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STUDIO KAMADA

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News and updates, June 2007

Jun 30, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
9·10¹⁶²+1 = 9(0)₁₆₁1_<163> = 17 · 233 · 5693 · 199673 · 3207278521_<10> · 118788802665563673626749_<24> · C118
C118 = P51 · P68
P51 = 152599297155465124131657187052166911440245078117469_<51>
P68 = 34380518818628962059427663768446076926280486458367419362075072569669_<68>

Number: 90001_162 N=5246443007563021739957261207032237060105169135561012564450700562709375031236031853655679900656876972792186038868447761 ( 118 digits) SNFS difficulty: 162 digits. Divisors found: r1=152599297155465124131657187052166911440245078117469 (pp51) r2=34380518818628962059427663768446076926280486458367419362075072569669 (pp68) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 87.52 hours. Scaled time: 59.60 units (timescale=0.681). Factorization parameters were as follows: name: 90001_162 n: 5246443007563021739957261207032237060105169135561012564450700562709375031236031853655679900656876972792186038868447761 m: 100000000000000000000000000000000 c5: 900 c0: 1 skew: 0.26 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4350001) Primes: RFBsize:315948, AFBsize:315061, largePrimes:5796639 encountered Relations: rels:5953554, finalFF:716636 Max relations in full relation-set: 0 Initial matrix: 631072 x 716636 with sparse part having weight 34710609. Pruned matrix : 561549 x 564768 with weight 26227273. Total sieving time: 75.30 hours. Total relation processing time: 0.36 hours. Matrix solve time: 11.66 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 87.52 hours. --------- CPU info (if available) ----------

Jun 29, 2007

100...001 was updated.
Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jun 27, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(46·10¹⁶⁴-1)/9 = 5(1)_164<165> = 7 · 149 · C162
C162 = P65 · P97
P65 = 92242528670324886100687746039495178044373011581100025580286480497_<65>
P97 = 5312510652925782344961262133689200030431493691271417414388712363170017984463868615627801357604941_<97>

Number: n N=490039416213912858208160221583040374986683711515926281026952167891765207201448812187067220624267604133375945456482369234047086396079684670288697134334718227335677 ( 162 digits) SNFS difficulty: 166 digits. Divisors found: r1=92242528670324886100687746039495178044373011581100025580286480497 (pp65) r2=5312510652925782344961262133689200030431493691271417414388712363170017984463868615627801357604941 (pp97) Version: GGNFS-0.77.1-20051202-athlon Total time: 58.95 hours. Scaled time: 85.31 units (timescale=1.447). Factorization parameters were as follows: name: KA_5_1_164 n: 490039416213912858208160221583040374986683711515926281026952167891765207201448812187067220624267604133375945456482369234047086396079684670288697134334718227335677 skew: 0.74 deg: 5 c5: 23 c0: -5 m: 1000000000000000000000000000000000 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, 2600001) Primes: RFBsize:315948, AFBsize:316461, largePrimes:6886645 encountered Relations: rels:6655180, finalFF:711185 Max relations in full relation-set: 28 Initial matrix: 632474 x 711185 with sparse part having weight 40763719. Pruned matrix : 559689 x 562915 with weight 26736168. Total sieving time: 51.88 hours. Total relation processing time: 0.26 hours. Matrix solve time: 6.55 hours. Total square root time: 0.26 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 58.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 26, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(4·10¹⁶⁴-13)/9 = (4)₁₆₃3_<164> = 367 · C162
C162 = P79 · P84
P79 = 1024998888971229736671457541060040483691797694445518916330624823174235310567513_<79>
P84 = 118148448512489899718403228417122472387954784945079796830310415633311893761115829533_<84>

Number: n N=121102028458976687859521646987587042082954889494399031183772328186497123826824099303663336360884044807750529821374508023009385407205570693309112927641537995761429 ( 162 digits) SNFS difficulty: 165 digits. Divisors found: r1=1024998888971229736671457541060040483691797694445518916330624823174235310567513 (pp79) r2=118148448512489899718403228417122472387954784945079796830310415633311893761115829533 (pp84) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 72.53 hours. Scaled time: 98.93 units (timescale=1.364). Factorization parameters were as follows: name: KA_4_163_3 n: 121102028458976687859521646987587042082954889494399031183772328186497123826824099303663336360884044807750529821374508023009385407205570693309112927641537995761429 skew: 2.01 deg: 5 c5: 2 c0: -65 m: 1000000000000000000000000000000000 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, 2900001) Primes: RFBsize:315948, AFBsize:315216, largePrimes:6629143 encountered Relations: rels:6530594, finalFF:741465 Max relations in full relation-set: 28 Initial matrix: 631229 x 741465 with sparse part having weight 44081270. Pruned matrix : 534485 x 537705 with weight 27414349. Total sieving time: 66.44 hours. Total relation processing time: 0.31 hours. Matrix solve time: 5.63 hours. Total square root time: 0.15 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 72.53 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 26, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(73·10¹⁵⁷-1)/9 = 8(1)_157<158> = 3 · 557 · 12503 · 21121 · 198623 · 24027128221834955244829_<23> · C119
C119 = P48 · P71
P48 = 709366404715725202134278510977230883791091516457_<48>
P71 = 54296667246476640184537223444832866376469118179207748377776959859458053_<71>

Number: 81111_157 N=38516231632679209057909219312447870443031509684067141874491405901558633307604267425485343175874835928384687741950678221 ( 119 digits) SNFS difficulty: 158 digits. Divisors found: r1=709366404715725202134278510977230883791091516457 (pp48) r2=54296667246476640184537223444832866376469118179207748377776959859458053 (pp71) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 81.74 hours. Scaled time: 55.66 units (timescale=0.681). Factorization parameters were as follows: name: 81111_157 n: 38516231632679209057909219312447870443031509684067141874491405901558633307604267425485343175874835928384687741950678221 m: 10000000000000000000000000000000 c5: 7300 c0: -1 skew: 0.17 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 4000001) Primes: RFBsize:283146, AFBsize:284167, largePrimes:5778061 encountered Relations: rels:5850073, finalFF:638910 Max relations in full relation-set: 0 Initial matrix: 567380 x 638910 with sparse part having weight 36945897. Pruned matrix : 516655 x 519555 with weight 28801074. Total sieving time: 70.46 hours. Total relation processing time: 0.34 hours. Matrix solve time: 10.71 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 81.74 hours. --------- CPU info (if available) ----------

Jun 25, 2007 (2nd)

By Alfred Reich / GMP-ECM / Jun 24, 2007
10¹⁵⁰⁶+1 is divisible by 104384225205357273799356477841_<30>
Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jun 25, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(5·10¹⁷³-41)/9 = (5)₁₇₂1_<173> = 3 · 179 · C171
C171 = P42 · P129
P42 = 114384483875150871829057541898587264239841_<42>
P129 = 904453184672326204317688425492042339266607258173108466450183893916706681010256982023307530563855324688384934286035740785881630103_<129>

Number: n N=103455410717980550382785019656528036416304572729153734740326919097868818539209600662114628595075522449824125801779433064349265466583902338092282226360438650941444237533623 ( 171 digits) SNFS difficulty: 174 digits. Divisors found: r1=114384483875150871829057541898587264239841 (pp42) r2=904453184672326204317688425492042339266607258173108466450183893916706681010256982023307530563855324688384934286035740785881630103 (pp129) Version: GGNFS-0.77.1-20051202-athlon Total time: 204.90 hours. Scaled time: 268.42 units (timescale=1.310). Factorization parameters were as follows: name: KA_5_172_1 n: 103455410717980550382785019656528036416304572729153734740326919097868818539209600662114628595075522449824125801779433064349265466583902338092282226360438650941444237533623 skew: 1.91 deg: 5 c5: 8 c0: -205 m: 50000000000000000000000000000000000 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, 8100001) Primes: RFBsize:348513, AFBsize:348437, largePrimes:8931314 encountered Relations: rels:8460683, finalFF:782229 Max relations in full relation-set: 48 Initial matrix: 697015 x 782229 with sparse part having weight 77788583. Pruned matrix : 641763 x 645312 with weight 59397651. Total sieving time: 185.11 hours. Total relation processing time: 0.60 hours. Matrix solve time: 19.04 hours. Total square root time: 0.14 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,174,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 204.90 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 24, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(8·10¹⁶⁴+1)/9 = (8)₁₆₃9_<164> = 881 · C162
C162 = P57 · P105
P57 = 438099651139842378074782985862900871663962476527603599689_<57>
P105 = 230302504990454513418307626464605022752045200943246897387527811045552664240151617880164349500151770360321_<105>

