 58.00 units (timescale=0.725). Factorization parameters were as follows: name: KA_4_9_169 n: 60024009603841536614645858343337334933973589435774309723889555822328931572629051620648259303721488595438175270108043217286914765906362545018007202881152460984393757503 skew: 1.15 deg: 5 c5: 1 c0: -2 m: 10000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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: 48/48 Sieved algebraic special-q in [100000, 3100001) Primes: RFBsize:348513, AFBsize:348176, largePrimes:7957180 encountered Relations: rels:7622391, finalFF:810632 Max relations in full relation-set: 48 Initial matrix: 696753 x 810632 with sparse part having weight 43718412. Pruned matrix : 593010 x 596557 with weight 26495728. Total sieving time: 70.42 hours. Total relation processing time: 0.28 hours. Matrix solve time: 8.76 hours. Total square root time: 0.54 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 80.00 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 22, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs
(10¹⁷⁸+17)/9 = (1)₁₇₇3_<178> = 3² · 7² · 1046641 · 1290857 · 468836928921920538313_<21> · 297082579660968821734851624509405183_<36> · C107
C107 = P34 · P73
P34 = 6351389277783512750660674500861871_<34>
P73 = 2108022748500441599748310376090833021700915012375759080181462532721767521_<73>

Number: 11113_178 N=13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791 ( 107 digits) Divisors found: r1=6351389277783512750660674500861871 (pp34) r2=2108022748500441599748310376090833021700915012375759080181462532721767521 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.91 hours. Scaled time: 10.20 units (timescale=0.935). Factorization parameters were as follows: name: 11113_178 n: 13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791 skew: 24447.50 # norm 1.03e+15 c5: 11040 c4: 634721972 c3: -57395841951390 c2: -297909801429328773 c1: 7360634883314650193640 c0: 44733769501169737130602075 # alpha -6.20 Y1: 59180280269 Y0: -261068129944292921856 # Murphy_E 1.60e-09 # M 1848511566881534751075889082385374038136846422142820742013036141739596195580891966762660131878038833277554 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1440001) Primes: RFBsize:135072, AFBsize:135129, largePrimes:4628918 encountered Relations: rels:4758229, finalFF:429445 Max relations in full relation-set: 28 Initial matrix: 270283 x 429445 with sparse part having weight 42261017. Pruned matrix : 196380 x 197795 with weight 17946254. Total sieving time: 10.57 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.19 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 10.91 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 22, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
2·10¹⁴⁷-3 = 1(9)₁₄₆7_<148> = 6328193 · 2807442959_<10> · 9315019792951667720337833_<25> · C107
C107 = P38 · P69
P38 = 19847917526656775016866295121378364453_<38>
P69 = 608892479187265731705994468981721335175199066679255978067665568322719_<69>

Number: n N=12085247709510427120634598202262732105264237067773714462472119550932718546531305768674719902899358701907707 ( 107 digits) SNFS difficulty: 147 digits. Divisors found: r1=19847917526656775016866295121378364453 (pp38) r2=608892479187265731705994468981721335175199066679255978067665568322719 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 12.22 hours. Scaled time: 17.76 units (timescale=1.454). Factorization parameters were as follows: name: KA_1_9_146_7 n: 12085247709510427120634598202262732105264237067773714462472119550932718546531305768674719902899358701907707 skew: 0.43 deg: 5 c5: 200 c0: -3 m: 100000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:183072, AFBsize:183041, largePrimes:6840115 encountered Relations: rels:6269711, finalFF:436586 Max relations in full relation-set: 28 Initial matrix: 366178 x 436586 with sparse part having weight 29446300. Pruned matrix : 310612 x 312506 with weight 17873574. Total sieving time: 9.61 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.38 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 12.22 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 22, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹⁴⁷+3 = 2(0)₁₄₆3_<148> = 1689189684351792543788723_<25> · C124
C124 = P32 · P92
P32 = 37217298101001103011342694765763_<32>
P92 = 31813154456124267948681707302764451170058560372489661494512147777300060017072412206709935547_<92>

Number: 20003_147 N=1183999652926768495616698876252051229605874742718666658960661269213398956494208102909274279905772503661905475316163992277361 ( 124 digits) SNFS difficulty: 147 digits. Divisors found: r1=37217298101001103011342694765763 (pp32) r2=31813154456124267948681707302764451170058560372489661494512147777300060017072412206709935547 (pp92) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.66 hours. Scaled time: 15.51 units (timescale=0.931). Factorization parameters were as follows: n: 1183999652926768495616698876252051229605874742718666658960661269213398956494208102909274279905772503661905475316163992277361 m: 200000000000000000000000000000 c5: 25 c0: 12 skew: 1 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [900000, 1950001) Primes: RFBsize:135072, AFBsize:135133, largePrimes:2850480 encountered Relations: rels:2879930, finalFF:356257 Max relations in full relation-set: 28 Initial matrix: 270269 x 356257 with sparse part having weight 24048209. Pruned matrix : 233955 x 235370 with weight 13959048. Total sieving time: 16.36 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.21 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,45,45,2.3,2.3,75000 total time: 16.66 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 21, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹⁶⁷+3 = 2(0)₁₆₆3_<168> = C168
C168 = P51 · P58 · P60
P51 = 337473788641314954387395638036113417304047480856561_<51>
P58 = 4690700023174550771994364525354487199388452766958125990189_<58>
P60 = 126343321023855007144178242728859599541361819987460022346207_<60>

Number: 20003_167 N=200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 168 digits) SNFS difficulty: 167 digits. Divisors found: r1=337473788641314954387395638036113417304047480856561 (pp51) r2=4690700023174550771994364525354487199388452766958125990189 (pp58) r3=126343321023855007144178242728859599541361819987460022346207 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 86.06 hours. Scaled time: 79.78 units (timescale=0.927). Factorization parameters were as follows: n: 200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 m: 2000000000000000000000000000000000 c5: 25 c0: 12 skew: 1 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 7200001) Primes: RFBsize:412849, AFBsize:413001, largePrimes:6107027 encountered Relations: rels:6383488, finalFF:940116 Max relations in full relation-set: 28 Initial matrix: 825914 x 940116 with sparse part having weight 55379558. Pruned matrix : 732130 x 736323 with weight 40746913. Total sieving time: 81.90 hours. Total relation processing time: 0.13 hours. Matrix solve time: 3.96 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.5,2.5,100000 total time: 86.06 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 21, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
2·10¹⁴⁶-3 = 1(9)₁₄₅7_<147> = 149 · 1570076584418759_<16> · 2011840031262686851_<19> · C111
C111 = P46 · P65
P46 = 4448748130740857754356733813222510745804262837_<46>
P65 = 95519408968726075748994090904376099816839216393188114257850974641_<65>

Number: n N=424941792099091652796628671010700958506423837145816971878241180930695799833275848461352158847044391932985716517 ( 111 digits) SNFS difficulty: 146 digits. Divisors found: r1=4448748130740857754356733813222510745804262837 (pp46) r2=95519408968726075748994090904376099816839216393188114257850974641 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 11.06 hours. Scaled time: 16.04 units (timescale=1.450). Factorization parameters were as follows: name: KA_1_9_145_7 n: 424941792099091652796628671010700958506423837145816971878241180930695799833275848461352158847044391932985716517 skew: 0.68 deg: 5 c5: 20 c0: -3 m: 100000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:183072, AFBsize:182801, largePrimes:6838353 encountered Relations: rels:6284624, finalFF:453514 Max relations in full relation-set: 28 Initial matrix: 365939 x 453514 with sparse part having weight 30588863. Pruned matrix : 295556 x 297449 with weight 17145080. Total sieving time: 8.83 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.91 hours. Total square root time: 0.16 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 11.06 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

2·10¹⁵⁷+3 = 2(0)₁₅₆3_<158> = 8678368395079_<13> · C145
C145 = P44 · P101
P44 = 59573402681404398007654718102866364909302643_<44>
P101 = 38684724398115424654512004896712075071304442379362845270019006771965113736013768988351468162809875399_<101>

Number: n N=2304580664188079575933828712914557890427023054102125976725828086702081005763818534064969056410847081186110800103490795263920600961553242811379557 ( 145 digits) SNFS difficulty: 157 digits. Divisors found: r1=59573402681404398007654718102866364909302643 (pp44) r2=38684724398115424654512004896712075071304442379362845270019006771965113736013768988351468162809875399 (pp101) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 44.23 hours. Scaled time: 60.55 units (timescale=1.369). Factorization parameters were as follows: name: KA_2_0_156_3 n: 2304580664188079575933828712914557890427023054102125976725828086702081005763818534064969056410847081186110800103490795263920600961553242811379557 skew: 0.43 deg: 5 c5: 200 c0: 3 m: 10000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:315948, AFBsize:316266, largePrimes:7406177 encountered Relations: rels:7093105, finalFF:765139 Max relations in full relation-set: 28 Initial matrix: 632279 x 765139 with sparse part having weight 36970198. Pruned matrix : 503294 x 506519 with weight 19243383. Total sieving time: 39.27 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.31 hours. Total square root time: 0.43 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 44.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 21, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs
2·10¹⁴³+3 = 2(0)₁₄₂3_<144> = 31 · 79869969541_<11> · 213191226127907995641964733297_<30> · C102
C102 = P30 · P73
P30 = 228969479001528543632608227557_<30>
P73 = 1654770841768982551074895703714451566312262310294250115213002864298336917_<73>

Number: 20003_143 N=352782624717439820453701966298868758723803154243973650848982107895441604203274505013730356962554225349 ( 102 digits) Divisors found: r1=213191226127907995641964733297 (pp30) r2=1654770841768982551074895703714451566312262310294250115213002864298336917 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.26 hours. Scaled time: 4.92 units (timescale=0.935). Factorization parameters were as follows: name: 20003_143 n: 352782624717439820453701966298868758723803154243973650848982107895441604203274505013730356962554225349 skew: 4896.42 # norm 1.65e+14 c5: 414540 c4: -1516615299 c3: -29953559408092 c2: 22157126830643012 c1: 319304041463428098440 c0: -322389009793145912969625 # alpha -6.51 Y1: 29065820179 Y0: -15345772329994469954 # Murphy_E 2.97e-09 # M 71309661546094854819531043168860349419349509853588268376742292160086044115824039856088598435052274054 type: gnfs rlim: 1700000 alim: 1700000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1700000/1700000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [850000, 1450001) Primes: RFBsize:128141, AFBsize:128124, largePrimes:4351260 encountered Relations: rels:4289278, finalFF:336862 Max relations in full relation-set: 28 Initial matrix: 256353 x 336862 with sparse part having weight 27590776. Pruned matrix : 202920 x 204265 with weight 14425353. Polynomial selection time: 0.31 hours. Total sieving time: 4.63 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.17 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1700000,1700000,26,26,49,49,2.6,2.6,50000 total time: 5.26 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 21, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=1035500, GGNFS-0.77.1-20051202-athlon gnfs
2·10¹⁵⁹-3 = 1(9)₁₅₈7_<160> = 52589677955822857981_<20> · C140
C140 = P37 · P49 · P55
P37 = 3896040234710280092225221728653869867_<37>
P49 = 5874207548035032880370430336726048734418437859121_<49>
P55 = 1661715856862486631625209578684315662965911900561608691_<55>

Number: n N=9761263829071121262365012249257222672340375008383646695682227981460573838578364015976442972225787220611 ( 103 digits) Divisors found: r1=5874207548035032880370430336726048734418437859121 (pp49) r2=1661715856862486631625209578684315662965911900561608691 (pp55) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.26 hours. Scaled time: 11.92 units (timescale=1.443). Factorization parameters were as follows: name: KA_1_9_158_7 n: 9761263829071121262365012249257222672340375008383646695682227981460573838578364015976442972225787220611 skew: 17806.85 # norm 3.92e+14 c5: 24840 c4: 1198081196 c3: -24357592265018 c2: -210683013743336014 c1: 4490637563116177810311 c0: -6227635109584928607029385 # alpha -6.39 Y1: 15093872179 Y0: -52344334656327314746 # Murphy_E 2.17e-09 # M 5247268042512921953463320309399432360648469461756698860444742486375840947181248944205613969233916838496 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:169511, AFBsize:168934, largePrimes:4068833 encountered Relations: rels:4045535, finalFF:435835 Max relations in full relation-set: 28 Initial matrix: 338529 x 435835 with sparse part having weight 25375260. Pruned matrix : 245530 x 247286 with weight 10481944. Total sieving time: 7.28 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.75 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 8.26 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 20, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(4·10¹⁶⁸-13)/9 = (4)₁₆₇3_<168> = 17 · 419 · C164
C164 = P35 · P52 · P78
P35 = 57223726068551403899392214060994719_<35>
P52 = 2958022467640268007405799325268632922692503207747423_<52>
P78 = 368618337536960736026589540264509215386289010356520617633489625535863749834393_<78>

Number: n N=62395682218790459700188746938711841140593070959489603319450294039652456050041337139469948679551375044846896594755642909510661862199135819801269752133152385854898841 ( 164 digits) SNFS difficulty: 168 digits. Divisors found: r1=57223726068551403899392214060994719 (pp35) r2=2958022467640268007405799325268632922692503207747423 (pp52) r3=368618337536960736026589540264509215386289010356520617633489625535863749834393 (pp78) Version: GGNFS-0.77.1-20051202-athlon Total time: 82.39 hours. Scaled time: 98.53 units (timescale=1.196). Factorization parameters were as follows: name: KA_4_167_3 n: 62395682218790459700188746938711841140593070959489603319450294039652456050041337139469948679551375044846896594755642909510661862199135819801269752133152385854898841 type: snfs skew: 0.64 deg: 5 c5: 125 c0: -13 m: 2000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2800001) Primes: RFBsize:348513, AFBsize:348691, largePrimes:7837578 encountered Relations: rels:7490877, finalFF:784720 Max relations in full relation-set: 28 Initial matrix: 697269 x 784720 with sparse part having weight 41841324. Pruned matrix : 613981 x 617531 with weight 27192773. Total sieving time: 73.63 hours. Total relation processing time: 0.33 hours. Matrix solve time: 7.84 hours. Total square root time: 0.59 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000 total time: 82.39 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

May 20, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹³⁷+3 = 2(0)₁₃₆3_<138> = 17 · C137
C137 = P58 · P79
P58 = 1328613771450100770246781828785320550322299965818189662049_<58>
P79 = 8854872751704570530521108482218419399537655969341394293738394189902236177869491_<79>

Number: 20003_137 N=11764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647059 ( 137 digits) SNFS difficulty: 137 digits. Divisors found: r1=1328613771450100770246781828785320550322299965818189662049 (pp58) r2=8854872751704570530521108482218419399537655969341394293738394189902236177869491 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.22 hours. Scaled time: 5.78 units (timescale=0.928). Factorization parameters were as follows: n: 11764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647059 m: 2000000000000000000000000000 c5: 25 c0: 12 skew: 1 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [650000, 1850001) Primes: RFBsize:100021, AFBsize:100128, largePrimes:1640721 encountered Relations: rels:1668665, finalFF:226443 Max relations in full relation-set: 28 Initial matrix: 200213 x 226443 with sparse part having weight 12812781. Pruned matrix : 188889 x 189954 with weight 9261748. Total sieving time: 6.07 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000 total time: 6.22 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹⁴¹+3 = 2(0)₁₄₀3_<142> = 19 · 167 · 511171 · 31993217 · 416824282517_<12> · 40464415611439_<14> · C100
C100 = P35 · P65
P35 = 40059260051938443901187811141767299_<35>
P65 = 57043556884754993123007599776067037686087494765852279033731828829_<65>

Number: 20003_141 N=2285122679533943884995836369403375958380690166981928865619552380550189111322270262039694582417662871 ( 100 digits) Divisors found: r1=40059260051938443901187811141767299 (pp35) r2=57043556884754993123007599776067037686087494765852279033731828829 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.69 hours. Scaled time: 3.44 units (timescale=0.933). Factorization parameters were as follows: name: 20003_141 n: 2285122679533943884995836369403375958380690166981928865619552380550189111322270262039694582417662871 skew: 31367.47 # norm 6.42e+13 c5: 1440 c4: 75236316 c3: -4337450867666 c2: -75939829829144874 c1: 1832361831257217421219 c0: 16270129288624735982981380 # alpha -6.20 Y1: 10815828199 Y0: -17382273622225387341 # Murphy_E 3.72e-09 # M 1528662353311578042268050061954235525428090049383327581993882190980449819514204253607283249127063063 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [750000, 1200001) Primes: RFBsize:114155, AFBsize:113995, largePrimes:3892638 encountered Relations: rels:3880924, finalFF:363769 Max relations in full relation-set: 28 Initial matrix: 228229 x 363769 with sparse part having weight 27334851. Pruned matrix : 151504 x 152709 with weight 10165771. Polynomial selection time: 0.25 hours. Total sieving time: 3.25 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000 total time: 3.69 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 20, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹³⁵+3 = 2(0)₁₃₄3_<136> = 257 · 1039 · 99257 · C125
C125 = P46 · P80
P46 = 7020006299581572894488170104402102406297674139_<46>
P80 = 10749361742827382298904906120880763303050229911440763032084434365062835850279407_<80>