Number: n N=100895447092949930634380123596922688863665027115651406230293857989658216672972632109976037331315424391474334720645730861394879556060032791020305208727456173540169 ( 162 digits) SNFS difficulty: 165 digits. Divisors found: r1=438099651139842378074782985862900871663962476527603599689 (pp57) r2=230302504990454513418307626464605022752045200943246897387527811045552664240151617880164349500151770360321 (pp105) Version: GGNFS-0.77.1-20051202-athlon Total time: 45.31 hours. Scaled time: 65.87 units (timescale=1.454). Factorization parameters were as follows: name: KA_8_163_9 n: 100895447092949930634380123596922688863665027115651406230293857989658216672972632109976037331315424391474334720645730861394879556060032791020305208727456173540169 skew: 1.05 deg: 5 c5: 4 c0: 5 m: 1000000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 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: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:283146, AFBsize:283197, largePrimes:5489253 encountered Relations: rels:5506229, finalFF:648965 Max relations in full relation-set: 28 Initial matrix: 566407 x 648965 with sparse part having weight 37677844. Pruned matrix : 491814 x 494710 with weight 23543322. Total sieving time: 39.96 hours. Total relation processing time: 0.18 hours. Matrix solve time: 5.09 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.5,2.5,100000 total time: 45.31 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 24, 2007 (2nd)

By JMB / GMP-ECM 6.0.1 B1=1000000
(7·10¹⁵⁹-61)/9 = (7)₁₅₈1_<159> = 3³ · 43 · 263 · 349831 · 17126917 · C141
C141 = P35 · C107
P35 = 28619057539265783684510425072387757_<35>
C107 = [14855071619085049328530992857412182242694733285669768452444236785568599716426578493792762350613756076351523_<107>]

Jun 24, 2007

11...11 (Repunit) and 100...001 were updated.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jun 23, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(16·10¹⁶³-61)/9 = 1(7)₁₆₂1_<164> = 11 · 347 · C160
C160 = P42 · P48 · P71
P42 = 646634560597002933420775479995833343960443_<42>
P48 = 398763057690552657144449211172587774514959984401_<48>
P71 = 18062650687187667320018671801554696018440996733928315494676273037001241_<71>

Number: n N=4657526271359124385060984484615608534916892265595435624254068058102640235205076703635781445579716473088231013303059412569499024830436934183331877856373533606963 ( 160 digits) SNFS difficulty: 164 digits. Divisors found: r1=646634560597002933420775479995833343960443 (pp42) r2=398763057690552657144449211172587774514959984401 (pp48) r3=18062650687187667320018671801554696018440996733928315494676273037001241 (pp71) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 57.05 hours. Scaled time: 77.82 units (timescale=1.364). Factorization parameters were as follows: name: KA_1_7_162_1 n: 4657526271359124385060984484615608534916892265595435624254068058102640235205076703635781445579716473088231013303059412569499024830436934183331877856373533606963 skew: 0.66 deg: 5 c5: 500 c0: -61 m: 200000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 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: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2300001) Primes: RFBsize:283146, AFBsize:283473, largePrimes:5594710 encountered Relations: rels:5651279, finalFF:678375 Max relations in full relation-set: 28 Initial matrix: 566685 x 678375 with sparse part having weight 40831702. Pruned matrix : 469314 x 472211 with weight 24216609. Total sieving time: 52.65 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.92 hours. Total square root time: 0.26 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.5,2.5,100000 total time: 57.05 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 22, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(25·10¹⁶³-7)/9 = 2(7)_163<164> = 3³ · 53 · C161
C161 = P52 · P109
P52 = 5784099087847801999595098935811677620966410670797411_<52>
P109 = 3356001460754311479240774153689287838703249898666255530643269682857515657144061974783366037668112153528135197_<109>

Number: n N=19411444987964904107461759453373709138908300333876853792996350648342262598027797189222765742681885239537231151486916686078111654631570774128426120040375805574967 ( 161 digits) SNFS difficulty: 164 digits. Divisors found: r1=5784099087847801999595098935811677620966410670797411 (pp52) r2=3356001460754311479240774153689287838703249898666255530643269682857515657144061974783366037668112153528135197 (pp109) Version: GGNFS-0.77.1-20051202-athlon Total time: 55.82 hours. Scaled time: 81.11 units (timescale=1.453). Factorization parameters were as follows: name: KA_2_7_163 n: 19411444987964904107461759453373709138908300333876853792996350648342262598027797189222765742681885239537231151486916686078111654631570774128426120040375805574967 skew: 0.97 deg: 5 c5: 8 c0: -7 m: 500000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 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: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2100001) Primes: RFBsize:283146, AFBsize:282602, largePrimes:5499517 encountered Relations: rels:5503640, finalFF:637582 Max relations in full relation-set: 28 Initial matrix: 565813 x 637582 with sparse part having weight 38094152. Pruned matrix : 501050 x 503943 with weight 25009807. Total sieving time: 41.68 hours. Total relation processing time: 0.19 hours. Matrix solve time: 13.81 hours. Total square root time: 0.14 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.5,2.5,100000 total time: 55.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 21, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(55·10¹⁶³-1)/9 = 6(1)_163<164> = 503 · C162
C162 = P43 · P44 · P76
P43 = 1487407993549019848776612935809194872068909_<43>
P44 = 11413058107787456233245536501918521595780953_<44>
P76 = 7156819357030125486732946829220674112434544047932731153794325074222174276381_<76>

Number: n N=121493262646344157278550916721890876960459465429644356085707974375966423680141373978352109564833222884912745747735807377954495250717914733819306383918709962447537 ( 162 digits) SNFS difficulty: 165 digits. Divisors found: r1=1487407993549019848776612935809194872068909 (pp43) r2=11413058107787456233245536501918521595780953 (pp44) r3=7156819357030125486732946829220674112434544047932731153794325074222174276381 (pp76) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 63.80 hours. Scaled time: 87.34 units (timescale=1.369). Factorization parameters were as follows: name: KA_6_1_163 n: 121493262646344157278550916721890876960459465429644356085707974375966423680141373978352109564833222884912745747735807377954495250717914733819306383918709962447537 skew: 0.56 deg: 5 c5: 88 c0: -5 m: 500000000000000000000000000000000 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, 2600001) Primes: RFBsize:250150, AFBsize:250657, largePrimes:7570457 encountered Relations: rels:7122095, finalFF:594860 Max relations in full relation-set: 28 Initial matrix: 500873 x 594860 with sparse part having weight 44530909. Pruned matrix : 429195 x 431763 with weight 29739754. Total sieving time: 58.27 hours. Total relation processing time: 0.28 hours. Matrix solve time: 4.83 hours. Total square root time: 0.42 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 63.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(16·10¹⁷³-1)/3 = 5(3)_173<174> = 67 · C172
C172 = P68 · P104
P68 = 96371276020696526133446288272274025697919084102770639532241766004453_<68>
P104 = 82599290303737453966408350950661246292450859283670030355136080034796461939594945728788702602573657900283_<104>

Number: n N=7960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199 ( 172 digits) SNFS difficulty: 174 digits. Divisors found: r1=96371276020696526133446288272274025697919084102770639532241766004453 (pp68) r2=82599290303737453966408350950661246292450859283670030355136080034796461939594945728788702602573657900283 (pp104) Version: GGNFS-0.77.1-20051202-athlon Total time: 172.53 hours. Scaled time: 206.34 units (timescale=1.196). Factorization parameters were as follows: name: KA_5_3_173 n: 7960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199 type: snfs skew: 0.29 deg: 5 c5: 500 c0: -1 m: 20000000000000000000000000000000000 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, 6100001) Primes: RFBsize:348513, AFBsize:348381, largePrimes:8606327 encountered Relations: rels:8178018, finalFF:784475 Max relations in full relation-set: 28 Initial matrix: 696960 x 784475 with sparse part having weight 56036078. Pruned matrix : 632811 x 636359 with weight 42788642. Total sieving time: 158.37 hours. Total relation processing time: 0.66 hours. Matrix solve time: 13.29 hours. Total square root time: 0.20 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,174,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000 total time: 172.53 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Jun 21, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(8·10¹⁵⁷-53)/9 = (8)₁₅₆3_<157> = 3² · 99259 · 298883603 · 412769895811232603033399_<24> · C119
C119 = P41 · P78
P41 = 91704661940135167282070266149538417976081_<41>
P78 = 879495360224213103544482307466419072309436217083572482010934548798414923507149_<78>