Number: 20003_135 N=75460587151129379230670063280857121792718817008604043048671091197504696349160888652369718619579296555750824669583497388155573 ( 125 digits) SNFS difficulty: 135 digits. Divisors found: r1=7020006299581572894488170104402102406297674139 (pp46) r2=10749361742827382298904906120880763303050229911440763032084434365062835850279407 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.55 hours. Scaled time: 3.32 units (timescale=0.934). Factorization parameters were as follows: n: 75460587151129379230670063280857121792718817008604043048671091197504696349160888652369718619579296555750824669583497388155573 m: 1000000000000000000000000000 c5: 2 c0: 3 skew: 1.08 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [650000, 1300001) Primes: RFBsize:100021, AFBsize:100078, largePrimes:1574128 encountered Relations: rels:1626678, finalFF:245535 Max relations in full relation-set: 28 Initial matrix: 200164 x 245535 with sparse part having weight 8965702. Pruned matrix : 173620 x 174684 with weight 5510812. Total sieving time: 3.45 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000 total time: 3.55 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 19, 2007 (5th)

By Yousuke Koide / GMP-ECM B1=1250000 / May 15, 2007
(10⁸⁹³-1)/9 = (1)_893<893> = 1787 · 37507 · 35121409 · 965588399 · 1111111111111111111_<19> · 21638150846892565213405304766721_<32> · 316362908763458525001406154038726382279_<39> · C780
C780 = P41 · C740
P41 = 10493490498099374383685787869090487099769_<41>
By Yousuke Koide / GMP-ECM B1=1250000 / May 15, 2007
(10⁸⁹⁹-1)/9 = (1)_899<899> = 2791 · 3191 · 16763 · 43037 · 62003 · 6943319 · 77843839397_<11> · 480833853881_<12> · 57336415063790604359_<20> · 2257918530532265915349804384025799_<34> · C795
C795 = P36 · C760
P36 = 323713506321948847919927778598102721_<36>
By Yousuke Koide / GMP-ECM B1=1250000 / May 17, 2007
(10⁹²³-1)/9 = (1)_923<923> = 53 · 79 · 265371653 · 1632253507_<10> · 104900736929_<12> · 95520614386871982749923_<23> · 241573142393627673576957439049_<30> · 45994811347886846310221728895223034301839_<41> · C797
C797 = P31 · C766
P31 = 7487500179911376323952478489837_<31>
By Yousuke Koide / GMP-ECM B1=1000000 / May 18, 2007
10¹²²¹+1 = 1(0)₁₂₂₀1_<1222> = 7 · 11² · 13 · 23 · 223 · 4093 · 4663 · 7253 · 8779 · 599144041 · 183411838171_<12> · 409038414731_<12> · 422650073734453_<15> · 296557347313446299_<18> · 182160098613913582339_<21> · 21606064498691505246200058094681_<32> · 84713181371149698699040859437321_<32> · 48911689110891303706174193415115219_<35> · 219750014263062386251162088588835607771_<39> · C279 · C700
C700 = P38 · C663
P38 = 19505047835248219128488737914962029531_<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

May 19, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
2·10¹⁵⁴+3 = 2(0)₁₅₃3_<155> = 241 · 141906841 · C144
C144 = P53 · P92
P53 = 32826981394635607932036482961957538515492937504121287_<53>
P92 = 17814706504328977485410892424619338104938573843248529336228689546358190125162267028033028349_<92>

Number: n N=584803038968501293129681695754773285044568217236351897459123080525426305698095361365508658479597554195571988051288752034745016639946342805365163 ( 144 digits) SNFS difficulty: 155 digits. Divisors found: r1=32826981394635607932036482961957538515492937504121287 (pp53) r2=17814706504328977485410892424619338104938573843248529336228689546358190125162267028033028349 (pp92) Version: GGNFS-0.77.1-20051202-athlon Total time: 20.71 hours. Scaled time: 30.05 units (timescale=1.451). Factorization parameters were as follows: name: KA_2_0_153_3 n: 584803038968501293129681695754773285044568217236351897459123080525426305698095361365508658479597554195571988051288752034745016639946342805365163 skew: 1.72 deg: 5 c5: 1 c0: 15 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:183072, AFBsize:182886, largePrimes:6936703 encountered Relations: rels:6500743, finalFF:530318 Max relations in full relation-set: 28 Initial matrix: 366022 x 530318 with sparse part having weight 39481451. Pruned matrix : 243009 x 244903 with weight 21177995. Total sieving time: 18.57 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.83 hours. Total square root time: 0.15 hours, sqrts: 3. [2 more had ODD EXPONENTS!] Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 20.71 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

2·10¹⁴⁸+3 = 2(0)₁₄₇3_<149> = 151 · 54917 · 79496880961_<11> · 360248308916767_<15> · C116
C116 = P50 · P67
P50 = 22142194087798266515774322687941954125664442651683_<50>
P67 = 3803413556430766247732445539023188610808389140958333384583058412229_<67>

Number: n N=84215921162653090923161345791936118708491721223162198728702917790987256948208915116143433713706768557404516474631407 ( 116 digits) SNFS difficulty: 148 digits. Divisors found: r1=22142194087798266515774322687941954125664442651683 (pp50) r2=3803413556430766247732445539023188610808389140958333384583058412229 (pp67) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 12.42 hours. Scaled time: 16.92 units (timescale=1.363). Factorization parameters were as follows: name: KA_2_0_147_3 n: 84215921162653090923161345791936118708491721223162198728702917790987256948208915116143433713706768557404516474631407 skew: 0.54 deg: 5 c5: 125 c0: 6 m: 200000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:315948, AFBsize:315516, largePrimes:7024094 encountered Relations: rels:6715776, finalFF:774140 Max relations in full relation-set: 28 Initial matrix: 631529 x 774140 with sparse part having weight 27775308. Pruned matrix : 477072 x 480293 with weight 12291778. Total sieving time: 10.14 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.01 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 12.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

2·10¹³⁴+3 = 2(0)₁₃₃3_<135> = 7 · 157756740409116882389_<21> · C114
C114 = P36 · P78
P36 = 245627325886145161242134796623575019_<36>
P78 = 737339247296593171731659164098751163305183427019906464474193591876106604044019_<78>

Number: n N=181110667584365268571506917891704517125360677457662669626156617049442655401350747509071891750331736847898624761361 ( 114 digits) SNFS difficulty: 135 digits. Divisors found: r1=245627325886145161242134796623575019 (pp36) r2=737339247296593171731659164098751163305183427019906464474193591876106604044019 (pp78) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.54 hours. Scaled time: 5.12 units (timescale=1.448). Factorization parameters were as follows: name: KA_2_0_133_3 n: 181110667584365268571506917891704517125360677457662669626156617049442655401350747509071891750331736847898624761361 skew: 1.72 deg: 5 c5: 1 c0: 15 m: 1000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 500001) Primes: RFBsize:148933, AFBsize:148925, largePrimes:5017314 encountered Relations: rels:4491776, finalFF:346937 Max relations in full relation-set: 28 Initial matrix: 297922 x 346937 with sparse part having weight 14433488. Pruned matrix : 245580 x 247133 with weight 7586313. Total sieving time: 2.78 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.61 hours. Total square root time: 0.05 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000 total time: 3.54 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 19, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v. 1.21
2·10¹²⁶+3 = 2(0)₁₂₅3_<127> = 9496596035573_<13> · 72990180616825855013_<20> · C94
C94 = P34 · P61
P34 = 1363935016086710284190348118562849_<34>
P61 = 2115455595883918282267614450587132366299796154935856176143403_<61>

Number: 20003_126 N=2885343962202653372378528009811363064619245247881531993159016967031147098713516972051692235147 ( 94 digits) SNFS difficulty: 126 digits. Divisors found: r1=1363935016086710284190348118562849 (pp34) r2=2115455595883918282267614450587132366299796154935856176143403 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.12 hours. Scaled time: 1.97 units (timescale=0.932). Factorization parameters were as follows: n: 2885343962202653372378528009811363064619245247881531993159016967031147098713516972051692235147 m: 10000000000000000000000000 c5: 20 c0: 3 skew: 1 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78241, largePrimes:1570656 encountered Relations: rels:1629783, finalFF:230731 Max relations in full relation-set: 28 Initial matrix: 156805 x 230731 with sparse part having weight 11797616. Pruned matrix : 123689 x 124537 with weight 5161895. Total sieving time: 2.04 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.12 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹²⁷+3 = 2(0)₁₂₆3_<128> = 79 · 83 · 32843 · 3835231 · 1195589420583881466001_<22> · C92
C92 = P37 · P55
P37 = 8927757006598681262632931194240133629_<37>
P55 = 2268642375519091333458799446695979155571481664083795247_<55>

Sat May 19 19:31:19 2007 Sat May 19 19:31:19 2007 Sat May 19 19:31:19 2007 Msieve v. 1.21 Sat May 19 19:31:19 2007 random seeds: d716045e 858ea74d Sat May 19 19:31:19 2007 factoring 20253887863507244220879021005238400509953820135797606636390564270556960616638635630755061363 (92 digits) Sat May 19 19:31:20 2007 commencing quadratic sieve (92-digit input) Sat May 19 19:31:20 2007 using multiplier of 17 Sat May 19 19:31:20 2007 using 32kb Intel Core sieve core Sat May 19 19:31:20 2007 sieve interval: 36 blocks of size 32768 Sat May 19 19:31:20 2007 processing polynomials in batches of 6 Sat May 19 19:31:20 2007 using a sieve bound of 1783751 (67059 primes) Sat May 19 19:31:20 2007 using large prime bound of 187293855 (27 bits) Sat May 19 19:31:20 2007 using double large prime bound of 777217055970600 (42-50 bits) Sat May 19 19:31:20 2007 using trial factoring cutoff of 50 bits Sat May 19 19:31:20 2007 polynomial 'A' values have 12 factors Sat May 19 21:02:32 2007 67423 relations (17378 full + 50045 combined from 830306 partial), need 67155 Sat May 19 21:02:33 2007 begin with 847684 relations Sat May 19 21:02:33 2007 reduce to 169734 relations in 10 passes Sat May 19 21:02:33 2007 attempting to read 169734 relations Sat May 19 21:02:35 2007 recovered 169734 relations Sat May 19 21:02:35 2007 recovered 151296 polynomials Sat May 19 21:02:35 2007 attempting to build 67423 cycles Sat May 19 21:02:35 2007 found 67422 cycles in 5 passes Sat May 19 21:02:35 2007 distribution of cycle lengths: Sat May 19 21:02:35 2007 length 1 : 17378 Sat May 19 21:02:35 2007 length 2 : 12280 Sat May 19 21:02:35 2007 length 3 : 11630 Sat May 19 21:02:35 2007 length 4 : 8996 Sat May 19 21:02:35 2007 length 5 : 6589 Sat May 19 21:02:35 2007 length 6 : 4405 Sat May 19 21:02:35 2007 length 7 : 2691 Sat May 19 21:02:35 2007 length 9+: 3453 Sat May 19 21:02:35 2007 largest cycle: 19 relations Sat May 19 21:02:35 2007 matrix is 67059 x 67422 with weight 4070500 (avg 60.37/col) Sat May 19 21:02:35 2007 filtering completed in 3 passes Sat May 19 21:02:35 2007 matrix is 65530 x 65594 with weight 3893561 (avg 59.36/col) Sat May 19 21:02:36 2007 saving the first 48 matrix rows for later Sat May 19 21:02:36 2007 matrix is 65482 x 65594 with weight 2931664 (avg 44.69/col) Sat May 19 21:02:36 2007 matrix includes 32 packed rows Sat May 19 21:02:36 2007 using block size 26237 for processor cache size 4096 kB Sat May 19 21:02:56 2007 lanczos halted after 1037 iterations Sat May 19 21:02:57 2007 recovered 16 nontrivial dependencies Sat May 19 21:02:57 2007 prp37 factor: 8927757006598681262632931194240133629 Sat May 19 21:02:57 2007 prp55 factor: 2268642375519091333458799446695979155571481664083795247 Sat May 19 21:02:57 2007 elapsed time 01:31:38

May 19, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=11000000
(10¹⁷⁸+17)/9 = (1)₁₇₇3_<178> = 3² · 7² · 1046641 · 1290857 · 468836928921920538313_<21> · C142
C142 = P36 · C107
P36 = 297082579660968821734851624509405183_<36>
C107 = [13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791_<107>]

May 19, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
(2·10¹⁶⁸+43)/9 = (2)₁₆₇7_<168> = 47 · C166
C166 = P41 · P55 · P71
P41 = 45965997803609570676069581691927428510183_<41>
P55 = 2946919768053066098412187258879318843529311861174818097_<55>
P71 = 34904757433689170732652558228154689367498858601950291450197647933335691_<71>

Number: n N=4728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749408983451536643026004728132387706855791962174941 ( 166 digits) SNFS difficulty: 168 digits. Divisors found: r1=45965997803609570676069581691927428510183 (pp41) r2=2946919768053066098412187258879318843529311861174818097 (pp55) r3=34904757433689170732652558228154689367498858601950291450197647933335691 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 101.82 hours. Scaled time: 134.81 units (timescale=1.324). Factorization parameters were as follows: name: KA_2_167_7 n: 4728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749408983451536643026004728132387706855791962174941 skew: 0.93 deg: 5 c5: 125 c0: 86 m: 2000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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: 48/48 Sieved algebraic special-q in [100000, 4000001) Primes: RFBsize:348513, AFBsize:349516, largePrimes:8195682 encountered Relations: rels:7828220, finalFF:805085 Max relations in full relation-set: 48 Initial matrix: 698094 x 805085 with sparse part having weight 48480685. Pruned matrix : 604878 x 608432 with weight 31850567. Total sieving time: 92.31 hours. Total relation processing time: 0.35 hours. Matrix solve time: 8.93 hours. Total square root time: 0.22 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 101.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

2·10¹⁵⁰+3 = 2(0)₁₄₉3_<151> = 487 · C148
C148 = P64 · P85
P64 = 1824453361909318934020125483109157972584403451163125882265065433_<64>
P85 = 2250962543871412830161298255938234659251521136933600855735504876723568950774217694093_<85>

Number: n N=4106776180698151950718685831622176591375770020533880903490759753593429158110882956878850102669404517453798767967145790554414784394250513347022587269 ( 148 digits) SNFS difficulty: 150 digits. Divisors found: r1=1824453361909318934020125483109157972584403451163125882265065433 (pp64) r2=2250962543871412830161298255938234659251521136933600855735504876723568950774217694093 (pp85) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 16.18 hours. Scaled time: 22.14 units (timescale=1.368). Factorization parameters were as follows: name: KA_2_0_149_3 n: 4106776180698151950718685831622176591375770020533880903490759753593429158110882956878850102669404517453798767967145790554414784394250513347022587269 skew: 1.08 deg: 5 c5: 2 c0: 3 m: 1000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 600001) Primes: RFBsize:315948, AFBsize:315821, largePrimes:6583994 encountered Relations: rels:6446442, finalFF:849439 Max relations in full relation-set: 28 Initial matrix: 631834 x 849439 with sparse part having weight 29055982. Pruned matrix : 406919 x 410142 with weight 10416091. Total sieving time: 14.39 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.56 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 16.18 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
2·10¹⁹¹-3 = 1(9)₁₉₀7_<192> = 7 · 53 · 829 · 1031 · 12110972033_<11> · 1278085313563_<13> · 18580007275894843_<17> · 117121349237684572025004166361887_<33> · C113
C113 = P47 · P66
P47 = 49371617551587041843675930397116659530937545163_<47>
P66 = 379266725313477244975216442892897216971059794842475211319820147649_<66>

Number: 19997_191 N=18725011712219814562530479034837840702529034807249997949068275863786847663649064207303543066082563170428265771787 ( 113 digits) Divisors found: r1=49371617551587041843675930397116659530937545163 (pp47) r2=379266725313477244975216442892897216971059794842475211319820147649 (pp66) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 56.52 hours. Scaled time: 38.15 units (timescale=0.675). Factorization parameters were as follows: name: 19997_191 n: 18725011712219814562530479034837840702529034807249997949068275863786847663649064207303543066082563170428265771787 skew: 59546.05 # norm 6.66e+15 c5: 10560 c4: -2374857106 c3: -195238124648465 c2: 1713791335976812382 c1: 286960883326780791878154 c0: -869102931125208602582566965 # alpha -6.63 Y1: 1066141682921 Y0: -4464330115947638126804 # Murphy_E 7.39e-10 # M 15931944624871609380286614016751846664857168747787310376807033596899975510455931096032109076919995223638073753024 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, 2750001) Primes: RFBsize:250150, AFBsize:249696, largePrimes:7656920 encountered Relations: rels:7706870, finalFF:571600 Max relations in full relation-set: 0 Initial matrix: 499929 x 571600 with sparse part having weight 34433582. Pruned matrix : 435540 x 438103 with weight 23881885. Polynomial selection time: 2.15 hours. Total sieving time: 46.66 hours. Total relation processing time: 0.59 hours. Matrix solve time: 6.79 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 56.52 hours. --------- CPU info (if available) ----------