Number: 88883_157 N=80653824687278864260499882306813850511268547403444054213087351371389500573348614528160269592553396427774786594914503069 ( 119 digits) SNFS difficulty: 157 digits. Divisors found: r1=91704661940135167282070266149538417976081 (pp41) r2=879495360224213103544482307466419072309436217083572482010934548798414923507149 (pp78) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 62.70 hours. Scaled time: 42.70 units (timescale=0.681). Factorization parameters were as follows: name: 88883_157 n: 80653824687278864260499882306813850511268547403444054213087351371389500573348614528160269592553396427774786594914503069 m: 20000000000000000000000000000000 c5: 25 c0: -53 skew: 1.16 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:217081, largePrimes:5636168 encountered Relations: rels:5570899, finalFF:488151 Max relations in full relation-set: 0 Initial matrix: 433961 x 488151 with sparse part having weight 34548626. Pruned matrix : 409449 x 411682 with weight 26681522. Total sieving time: 55.38 hours. Total relation processing time: 0.30 hours. Matrix solve time: 6.84 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 62.70 hours. --------- CPU info (if available) ----------

Jun 20, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=203500, B1=1024000
(14·10¹⁶²-41)/9 = 1(5)₁₆₁1_<163> = 3 · 214219 · 10324063 · C150
C150 = P36 · P41 · P74
P36 = 110021344519261749564662722162683047_<36>
P41 = 34504949858484862052592280714802542174189_<41>
P74 = 61758578210491351731564901830521726152917416595997540856609496672738529267_<74>

Jun 19, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(34·10¹⁶⁰-7)/9 = 3(7)_160<161> = 37 · 739 · 1061 · 6359 · C150
C150 = P40 · P111
P40 = 1122510875599841509819333162942527354919_<40>
P111 = 182429672649887044863888718305726909178631224196066040957083526804690245217425139299330145938851723157067710419_<111>

Number: n N=204779291581617165659482935465497566962336896463508396519683855623161916137193553474407168443864391313760716948157646481601056640075903959403527201061 ( 150 digits) SNFS difficulty: 161 digits. Divisors found: r1=1122510875599841509819333162942527354919 (pp40) r2=182429672649887044863888718305726909178631224196066040957083526804690245217425139299330145938851723157067710419 (pp111) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.46 hours. Scaled time: 58.47 units (timescale=1.445). Factorization parameters were as follows: name: KA_3_7_160 n: 204779291581617165659482935465497566962336896463508396519683855623161916137193553474407168443864391313760716948157646481601056640075903959403527201061 skew: 0.73 deg: 5 c5: 34 c0: -7 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, 1800001) Primes: RFBsize:250150, AFBsize:249466, largePrimes:7231529 encountered Relations: rels:6757696, finalFF:567845 Max relations in full relation-set: 28 Initial matrix: 499682 x 567845 with sparse part having weight 37971589. Pruned matrix : 441964 x 444526 with weight 24954498. Total sieving time: 35.43 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.60 hours. Total square root time: 0.22 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 40.46 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 18, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(17·10¹⁶²-71)/9 = 1(8)₁₆₁1_<163> = 3 · 1439 · C159
C159 = P70 · P90
P70 = 2583124372509618337040968830299059261714173907429069612978604367206603_<70>
P90 = 169386598202867977225527166176651263517709056741805060006511940185061380465616968087449231_<90>

Number: n N=437546650194322188762772501479937199186677991403495225593905232543175559158880910097032404190152626566803078269374308290222119270069235322883689805163050472293 ( 159 digits) SNFS difficulty: 163 digits. Divisors found: r1=2583124372509618337040968830299059261714173907429069612978604367206603 (pp70) r2=169386598202867977225527166176651263517709056741805060006511940185061380465616968087449231 (pp90) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 57.94 hours. Scaled time: 78.51 units (timescale=1.355). Factorization parameters were as follows: name: KA_1_8_161_1 n: 437546650194322188762772501479937199186677991403495225593905232543175559158880910097032404190152626566803078269374308290222119270069235322883689805163050472293 skew: 0.53 deg: 5 c5: 1700 c0: -71 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, 2400001) Primes: RFBsize:250150, AFBsize:250202, largePrimes:7459585 encountered Relations: rels:6986844, finalFF:572535 Max relations in full relation-set: 28 Initial matrix: 500419 x 572535 with sparse part having weight 41248883. Pruned matrix : 442792 x 445358 with weight 28101844. Total sieving time: 52.51 hours. Total relation processing time: 0.27 hours. Matrix solve time: 4.81 hours. Total square root time: 0.34 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 57.94 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 17, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=11000000
4·10¹⁶⁶-3 = 3(9)₁₆₅7_<167> = 37 · 109 · 467 · 21467 · C156
C156 = P35 · P122
P35 = 10558902718487179894422921589845289_<35>
P122 = 93696796766281288719136025075673968299994681684211285870697078809182558148593470010534568057803410687480015936158750023029_<122>

Jun 17, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(83·10¹⁶¹+61)/9 = 9(2)₁₆₀9_<162> = 7 · 11 · 12377 · 19541 · C152
C152 = P55 · P98
P55 = 1253925579802704887847319737479996409450417957300062431_<55>
P98 = 39492162932172239037026100445899515906877612660361618281345600460588359473016205661201392275400531_<98>

Number: n N=49520233302386964779546750368695160262255294423154139840175164473697688657347976477513615143791891804577561756279764230158227764030719676476471830550861 ( 152 digits) SNFS difficulty: 162 digits. Divisors found: r1=1253925579802704887847319737479996409450417957300062431 (pp55) r2=39492162932172239037026100445899515906877612660361618281345600460588359473016205661201392275400531 (pp98) Version: GGNFS-0.77.1-20051202-athlon Total time: 65.76 hours. Scaled time: 95.42 units (timescale=1.451). Factorization parameters were as follows: name: KA_9_2_160_9 n: 49520233302386964779546750368695160262255294423154139840175164473697688657347976477513615143791891804577561756279764230158227764030719676476471830550861 skew: 0.59 deg: 5 c5: 830 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, 2900001) Primes: RFBsize:250150, AFBsize:249517, largePrimes:7668454 encountered Relations: rels:7187894, finalFF:565601 Max relations in full relation-set: 28 Initial matrix: 499734 x 565601 with sparse part having weight 45402229. Pruned matrix : 454050 x 456612 with weight 33560178. Total sieving time: 58.49 hours. Total relation processing time: 0.26 hours. Matrix solve time: 6.82 hours. Total square root time: 0.19 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 65.76 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 17, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8
4·10¹⁸⁰+3 = 4(0)₁₇₉3_<181> = 7 · C180
C180 = P86 · P94
P86 = 83826283922298951250679670902394172492665030066721447476491438645405060824416416839171_<86>
P94 = 6816818600216674079721080459803918316770769056707557617751767138646831184079876164364702748599_<94>

Number: 40003_180 N=571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 ( 180 digits) SNFS difficulty: 180 digits. Divisors found: r1=83826283922298951250679670902394172492665030066721447476491438645405060824416416839171 (pp86) r2=6816818600216674079721080459803918316770769056707557617751767138646831184079876164364702748599 (pp94) Version: GGNFS-0.77.1-20060513-k8 Total time: 402.02 hours. Scaled time: 805.24 units (timescale=2.003). Factorization parameters were as follows: name: 40003_180 n: 571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 m: 1000000000000000000000000000000000000 c5: 4 c0: 3 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, 8200001) Primes: RFBsize:501962, AFBsize:502056, largePrimes:6501623 encountered Relations: rels:7055323, finalFF:1224296 Max relations in full relation-set: 28 Initial matrix: 1004085 x 1224296 with sparse part having weight 64791188. Pruned matrix : 810729 x 815813 with weight 46491843. Total sieving time: 393.70 hours. Total relation processing time: 0.32 hours. Matrix solve time: 7.71 hours. Time per square root: 0.28 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: 402.02 hours. --------- CPU info (if available) ----------

P86 is the largest factor found by GGNFS so far in our tables. Congratulations!