May 18, 2007 (2nd)

By Jo Yeong Uk / Msieve v. 1.21, GMP-ECM 6.1.2
2·10¹⁴²+3 = 2(0)₁₄₁3_<143> = 29 · 18121 · 10062555889_<11> · 5499130730309_<13> · 142203315288161311512583_<24> · C91
C91 = P40 · P52
P40 = 1628892178337141932454034590460430447783_<40>
P52 = 2969240859409506695099012352547967144102089819518203_<52>

Thu May 17 23:56:51 2007 Thu May 17 23:56:51 2007 Thu May 17 23:56:51 2007 Msieve v. 1.21 Thu May 17 23:56:51 2007 random seeds: ac10f82d 2d0dace6 Thu May 17 23:56:51 2007 factoring 4836573211491198755748211680523749919543813705587359988916604311081614199708621860609493949 (91 digits) Thu May 17 23:56:52 2007 commencing quadratic sieve (91-digit input) Thu May 17 23:56:52 2007 using multiplier of 29 Thu May 17 23:56:52 2007 using 32kb Intel Core sieve core Thu May 17 23:56:52 2007 sieve interval: 36 blocks of size 32768 Thu May 17 23:56:52 2007 processing polynomials in batches of 6 Thu May 17 23:56:52 2007 using a sieve bound of 1719869 (64560 primes) Thu May 17 23:56:52 2007 using large prime bound of 165107424 (27 bits) Thu May 17 23:56:52 2007 using double large prime bound of 619412223763104 (42-50 bits) Thu May 17 23:56:52 2007 using trial factoring cutoff of 50 bits Thu May 17 23:56:52 2007 polynomial 'A' values have 12 factors Fri May 18 01:24:55 2007 64901 relations (16394 full + 48507 combined from 770121 partial), need 64656 Fri May 18 01:24:55 2007 begin with 786515 relations Fri May 18 01:24:55 2007 reduce to 162698 relations in 10 passes Fri May 18 01:24:56 2007 attempting to read 162698 relations Fri May 18 01:24:57 2007 recovered 162698 relations Fri May 18 01:24:57 2007 recovered 145537 polynomials Fri May 18 01:24:57 2007 attempting to build 64901 cycles Fri May 18 01:24:57 2007 found 64901 cycles in 5 passes Fri May 18 01:24:57 2007 distribution of cycle lengths: Fri May 18 01:24:57 2007 length 1 : 16394 Fri May 18 01:24:57 2007 length 2 : 12017 Fri May 18 01:24:57 2007 length 3 : 11335 Fri May 18 01:24:57 2007 length 4 : 8916 Fri May 18 01:24:57 2007 length 5 : 6442 Fri May 18 01:24:57 2007 length 6 : 4126 Fri May 18 01:24:57 2007 length 7 : 2645 Fri May 18 01:24:57 2007 length 9+: 3026 Fri May 18 01:24:57 2007 largest cycle: 17 relations Fri May 18 01:24:57 2007 matrix is 64560 x 64901 with weight 3877029 (avg 59.74/col) Fri May 18 01:24:57 2007 filtering completed in 4 passes Fri May 18 01:24:57 2007 matrix is 63178 x 63242 with weight 3716626 (avg 58.77/col) Fri May 18 01:24:58 2007 saving the first 48 matrix rows for later Fri May 18 01:24:59 2007 matrix is 63130 x 63242 with weight 2795295 (avg 44.20/col) Fri May 18 01:24:59 2007 matrix includes 32 packed rows Fri May 18 01:24:59 2007 using block size 25296 for processor cache size 4096 kB Fri May 18 01:25:17 2007 lanczos halted after 1000 iterations Fri May 18 01:25:17 2007 recovered 17 nontrivial dependencies Fri May 18 01:25:17 2007 prp40 factor: 1628892178337141932454034590460430447783 Fri May 18 01:25:17 2007 prp52 factor: 2969240859409506695099012352547967144102089819518203 Fri May 18 01:25:17 2007 elapsed time 01:28:26

2·10¹⁸¹+3 = 2(0)₁₈₀3_<182> = C182
C182 = P34 · C148
P34 = 5511837461824511266624821670808689_<34>
C148 = [3628554023684809875041241575766798527068771437488933383862974033044444603054287454851457985502624509381866036022786923582580265165248809496728968627_<148>]

May 18, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
3·10¹⁵⁸+1 = 3(0)₁₅₇1_<159> = 7 · 518209 · 1248630547_<10> · C143
C143 = P68 · P76
P68 = 14187037984758391993529228654317591874792986868087928456850474187179_<68>
P76 = 4668663539228271717902874354562882580267735906322278836949839530064145731879_<76>

Number: n N=66234506969088041957193564483376377591189005460744403342598632681083858520789395982329953995232154901773260034664510126060898123874794593379341 ( 143 digits) SNFS difficulty: 158 digits. Divisors found: r1=14187037984758391993529228654317591874792986868087928456850474187179 (pp68) r2=4668663539228271717902874354562882580267735906322278836949839530064145731879 (pp76) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.69 hours. Scaled time: 51.68 units (timescale=1.448). Factorization parameters were as follows: name: KA_3_0_157_1 n: 66234506969088041957193564483376377591189005460744403342598632681083858520789395982329953995232154901773260034664510126060898123874794593379341 skew: 0.20 deg: 5 c5: 3000 c0: 1 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:183072, AFBsize:183066, largePrimes:7144631 encountered Relations: rels:6604207, finalFF:421676 Max relations in full relation-set: 28 Initial matrix: 366205 x 421676 with sparse part having weight 37286804. Pruned matrix : 331020 x 332915 with weight 26592023. Total sieving time: 31.64 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.56 hours. Total square root time: 0.27 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 35.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(37·10¹⁵⁸-1)/9 = 4(1)_158<159> = 3³ · 1113503211871_<13> · C146
C146 = P51 · P95
P51 = 437047077000875706556100910362101256688838117136603_<51>
P95 = 31287852560125735966912304307179361487093589834503079004811219125764118303034275852798460927361_<95>

Number: n N=13674264507037318634426012072489013175752521746264239263365882696289761263584377804407017898506229087375374061783811632623995055437253177297294683 ( 146 digits) SNFS difficulty: 159 digits. Divisors found: r1=437047077000875706556100910362101256688838117136603 (pp51) r2=31287852560125735966912304307179361487093589834503079004811219125764118303034275852798460927361 (pp95) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 49.75 hours. Scaled time: 67.76 units (timescale=1.362). Factorization parameters were as follows: name: KA_4_1_158 n: 13674264507037318634426012072489013175752521746264239263365882696289761263584377804407017898506229087375374061783811632623995055437253177297294683 skew: 0.12 deg: 5 c5: 37000 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:315948, AFBsize:316896, largePrimes:7462039 encountered Relations: rels:7093511, finalFF:723313 Max relations in full relation-set: 28 Initial matrix: 632911 x 723313 with sparse part having weight 38195405. Pruned matrix : 545249 x 548477 with weight 23406323. Total sieving time: 44.78 hours. Total relation processing time: 0.25 hours. Matrix solve time: 4.31 hours. Total square root time: 0.41 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 49.75 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

2·10¹⁴⁴+3 = 2(0)₁₄₃3_<145> = 1201 · C142
C142 = P55 · P88
P55 = 1168960033824751568738318599288806794044795142960334049_<55>
P88 = 1424581581949223240674405227318668880791852510435284297667922774714016704281163739428947_<88>

Number: n N=1665278934221482098251457119067443796835970024979184013322231473771856786011656952539550374687760199833472106577851790174854288093255620316403 ( 142 digits) SNFS difficulty: 145 digits. Divisors found: r1=1168960033824751568738318599288806794044795142960334049 (pp55) r2=1424581581949223240674405227318668880791852510435284297667922774714016704281163739428947 (pp88) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 9.47 hours. Scaled time: 12.92 units (timescale=1.364). Factorization parameters were as follows: name: KA_2_0_143_3 n: 1665278934221482098251457119067443796835970024979184013322231473771856786011656952539550374687760199833472106577851790174854288093255620316403 skew: 1.72 deg: 5 c5: 1 c0: 15 m: 100000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:283146, AFBsize:282687, largePrimes:6448372 encountered Relations: rels:6058655, finalFF:650499 Max relations in full relation-set: 28 Initial matrix: 565897 x 650499 with sparse part having weight 22096768. Pruned matrix : 435350 x 438243 with weight 11275494. Total sieving time: 7.48 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.61 hours. Total square root time: 0.22 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 9.47 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

2·10¹⁵⁵+3 = 2(0)₁₅₄3_<156> = 23 · C154
C154 = P76 · P79
P76 = 1111621257288759311574554337362336029819886569891919818320899807496833211589_<76>
P79 = 7822495402005635711932598925376137473625943127630073484216479297850123896513649_<79>

Number: n N=8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261 ( 154 digits) SNFS difficulty: 155 digits. Divisors found: r1=1111621257288759311574554337362336029819886569891919818320899807496833211589 (pp76) r2=7822495402005635711932598925376137473625943127630073484216479297850123896513649 (pp79) Version: GGNFS-0.77.1-20051202-athlon Total time: 18.69 hours. Scaled time: 27.04 units (timescale=1.447). Factorization parameters were as follows: name: KA_2_0_154_3 n: 8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261 skew: 1.08 deg: 5 c5: 2 c0: 3 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:183072, AFBsize:183201, largePrimes:6621471 encountered Relations: rels:6096384, finalFF:453480 Max relations in full relation-set: 28 Initial matrix: 366338 x 453480 with sparse part having weight 31199933. Pruned matrix : 295381 x 297276 with weight 17548748. Total sieving time: 16.52 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.97 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 18.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 17, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹¹⁹+3 = 2(0)₁₁₈3_<120> = C120
C120 = P49 · P71
P49 = 5228659514109126391498531522208323958331928046131_<49>
P71 = 38250721711810786837816564744277352704880578237524903785562032046531313_<71>

Number: 20003_119 N=200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 120 digits) SNFS difficulty: 120 digits. Divisors found: r1=5228659514109126391498531522208323958331928046131 (pp49) r2=38250721711810786837816564744277352704880578237524903785562032046531313 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.03 hours. Scaled time: 0.96 units (timescale=0.933). Factorization parameters were as follows: n: 200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 m: 1000000000000000000000000 c5: 1 c0: 15 skew: 1.72 type: snfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [350000, 490001) Primes: RFBsize:56543, AFBsize:56578, largePrimes:2095809 encountered Relations: rels:2212502, finalFF:259212 Max relations in full relation-set: 28 Initial matrix: 113185 x 259212 with sparse part having weight 21628126. Pruned matrix : 80815 x 81444 with weight 4666548. Total sieving time: 0.97 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000 total time: 1.03 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁰+3 = 2(0)₁₀₉3_<111> = 7 · C110
C110 = P35 · P76
P35 = 26184862097599361168293556342151923_<35>
P76 = 1091142984253028074855253881145711454222019861072878061773867745555021996423_<76>

Number: 20003_110 N=28571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 ( 110 digits) SNFS difficulty: 110 digits. Divisors found: r1=26184862097599361168293556342151923 (pp35) r2=1091142984253028074855253881145711454222019861072878061773867745555021996423 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.48 hours. Scaled time: 0.44 units (timescale=0.935). Factorization parameters were as follows: n: 28571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 m: 10000000000000000000000 c5: 2 c0: 3 skew: 1.08 type: snfs Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 325001) Primes: RFBsize:41538, AFBsize:41512, largePrimes:1111312 encountered Relations: rels:1064225, finalFF:121436 Max relations in full relation-set: 28 Initial matrix: 83115 x 121436 with sparse part having weight 4674144. Pruned matrix : 63518 x 63997 with weight 1815360. Total sieving time: 0.45 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,25000 total time: 0.48 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁴+3 = 2(0)₁₁₃3_<115> = 29 · 79 · 269 · 46091 · C104
C104 = P33 · P72
P33 = 141642068744903728734080380860557_<33>
P72 = 497100539534504959831516767690043182490203130774494939527873200330969211_<72>

Number: 20003_114 N=70410348793875085321768849152758164549236425820919737153313863018456745454803368293180589836398051310527 ( 104 digits) SNFS difficulty: 115 digits. Divisors found: r1=141642068744903728734080380860557 (pp33) r2=497100539534504959831516767690043182490203130774494939527873200330969211 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.64 hours. Scaled time: 0.60 units (timescale=0.930). Factorization parameters were as follows: n: 70410348793875085321768849152758164549236425820919737153313863018456745454803368293180589836398051310527 m: 100000000000000000000000 c5: 1 c0: 15 skew: 1.72 type: snfs Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 375001) Primes: RFBsize:41538, AFBsize:41382, largePrimes:1149521 encountered Relations: rels:1106102, finalFF:125588 Max relations in full relation-set: 28 Initial matrix: 82983 x 125588 with sparse part having weight 5422596. Pruned matrix : 65702 x 66180 with weight 2045419. Total sieving time: 0.61 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,25000 total time: 0.64 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁸+3 = 2(0)₁₁₇3_<119> = 714997972759321_<15> · C104
C104 = P39 · P65
P39 = 991811671612623385550841555017839892819_<39>
P65 = 28203043059484251487882072762043305121719614244673667495654922297_<65>

Number: 20003_118 N=27972107281389871588317961432884759576381723602570236734004002563659504714454632356237779796988253285243 ( 104 digits) SNFS difficulty: 118 digits. Divisors found: r1=991811671612623385550841555017839892819 (pp39) r2=28203043059484251487882072762043305121719614244673667495654922297 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.96 hours. Scaled time: 0.82 units (timescale=0.853). Factorization parameters were as follows: n: 27972107281389871588317961432884759576381723602570236734004002563659504714454632356237779796988253285243 m: 200000000000000000000000 c5: 125 c0: 6 skew: 1 type: snfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [350000, 455001) Primes: RFBsize:56543, AFBsize:56408, largePrimes:1928404 encountered Relations: rels:1883991, finalFF:137232 Max relations in full relation-set: 28 Initial matrix: 113016 x 137232 with sparse part having weight 10203633. Pruned matrix : 104024 x 104653 with weight 5985437. Total sieving time: 0.89 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000 total time: 0.96 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 17, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=11000000
(64·10²³⁵+53)/9 = 7(1)₂₃₄7_<236> = 7 · 11 · 193 · C232
C232 = P32 · C201
P32 = 28107359195838759279509711482249_<32>
C201 = [170243048162211606139168092899412373887432262726392638811930752489088113456154186085588507167609348929816413787030872916649323684810730559987175370389656582406055523330513546443606392638754557740210553_<201>]

May 17, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(35·10¹⁶⁷-53)/9 = 3(8)₁₆₆3_<168> = 11 · 113 · C165
C165 = P46 · P120
P46 = 1481894566930897165561217886297315643190412863_<46>
P120 = 211123754485119892507236798299021028208278038771361562866186890465260883878836081438303807062657374164385131676699256887_<120>

Number: n N=312863144721551801197818896933941181728792348261374810047376419057834987038526861535711093233217127022436756950031286314472155180119781889693394118172879234826137481 ( 165 digits) SNFS difficulty: 168 digits. Divisors found: r1=1481894566930897165561217886297315643190412863 (pp46) r2=211123754485119892507236798299021028208278038771361562866186890465260883878836081438303807062657374164385131676699256887 (pp120) Version: GGNFS-0.77.1-20051202-athlon Total time: 94.40 hours. Scaled time: 112.80 units (timescale=1.195). Factorization parameters were as follows: name: KA_3_8_166_3 n: 312863144721551801197818896933941181728792348261374810047376419057834987038526861535711093233217127022436756950031286314472155180119781889693394118172879234826137481 type: snfs skew: 0.43 deg: 5 c5: 3500 c0: -53 m: 1000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3200001) Primes: RFBsize:348513, AFBsize:348001, largePrimes:7992903 encountered Relations: rels:7653020, finalFF:801438 Max relations in full relation-set: 28 Initial matrix: 696581 x 801438 with sparse part having weight 45326608. Pruned matrix : 601811 x 605357 with weight 28677270. Total sieving time: 85.35 hours. Total relation processing time: 0.37 hours. Matrix solve time: 8.34 hours. Total square root time: 0.33 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000 total time: 94.40 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