Jun 16, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GMP-ECM 5.0 B1=555500, GGNFS-0.77.1-20051202-athlon
(64·10¹⁶¹-1)/9 = 7(1)_161<162>= 3 · 7001 · 16644197 · C151
C151 = P60 · P91
P60 = 242234408783777373086114783431817508160131008952509616569639_<60>
P91 = 8397643833649287842181389119448886552064945552482189671050550356474674679669138218340127239_<91>

Number: n N=2034198289220768944122855330305356229027758545561694863312919801308175051845084868498046294285027792142932415919483934510480134883453891368081964296721 ( 151 digits) SNFS difficulty: 162 digits. Divisors found: r1=242234408783777373086114783431817508160131008952509616569639 (pp60) r2=8397643833649287842181389119448886552064945552482189671050550356474674679669138218340127239 (pp91) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 38.61 hours. Scaled time: 52.75 units (timescale=1.366). Factorization parameters were as follows: name: KA_7_1_161 n: 2034198289220768944122855330305356229027758545561694863312919801308175051845084868498046294285027792142932415919483934510480134883453891368081964296721 skew: 0.55 deg: 5 c5: 20 c0: -1 m: 200000000000000000000000000000000 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, 1700001) Primes: RFBsize:250150, AFBsize:249621, largePrimes:7178047 encountered Relations: rels:6706081, finalFF:569137 Max relations in full relation-set: 28 Initial matrix: 499837 x 569137 with sparse part having weight 35817686. Pruned matrix : 439711 x 442274 with weight 23181566. Total sieving time: 34.90 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.38 hours. Total square root time: 0.12 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 38.61 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(4·10¹⁷¹-7)/3 = 1(3)₁₇₀1_<172> = 11 · 509 · C168
C168 = P31 · P62 · P76
P31 = 1579581662729255260822279089299_<31>
P62 = 15140952069917912762805059248526017411056580054721603176641137_<62>
P76 = 9957103032241894992392055264616753554079600537545293015777629476295758102863_<76>

Number: n N=150760019766408845647399019187174726946819254572510064535376429497480082829008432013771344824709618636211004729226783886499508955683275231 ( 138 digits) SNFS difficulty: 171 digits. Divisors found: r1=15140952069917912762805059248526017411056580054721603176641137 (pp62) r2=9957103032241894992392055264616753554079600537545293015777629476295758102863 (pp76) Version: GGNFS-0.77.1-20051202-athlon Total time: 92.21 hours. Scaled time: 122.09 units (timescale=1.324). Factorization parameters were as follows: name: KA_1_3_170_1 n: 150760019766408845647399019187174726946819254572510064535376429497480082829008432013771344824709618636211004729226783886499508955683275231 # n: 238137762695719473715544442459963088646782163481574090611418705721259748764660356015955230100613204738941477644817526939334404953265464070965053283324403167232243853069 skew: 0.71 deg: 5 c5: 40 c0: -7 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, 3700001) Primes: RFBsize:348513, AFBsize:348246, largePrimes:8112542 encountered Relations: rels:7771094, finalFF:817458 Max relations in full relation-set: 48 Initial matrix: 696825 x 817458 with sparse part having weight 48005762. Pruned matrix : 589738 x 593286 with weight 30161766. Total sieving time: 83.41 hours. Total relation processing time: 0.35 hours. Matrix solve time: 8.15 hours. Total square root time: 0.31 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 92.21 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 14, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
(4·10¹⁷⁷+41)/9 = (4)₁₇₆9_<177> = C177
C177 = P42 · P136
P42 = 168147754451668131804909254590792523405537_<42>
P136 = 2643177994816423045994801272196432548527495305343780758343199586659007613587966246673472391393843105829320609766702837229594492464461377_<136>

Number: 44449_177 N=444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 ( 177 digits) SNFS difficulty: 177 digits. Divisors found: r1=168147754451668131804909254590792523405537 (pp42) r2=2643177994816423045994801272196432548527495305343780758343199586659007613587966246673472391393843105829320609766702837229594492464461377 (pp136) Version: GGNFS-0.77.1-20050930-nocona Total time: 183.14 hours. Scaled time: 391.19 units (timescale=2.136). Factorization parameters were as follows: n: 444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 m: 200000000000000000000000000000000000 c5: 25 c0: 82 skew: 1.27 type: snfs Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [5000000, 7900001) Primes: RFBsize:664579, AFBsize:665706, largePrimes:10888385 encountered Relations: rels:11167090, finalFF:1501554 Max relations in full relation-set: 28 Initial matrix: 1330349 x 1501554 with sparse part having weight 84723705. Pruned matrix : 1171071 x 1177786 with weight 56372503. Total sieving time: 173.41 hours. Total relation processing time: 0.25 hours. Matrix solve time: 9.37 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,177,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000 total time: 183.14 hours. --------- CPU info (if available) ----------

Jun 14, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=235000, GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0 B1=148000, GGNFS-0.77.1-20060513-athlon-xp
8·10¹⁷³-3 = 7(9)₁₇₂7_<174> = 11 · 17 · C172
C172 = P32 · P141
P32 = 16714781670858896574412244553011_<32>
P141 = 255945602554216888346456751285955406140848117378586326431440585310105420050084687172161632857854573720137957976799629434184623898942614879421_<141>
(5·10¹⁶⁰-41)/9 = (5)₁₅₉1_<160> = 7 · 13 · 38339629 · C151
C151 = P59 · P92
P59 = 93930422496056102672951745999929180207457761507108874860957_<59>
P92 = 16952428477316522540754897578493590824200183248034476666556039573794818514422723747420375637_<92>

Number: n N=1592348769208513991125215662625766411590734512586468952556897748021011107359699830430311416447197781962393273577322854377674078720220820343907085304609 ( 151 digits) SNFS difficulty: 160 digits. Divisors found: r1=93930422496056102672951745999929180207457761507108874860957 (pp59) r2=16952428477316522540754897578493590824200183248034476666556039573794818514422723747420375637 (pp92) Version: GGNFS-0.77.1-20051202-athlon Total time: 34.68 hours. Scaled time: 50.01 units (timescale=1.442). Factorization parameters were as follows: name: KA_5_159_1 n: 1592348769208513991125215662625766411590734512586468952556897748021011107359699830430311416447197781962393273577322854377674078720220820343907085304609 skew: 1.52 deg: 5 c5: 5 c0: -41 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:250147, largePrimes:7174417 encountered Relations: rels:6714797, finalFF:578820 Max relations in full relation-set: 28 Initial matrix: 500362 x 578820 with sparse part having weight 36630150. Pruned matrix : 431983 x 434548 with weight 22708070. Total sieving time: 30.10 hours. Total relation processing time: 0.31 hours. Matrix solve time: 4.13 hours. Total square root time: 0.14 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: 34.68 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(16·10¹⁶¹-1)/3 = 5(3)_161<162> = 371464902031_<12> · C151
C151 = P38 · P53 · P61
P38 = 21296628673706037218941669897405375529_<38>
P53 = 18789442466366541078334745181943959375398817645988163_<53>
P61 = 3588031028791720530702891116571104480395193265875079747911009_<61>