May 17, 2007

The factor table of 200...003 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 16, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
2·10¹³⁷-3 = 1(9)₁₃₆7_<138> = 7² · 283 · 317 · 653 · 17264088293_<11> · C118
C118 = P58 · P60
P58 = 7000751848412477959806057766604418499857831431396426422451_<58>
P60 = 576483264949148720398224057113036271804100390023761971950737_<60>

Number: n N=4035816282671613171343262279759201422385931092225366246725375548600017972927485571480526777015219311635458678522796387 ( 118 digits) SNFS difficulty: 137 digits. Divisors found: r1=7000751848412477959806057766604418499857831431396426422451 (pp58) r2=576483264949148720398224057113036271804100390023761971950737 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.31 hours. Scaled time: 7.68 units (timescale=1.447). Factorization parameters were as follows: name: KA_1_9_136_7 n: 4035816282671613171343262279759201422385931092225366246725375548600017972927485571480526777015219311635458678522796387 skew: 0.43 deg: 5 c5: 200 c0: -3 m: 1000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:114155, AFBsize:114342, largePrimes:6384288 encountered Relations: rels:5895003, finalFF:424935 Max relations in full relation-set: 28 Initial matrix: 228562 x 424935 with sparse part having weight 33701210. Pruned matrix : 150857 x 152063 with weight 10360660. Total sieving time: 4.55 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.44 hours. Total square root time: 0.17 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000 total time: 5.31 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 16, 2007 (4th)

By suberi / GMP-ECM 6.1.2 B1=3000000
2·10¹⁷⁷-3 = 1(9)₁₇₆7_<178> = 17 · 66090659226826860491_<20> · C157
C157 = P33 · C124
P33 = 314129679887073807583524645188651_<33>
C124 = [5666723452861111419953301719983874645151689206796263127100108210064996380732130563446722510620008860655369666194925533653301_<124>]
2·10¹⁸⁴-3 = 1(9)₁₈₃7_<185> = 29² · 2713 · 5237 · 66857737 · C167
C167 = P32 · P135
P32 = 89177151216694919128342839012937_<32>
P135 = 280734873559781758253348251445739908956056985830730029555749391702366572037148720479831472201011105110825184173089405824194320945511353_<135>
2·10¹⁸⁵-3 = 1(9)₁₈₄7_<186> = 7 · 10139 · C181
C181 = P34 · C148
P34 = 1629098585915315381840811732409037_<34>
C148 = [1729774401844928654956193898363519632991312797796196776125859358920365912442809486382638218734874672877056576604898068320294799461787530626132748997_<148>]

May 16, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(55·10¹⁷⁸-1)/9 = 6(1)_178<179> = C179
C179 = P71 · P109
P71 = 10844535479140675215472164272317404597918151109866534169729050994698157_<71>
P109 = 5635198596441272091330699355272671552551459731965648263799402079769287090412428090080019459707087511004675523_<109>

Number: 61111_178 N=61111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 ( 179 digits) SNFS difficulty: 180 digits. Divisors found: r1=10844535479140675215472164272317404597918151109866534169729050994698157 (pp71) r2=5635198596441272091330699355272671552551459731965648263799402079769287090412428090080019459707087511004675523 (pp109) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 699.57 hours. Scaled time: 471.51 units (timescale=0.674). Factorization parameters were as follows: name: 61111_178 n: 61111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 m: 500000000000000000000000000000000000 c5: 88 c0: -5 skew: 1 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, 8500001) Primes: RFBsize:501962, AFBsize:502697, largePrimes:6420312 encountered Relations: rels:6865276, finalFF:1126019 Max relations in full relation-set: 0 Initial matrix: 1004725 x 1126019 with sparse part having weight 61341522. Pruned matrix : 900119 x 905206 with weight 47244858. Total sieving time: 650.72 hours. Total relation processing time: 0.72 hours. Matrix solve time: 47.78 hours. Time per square root: 0.35 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: 699.57 hours. --------- CPU info (if available) ----------

May 16, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
2·10¹³⁹-3 = 1(9)₁₃₈7_<140> = 53 · 113 · 241 · C134
C134 = P38 · P96
P38 = 41803841074986331004467759752042705661_<38>
P96 = 331468644256359068076837242793801952073119679096103445167011822018914725489819506339762119501373_<96>

Number: n N=13856662525834015196601792082164466113185376509769986330402418264744008552332110944754179342626073111908485058014381830035563124372553 ( 134 digits) SNFS difficulty: 140 digits. Divisors found: r1=41803841074986331004467759752042705661 (pp38) r2=331468644256359068076837242793801952073119679096103445167011822018914725489819506339762119501373 (pp96) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.88 hours. Scaled time: 7.08 units (timescale=1.451). Factorization parameters were as follows: name: KA_1_9_138_7 n: 13856662525834015196601792082164466113185376509769986330402418264744008552332110944754179342626073111908485058014381830035563124372553 skew: 1.72 deg: 5 c5: 1 c0: -15 m: 10000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 600001) Primes: RFBsize:148933, AFBsize:148925, largePrimes:5871911 encountered Relations: rels:5357002, finalFF:416257 Max relations in full relation-set: 28 Initial matrix: 297922 x 416257 with sparse part having weight 22774580. Pruned matrix : 197183 x 198736 with weight 9498448. Total sieving time: 4.11 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.59 hours. Total square root time: 0.06 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000 total time: 4.88 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(2·10¹⁵⁸+1)/3 = (6)₁₅₇7_<158> = 17 · 277897 · 488347 · C146
C146 = P41 · P106
P41 = 21031561607724268249695576438281644154827_<41>
P106 = 1373965780486348413798444543281701321099663088692889197539420932838074370643421175688293752426150951769707_<106>

Number: n N=28896645959203594878243179450779359727070264879734381614242857401731103885737949305946301799304495401978678162311838251115093256907566767956425689 ( 146 digits) SNFS difficulty: 158 digits. Divisors found: r1=21031561607724268249695576438281644154827 (pp41) r2=1373965780486348413798444543281701321099663088692889197539420932838074370643421175688293752426150951769707 (pp106) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 29.31 hours. Scaled time: 40.01 units (timescale=1.365). Factorization parameters were as follows: name: KA_6_157_7 n: 28896645959203594878243179450779359727070264879734381614242857401731103885737949305946301799304495401978678162311838251115093256907566767956425689 skew: 0.44 deg: 5 c5: 125 c0: 2 m: 20000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:315948, AFBsize:316326, largePrimes:7115036 encountered Relations: rels:6794108, finalFF:747296 Max relations in full relation-set: 28 Initial matrix: 632339 x 747296 with sparse part having weight 32157852. Pruned matrix : 514318 x 517543 with weight 16887335. Total sieving time: 25.80 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.22 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 29.31 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

2·10¹³³-3 = 1(9)₁₃₂7_<134> = 557 · 71162352319717499_<17> · C114
C114 = P40 · P74
P40 = 5387015255111323942626049346281287077863_<40>
P74 = 93664776152606764401059753977917406656658975593547100495177002729005709733_<74>

Number: n N=504573578000679980011194383314501795810950700707844710097611496380308437105732388873064306717211277180237947940579 ( 114 digits) SNFS difficulty: 133 digits. Divisors found: r1=5387015255111323942626049346281287077863 (pp40) r2=93664776152606764401059753977917406656658975593547100495177002729005709733 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.51 hours. Scaled time: 5.09 units (timescale=1.448). Factorization parameters were as follows: name: KA_1_9_132_7 n: 504573578000679980011194383314501795810950700707844710097611496380308437105732388873064306717211277180237947940579 skew: 0.54 deg: 5 c5: 125 c0: -6 m: 200000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 400001) Primes: RFBsize:114155, AFBsize:113572, largePrimes:5040741 encountered Relations: rels:4461042, finalFF:289507 Max relations in full relation-set: 28 Initial matrix: 227792 x 289507 with sparse part having weight 14730733. Pruned matrix : 176541 x 177743 with weight 6872155. Total sieving time: 3.03 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.36 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000 total time: 3.51 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 16, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹²⁴-3 = 1(9)₁₂₃7_<125> = 31536909893_<11> · C114
C114 = P40 · P74
P40 = 9336975976397637344374611852234644275771_<40>
P74 = 67921085334223439767801410472062272050391919676586092874931678368742117499_<74>

Number: 19997_124 N=634177542056498147727386792391213558521105928315688960325495387938387321694086180962789993154640998992817840816729 ( 114 digits) SNFS difficulty: 125 digits. Divisors found: r1=9336975976397637344374611852234644275771 (pp40) r2=67921085334223439767801410472062272050391919676586092874931678368742117499 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.37 hours. Scaled time: 1.28 units (timescale=0.933). Factorization parameters were as follows: n: 634177542056498147727386792391213558521105928315688960325495387938387321694086180962789993154640998992817840816729 m: 10000000000000000000000000 c5: 1 c0: -15 skew: 1.72 type: snfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [350000, 560001) Primes: RFBsize:56543, AFBsize:56578, largePrimes:2126235 encountered Relations: rels:2218039, finalFF:221963 Max relations in full relation-set: 28 Initial matrix: 113185 x 221963 with sparse part having weight 20278707. Pruned matrix : 90696 x 91325 with weight 5816729. Total sieving time: 1.30 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000 total time: 1.37 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹²⁵-3 = 1(9)₁₂₄7_<126> = 7 · 233 · 144593 · 10817778017_<11> · C107
C107 = P32 · P76
P32 = 70950032524214449038440162186879_<32>
P76 = 1104938488904480115616998648501886905041655534575552950019302930656654642413_<76>

Number: 19997_125 N=78395421725029230328818426014800087569324238426422046695751860537037254334678996299996708647592753825499027 ( 107 digits) SNFS difficulty: 125 digits. Divisors found: r1=70950032524214449038440162186879 (pp32) r2=1104938488904480115616998648501886905041655534575552950019302930656654642413 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.41 hours. Scaled time: 1.31 units (timescale=0.929). Factorization parameters were as follows: n: 78395421725029230328818426014800087569324238426422046695751860537037254334678996299996708647592753825499027 m: 10000000000000000000000000 c5: 2 c0: -3 skew: 1.08 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 750001) Primes: RFBsize:78498, AFBsize:78591, largePrimes:1530358 encountered Relations: rels:1610360, finalFF:249014 Max relations in full relation-set: 28 Initial matrix: 157154 x 249014 with sparse part having weight 10838770. Pruned matrix : 105018 x 105867 with weight 4177813. Total sieving time: 1.36 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.41 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹³²-3 = 1(9)₁₃₁7_<133> = 19 · 883 · 312007369 · 2035213286473_<13> · C108
C108 = P48 · P60
P48 = 224921079033736342221790746096952105532091294451_<48>
P60 = 834662212681919642405556463667806222934803506974724243740903_<60>

Number: 19997_132 N=187733125505103299807786248565954705912786141137724869511999365125813198339801086514367050241684111925629253 ( 108 digits) SNFS difficulty: 132 digits. Divisors found: r1=224921079033736342221790746096952105532091294451 (pp48) r2=834662212681919642405556463667806222934803506974724243740903 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.24 hours. Scaled time: 3.02 units (timescale=0.930). Factorization parameters were as follows: n: 187733125505103299807786248565954705912786141137724869511999365125813198339801086514367050241684111925629253 m: 200000000000000000000000000 c5: 25 c0: -12 skew: 1 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 1150001) Primes: RFBsize:78498, AFBsize:78531, largePrimes:1574002 encountered Relations: rels:1587278, finalFF:187947 Max relations in full relation-set: 28 Initial matrix: 157093 x 187947 with sparse part having weight 12103751. Pruned matrix : 146454 x 147303 with weight 7639030. Total sieving time: 3.14 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 3.24 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 15, 2007 (6th)

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000
9·10¹⁸⁶+1 = 9(0)₁₈₅1_<187> = 61 · 161271954417042232580477_<24> · C162
C162 = P35 · P128
P35 = 71338953778563773721289257398483341_<35>
P128 = 12824105714440400124634673307313813672129762979860127394144076399375268657498186011572935151644208597728853041885465975326330013_<128>

May 15, 2007 (5th)

By suberi / GMP-ECM 6.1.2 B1=3000000
(64·10²¹⁰+53)/9 = 7(1)₂₀₉7_<211> = 13 · 1901 · 215887165601_<12> · C196
C196 = P36 · C161
P36 = 120353750687524054661558403071957407_<36>
C161 = [11074536064618948013173809104218434495785079170068678862536218619877065401976868698025916479343294712320399742216591613798301642308351142097007338459987719559387_<161>]
(64·10²²¹+53)/9 = 7(1)₂₂₀7_<222> = 3² · 11 · 128239 · 503398933 · 1004825417137_<13> · 27740572834433626007911111_<26> · C169
C169 = P38 · C132
P38 = 38068287072532520234581880952761336179_<38>
C132 = [104857737776937132831500531794436978547677820037074899064862334390039119428558654617425288051798995857403608343118733866481109955753_<132>]

May 15, 2007 (4th)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, GGNFS-0.77.1-20050930-nocona
2·10¹⁸⁹-3 = 1(9)₁₈₈7_<190> = C190
C190 = P38 · C152
P38 = 26515433818872756128486451063540368813_<38>
C152 = [75427768357931602931753276660580155235389614555331854484100658108640121572138298453489837951680283043601403057326275895068893330216499198205413743316369_<152>]
2·10¹³⁸-3 = 1(9)₁₃₇7_<139> = C139
C139 = P43 · P96
P43 = 2792516776165070836944026656509845283656971_<43>
P96 = 716199815546524866079650590503056034131183398218468977769146136824078266907549975600350599517207_<96>

Number: 19997_138 N=1999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 139 digits) SNFS difficulty: 140 digits. Divisors found: r1=2792516776165070836944026656509845283656971 (pp43) r2=716199815546524866079650590503056034131183398218468977769146136824078266907549975600350599517207 (pp96) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.55 hours. Scaled time: 7.97 units (timescale=0.932). Factorization parameters were as follows: n: 1999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 10000000000000000000000000000 c5: 1 c0: -150 skew: 1 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [650000, 1200001) Primes: RFBsize:100021, AFBsize:99568, largePrimes:1619547 encountered Relations: rels:1694434, finalFF:263039 Max relations in full relation-set: 28 Initial matrix: 199653 x 263039 with sparse part having weight 10868421. Pruned matrix : 161528 x 162590 with weight 6105713. Total sieving time: 8.45 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000 total time: 8.55 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹⁰⁸-3 = 1(9)₁₀₇7_<109> = 97 · 907 · 2334911 · 62038633 · C90
C90 = P40 · P50
P40 = 9795426399848232136433658361416964220351_<40>
P50 = 16021201316639818235833142024355288672757596038111_<50>

Number: 19997_108 N=156934498334296931342888700420223926738874127226828735072542912178143222401314959597796961 ( 90 digits) SNFS difficulty: 110 digits. Divisors found: r1=9795426399848232136433658361416964220351 (pp40) r2=16021201316639818235833142024355288672757596038111 (pp50) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.51 hours. Scaled time: 0.46 units (timescale=0.909). Factorization parameters were as follows: n: 156934498334296931342888700420223926738874127226828735072542912178143222401314959597796961 m: 10000000000000000000000 c5: 1 c0: -150 skew: 2.72 type: snfs Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 325001) Primes: RFBsize:41538, AFBsize:41357, largePrimes:1146010 encountered Relations: rels:1115866, finalFF:136839 Max relations in full relation-set: 28 Initial matrix: 82959 x 136839 with sparse part having weight 5203852. Pruned matrix : 58367 x 58845 with weight 1641515. Total sieving time: 0.48 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,25000 total time: 0.51 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁴-3 = 1(9)₁₁₃7_<115> = 19 · 211 · C111
C111 = P50 · P61
P50 = 66720394280058370841709380872145894939733576500903_<50>
P61 = 7477136952660057610131641830487159799848955980602003638351811_<61>

Number: 19997_114 N=498877525567473185333000748316288351209777999501122474432526814666999251683711648790222000498877525567473185333 ( 111 digits) SNFS difficulty: 115 digits. Divisors found: r1=66720394280058370841709380872145894939733576500903 (pp50) r2=7477136952660057610131641830487159799848955980602003638351811 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.65 hours. Scaled time: 0.60 units (timescale=0.929). Factorization parameters were as follows: n: 498877525567473185333000748316288351209777999501122474432526814666999251683711648790222000498877525567473185333 m: 100000000000000000000000 c5: 1 c0: -15 skew: 1.72 type: snfs Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 375001) Primes: RFBsize:41538, AFBsize:41382, largePrimes:1141363 encountered Relations: rels:1093722, finalFF:121200 Max relations in full relation-set: 28 Initial matrix: 82984 x 121200 with sparse part having weight 5257052. Pruned matrix : 66846 x 67324 with weight 2100764. Total sieving time: 0.62 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,25000 total time: 0.65 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁸-3 = 1(9)₁₁₇7_<119> = 191 · 8248949 · C110
C110 = P32 · P78
P32 = 22950984299621533137884728246439_<32>
P78 = 553091130404568883549143340580413178416536717655739844547962308344784263446097_<78>

Number: 19997_118 N=12693985850175186430016911327810157663880441074803615518059787935833747232907048068371437696826716606008698583 ( 110 digits) SNFS difficulty: 120 digits. Divisors found: r1=22950984299621533137884728246439 (pp32) r2=553091130404568883549143340580413178416536717655739844547962308344784263446097 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.06 hours. Scaled time: 0.98 units (timescale=0.927). Factorization parameters were as follows: n: 12693985850175186430016911327810157663880441074803615518059787935833747232907048068371437696826716606008698583 m: 1000000000000000000000000 c5: 1 c0: -150 skew: 2.72 type: snfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [350000, 490001) Primes: RFBsize:56543, AFBsize:56408, largePrimes:2190525 encountered Relations: rels:2411404, finalFF:354493 Max relations in full relation-set: 28 Initial matrix: 113015 x 354493 with sparse part having weight 29047533. Pruned matrix : 69719 x 70348 with weight 4777254. Total sieving time: 1.00 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000 total time: 1.06 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹²²-3 = 1(9)₁₂₁7_<123> = 23 · 67 · 6389 · C116
C116 = P48 · P69
P48 = 171991496996710309484092016279706178541733683213_<48>
P69 = 118110223750443992209744996157769492200408400398154132891719193722281_<69>

Number: 19997_122 N=20313954193455270551906774388857227334172367354703680858028922804841099679659099346307111031706121274915953553768853 ( 116 digits) SNFS difficulty: 122 digits. Divisors found: r1=171991496996710309484092016279706178541733683213 (pp48) r2=118110223750443992209744996157769492200408400398154132891719193722281 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.36 hours. Scaled time: 1.27 units (timescale=0.929). Factorization parameters were as follows: n: 20313954193455270551906774388857227334172367354703680858028922804841099679659099346307111031706121274915953553768853 m: 2000000000000000000000000 c5: 25 c0: -12 skew: 1 type: snfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [350000, 560001) Primes: RFBsize:56543, AFBsize:56628, largePrimes:2122377 encountered Relations: rels:2193156, finalFF:202049 Max relations in full relation-set: 28 Initial matrix: 113235 x 202049 with sparse part having weight 18248550. Pruned matrix : 93995 x 94625 with weight 5931908. Total sieving time: 1.29 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000 total time: 1.36 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 15, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
2·10¹⁴³-3 = 1(9)₁₄₂7_<144> = 7 · 367 · C140
C140 = P36 · P105
P36 = 300364480242690431385063688008727003_<36>
P105 = 259189448587394079995709224242217573207735348894143323496982198581906017312796640460823662146191460771471_<105>

Number: n N=77851304009342156481121058777734527053328143246399377189567925262748151031529778123783573374854028804982483456597898014791747761775009731413 ( 140 digits) SNFS difficulty: 143 digits. Divisors found: r1=300364480242690431385063688008727003 (pp36) r2=259189448587394079995709224242217573207735348894143323496982198581906017312796640460823662146191460771471 (pp105) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.88 hours. Scaled time: 9.96 units (timescale=1.448). Factorization parameters were as follows: name: KA_1_9_142_7 n: 77851304009342156481121058777734527053328143246399377189567925262748151031529778123783573374854028804982483456597898014791747761775009731413 skew: 0.54 deg: 5 c5: 125 c0: -6 m: 20000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:183072, AFBsize:182636, largePrimes:6536042 encountered Relations: rels:6097591, finalFF:542478 Max relations in full relation-set: 28 Initial matrix: 365773 x 542478 with sparse part having weight 28309689. Pruned matrix : 211117 x 213009 with weight 11522988. Total sieving time: 5.77 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.85 hours. Total square root time: 0.11 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 6.88 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 15, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000
9·10¹⁸⁵+1 = 9(0)₁₈₄1_<186> = C186
C186 = P38 · C149
P38 = 14221071273845475492291671003825582287_<38>
C149 = [63286371516555504143607328750089379622990817116008869593801609303856339184629344856413421757600029944178214967248795969528509796283408631275118450223_<149>]

May 15, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(85·10¹⁵⁶+41)/9 = 9(4)₁₅₅9_<157> = 7 · 43 · 1829647 · 59981311102477643861_<20> · C129
C129 = P45 · P84
P45 = 623026004262418045585258199687571169731749999_<45>
P84 = 458902564109778259210141897723342450686101445324350532928974904781714443488055487153_<84>

Number: n N=285908230863093280149522567479878460620220761033945807669254236564669687489493297610088438129173451686543805526322851093152262847 ( 129 digits) SNFS difficulty: 157 digits. Divisors found: r1=623026004262418045585258199687571169731749999 (pp45) r2=458902564109778259210141897723342450686101445324350532928974904781714443488055487153 (pp84) Version: GGNFS-0.77.1-20051202-athlon Total time: 33.23 hours. Scaled time: 47.88 units (timescale=1.441). Factorization parameters were as follows: name: KA_9_4_155_9 n: 285908230863093280149522567479878460620220761033945807669254236564669687489493297610088438129173451686543805526322851093152262847 skew: 0.55 deg: 5 c5: 850 c0: 41 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:216852, largePrimes:7158635 encountered Relations: rels:6684140, finalFF:532075 Max relations in full relation-set: 28 Initial matrix: 433735 x 532075 with sparse part having weight 38484696. Pruned matrix : 354237 x 356469 with weight 22829842. Total sieving time: 29.61 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.29 hours. Total square root time: 0.13 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 33.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

2·10¹⁰⁴-3 = 1(9)₁₀₃7_<105> = 397633 · C99
C99 = P47 · P52
P47 = 81143272388834334896650363044075567399043782163_<47>
P52 = 6198620635061424030493749864953890386771151005333743_<52>

Number: n N=502976362625838398724451944380873820834789869050103990362972892088936280439500745662457592805426109 ( 99 digits) SNFS difficulty: 105 digits. Divisors found: r1=81143272388834334896650363044075567399043782163 (pp47) r2=6198620635061424030493749864953890386771151005333743 (pp52) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.86 hours. Scaled time: 1.25 units (timescale=1.449). Factorization parameters were as follows: name: KA_1_9_103_7 n: 502976362625838398724451944380873820834789869050103990362972892088936280439500745662457592805426109 skew: 1.72 deg: 5 c5: 1 c0: -15 m: 1000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:114155, AFBsize:114187, largePrimes:4382413 encountered Relations: rels:4136356, finalFF:487915 Max relations in full relation-set: 28 Initial matrix: 228406 x 487915 with sparse part having weight 13647573. Pruned matrix : 114742 x 115948 with weight 3325133. Total sieving time: 0.71 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.05 hours. Total square root time: 0.04 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,105,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,20000 total time: 0.86 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

2·10¹⁰⁶-3 = 1(9)₁₀₅7_<107> = 53299 · 42876259 · C94
C94 = P43 · P52
P43 = 5159197730271147217349752990276548876845323_<43>
P52 = 1696335989904637732334935062814384104990952215712079_<52>

Number: n N=8751732788893266688487625777268063114486632739211302698544914987497525049574361686915585756517 ( 94 digits) SNFS difficulty: 106 digits. Divisors found: r1=5159197730271147217349752990276548876845323 (pp43) r2=1696335989904637732334935062814384104990952215712079 (pp52) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.03 hours. Scaled time: 1.49 units (timescale=1.449). Factorization parameters were as follows: name: KA_1_9_105_7 n: 8751732788893266688487625777268063114486632739211302698544914987497525049574361686915585756517 skew: 0.68 deg: 5 c5: 20 c0: -3 m: 1000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:114155, AFBsize:113992, largePrimes:4623427 encountered Relations: rels:4344731, finalFF:480702 Max relations in full relation-set: 28 Initial matrix: 228213 x 480702 with sparse part having weight 15679088. Pruned matrix : 114549 x 115754 with weight 4184415. Total sieving time: 0.87 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.07 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,106,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000 total time: 1.03 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 14, 2007 (3rd)

The factor table of 199...997 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 14, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(37·10¹⁶⁷-1)/9 = 4(1)_167<168> = 3² · 373 · C165
C165 = P81 · P84
P81 = 918223766473056927120072370892676793977105023306840968715720117517723479949296603_<81>
P84 = 133370366287984710553342761808911401909229691328395596089306523023084095806001884041_<84>

Number: n N=122463840068844537119782874921391454009863303875815046503160891007182338728361963393241319961605931221659550524608612186807003607718531757852580015225234170721212723 ( 165 digits) SNFS difficulty: 168 digits. Divisors found: r1=918223766473056927120072370892676793977105023306840968715720117517723479949296603 (pp81) r2=133370366287984710553342761808911401909229691328395596089306523023084095806001884041 (pp84) Version: GGNFS-0.77.1-20051202-athlon Total time: 92.87 hours. Scaled time: 122.86 units (timescale=1.323). Factorization parameters were as follows: name: KA_4_1_167 n: 122463840068844537119782874921391454009863303875815046503160891007182338728361963393241319961605931221659550524608612186807003607718531757852580015225234170721212723 skew: 0.19 deg: 5 c5: 3700 c0: -1 m: 1000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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: 48/48 Sieved algebraic special-q in [100000, 3600001) Primes: RFBsize:348513, AFBsize:348256, largePrimes:8066454 encountered Relations: rels:7685936, finalFF:786082 Max relations in full relation-set: 48 Initial matrix: 696836 x 786082 with sparse part having weight 45848187. Pruned matrix : 617807 x 621355 with weight 30540514. Total sieving time: 83.57 hours. Total relation processing time: 0.32 hours. Matrix solve time: 8.75 hours. Total square root time: 0.22 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 92.87 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

P81 is the second largest factor found by GGNFS so far in our tables. Congratulations!
See also Records.

May 14, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GMP-ECM 5.0 B1=865000
(5·10¹⁵⁹-17)/3 = 1(6)₁₅₈1_<160> = 11 · 10526074387_<11> · C149
C149 = P49 · P100
P49 = 4281777787034366358534397847460791774293780003501_<49>
P100 = 3361750706608769880083150153142444008856468108643668619700589506468289143083298686757456257443067273_<100>

Number: n N=14394269501104516102021268331661041980010011828843017576094121090800487723317012837974305221059535679220116378939584964492187105376490962770118522773 ( 149 digits) SNFS difficulty: 160 digits. Divisors found: r1=4281777787034366358534397847460791774293780003501 (pp49) r2=3361750706608769880083150153142444008856468108643668619700589506468289143083298686757456257443067273 (pp100) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 28.58 hours. Scaled time: 39.01 units (timescale=1.365). Factorization parameters were as follows: name: KA_1_6_158_1 n: 14394269501104516102021268331661041980010011828843017576094121090800487723317012837974305221059535679220116378939584964492187105376490962770118522773 skew: 2.02 deg: 5 c5: 1 c0: -34 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:315948, AFBsize:315621, largePrimes:7083979 encountered Relations: rels:6741752, finalFF:731785 Max relations in full relation-set: 28 Initial matrix: 631633 x 731785 with sparse part having weight 31162081. Pruned matrix : 526231 x 529453 with weight 17073243. Total sieving time: 25.13 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.17 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 28.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(5·10¹⁵⁸-41)/9 = (5)₁₅₇1_<158> = 3 · 139 · 823 · 1460911 · C147
C147 = P33 · P114
P33 = 345932055663238901623643181254069_<33>
P114 = 320314823938951775915028322935805675020923974788887849647682117084206664427032851449437721142740924025642142485979_<114>

May 13, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(5·10¹⁵⁹-23)/9 = (5)₁₅₈3_<159> = 7² · 79 · 941 · C153
C153 = P40 · P52 · P62
P40 = 1365275107933766940502292838105456569269_<40>
P52 = 5993070696988687498185746545206764928030823906718791_<52>
P62 = 18639966485678882898966502221797396041802923662890668936753337_<62>

Number: n N=152515751903114429609847319836116334013035033264753100332578898914969387495825262581032000275504454237785905647228198551960545761146484089450000440770523 ( 153 digits) SNFS difficulty: 160 digits. Divisors found: r1=1365275107933766940502292838105456569269 (pp40) r2=5993070696988687498185746545206764928030823906718791 (pp52) r3=18639966485678882898966502221797396041802923662890668936753337 (pp62) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 37.16 hours. Scaled time: 50.72 units (timescale=1.365). Factorization parameters were as follows: name: KA_5_158_3 n: 152515751903114429609847319836116334013035033264753100332578898914969387495825262581032000275504454237785905647228198551960545761146484089450000440770523 skew: 2.15 deg: 5 c5: 1 c0: -46 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:315948, AFBsize:316251, largePrimes:7486977 encountered Relations: rels:7195105, finalFF:785470 Max relations in full relation-set: 28 Initial matrix: 632263 x 785470 with sparse part having weight 38165133. Pruned matrix : 485256 x 488481 with weight 18851472. Total sieving time: 33.59 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.14 hours. Total square root time: 0.22 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 37.16 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(10¹⁶⁶+71)/9 = (1)₁₆₅9_<166> = 3 · 853 · C162
C162 = P52 · P54 · P57
P52 = 2941450565776713211063703481417686180142901689698887_<52>
P54 = 444247718689605355281288325170529968377748965603234359_<54>
P57 = 332277125209997397567433286536766521100002249200099342577_<57>

Number: n N=434197386131735486952368546741348617081325170422474056706178628804654595979332204420129390821067257175111805826928921887890234900785897268898441231383787069601841 ( 162 digits) SNFS difficulty: 166 digits. Divisors found: r1=2941450565776713211063703481417686180142901689698887 (pp52) r2=444247718689605355281288325170529968377748965603234359 (pp54) r3=332277125209997397567433286536766521100002249200099342577 (pp57) Version: GGNFS-0.77.1-20051202-athlon Total time: 71.23 hours. Scaled time: 84.90 units (timescale=1.192). Factorization parameters were as follows: name: KA_1_165_9 n: 434197386131735486952368546741348617081325170422474056706178628804654595979332204420129390821067257175111805826928921887890234900785897268898441231383787069601841 type: snfs skew: 1.48 deg: 5 c5: 10 c0: 71 m: 1000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2500001) Primes: RFBsize:348513, AFBsize:347947, largePrimes:7816338 encountered Relations: rels:7510687, finalFF:820417 Max relations in full relation-set: 28 Initial matrix: 696526 x 820417 with sparse part having weight 42457592. Pruned matrix : 578274 x 581820 with weight 24476107. Total sieving time: 63.39 hours. Total relation processing time: 0.32 hours. Matrix solve time: 7.07 hours. Total square root time: 0.43 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 71.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(64·10¹⁵⁶+53)/9 = 7(1)₁₅₅7_<157> = 13 · 113 · 239 · 52860592215645665953858467693317_<32> · C120
C120 = P50 · P70
P50 = 49077828529847726066736868936370114562389265709103_<50>
P70 = 7807291673078649995782734630227484536649932164015296032914517722906237_<70>

Number: n N=383164922013861954685718096101603237579244787814536099238125074662505933186233933720729459506399443843513551211786375411 ( 120 digits) SNFS difficulty: 157 digits. Divisors found: r1=49077828529847726066736868936370114562389265709103 (pp50) r2=7807291673078649995782734630227484536649932164015296032914517722906237 (pp70) Version: GGNFS-0.77.1-20051202-athlon Total time: 30.78 hours. Scaled time: 44.47 units (timescale=1.445). Factorization parameters were as follows: name: KA_7_1_155_7 n: 383164922013861954685718096101603237579244787814536099238125074662505933186233933720729459506399443843513551211786375411 skew: 1.22 deg: 5 c5: 20 c0: 53 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:215751, largePrimes:7121172 encountered Relations: rels:6653609, finalFF:535901 Max relations in full relation-set: 28 Initial matrix: 432633 x 535901 with sparse part having weight 37968592. Pruned matrix : 347961 x 350188 with weight 22254553. Total sieving time: 27.34 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.18 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 30.78 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 12, 2007 (4th)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000
5·10¹⁹⁰-1 = 4(9)_190<191> = C191
C191 = P35 · P156
P35 = 99540974625765465275232034702200919_<35>
P156 = 502305710668196126484659145583463988849571937897513433848127456075026044866256022945692253079700553166877184985681787449184093822883155280824677517509895321_<156>

May 12, 2007 (3rd)