Number: n N=67417102583019983171184801555027292869246270062017192633036181651915613927135668150787776143695353707888791386467 ( 113 digits) SNFS difficulty: 162 digits. Divisors found: r1=18789442466366541078334745181943959375398817645988163 (pp53) r2=3588031028791720530702891116571104480395193265875079747911009 (pp61) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 35.56 hours. Scaled time: 48.54 units (timescale=1.365). Factorization parameters were as follows: name: KA_5_3_161 n: 67417102583019983171184801555027292869246270062017192633036181651915613927135668150787776143695353707888791386467 # n: 1435756999967724720152252411207919472795542416216408834314647200422664077480544169773101373842224239920853631269279030738644813825332397365358703566043 skew: 0.72 deg: 5 c5: 5 c0: -1 m: 200000000000000000000000000000000 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, 1500001) Primes: RFBsize:250150, AFBsize:249616, largePrimes:7109746 encountered Relations: rels:6650928, finalFF:579476 Max relations in full relation-set: 28 Initial matrix: 499831 x 579476 with sparse part having weight 35607840. Pruned matrix : 430167 x 432730 with weight 21710821. Total sieving time: 31.47 hours. Total relation processing time: 0.37 hours. Matrix solve time: 3.37 hours. Total square root time: 0.34 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 35.56 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 13, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=11000000
4·10¹⁷⁹-3 = 3(9)₁₇₈7_<180> = 13 · 751609465955754276518902944827_<30> · C149
C149 = P31 · P118
P31 = 5440737829768967253704195829959_<31>
P118 = 7524308589497537700550163236387070963072198888286762101154838011070880004644191216696466958842086243668442125836776933_<118>

Jun 13, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(25·10¹⁷¹-1)/3 = 8(3)_171<172> = 13 · 479 · C169
C169 = P68 · P101
P68 = 29118448070168224831416797259913943918883957045985714959238024271677_<68>
P101 = 45959115678209855991045867600068525726469370895875466784175162434036104055601120929335967260638369027_<101>

Number: n N=1338258123226807986724479417590064771693164177506557464803811359134949949146191317381296504469782131577538675659761254750816337455168352871901932444729939510732830148279 ( 169 digits) SNFS difficulty: 172 digits. Divisors found: r1=29118448070168224831416797259913943918883957045985714959238024271677 (pp68) r2=45959115678209855991045867600068525726469370895875466784175162434036104055601120929335967260638369027 (pp101) Version: GGNFS-0.77.1-20051202-athlon Total time: 134.87 hours. Scaled time: 158.06 units (timescale=1.172). Factorization parameters were as follows: name: KA_8_3_171 n: 1338258123226807986724479417590064771693164177506557464803811359134949949146191317381296504469782131577538675659761254750816337455168352871901932444729939510732830148279 type: snfs skew: 0.33 deg: 5 c5: 250 c0: -1 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 special-q in [100000, 4800000) Primes: RFBsize:348513, AFBsize:348111, largePrimes:8295364 encountered Relations: rels:7898851, finalFF:788404 Max relations in full relation-set: 28 Initial matrix: 696690 x 788404 with sparse part having weight 47562588. Pruned matrix : 621809 x 625356 with weight 34416063. Total sieving time: 122.44 hours. Total relation processing time: 0.44 hours. Matrix solve time: 10.69 hours. Total square root time: 1.30 hours, sqrts: 7. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000 total time: 134.87 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Jun 12, 2007 (2nd)

By honeycrack7 / GGNFS-0.77.1-20060513-pentium4
2·10¹⁶⁶+3 = 2(0)₁₆₅3_<167> = 79 · 729941 · 1137496712761_<13> · 3151934443985899535720514258097_<31> · C116
C116 = P38 · P39 · P41
P38 = 29139773847805639821445881025078673003_<38>
P39 = 245334893549794309989767836564265608087_<39>
P41 = 13531387192579406360450949532177073435621_<41>

Number: 20003_166 N=96735931896521673246753209867323320086123873399038844839615081198086925909914926262118324884197380820104433849572081 ( 116 digits) SNFS difficulty: 166 digits. Divisors found: r1=29139773847805639821445881025078673003 (pp38) r2=245334893549794309989767836564265608087 (pp39) r3=13531387192579406360450949532177073435621 (pp41) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 149.93 hours. Scaled time: 223.25 units (timescale=1.489). Factorization parameters were as follows: n: 96735931896521673246753209867323320086123873399038844839615081198086925909914926262118324884197380820104433849572081 m: 1000000000000000000000000000000000 c5: 20 c0: 3 skew: 1 type: snfsFactor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 6300001) Primes: RFBsize:348513, AFBsize:348151, largePrimes:6025351 encountered Relations: rels:6221740, finalFF:823022 Max relations in full relation-set: 28 Initial matrix: 696730 x 823022 with sparse part having weight 62738206. Pruned matrix : 600136 x 603683 with weight 46382057. Total sieving time: 130.43 hours. Total relation processing time: 0.54 hours. Matrix solve time: 18.63 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 149.93 hours. --------- CPU info (if available) ----------

Jun 12, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0 B1=1739000
(7·10¹⁷⁰-1)/3 = 2(3)_170<171> = 311 · C168
C168 = P74 · P95
P74 = 11932010618769729868493135550576478670582273449378145996805715014527203523_<74>
P95 = 62878585748162680828932573824793216019304952212408377491474470576966134103734657544119040624561_<95>

Number: n N=750267952840300107181136120042872454448017148981779206859592711682743837084673097534833869239013933547695605573419078242229367631296891747052518756698821007502679528403 ( 168 digits) SNFS difficulty: 170 digits. Divisors found: r1=11932010618769729868493135550576478670582273449378145996805715014527203523 (pp74) r2=62878585748162680828932573824793216019304952212408377491474470576966134103734657544119040624561 (pp95) Version: GGNFS-0.77.1-20051202-athlon Total time: 89.70 hours. Scaled time: 118.41 units (timescale=1.320). Factorization parameters were as follows: name: KA_2_3_170 n: 750267952840300107181136120042872454448017148981779206859592711682743837084673097534833869239013933547695605573419078242229367631296891747052518756698821007502679528403 skew: 0.68 deg: 5 c5: 7 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, 3600001) Primes: RFBsize:348513, AFBsize:348031, largePrimes:8026856 encountered Relations: rels:7665683, finalFF:795791 Max relations in full relation-set: 48 Initial matrix: 696611 x 795791 with sparse part having weight 46042124. Pruned matrix : 608294 x 611841 with weight 29860162. Total sieving time: 80.68 hours. Total relation processing time: 0.41 hours. Matrix solve time: 8.40 hours. Total square root time: 0.21 hours, sqrts: 2. 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: 89.70 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(65·10¹⁶¹+43)/9 = 7(2)₁₆₀7_<162> = 11 · 3407 · C158
C158 = P44 · P114
P44 = 52947769774827685110950551656087356218398433_<44>
P114 = 363963939109135155217567052297823083527155953215564045576179453409875651685542451308909281653467079298253731913847_<114>

Number: n N=19271078854289890392033039523500339467465971721915367351234683198287542285194178355317187134034800603629485343603335971988745689949094704011052704918275801751 ( 158 digits) SNFS difficulty: 162 digits. Divisors found: r1=52947769774827685110950551656087356218398433 (pp44) r2=363963939109135155217567052297823083527155953215564045576179453409875651685542451308909281653467079298253731913847 (pp114) Version: GGNFS-0.77.1-20051202-athlon Total time: 51.24 hours. Scaled time: 74.29 units (timescale=1.450). Factorization parameters were as follows: name: KA_7_2_160_7 n: 19271078854289890392033039523500339467465971721915367351234683198287542285194178355317187134034800603629485343603335971988745689949094704011052704918275801751 skew: 0.58 deg: 5 c5: 650 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, 2300001) Primes: RFBsize:250150, AFBsize:249736, largePrimes:7540584 encountered Relations: rels:7113733, finalFF:609923 Max relations in full relation-set: 28 Initial matrix: 499953 x 609923 with sparse part having weight 44644601. Pruned matrix : 412583 x 415146 with weight 28053407. Total sieving time: 45.96 hours. Total relation processing time: 0.24 hours. Matrix solve time: 4.95 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 51.24 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(83·10¹⁵⁹+61)/9 = 9(2)₁₅₈9_<160> = 11 · 67 · 151901 · C152
C152 = P38 · P115
P38 = 79242765343021762777586110766574321493_<38>
P115 = 1039555880362478945347803022950014270999726058613258831222612147118945027723605412596578155237411757742769127379669_<115>

Jun 11, 2007 (2nd)