By Yousuke Koide / GMP-ECM B1=1000000 / Apr 30, 2007
(10¹¹⁶⁷-1)/9 = (1)_1167<1167> = 3 · 37 · 466801 · 1991681 · 25779031 · 9673567199_<10> · 7657037673276648858853_<22> · 30613946219676519851696681_<26> · 534106762532886493971950663223965323_<36> · 295666607855148525951669299929669849601357_<42> · C270 · C741
C741 = P32 · C710
P32 = 90840806850908670531036620137129_<32>
By Yousuke Koide / GMP-ECM B1=1000000 / May 4, 2007
10⁸⁷⁴+1 = 1(0)₈₇₃1_<875> = 101 · 1289 · 8259301 · 1440247121_<10> · 21631222069_<11> · 18371524594609_<14> · 722817036322379041_<18> · 1369778187490592461_<19> · 4181003300071669867932658901_<28> · C766
C766 = P31 · C735
P31 = 8177669991059740173635806566781_<31>
By Yousuke Koide / GMP-ECM B1=1000000 / May 8, 2007
10⁹¹⁷+1 = 1(0)₉₁₆1_<918> = 11 · 263 · 144887 · 909091 · 288840329 · 1397382241_<10> · 306662501757259_<15> · 525786373041914526306757_<24> · 112506283680098168752627601991569_<33> · 1363608083180796048411168783196497071688492468691_<49> · C767
C767 = P33 · C735
P33 = 223908687382121511269398989390133_<33>
By Yousuke Koide / GMP-ECM B1=1000000 / May 8, 2007
10¹⁰⁷⁷+1 = 1(0)₁₀₇₆1_<1078> = 7 · 11 · 13 · 10771 · 25849 · 91631161 · 19210610797963667218565939_<26> · C329 · C705
C705 = P34 · C671
P34 = 2586114064209667728427534023689533_<34>
By Torbjorn Granlund / GMP-ECM P-1 B1=100000000 / May 9, 2007
(10⁶¹⁵-1)/9 = (1)_615<615> = 3 · 31 · 37 · 41² · 83 · 271 · 1231 · 11071 · 275521 · 538987 · 1364071 · 1811791 · 2906161 · 21158848681_<11> · 626920594693_<12> · 9425856976319889649_<19> · 201763709900322803748657942361_<30> · 5440907236518498609451112390256369995629321_<43> · 8414640003465161203119978906558054839526493_<43> · 37654445534598090531061637404570516695225922222356909916889395661871779838862063550827086195341481919418156260385301045484576632937146377914151_<143> · C268
C268 = P36 · C232
P36 = 234065099292222402013296307835793151_<36>
By Torbjorn Granlund / GMP-ECM P-1 B1=10000000 / May 9, 2007
10⁷²²+1 = 1(0)₇₂₁1_<723> = 101 · 1097441 · 722817036322379041_<18> · 1369778187490592461_<19> · C678
C678 = P34 · C645
P34 = 6309203540697794137728747763478561_<34>
By Yousuke Koide / GMP-ECM B1=1000000 / May 7, 2007
10⁷⁵⁸+1 = 1(0)₇₅₇1_<759> = 101 · 4549 · C753
C753 = P32 · C721
P32 = 70488629165410024923533836947449_<32>
By Yousuke Koide / GMP-ECM B1=1000000 / May 12, 2007
10⁷⁷³+1 = 1(0)₇₇₂1_<774> = 11 · 2514771527_<10> · C763
C763 = P35 · C729
P35 = 27542107953980594633792218895027329_<35>
By Yousuke Koide / GMP-ECM B1=1000000 / May 12, 2007
10⁷⁷⁸+1 = 1(0)₇₇₇1_<779> = 101 · 68050337401_<11> · C766
C766 = P37 · C729
P37 = 1763722658625922307781888583674044509_<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

May 12, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(4·10¹⁵⁷-13)/9 = (4)₁₅₆3_<157> = 3 · 1607 · 1605739 · 72888289607101616827_<20> · C127
C127 = P38 · P90
P38 = 34994546482661762527459864491196336061_<38>
P90 = 225085369058061657663884263348948816998805899513451328210121428150671196588503313350746851_<90>

Number: n N=7876760410069416298662868647448204377450768132958815838678289103538428666499430415564938481187821565345250560533702189133493911 ( 127 digits) SNFS difficulty: 157 digits. Divisors found: r1=34994546482661762527459864491196336061 (pp38) r2=225085369058061657663884263348948816998805899513451328210121428150671196588503313350746851 (pp90) Version: GGNFS-0.77.1-20051202-athlon Total time: 31.88 hours. Scaled time: 46.19 units (timescale=1.449). Factorization parameters were as follows: name: KA_4_156_3 n: 7876760410069416298662868647448204377450768132958815838678289103538428666499430415564938481187821565345250560533702189133493911 skew: 1.01 deg: 5 c5: 25 c0: -26 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:217511, largePrimes:7047079 encountered Relations: rels:6530657, finalFF:496297 Max relations in full relation-set: 28 Initial matrix: 434391 x 496297 with sparse part having weight 34658844. Pruned matrix : 383891 x 386126 with weight 22977837. Total sieving time: 27.71 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.91 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 31.88 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 12, 2007

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000
(23·10¹⁸⁴+1)/3 = 7(6)₁₈₃7_<185> = C185
C185 = P37 · C149
P37 = 5774670075341229996045635806441711249_<37>
C149 = [13276371752222809090293402882959411707829163970866879125339397751880657325581180279608246723848888791937781266906345533410485228874392140408836617083_<149>]

May 11, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=3000000
(64·10¹⁹¹+53)/9 = 7(1)₁₉₀7_<192> = 3 · 11 · 239 · 2437 · 6599 · 244033 · C176
C176 = P34 · C143
P34 = 1215130975899590906278442010355229_<34>
C143 = [18906899481973526282026704495069056756649983846456749409752956664140620093099092451844621769773689315721058796527997944133334364541384120005301_<143>]
(64·10²³⁶+53)/9 = 7(1)₂₃₅7_<237> = 3 · 563 · 2383 · 20431 · 86381 · C222
C222 = P37 · C185
P37 = 6439440434086891745591132827876208899_<37>
C185 = [15546326742142275797343802733855931211964187662623718039519045945410959794410303852402574597376122760199834255719754439546665593662708368862695746542115188846097476249599680897257390819_<185>]

May 11, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
2·10¹⁶⁰-1 = 1(9)_160<161> = 7 · 719 · C157
C157 = P46 · P112
P46 = 3521112583666989208128791647491651766924820281_<46>
P112 = 1128556103542058996746525728749181096617698429611282103116231114503378579024061149030723533547291222035342709663_<112>

Number: n N=3973773097556129545002980329823167097158752235247367375322869064176435525531492151798132326644148619113848599244983111464335386449433737333598251539837075303 ( 157 digits) SNFS difficulty: 160 digits. Divisors found: r1=3521112583666989208128791647491651766924820281 (pp46) r2=1128556103542058996746525728749181096617698429611282103116231114503378579024061149030723533547291222035342709663 (pp112) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 35.80 hours. Scaled time: 26.88 units (timescale=0.751). Factorization parameters were as follows: name: KA_1_9_160 n: 3973773097556129545002980329823167097158752235247367375322869064176435525531492151798132326644148619113848599244983111464335386449433737333598251539837075303 skew: 0.87 deg: 5 c5: 2 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:315948, AFBsize:315591, largePrimes:7290686 encountered Relations: rels:6987505, finalFF:769990 Max relations in full relation-set: 28 Initial matrix: 631604 x 769990 with sparse part having weight 35494138. Pruned matrix : 494564 x 497786 with weight 17860283. Total sieving time: 30.25 hours. Total relation processing time: 0.20 hours. Matrix solve time: 5.14 hours. Total square root time: 0.20 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 35.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 11, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
(5·10¹⁶⁹+13)/9 = (5)₁₆₈7_<169> = 7 · 25841 · 708371 · 14831317 · 13419206138394747668082246000933204319_<38> · C114
C114 = P47 · P68
P47 = 18984589447258019171106580625816675813439927361_<47>
P68 = 11474971458647067240492312991607096103710342389767647453209132372147_<68>

Number: 55557_169 N=217847622061418072255581563015349258221880416028325068401083564087901225152792849614952022038191434366089299614067 ( 114 digits) Divisors found: r1=18984589447258019171106580625816675813439927361 (pp47) r2=11474971458647067240492312991607096103710342389767647453209132372147 (pp68) Version: GGNFS-0.77.1-20050930-nocona Total time: 23.52 hours. Scaled time: 21.99 units (timescale=0.935). Factorization parameters were as follows: name: 55557_169 n: 217847622061418072255581563015349258221880416028325068401083564087901225152792849614952022038191434366089299614067 skew: 93167.72 # norm 9.99e+15 c5: 7560 c4: 181240904 c3: -215160469783062 c2: 731926613668539534 c1: -336079217051183466131105 c0: -1719014552327535177050257095 # alpha -6.46 Y1: 515317817773 Y0: -7796973677105581012586 # Murphy_E 6.25e-10 # M 45979753848971241218306109270075070205023824708408177579147395268527404710642628807455036499266215840949482224176 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 2925001) Primes: RFBsize:256726, AFBsize:256868, largePrimes:7423035 encountered Relations: rels:7314425, finalFF:614838 Max relations in full relation-set: 28 Initial matrix: 513674 x 614838 with sparse part having weight 50290626. Pruned matrix : 428623 x 431255 with weight 30957143. Total sieving time: 22.00 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.24 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 23.52 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 10, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000
(5·10¹⁶⁰+13)/9 = (5)₁₅₉7_<160> = 443 · 149446961 · 954266828377_<12> · C137
C137 = P34 · P104
P34 = 2950675052531348964676339874534843_<34>
P104 = 29802003977964361400935073001776486894276408425662155711272488748993451457322768666516195405066304062469_<104>
(5·10¹⁶⁵+13)/9 = (5)₁₆₄7_<165> = 113 · 140207 · 7409646089513737_<16> · C142
C142 = P42 · P101
P42 = 120251587054056382828063467457919777275513_<42>
P101 = 39354198578549811165548493668314300005448817734165049827333990543389183856876706209828094658780016667_<101>

May 10, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0 B1=988000
(16·10¹⁶⁶-61)/9 = 1(7)₁₆₅1_<167> = 13 · 257 · C163
C163 = P41 · P51 · P72
P41 = 15109262159303914200235970117303182989937_<41>
P51 = 583000610683684808553479287729266199706051525409391_<51>
P72 = 604072035468266231595132183421912411669884078283681280966762593973524393_<72>

Number: n N=5321094815258239382753001430044231600651834114869134324387242675180418371079849679071468954737437227709601250457281585686254946955336060394426153181016994246566231 ( 163 digits) SNFS difficulty: 167 digits. Divisors found: r1=15109262159303914200235970117303182989937 (pp41) r2=583000610683684808553479287729266199706051525409391 (pp51) r3=604072035468266231595132183421912411669884078283681280966762593973524393 (pp72) Version: GGNFS-0.77.1-20051202-athlon Total time: 69.44 hours. Scaled time: 82.77 units (timescale=1.192). Factorization parameters were as follows: name: KA_1_7_165_1 n: 5321094815258239382753001430044231600651834114869134324387242675180418371079849679071468954737437227709601250457281585686254946955336060394426153181016994246566231 type: snfs skew: 1.65 deg: 5 c5: 5 c0: -61 m: 2000000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2300001) Primes: RFBsize:348513, AFBsize:348832, largePrimes:7702629 encountered Relations: rels:7363647, finalFF:782908 Max relations in full relation-set: 28 Initial matrix: 697410 x 782908 with sparse part having weight 38983048. Pruned matrix : 613328 x 616879 with weight 24922462. Total sieving time: 61.20 hours. Total relation processing time: 0.31 hours. Matrix solve time: 7.66 hours. Total square root time: 0.28 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000 total time: 69.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(2·10¹⁵⁶+61)/9 = (2)₁₅₅9_<156> = 7 · 43651 · 6364525991_<10> · 7275092106669707_<16> · C125
C125 = P38 · P87
P38 = 16178975375611820184681864685192671467_<38>
P87 = 970822145125557723186204385444462181385283099465504350555333554320195494843596374000943_<87>

Number: n N=15706907580085043270694630057489479125382622982598428533807291223433624832987908942174576079356758981977113837332597347193381 ( 125 digits) SNFS difficulty: 156 digits. Divisors found: r1=16178975375611820184681864685192671467 (pp38) r2=970822145125557723186204385444462181385283099465504350555333554320195494843596374000943 (pp87) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.90 hours. Scaled time: 35.95 units (timescale=1.444). Factorization parameters were as follows: name: KA_2_155_9 n: 15706907580085043270694630057489479125382622982598428533807291223433624832987908942174576079356758981977113837332597347193381 skew: 1.25 deg: 5 c5: 20 c0: 61 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:217357, largePrimes:6745421 encountered Relations: rels:6220624, finalFF:488017 Max relations in full relation-set: 28 Initial matrix: 434239 x 488017 with sparse part having weight 29966477. Pruned matrix : 386169 x 388404 with weight 19662895. Total sieving time: 21.52 hours. Total relation processing time: 0.17 hours. Matrix solve time: 3.09 hours. Total square root time: 0.12 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 24.90 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

3·10¹⁵⁶+1 = 3(0)₁₅₅1_<157> = 1297177961174555143_<19> · 2667221954249769199_<19> · C120
C120 = P44 · P77
P44 = 14120876924458604253497663539366736456941609_<44>
P77 = 61404594566872242448503276730228599364013338843483356019440687469832045039377_<77>
(83·10¹⁶⁷+61)/9 = 9(2)₁₆₆9_<168> = 7 · 11 · 17 · C165
C165 = P36(1440...) · P36(2519...) · P46 · P49
P36(1440...) = 144036627455472159894503296079104823_<36>
P36(2519...) = 251944573572582320400006996542619031_<36>
P46 = 7807715710023051816711416095697929674094210463_<46>
P49 = 2486531651431884079209006357389967329362985364599_<49>

Number: n N=704524233935998641880994822171292759528053645700704524233935998641880994822171292759528053645700704524233935998641880994822171292759528053645700704524233935998641881 ( 165 digits) SNFS difficulty: 168 digits. Divisors found: r1=144036627455472159894503296079104823 (pp36) r2=251944573572582320400006996542619031 (pp36) r3=7807715710023051816711416095697929674094210463 (pp46) r4=2486531651431884079209006357389967329362985364599 (pp49) Version: GGNFS-0.77.1-20051202-athlon Total time: 124.98 hours. Scaled time: 164.85 units (timescale=1.319). Factorization parameters were as follows: name: KA_9_2_166_9 n: 704524233935998641880994822171292759528053645700704524233935998641880994822171292759528053645700704524233935998641880994822171292759528053645700704524233935998641881 skew: 0.37 deg: 5 c5: 8300 c0: 61 m: 1000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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: 48/48 Sieved algebraic special-q in [100000, 4900001) Primes: RFBsize:348513, AFBsize:348547, largePrimes:8346543 encountered Relations: rels:7970546, finalFF:806767 Max relations in full relation-set: 48 Initial matrix: 697127 x 806767 with sparse part having weight 49889352. Pruned matrix : 609729 x 613278 with weight 34943447. Total sieving time: 112.71 hours. Total relation processing time: 0.41 hours. Matrix solve time: 10.22 hours. Total square root time: 1.64 hours, sqrts: 13. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 124.98 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 9, 2007 (2nd)

By Robert Backstrom / GMP-ECM 5.0 B1=803000, GGNFS-0.77.1-20051202-athlon
(13·10¹⁵⁶-31)/9 = 1(4)₁₅₅1_<157> = 81223 · 33503305313_<11> · 109654833847764713_<18> · C124
C124 = P32 · P93
P32 = 33221106335396792559728583649939_<32>
P93 = 145710983338393792427706737229266963776824439301949657734730802429613705232080064468338379037_<93>
(16·10¹⁵⁵-1)/3 = 5(3)_155<156> = 241 · 563 · 9720432861379084146529_<22> · C129
C129 = P56 · P73
P56 = 90029914555725552917405713267859877539437849056631020317_<56>
P73 = 4491597666962551358812885925456249780291015698726653486747753928606021907_<73>

Number: n N=404378154175334737009800640537312448779192500233832940020546894325311977216650147743526077094343949934288407943962237103864084519 ( 129 digits) SNFS difficulty: 156 digits. Divisors found: r1=90029914555725552917405713267859877539437849056631020317 (pp56) r2=4491597666962551358812885925456249780291015698726653486747753928606021907 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 22.14 hours. Scaled time: 16.09 units (timescale=0.727). Factorization parameters were as follows: name: KA_5_3_155 n: 404378154175334737009800640537312448779192500233832940020546894325311977216650147743526077094343949934288407943962237103864084519 skew: 1.15 deg: 5 c5: 1 c0: -2 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:216816, AFBsize:216491, largePrimes:6892018 encountered Relations: rels:6481806, finalFF:584788 Max relations in full relation-set: 28 Initial matrix: 433371 x 584788 with sparse part having weight 34883238. Pruned matrix : 301211 x 303441 with weight 16933179. Total sieving time: 18.50 hours. Total relation processing time: 0.17 hours. Matrix solve time: 3.30 hours. Total square root time: 0.17 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 22.14 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(5·10¹⁵⁹+31)/9 = (5)₁₅₈9_<159> = 13 · 97 · C156
C156 = P67 · P90
P67 = 1385395064995660441245964715337390478851164754214255342899601827751_<67>
P90 = 318008532012570179000633455554438524970194717548867326486492267515298642222528842549960869_<90>

Number: n N=440567450876729227244691162216935412811701471495285928275618997268481804564278791082914794255000440567450876729227244691162216935412811701471495285928275619 ( 156 digits) SNFS difficulty: 160 digits. Divisors found: r1=1385395064995660441245964715337390478851164754214255342899601827751 (pp67) r2=318008532012570179000633455554438524970194717548867326486492267515298642222528842549960869 (pp90) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 32.40 hours. Scaled time: 44.32 units (timescale=1.368). Factorization parameters were as follows: name: KA_5_158_9 n: 440567450876729227244691162216935412811701471495285928275618997268481804564278791082914794255000440567450876729227244691162216935412811701471495285928275619 skew: 2.28 deg: 5 c5: 1 c0: 62 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:315948, AFBsize:316092, largePrimes:7163062 encountered Relations: rels:6818762, finalFF:732797 Max relations in full relation-set: 28 Initial matrix: 632104 x 732797 with sparse part having weight 32214102. Pruned matrix : 527782 x 531006 with weight 17799091. Total sieving time: 28.25 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.53 hours. Total square root time: 0.41 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 32.40 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 9, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
6·10¹⁶²+1 = 6(0)₁₆₁1_<163> = 7 · 409 · 461 · 1297 · 71355177903228522649_<20> · 105440523536650831469_<21> · C114
C114 = P52 · P63
P52 = 2635929378062082616090181215642985097332592374330359_<52>
P63 = 176734845085883901472849673672121748213269636335439399849960889_<63>

Number: 60001_162 N=465860570289132470526766504662099277577757656808920530081522403634714863130373216991557016779244393574693715329151 ( 114 digits) Divisors found: r1=2635929378062082616090181215642985097332592374330359 (pp52) r2=176734845085883901472849673672121748213269636335439399849960889 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 25.27 hours. Scaled time: 23.50 units (timescale=0.930). Factorization parameters were as follows: name: 60001_162 n: 465860570289132470526766504662099277577757656808920530081522403634714863130373216991557016779244393574693715329151 skew: 52979.34 # norm 6.29e+15 c5: 28800 c4: -4744474328 c3: -240924644592942 c2: 12887096438141057377 c1: 343182609850863365434888 c0: -2211251175528614193036100335 # alpha -6.42 Y1: 962944882867 Y0: -6946638145470387030218 # Murphy_E 6.24e-10 # M 422905541741467303181853397627552337882467775546056669673492939882919014769355778867593327900220590802340709537733 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 2925001) Primes: RFBsize:256726, AFBsize:256259, largePrimes:7444354 encountered Relations: rels:7318652, finalFF:599647 Max relations in full relation-set: 28 Initial matrix: 513063 x 599647 with sparse part having weight 48328634. Pruned matrix : 441183 x 443812 with weight 30948811. Total sieving time: 21.86 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.08 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 25.27 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 8, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000
(5·10¹⁶⁹+13)/9 = (5)₁₆₈7_<169> = 7 · 25841 · 708371 · 14831317 · C151
C151 = P38 · C114
P38 = 13419206138394747668082246000933204319_<38>
C114 = [217847622061418072255581563015349258221880416028325068401083564087901225152792849614952022038191434366089299614067_<114>]

May 8, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=618000, B1=522500, GGNFS-0.77.1-20060513-athlon-xp
3·10¹⁵⁷+1 = 3(0)₁₅₆1_<158> = 17 · 772006355756021_<15> · 7401761985090177770309_<22> · C120
C120 = P36 · P85
P36 = 248529780208636811981353203838303673_<36>
P85 = 1242618760787690302557066234608127824342363929964979635799811131131051551936554388849_<85>
(34·10¹⁵⁶-7)/9 = 3(7)_156<157> = 3 · 131 · 3931 · 11472824853206904594929_<23> · C129
C129 = P34 · P95
P34 = 6782564829732305170470333318140549_<34>
P95 = 31425087546025715646735982184029372225640172487522725906443903355358448487384609969906116186239_<95>
(10¹⁶⁷+71)/9 = (1)₁₆₆9_<167> = 89 · C165
C165 = P59 · P106
P59 = 91311343163343446323968739512561574329110904059483452421063_<59>
P106 = 1367233694562301051553984933575756012125192786758201704704070474144368666604173622117402417959850492600417_<106>

Number: n N=124843945068664169787765293383270911360799001248439450686641697877652933832709113607990012484394506866416978776529338327091136079900124843945068664169787765293383271 ( 165 digits) SNFS difficulty: 167 digits. Divisors found: r1=91311343163343446323968739512561574329110904059483452421063 (pp59) r2=1367233694562301051553984933575756012125192786758201704704070474144368666604173622117402417959850492600417 (pp106) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 108.25 hours. Scaled time: 147.65 units (timescale=1.364). Factorization parameters were as follows: name: KA_1_166_9 n: 124843945068664169787765293383270911360799001248439450686641697877652933832709113607990012484394506866416978776529338327091136079900124843945068664169787765293383271 skew: 0.93 deg: 5 c5: 100 c0: 71 m: 1000000000000000000000000000000000 type: snfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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: 48/48 Sieved algebraic special-q in [100000, 4500001) Primes: RFBsize:348513, AFBsize:350387, largePrimes:7881774 encountered Relations: rels:7565246, finalFF:794688 Max relations in full relation-set: 28 Initial matrix: 698964 x 794688 with sparse part having weight 43936217. Pruned matrix : 616009 x 619567 with weight 29724900. Total sieving time: 98.17 hours. Total relation processing time: 0.59 hours. Matrix solve time: 8.69 hours. Total square root time: 0.80 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 108.25 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(4·10¹⁵⁵-13)/9 = (4)₁₅₄3_<155> = 7 · 3808559 · 6125229081493124399_<19> · C129
C129 = P64 · P66
P64 = 1430852648491397818456316645370885067116465513802945727285403371_<64>
P66 = 190213574326970416645495975919797015608841251458428834035091173959_<66>

Number: n N=272167596604760973939922895849222045319822735977613961182574173096110354671336539629503110460161984822070057750007276533246015789 ( 129 digits) SNFS difficulty: 155 digits. Divisors found: r1=1430852648491397818456316645370885067116465513802945727285403371 (pp64) r2=190213574326970416645495975919797015608841251458428834035091173959 (pp66) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.66 hours. Scaled time: 35.49 units (timescale=1.439). Factorization parameters were as follows: name: KA_4_154_3 n: 272167596604760973939922895849222045319822735977613961182574173096110354671336539629503110460161984822070057750007276533246015789 skew: 1.27 deg: 5 c5: 4 c0: -13 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1100001) Primes: RFBsize:216816, AFBsize:216856, largePrimes:6824327 encountered Relations: rels:6301687, finalFF:489949 Max relations in full relation-set: 28 Initial matrix: 433736 x 489949 with sparse part having weight 31276439. Pruned matrix : 385079 x 387311 with weight 20380733. Total sieving time: 21.27 hours. Total relation processing time: 0.17 hours. Matrix solve time: 3.16 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 24.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 7, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=184500, B1=595000, GGNFS-0.77.1-20051202-athlon
8·10¹⁶⁷-3 = 7(9)₁₆₆7_<168> = 11 · 71 · C166
C166 = P31 · P35 · P100
P31 = 6263376936571872349805965794179_<31>
P35 = 48366409729269876335151280681703887_<35>
P100 = 3381322183264895436089159421503432927307771620830849708685343102501831818018700928611257460676963669_<100>
6·10¹⁵⁵-1 = 5(9)_155<156> = 17 · 855694920236157839951575243_<27> · C155
C155 = P38 · P91
P38 = 23563769814083175297504581851112348513_<38>
P91 = 1750405235111493782019464819415041844908100509751846238928281927522333980653932785261889133_<91>

Number: n N=41246146041533380581382937109329549557946829659714681794095420363066533915011986623900432662432693705651217155512046742663409229 ( 128 digits) SNFS difficulty: 155 digits. Divisors found: r1=23563769814083175297504581851112348513 (pp38) r2=1750405235111493782019464819415041844908100509751846238928281927522333980653932785261889133 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.30 hours. Scaled time: 28.06 units (timescale=1.454). Factorization parameters were as follows: name: KA_5_9_155 n: 41246146041533380581382937109329549557946829659714681794095420363066533915011986623900432662432693705651217155512046742663409229 skew: 0.70 deg: 5 c5: 6 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:216816, AFBsize:216821, largePrimes:6743866 encountered Relations: rels:6305075, finalFF:556166 Max relations in full relation-set: 28 Initial matrix: 433703 x 556166 with sparse part having weight 32299756. Pruned matrix : 326541 x 328773 with weight 16053392. Total sieving time: 16.97 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.06 hours. Total square root time: 0.10 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 19.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 6, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(86·10¹⁵⁵+31)/9 = 9(5)₁₅₄9_<156> = 11 · 17 · 19 · 107 · 3329 · 234547 · 49916499175544369_<17> · C125
C125 = P51 · P75
P51 = 146893790346276534914663990304041376179590078145821_<51>
P75 = 439021432742427786693807047121586584432982187601506537680594815438795711667_<75>

Number: n N=64489522298788131872083990903207589990122986848898622434996970678191618339288837124645592388512510110304876458442669496993607 ( 125 digits) SNFS difficulty: 156 digits. Divisors found: r1=146893790346276534914663990304041376179590078145821 (pp51) r2=439021432742427786693807047121586584432982187601506537680594815438795711667 (pp75) Version: GGNFS-0.77.1-20051202-athlon Total time: 25.08 hours. Scaled time: 36.31 units (timescale=1.448). Factorization parameters were as follows: name: KA_9_5_154_9 n: 64489522298788131872083990903207589990122986848898622434996970678191618339288837124645592388512510110304876458442669496993607 skew: 0.82 deg: 5 c5: 86 c0: 31 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:216816, AFBsize:217122, largePrimes:6799735 encountered Relations: rels:6278199, finalFF:494460 Max relations in full relation-set: 28 Initial matrix: 434004 x 494460 with sparse part having weight 30387568. Pruned matrix : 381067 x 383301 with weight 19287909. Total sieving time: 21.81 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.02 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 25.08 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(43·10¹⁶⁴-7)/9 = 4(7)_164<165> = 3² · C164
C164 = P40 · P54 · P71
P40 = 2631129533782044843927495361912765542751_<40>
P54 = 215880931151977979223281199254244241548167819075235827_<54>
P71 = 93460247031749192280709130483295872291224585644076339206811461233287789_<71>

Number: n N=53086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753 ( 164 digits) SNFS difficulty: 166 digits. Divisors found: r1=2631129533782044843927495361912765542751 (pp40) r2=215880931151977979223281199254244241548167819075235827 (pp54) r3=93460247031749192280709130483295872291224585644076339206811461233287789 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 117.61 hours. Scaled time: 140.90 units (timescale=1.198). Factorization parameters were as follows: name: KA_4_7_164 n: 53086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753 type: snfs skew: 1.10 deg: 5 c5: 43 c0: -70 m: 1000000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 4500001) Primes: RFBsize:250150, AFBsize:248761, largePrimes:8106263 encountered Relations: rels:7638338, finalFF:562340 Max relations in full relation-set: 28 Initial matrix: 498976 x 562340 with sparse part having weight 56255595. Pruned matrix : 471675 x 474233 with weight 44274525. Total sieving time: 106.62 hours. Total relation processing time: 0.42 hours. Matrix solve time: 9.71 hours. Total square root time: 0.86 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 117.61 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

May 5, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(16·10¹⁵⁵-61)/9 = 1(7)₁₅₄1_<156> = 3³ · 11 · 313 · 3413 · 564653293741502455894429_<24> · C123
C123 = P57 · P67
P57 = 147578844538555167154379562564198635879111107545264229249_<57>
P67 = 6724104070964062862708978830908866005677012688304296879046893860907_<67>

Number: n N=992335509349871354723416775422313367980880327033705308667135048478218116917002201583659164168205143446837552843965167068843 ( 123 digits) SNFS difficulty: 156 digits. Divisors found: r1=147578844538555167154379562564198635879111107545264229249 (pp57) r2=6724104070964062862708978830908866005677012688304296879046893860907 (pp67) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.42 hours. Scaled time: 28.06 units (timescale=1.445). Factorization parameters were as follows: name: KA_1_7_154_1 n: 992335509349871354723416775422313367980880327033705308667135048478218116917002201583659164168205143446837552843965167068843 skew: 2.61 deg: 5 c5: 1 c0: -122 m: 20000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:216816, AFBsize:216857, largePrimes:6849328 encountered Relations: rels:6484465, finalFF:621032 Max relations in full relation-set: 28 Initial matrix: 433737 x 621032 with sparse part having weight 35182490. Pruned matrix : 269851 x 272083 with weight 16048658. Total sieving time: 17.58 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.63 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 19.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(31·10¹⁶⁶-13)/9 = 3(4)₁₆₅3_<167> = 3² · C166
C166 = P44 · P55 · P68
P44 = 11249365279272105191944705856137109893341383_<44>
P55 = 4629217185850101516750522211783509052473169342352740507_<55>
P68 = 73492174772991205921386920343213336461480210780035033172068546448767_<68>

Number: n N=3827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827 ( 166 digits) SNFS difficulty: 167 digits. Divisors found: r1=11249365279272105191944705856137109893341383 (pp44) r2=4629217185850101516750522211783509052473169342352740507 (pp55) r3=73492174772991205921386920343213336461480210780035033172068546448767 (pp68) Version: GGNFS-0.77.1-20051202-athlon Total time: 84.72 hours. Scaled time: 112.08 units (timescale=1.323). Factorization parameters were as follows: name: KA_3_4_165_3 n: 3827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827 skew: 0.53 deg: 5 c5: 310 c0: -13 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3600001) Primes: RFBsize:216816, AFBsize:216917, largePrimes:7638831 encountered Relations: rels:7082488, finalFF:488644 Max relations in full relation-set: 48 Initial matrix: 433800 x 488644 with sparse part having weight 62247574. Pruned matrix : 416718 x 418951 with weight 46486994. Total sieving time: 74.95 hours. Total relation processing time: 0.30 hours. Matrix solve time: 8.93 hours. Total square root time: 0.54 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 84.72 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 4, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM 5.0.3 B1=3000000
(8·10¹⁸³-17)/9 = (8)₁₈₂7_<183> = C183
C183 = P31 · C153
P31 = 1259337356542822108306204266629_<31>
C153 = [705838577939987753279711060237017228585936509399199518627682834424778845002336309634782236276759532406698056060483434655977248535150104022612858176741003_<153>]

May 4, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(13·10¹⁵⁵-1)/3 = 4(3)_155<156> = 1217 · 1758541 · 451860930139252966767713_<24> · C123
C123 = P42 · P81
P42 = 664604448458801168137249105380355621156169_<42>
P81 = 674234521819545742193894263762175555094507255650621412062733023543616234671763137_<81>

Number: n N=448099262505762739810790562822297173729543427286178125601790590364287468716846509427825261974678202403285587890997654342153 ( 123 digits) SNFS difficulty: 156 digits. Divisors found: r1=664604448458801168137249105380355621156169 (pp42) r2=674234521819545742193894263762175555094507255650621412062733023543616234671763137 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.55 hours. Scaled time: 31.23 units (timescale=1.449). Factorization parameters were as follows: name: KA_4_3_155 n: 448099262505762739810790562822297173729543427286178125601790590364287468716846509427825261974678202403285587890997654342153 skew: 0.60 deg: 5 c5: 13 c0: -1 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:216816, AFBsize:215931, largePrimes:7088794 encountered Relations: rels:6747346, finalFF:648840 Max relations in full relation-set: 28 Initial matrix: 432812 x 648840 with sparse part having weight 40651871. Pruned matrix : 253312 x 255540 with weight 20462953. Total sieving time: 19.43 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.90 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 21.55 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 4, 2007

By suberi / GMP-ECM 6.1.2 B1=3000000
(5·10¹⁹⁰+13)/9 = (5)₁₈₉7_<190> = 811 · 907 · 10837804441_<11> · 2785656325929626661973_<22> · C153
C153 = P30 · C124
P30 = 141420727163771568086127494461_<30>
C124 = [1768957675798608538570697178394242001598658689261756493802670073290117602123758045787374992447868719160331461600669004667317_<124>]
(5·10¹⁷⁹+13)/9 = (5)₁₇₈7_<179> = 3 · 509 · 1067600111_<10> · C167
C167 = P30 · C137
P30 = 501390694625542533719253930763_<30>
C137 = [67967857156207860206815546895977987863005066787709361009704730235070830216414344853956065234054495527685695832614271671186671680546533287_<137>]