By suberi / Msieve v. 1.23
4·10¹⁸⁴+3 = 4(0)₁₈₃3_<185> = 643 · 44017 · 49859134658930905291_<20> · 3260581655841388369657396033_<28> · 5986920270178566508580072759197219_<34> · C97
C97 = P48 · P49
P48 = 598460262591086976314911215354850882063724060041_<48>
P49 = 2426330557371719231339466672548563551076810498249_<49>

Thu Jun 07 01:51:11 2007 Thu Jun 07 01:51:11 2007 Thu Jun 07 01:51:11 2007 Msieve v. 1.23 Thu Jun 07 01:51:11 2007 random seeds: 37e514e8 67c1b05e Thu Jun 07 01:51:11 2007 factoring 1451242577945435488202684730983697729965218073649465682642517742785018455031453318180555507115689620266670700586067 (115 digits) Thu Jun 07 01:51:12 2007 commencing quadratic sieve (114-digit input) Thu Jun 07 01:51:14 2007 using multiplier of 3 Thu Jun 07 01:51:14 2007 using 64kb Pentium 4 sieve core Thu Jun 07 01:51:14 2007 sieve interval: 35 blocks of size 65536 Thu Jun 07 01:51:14 2007 processing polynomials in batches of 3 Thu Jun 07 01:51:14 2007 using a sieve bound of 9160121 (306250 primes) Thu Jun 07 01:51:14 2007 using large prime bound of 1374018150 (30 bits) Thu Jun 07 01:51:14 2007 using double large prime bound of 28079309877748350 (47-55 bits) Thu Jun 07 01:51:14 2007 using trial factoring cutoff of 55 bits Thu Jun 07 01:51:14 2007 polynomial 'A' values have 15 factors Thu Jun 07 17:03:36 2007 2573 relations (2507 full + 66 combined from 147158 partial), need 306346 Thu Jun 07 17:03:36 2007 c115 factor: 1451242577945435488202684730983697729965218073649465682642517742785018455031453318180555507115689620266670700586067 Thu Jun 07 17:03:36 2007 elapsed time 15:12:25 Sun Jun 10 22:09:11 2007 Sun Jun 10 22:09:11 2007 Sun Jun 10 22:09:11 2007 Msieve v. 1.23 Sun Jun 10 22:09:11 2007 random seeds: c6371880 07cdeec2 Sun Jun 10 22:09:11 2007 factoring 1452062422497457515275178568841712183672090367974976058364101164379409367802639948011198401368209 (97 digits) Sun Jun 10 22:09:11 2007 commencing quadratic sieve (96-digit input) Sun Jun 10 22:09:12 2007 using multiplier of 1 Sun Jun 10 22:09:12 2007 using 64kb Pentium 4 sieve core Sun Jun 10 22:09:12 2007 sieve interval: 18 blocks of size 65536 Sun Jun 10 22:09:12 2007 processing polynomials in batches of 6 Sun Jun 10 22:09:12 2007 using a sieve bound of 2328947 (85882 primes) Sun Jun 10 22:09:12 2007 using large prime bound of 349342050 (28 bits) Sun Jun 10 22:09:12 2007 using double large prime bound of 2386995188843550 (43-52 bits) Sun Jun 10 22:09:12 2007 using trial factoring cutoff of 52 bits Sun Jun 10 22:09:12 2007 polynomial 'A' values have 12 factors Mon Jun 11 07:51:47 2007 86181 relations (21034 full + 65147 combined from 1292570 partial), need 85978 Mon Jun 11 07:51:49 2007 begin with 1313604 relations Mon Jun 11 07:51:52 2007 reduce to 225635 relations in 14 passes Mon Jun 11 07:51:52 2007 attempting to read 225635 relations Mon Jun 11 07:51:57 2007 recovered 225635 relations Mon Jun 11 07:51:57 2007 recovered 210860 polynomials Mon Jun 11 07:51:57 2007 attempting to build 86181 cycles Mon Jun 11 07:51:57 2007 found 86181 cycles in 6 passes Mon Jun 11 07:51:57 2007 distribution of cycle lengths: Mon Jun 11 07:51:57 2007 length 1 : 21034 Mon Jun 11 07:51:57 2007 length 2 : 15162 Mon Jun 11 07:51:57 2007 length 3 : 14263 Mon Jun 11 07:51:57 2007 length 4 : 11625 Mon Jun 11 07:51:57 2007 length 5 : 8916 Mon Jun 11 07:51:57 2007 length 6 : 6072 Mon Jun 11 07:51:57 2007 length 7 : 3792 Mon Jun 11 07:51:57 2007 length 9+: 5317 Mon Jun 11 07:51:57 2007 largest cycle: 20 relations Mon Jun 11 07:51:58 2007 matrix is 85882 x 86181 with weight 5832332 (avg 67.68/col) Mon Jun 11 07:52:00 2007 filtering completed in 3 passes Mon Jun 11 07:52:00 2007 matrix is 82073 x 82137 with weight 5580342 (avg 67.94/col) Mon Jun 11 07:52:01 2007 saving the first 48 matrix rows for later Mon Jun 11 07:52:02 2007 matrix is 82025 x 82137 with weight 4657748 (avg 56.71/col) Mon Jun 11 07:52:02 2007 matrix includes 64 packed rows Mon Jun 11 07:52:02 2007 using block size 21845 for processor cache size 512 kB Mon Jun 11 07:52:02 2007 commencing Lanczos iteration Mon Jun 11 07:53:56 2007 lanczos halted after 1299 iterations Mon Jun 11 07:53:57 2007 recovered 17 nontrivial dependencies Mon Jun 11 07:53:59 2007 prp48 factor: 598460262591086976314911215354850882063724060041 Mon Jun 11 07:53:59 2007 prp49 factor: 2426330557371719231339466672548563551076810498249 Mon Jun 11 07:53:59 2007 elapsed time 09:44:48

Jun 11, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=166500, B1=621000
(34·10¹⁶¹-43)/9 = 3(7)₁₆₀3_<162> = 11² · 62134973 · C152
C152 = P31 · P33 · P89
P31 = 4307682285413506208225521446163_<31>
P33 = 119609608489188908704802685341489_<33>
P89 = 97522581802448847543848204896401695824467527895737868563689707593989646588087900743901683_<89>

Jun 10, 2007 (4th)

By suberi / GGNFS-0.77.1-20060722-pentium4, GMP-ECM 6.1.2 B1=11000000
(4·10¹⁷¹-1)/3 = 1(3)_171<172> = 43 · 563075957 · C161
C161 = P62 · P100
P62 = 10565196783884673236263834339911427983584335421440205826081601_<62>
P100 = 5212255627583432316510330673884890259823438206542422559981296851838922765444865400476740562332250083_<100>

Number: 13333_171 N=55068506393329268228781801372382135819242644394692096548700842559697060441144881140842260739500877847149902384753995071567447570857215517700565083852457497022883 ( 161 digits) SNFS difficulty: 171 digits. Divisors found: r1=10565196783884673236263834339911427983584335421440205826081601 (pp62) r2=5212255627583432316510330673884890259823438206542422559981296851838922765444865400476740562332250083 (pp100) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 182.70 hours. Scaled time: 124.78 units (timescale=0.683). Factorization parameters were as follows: n: 55068506393329268228781801372382135819242644394692096548700842559697060441144881140842260739500877847149902384753995071567447570857215517700565083852457497022883 m: 10000000000000000000000000000000000 c5: 40 c0: -1 skew: 1 type: snfs Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [4200000, ) Primes: RFBsize:564877, AFBsize:564646, largePrimes:6291159 encountered Relations: rels:6883739, finalFF:1293233 Max relations in full relation-set: 32 Initial matrix: 1129589 x 1293233 with sparse part having weight 43585609. Pruned matrix : 977490 x 983201 with weight 30378877. Total sieving time: 140.70 hours. Total relation processing time: 0.70 hours. Matrix solve time: 41.01 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,8400000,8400000,27,27,48,48,2.6,2.6,100000 total time: 182.70 hours. --------- CPU info (if available) ----------

4·10¹⁷⁵+3 = 4(0)₁₇₄3_<176> = 17 · 6883 · 19412177 · 169757677820354209_<18> · C147
C147 = P31 · P116
P31 = 7869296226745426570552208159293_<31>
P116 = 13182377316446225748087882274614574555076488881805882086115583209285537401151576878380413502502112486527863046837877_<116>
4·10¹⁸⁴+3 = 4(0)₁₈₃3_<185> = 643 · 44017 · 49859134658930905291_<20> · 3260581655841388369657396033_<28> · C130
C130 = P34 · C97
P34 = 5986920270178566508580072759197219_<34>
C97 = [1452062422497457515275178568841712183672090367974976058364101164379409367802639948011198401368209_<97>]

Jun 10, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(65·10¹⁶⁰+43)/9 = 7(2)₁₅₉7_<161> = 1291 · 297457 · C153
C153 = P32 · P34 · P88
P32 = 17352541246944072825111665711753_<32>
P34 = 2342545412736254376314836515222427_<34>
P88 = 4626678339400851524807725560482691036987427405150010526072468457028149806517927931218291_<88>

Number: n N=188070384038043145789855963382740207328959180189136326467303443069361466091139927156978142277394156582511341411629330403090273249350352884837936146356521 ( 153 digits) SNFS difficulty: 161 digits. Divisors found: r1=17352541246944072825111665711753 (pp32) r2=2342545412736254376314836515222427 (pp34) r3=4626678339400851524807725560482691036987427405150010526072468457028149806517927931218291 (pp88) Version: GGNFS-0.77.1-20051202-athlon Total time: 39.23 hours. Scaled time: 56.69 units (timescale=1.445). Factorization parameters were as follows: name: KA_7_2_159_7 n: 188070384038043145789855963382740207328959180189136326467303443069361466091139927156978142277394156582511341411629330403090273249350352884837936146356521 skew: 0.92 deg: 5 c5: 65 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, 1700001) Primes: RFBsize:250150, AFBsize:250296, largePrimes:7171287 encountered Relations: rels:6695030, finalFF:564527 Max relations in full relation-set: 28 Initial matrix: 500512 x 564527 with sparse part having weight 35787677. Pruned matrix : 445479 x 448045 with weight 23699811. Total sieving time: 34.25 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.54 hours. Total square root time: 0.23 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 39.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 10, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000
(5·10¹⁸⁴-17)/3 = 1(6)₁₈₃1_<185> = C185
C185 = P42 · C143
P42 = 650396194789255960015809850516619718777599_<42>
C143 = [25625406175795767517350994169187890818937242743959519616955167305594370202781899645404855476406496245046648724032900205007202467374194220379739_<143>]

Jun 10, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GMP-ECM 5.0 B1=367500
6·10¹⁶⁰+1 = 6(0)₁₅₉1_<161> = 31 · 670853 · C154
C154 = P41 · P114
P41 = 27432596289301964073885280181487235430291_<41>
P114 = 105170824355437139403715973975995678497668642440971399521069843399452536718803322806044637013799975195072495150977_<114>

Number: n N=2885108765955793497955395545286278042836460061944246907992871665601660822478151672379743016630295863576285617689525078880075789883875814724662289604044307 ( 154 digits) SNFS difficulty: 160 digits. Divisors found: r1=27432596289301964073885280181487235430291 (pp41) r2=105170824355437139403715973975995678497668642440971399521069843399452536718803322806044637013799975195072495150977 (pp114) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 33.19 hours. Scaled time: 45.33 units (timescale=1.366). Factorization parameters were as follows: name: KA_6_0_159_1 n: 2885108765955793497955395545286278042836460061944246907992871665601660822478151672379743016630295863576285617689525078880075789883875814724662289604044307 skew: 0.70 deg: 5 c5: 6 c0: 1 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, 1400001) Primes: RFBsize:250150, AFBsize:250351, largePrimes:7044823 encountered Relations: rels:6590876, finalFF:582384 Max relations in full relation-set: 28 Initial matrix: 500567 x 582384 with sparse part having weight 34717814. Pruned matrix : 426273 x 428839 with weight 20692604. Total sieving time: 29.74 hours. Total relation processing time: 0.26 hours. Matrix solve time: 2.86 hours. Total square root time: 0.33 hours, sqrts: 3. 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: 33.19 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(8·10¹⁶⁰-17)/9 = (8)₁₅₉7_<160> = 6934331 · C154
C154 = P33 · P121
P33 = 968995160047131185467992972361627_<33>
P121 = 1322882591846643298048151628358822882762642650753662322011497085867674561864363575653354158395684834292581003964206621551_<121>

Jun 9, 2007 (2nd)

By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4
10¹⁷⁹+7 = 1(0)₁₇₈7_<180> = 167 · C177
C177 = P53 · P124
P53 = 60950560869098197619847712489744585923674505423726671_<53>
P124 = 9824395160130058065900701752890082125561413858734478820643602889430506537378449350699284748319422251954897604377774555118351_<124>

Number: 10007_109 N=598802395209580838323353293413173652694610778443113772455089820359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239521 ( 177 digits) SNFS difficulty: 180 digits. Divisors found: r1=60950560869098197619847712489744585923674505423726671 (pp53) r2=9824395160130058065900701752890082125561413858734478820643602889430506537378449350699284748319422251954897604377774555118351 (pp124) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 409.50 hours. Scaled time: 819.00 units (timescale=2.000). Factorization parameters were as follows: n: 598802395209580838323353293413173652694610778443113772455089820359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239521 m: 1000000000000000000000000000000000000 c5: 1 c0: 70 skew: 2.34 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 8700001) Primes: RFBsize:501962, AFBsize:503466, largePrimes:6469967 encountered Relations: rels:6943936, finalFF:1154759 Max relations in full relation-set: 28 Initial matrix: 1005492 x 1154759 with sparse part having weight 64569777. Pruned matrix : 877696 x 882787 with weight 48153746. Total sieving time: 382.49 hours. Total relation processing time: 0.69 hours. Matrix solve time: 26.02 hours. Time per square root: 0.30 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: 409.50 hours.

Jun 9, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(8·10¹⁶¹+1)/9 = (8)₁₆₀9_<161> = 2874007 · C155
C155 = P65 · P91
P65 = 20551810746861218705246366224186858134216473117184809940650521769_<65>
P91 = 1504906659159028468961208577641797976861017330391535785231117565171524456762298528051525783_<91>

Number: n N=30928556850727534375834466961593652655991752591030184995683339981040021436582753239254075890869051080560655867883720843021220508122940858838857695506270127 ( 155 digits) SNFS difficulty: 162 digits. Divisors found: r1=20551810746861218705246366224186858134216473117184809940650521769 (pp65) r2=1504906659159028468961208577641797976861017330391535785231117565171524456762298528051525783 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.08 hours. Scaled time: 50.90 units (timescale=1.451). Factorization parameters were as follows: name: KA_8_160_9 n: 30928556850727534375834466961593652655991752591030184995683339981040021436582753239254075890869051080560655867883720843021220508122940858838857695506270127 skew: 0.83 deg: 5 c5: 5 c0: 2 m: 200000000000000000000000000000000 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:249566, largePrimes:7153402 encountered Relations: rels:6692688, finalFF:576485 Max relations in full relation-set: 28 Initial matrix: 499781 x 576485 with sparse part having weight 35524689. Pruned matrix : 433288 x 435850 with weight 22114077. Total sieving time: 30.66 hours. Total relation processing time: 0.19 hours. Matrix solve time: 4.16 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 35.08 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 8, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GMP-ECM 5.0 B1=807000, GGNFS-0.77.1-20051202-athlon
8·10¹⁶¹-1 = 7(9)_161<162> = 11448961 · C155
C155 = P43 · P50 · P64
P43 = 4539588034558524737970606694078211509057811_<43>
P50 = 11816947682969491809277478418090336975083252421299_<50>
P64 = 1302573251363958712781218721583539351026194452662047110920669831_<64>