May 3, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
7·10¹⁵⁴+1 = 7(0)₁₅₃1_<155> = 43 · 5623 · 12401 · 79861933 · 1575233648179_<13> · C126
C126 = P51 · P75
P51 = 193370246682439687632641395275617696499919070409857_<51>
P75 = 959688618561589603204660736875782818852796083063317811556994979114317575491_<75>

Number: n N=185575224909584348798499980746588371732865042833545760086485528245996049062231370685862811259790810958949845914972371908014787 ( 126 digits) SNFS difficulty: 155 digits. Divisors found: r1=193370246682439687632641395275617696499919070409857 (pp51) r2=959688618561589603204660736875782818852796083063317811556994979114317575491 (pp75) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.11 hours. Scaled time: 40.70 units (timescale=1.448). Factorization parameters were as follows: name: KA_7_0_153_1 n: 185575224909584348798499980746588371732865042833545760086485528245996049062231370685862811259790810958949845914972371908014787 skew: 1.07 deg: 5 c5: 7 c0: 10 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:217031, largePrimes:7072813 encountered Relations: rels:6598043, finalFF:530393 Max relations in full relation-set: 28 Initial matrix: 433912 x 530393 with sparse part having weight 36370966. Pruned matrix : 353629 x 355862 with weight 21272652. Total sieving time: 24.79 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.07 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 28.11 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(4·10¹⁶³-13)/9 = (4)₁₆₂3_<163> = 3 · C163
C163 = P65 · P99
P65 = 11928511488576416652518926449031014706382259688259889449372428463_<65>
P99 = 124196676416856584831190356834443566414147381261107180590809616102721629362131706129660584348140487_<99>

Number: n N=1481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481 ( 163 digits) SNFS difficulty: 163 digits. Divisors found: r1=11928511488576416652518926449031014706382259688259889449372428463 (pp65) r2=124196676416856584831190356834443566414147381261107180590809616102721629362131706129660584348140487 (pp99) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 46.36 hours. Scaled time: 63.28 units (timescale=1.365). Factorization parameters were as follows: name: KA_4_162_3 n: 1481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481 skew: 0.64 deg: 5 c5: 125 c0: -13 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:216816, AFBsize:216271, largePrimes:7206086 encountered Relations: rels:6681195, finalFF:486083 Max relations in full relation-set: 28 Initial matrix: 433152 x 486083 with sparse part having weight 37948638. Pruned matrix : 394389 x 396618 with weight 27334391. Total sieving time: 42.09 hours. Total relation processing time: 0.26 hours. Matrix solve time: 3.88 hours. Total square root time: 0.13 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 46.36 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 3, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000
8·10¹⁸⁴-1 = 7(9)_184<185> = C185
C185 = P43 · C143
P43 = 1999080062901581503437318550484654902159553_<43>
C143 = [40018407208705453170393588274967598668194718998797708185694406998207268713775631752044327280691107243190075250207288752868081397525726798190783_<143>]

May 3, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs
(5·10¹⁵⁹+13)/9 = (5)₁₅₈7_<159> = 31 · 88422043643857462597_<20> · 1425603659062897082122821966839_<31> · C108
C108 = P42 · P66
P42 = 963375458771271206396670106466303330684323_<42>
P66 = 147574347817773759929890143833175414071639106091723198758761439283_<66>

Number: 55557_159 N=142169505031818941787456133521823682753734366848698561502053979968080314542932254864568794355447616804460409 ( 108 digits) Divisors found: r1=963375458771271206396670106466303330684323 (pp42) r2=147574347817773759929890143833175414071639106091723198758761439283 (pp66) Version: GGNFS-0.77.1-20050930-k8 Total time: 11.50 hours. Scaled time: 10.75 units (timescale=0.935). Factorization parameters were as follows: name: 55557_159 n: 142169505031818941787456133521823682753734366848698561502053979968080314542932254864568794355447616804460409 skew: 26374.85 # norm 2.40e+15 c5: 35280 c4: 934399884 c3: -89832636229180 c2: 1523184560386315315 c1: 18999259139000664323700 c0: -99692038060039600471149984 # alpha -8.27 Y1: 264069173159 Y0: -331935532854754032235 # Murphy_E 1.80e-09 # M 123395139583000001562421371741684712074865364389449685364637536523825175006068414011882084180445111450434185 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1380001) Primes: RFBsize:135072, AFBsize:134617, largePrimes:4669123 encountered Relations: rels:4865738, finalFF:485020 Max relations in full relation-set: 28 Initial matrix: 269770 x 485020 with sparse part having weight 47009771. Pruned matrix : 179665 x 181077 with weight 17208918. Polynomial selection time: 0.61 hours. Total sieving time: 10.58 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.16 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 11.50 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676) Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133) Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148) Total of 4 processors activated (19246.21 BogoMIPS).

May 2, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(8·10¹⁶³-71)/9 = (8)₁₆₂1_<163> = 107 · C161
C161 = P60 · P102
P60 = 331525272836625077861926530888596074621005958963348147811333_<60>
P102 = 250580377244662029958853007009725953486242048898063827611155437846422355414015990463558317384787413751_<102>

Number: n N=83073727933541017653167185877466251298026998961578400830737279335410176531671858774662512980269989615784008307372793354101765316718587746625129802699896157840083 ( 161 digits) SNFS difficulty: 163 digits. Divisors found: r1=331525272836625077861926530888596074621005958963348147811333 (pp60) r2=250580377244662029958853007009725953486242048898063827611155437846422355414015990463558317384787413751 (pp102) Version: GGNFS-0.77.1-20051202-athlon Total time: 76.77 hours. Scaled time: 111.16 units (timescale=1.448). Factorization parameters were as follows: name: KA_8_162_1 n: 83073727933541017653167185877466251298026998961578400830737279335410176531671858774662512980269989615784008307372793354101765316718587746625129802699896157840083 skew: 0.78 deg: 5 c5: 250 c0: -71 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3600001) Primes: RFBsize:216816, AFBsize:215722, largePrimes:7882612 encountered Relations: rels:7405836, finalFF:485486 Max relations in full relation-set: 28 Initial matrix: 432604 x 485486 with sparse part having weight 50002622. Pruned matrix : 413633 x 415860 with weight 39761888. Total sieving time: 68.97 hours. Total relation processing time: 0.28 hours. Matrix solve time: 7.34 hours. Total square root time: 0.18 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 76.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

May 2, 2007 (2nd)

By Jo Yeong Uk / Msieve v. 1.19
(5·10¹⁷⁸+13)/9 = (5)₁₇₇7_<178> = 1528613 · 9850196670187_<13> · 2526077546800091_<16> · 51897680774988553_<17> · 1936097886341375452565514421758559_<34> · C94
C94 = P44 · P50
P44 = 24797876921485497067144513611132264335092469_<44>
P50 = 58620376640769325233358205994469484508814376477459_<50>

Wed May 2 08:05:47 2007 Wed May 2 08:05:47 2007 Wed May 2 08:05:47 2007 Msieve v. 1.19 Wed May 2 08:05:47 2007 random seeds: 0e7d1e7b 64086647 Wed May 2 08:05:47 2007 factoring 1453660885028921178823036658094874193257359268776143901154311382982677794100725313703259156271 (94 digits) Wed May 2 08:05:47 2007 commencing quadratic sieve (93-digit input) Wed May 2 08:05:47 2007 using multiplier of 1 Wed May 2 08:05:47 2007 sieve interval: 9 blocks of size 65536 Wed May 2 08:05:47 2007 processing polynomials in batches of 6 Wed May 2 08:05:47 2007 using a sieve bound of 1990607 (74118 primes) Wed May 2 08:05:47 2007 using large prime bound of 256788303 (27 bits) Wed May 2 08:05:47 2007 using double large prime bound of 1371624962518986 (42-51 bits) Wed May 2 08:05:47 2007 using trial factoring cutoff of 53 bits Wed May 2 08:05:47 2007 polynomial 'A' values have 12 factors Wed May 2 10:35:55 2007 74609 relations (19982 full + 54627 combined from 1001183 partial), need 74214 Wed May 2 10:35:56 2007 begin with 1021165 relations Wed May 2 10:35:56 2007 reduce to 185310 relations in 10 passes Wed May 2 10:35:56 2007 attempting to read 185310 relations Wed May 2 10:35:57 2007 recovered 185310 relations Wed May 2 10:35:57 2007 recovered 165356 polynomials Wed May 2 10:35:58 2007 attempting to build 74609 cycles Wed May 2 10:35:58 2007 found 74609 cycles in 6 passes Wed May 2 10:35:58 2007 distribution of cycle lengths: Wed May 2 10:35:58 2007 length 1 : 19982 Wed May 2 10:35:58 2007 length 2 : 14145 Wed May 2 10:35:58 2007 length 3 : 12995 Wed May 2 10:35:58 2007 length 4 : 9919 Wed May 2 10:35:58 2007 length 5 : 6952 Wed May 2 10:35:58 2007 length 6 : 4552 Wed May 2 10:35:58 2007 length 7 : 2683 Wed May 2 10:35:58 2007 length 9+: 3381 Wed May 2 10:35:58 2007 largest cycle: 21 relations Wed May 2 10:35:58 2007 matrix is 74118 x 74609 with weight 4562903 (avg 61.16/col) Wed May 2 10:35:58 2007 filtering completed in 4 passes Wed May 2 10:35:58 2007 matrix is 72366 x 72430 with weight 4338494 (avg 59.90/col) Wed May 2 10:35:59 2007 saving the first 48 matrix rows for later Wed May 2 10:35:59 2007 matrix is 72318 x 72430 with weight 3394140 (avg 46.86/col) Wed May 2 10:35:59 2007 matrix includes 32 packed rows Wed May 2 10:35:59 2007 using block size 28972 for processor cache size 4096 kB Wed May 2 10:36:24 2007 lanczos halted after 1146 iterations Wed May 2 10:36:24 2007 recovered 17 nontrivial dependencies Wed May 2 10:36:24 2007 prp44 factor: 24797876921485497067144513611132264335092469 Wed May 2 10:36:24 2007 prp50 factor: 58620376640769325233358205994469484508814376477459 Wed May 2 10:36:24 2007 elapsed time 02:30:37

May 2, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(7·10¹⁶³+11)/9 = (7)₁₆₂9_<163> = 3² · 41 · C161
C161 = P54 · P107
P54 = 514515297087868502474983030087617316989796040442834827_<54>
P107 = 40966689769893610626476927258402725629496499459917386396791475858410644488358780719013787208922173833093833_<107>

Number: n N=21077988557663354411321890996687744655224330021077988557663354411321890996687744655224330021077988557663354411321890996687744655224330021077988557663354411321891 ( 161 digits) SNFS difficulty: 163 digits. Divisors found: r1=514515297087868502474983030087617316989796040442834827 (pp54) r2=40966689769893610626476927258402725629496499459917386396791475858410644488358780719013787208922173833093833 (pp107) Version: GGNFS-0.77.1-20051202-athlon Total time: 73.09 hours. Scaled time: 96.69 units (timescale=1.323). Factorization parameters were as follows: name: KA_7_162_9 n: 21077988557663354411321890996687744655224330021077988557663354411321890996687744655224330021077988557663354411321890996687744655224330021077988557663354411321891 skew: 0.27 deg: 5 c5: 7000 c0: 11 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3100001) Primes: RFBsize:216816, AFBsize:216287, largePrimes:7606035 encountered Relations: rels:7066578, finalFF:507191 Max relations in full relation-set: 48 Initial matrix: 433170 x 507191 with sparse part having weight 57968673. Pruned matrix : 408331 x 410560 with weight 39468405. Total sieving time: 65.31 hours. Total relation processing time: 0.29 hours. Matrix solve time: 7.28 hours. Total square root time: 0.20 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 73.09 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

May 1, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(34·10¹⁶³-43)/9 = 3(7)₁₆₂3_<164> = 3 · 11 · 127 · C160
C160 = P65 · P95
P65 = 91390426373664897185118886740810108717145752199108537782197799559_<65>
P95 = 98632046262711639984435686270799324642733520958702869493254441867094251159024695060193689043317_<95>

Number: n N=9014024762056258119250245234497203001140009014024762056258119250245234497203001140009014024762056258119250245234497203001140009014024762056258119250245234497203 ( 160 digits) SNFS difficulty: 164 digits. Divisors found: r1=91390426373664897185118886740810108717145752199108537782197799559 (pp65) r2=98632046262711639984435686270799324642733520958702869493254441867094251159024695060193689043317 (pp95) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 79.19 hours. Scaled time: 108.17 units (timescale=1.366). Factorization parameters were as follows: name: KA_3_7_162_3 n: 9014024762056258119250245234497203001140009014024762056258119250245234497203001140009014024762056258119250245234497203001140009014024762056258119250245234497203 skew: 0.53 deg: 5 c5: 2125 c0: -86 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3500001) Primes: RFBsize:216816, AFBsize:216441, largePrimes:7805786 encountered Relations: rels:7321063, finalFF:489799 Max relations in full relation-set: 28 Initial matrix: 433323 x 489799 with sparse part having weight 49107580. Pruned matrix : 412563 x 414793 with weight 38441893. Total sieving time: 73.32 hours. Total relation processing time: 0.31 hours. Matrix solve time: 5.20 hours. Total square root time: 0.36 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 79.19 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

8·10¹⁶³-3 = 7(9)₁₆₂7_<164> = 7 · 11 · C163
C163 = P47 · P52 · P64
P47 = 89581069649366015235300671433024669118796111357_<47>
P52 = 1328960328047374779277655762328347541585843851574289_<52>
P64 = 8727121078291846984177702899623421473981265858116567223440296757_<64>

Number: n N=1038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961 ( 163 digits) SNFS difficulty: 163 digits. Divisors found: r1=89581069649366015235300671433024669118796111357 (pp47) r2=1328960328047374779277655762328347541585843851574289 (pp52) r3=8727121078291846984177702899623421473981265858116567223440296757 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 56.88 hours. Scaled time: 68.02 units (timescale=1.196). Factorization parameters were as follows: name: KA_7_9_162_7 n: 1038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961 type: snfs skew: 0.41 deg: 5 c5: 250 c0: -3 m: 200000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2300001) Primes: RFBsize:216816, AFBsize:216651, largePrimes:7103403 encountered Relations: rels:6546431, finalFF:496607 Max relations in full relation-set: 28 Initial matrix: 433533 x 496607 with sparse part having weight 35754138. Pruned matrix : 386820 x 389051 with weight 24746569. Total sieving time: 51.96 hours. Total relation processing time: 0.26 hours. Matrix solve time: 4.31 hours. Total square root time: 0.34 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 56.88 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

May 1, 2007

By suberi / GMP-ECM 6.1.2 B1=3000000
(5·10¹⁹⁵+13)/9 = (5)₁₉₄7_<195> = C195
C195 = P39 · P157
P39 = 293923582732541876305980115142461713161_<39>
P157 = 1890136036008678464132934523184891613446562306896411362973575981503407833876886244603645696907973797637476002009415129925578694940419444733815604163115952637_<157>
(5·10¹⁷⁵+13)/9 = (5)₁₇₄7_<175> = 7 · 43 · 149 · 1499 · 14251 · C163
C163 = P31 · C133
P31 = 3245287931581745301311295513847_<31>
C133 = [1786794155374191302871466689817032767120466283217883352210266480367265472931130656381364399208145044807027729642278741101891201645531_<133>]
(5·10¹⁹⁷+13)/9 = (5)₁₉₆7_<197> = 3 · 151 · 4039753 · 51553300303_<11> · 33119551843253_<14> · C164
C164 = P31 · P133
P31 = 6580404024701852906940026053969_<31>
P133 = 2701972951016802964778536554653481812241749050896874603933106059438368263044746699896453605189606469163356710583422716412312190699563_<133>
(5·10¹⁵⁹+13)/9 = (5)₁₅₈7_<159> = 31 · 88422043643857462597_<20> · C138
C138 = P31 · C108
P31 = 1425603659062897082122821966839_<31>
C108 = [142169505031818941787456133521823682753734366848698561502053979968080314542932254864568794355447616804460409_<108>]
(5·10¹⁷⁸+13)/9 = (5)₁₇₇7_<178> = 1528613 · 9850196670187_<13> · 2526077546800091_<16> · 51897680774988553_<17> · C127
C127 = P34 · C94
P34 = 1936097886341375452565514421758559_<34>
C94 = [1453660885028921178823036658094874193257359268776143901154311382982677794100725313703259156271_<94>]