Number: n N=69875336285973897544065352305768182807156038002051015808334048827662178253555060585847047605455202441514125168213954087187474915846075464839123829664543359 ( 155 digits) SNFS difficulty: 162 digits. Divisors found: r1=4539588034558524737970606694078211509057811 (pp43) r2=11816947682969491809277478418090336975083252421299 (pp50) r3=1302573251363958712781218721583539351026194452662047110920669831 (pp64) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 39.71 hours. Scaled time: 54.29 units (timescale=1.367). Factorization parameters were as follows: name: KA_7_9_161 n: 69875336285973897544065352305768182807156038002051015808334048827662178253555060585847047605455202441514125168213954087187474915846075464839123829664543359 skew: 0.83 deg: 5 c5: 5 c0: -2 m: 200000000000000000000000000000000 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, 1700001) Primes: RFBsize:250150, AFBsize:249566, largePrimes:7182966 encountered Relations: rels:6717273, finalFF:574042 Max relations in full relation-set: 28 Initial matrix: 499781 x 574042 with sparse part having weight 36072684. Pruned matrix : 435510 x 438072 with weight 22844668. Total sieving time: 35.55 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.71 hours. Total square root time: 0.24 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 39.71 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(2·10¹⁷¹-11)/9 = (2)₁₇₀1_<171> = 13 · 23 · C168
C168 = P32 · P39 · P98
P32 = 27851033920037562716463233492393_<32>
P39 = 275686147181721751471622993232321660739_<39>
P98 = 96796584127055481810278948284165150853864843387232107130793898378385677491078494178075979521903877_<98>

Number: n N=26685477338339329039543211617052433617893367389355907405472169844555157404025928817956271993597584603028709449313596895296724931762785103 ( 137 digits) SNFS difficulty: 171 digits. Divisors found: r1=275686147181721751471622993232321660739 (pp39) r2=96796584127055481810278948284165150853864843387232107130793898378385677491078494178075979521903877 (pp98) Version: GGNFS-0.77.1-20051202-athlon Total time: 109.28 hours. Scaled time: 144.57 units (timescale=1.323). Factorization parameters were as follows: name: KA_2_170_1 n: 26685477338339329039543211617052433617893367389355907405472169844555157404025928817956271993597584603028709449313596895296724931762785103 # n: 743218134522482348569305091044221479004087699739873652917131178000743218134522482348569305091044221479004087699739873652917131178000743218134522482348569305091044221479 skew: 0.89 deg: 5 c5: 20 c0: -11 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, 4300001) Primes: RFBsize:348513, AFBsize:348817, largePrimes:8249964 encountered Relations: rels:7870823, finalFF:800899 Max relations in full relation-set: 48 Initial matrix: 697396 x 800899 with sparse part having weight 47329242. Pruned matrix : 610868 x 614418 with weight 32155254. Total sieving time: 98.90 hours. Total relation processing time: 0.35 hours. Matrix solve time: 9.69 hours. Total square root time: 0.33 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 109.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 8, 2007

By suberi / GMP-ECM 6.1.2 B1=11000000
4·10¹⁶³+3 = 4(0)₁₆₂3_<164> = 1316989799426812351_<19> · C146
C146 = P40 · P106
P40 = 9122825587223042642884812944337703070033_<40>
P106 = 3329263796544560932998781161768664065173476621162459775686753155158211188126981055831370511645586167117741_<106>
4·10¹⁶⁹+3 = 4(0)₁₆₈3_<170> = 23 · 43 · 2695744223_<10> · C158
C158 = P37 · P122
P37 = 1095863878505531791352248008590604473_<37>
P122 = 13690786705166299346121105341688039593329430814257896520268003985603036085194932170203623925361810203165403423559971573513_<122>
4·10¹⁷⁶+3 = 4(0)₁₇₅3_<177> = 13² · 14479 · 1727839 · C164
C164 = P38 · C127
P38 = 30175961085952909008534878737421283007_<38>
C127 = [3135236706631199341096636684750581017076426724373352960266683033160613553116178668067537726925834017042340630910117649030813861_<127>]

Jun 7, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8
2·10¹⁷¹+3 = 2(0)₁₇₀3_<172> = 8627 · C168
C168 = P41 · P127
P41 = 41713247973026961742658321646485423054431_<41>
P127 = 5557713951456074967962531890753686473889384220379793822875068616831334165905093911472798378503095080109303609626110094430409519_<127>

Number: 20003_171 N=231830300220238785209226845948765503651327228468760867045322823693056682508403848382983655963834473165642749507360612031992581430392952358873304740929639503883157528689 ( 168 digits) SNFS difficulty: 171 digits. Divisors found: r1=41713247973026961742658321646485423054431 (pp41) r2=5557713951456074967962531890753686473889384220379793822875068616831334165905093911472798378503095080109303609626110094430409519 (pp127) Version: GGNFS-0.77.1-20060513-k8 Total time: 206.25 hours. Scaled time: 413.12 units (timescale=2.003). Factorization parameters were as follows: name: 20003_171 n: 231830300220238785209226845948765503651327228468760867045322823693056682508403848382983655963834473165642749507360612031992581430392952358873304740929639503883157528689 m: 10000000000000000000000000000000000 c5: 20 c0: 3 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, 9300001) Primes: RFBsize:412849, AFBsize:412656, largePrimes:6353030 encountered Relations: rels:6686637, finalFF:976860 Max relations in full relation-set: 28 Initial matrix: 825571 x 976860 with sparse part having weight 78469523. Pruned matrix : 705516 x 709707 with weight 60130180. Total sieving time: 198.00 hours. Total relation processing time: 0.35 hours. Matrix solve time: 7.61 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 206.25 hours. --------- CPU info (if available) ----------

Jun 7, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(13·10¹⁷¹-1)/3 = 4(3)_171<172> = 7 · C171
C171 = P80 · P92
P80 = 41301678601887909281508978574307473779381336266973146191783297973077225039301321_<80>
P92 = 14988437274298150142827003772114850577864102899199141349041142889289160609017099225061284139_<92>

Number: n N=619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619 ( 171 digits) SNFS difficulty: 172 digits. Divisors found: r1=41301678601887909281508978574307473779381336266973146191783297973077225039301321 (pp80) r2=14988437274298150142827003772114850577864102899199141349041142889289160609017099225061284139 (pp92) Version: GGNFS-0.77.1-20051202-athlon Total time: 136.44 hours. Scaled time: 163.05 units (timescale=1.195). Factorization parameters were as follows: name: KA_4_3_171 n: 619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619 type: snfs skew: 0.38 deg: 5 c5: 130 c0: -1 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 special-q in [100000, 4800000) Primes: RFBsize:348513, AFBsize:349036, largePrimes:8355279 encountered Relations: rels:7958858, finalFF:790913 Max relations in full relation-set: 28 Initial matrix: 697616 x 790913 with sparse part having weight 49108257. Pruned matrix : 622652 x 626204 with weight 35955650. Total sieving time: 124.32 hours. Total relation processing time: 0.58 hours. Matrix solve time: 11.17 hours. Total square root time: 0.38 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000 total time: 136.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(4·10¹⁶¹-13)/9 = (4)₁₆₀3_<161> = 7 · 77867 · C155
C155 = P54 · P102
P54 = 319550413044553780518507753936684693865291403825034473_<54>
P102 = 255168238619378957640510165325532105096040257500576497491031577087931802511480908975140897813777669839_<102>

Number: n N=81539116046673805416276552958330861678878168533606652450321783929088692338849658381680932954257982832346811953063638630053157388228727820596006091787359847 ( 155 digits) SNFS difficulty: 161 digits. Divisors found: r1=319550413044553780518507753936684693865291403825034473 (pp54) r2=255168238619378957640510165325532105096040257500576497491031577087931802511480908975140897813777669839 (pp102) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.78 hours. Scaled time: 58.92 units (timescale=1.445). Factorization parameters were as follows: name: KA_4_160_3 n: 81539116046673805416276552958330861678878168533606652450321783929088692338849658381680932954257982832346811953063638630053157388228727820596006091787359847 skew: 0.80 deg: 5 c5: 40 c0: -13 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, 1800001) Primes: RFBsize:250150, AFBsize:250286, largePrimes:7303690 encountered Relations: rels:6857429, finalFF:592319 Max relations in full relation-set: 28 Initial matrix: 500502 x 592319 with sparse part having weight 38801200. Pruned matrix : 421594 x 424160 with weight 23783758. Total sieving time: 35.81 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.32 hours. Total square root time: 0.43 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 40.78 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 6, 2007 (3rd)

By suberi / Msieve 1.22
4·10¹⁵⁹+3 = 4(0)₁₅₈3_<160> = 17 · 29 · 409 · 4108499 · 39134819 · 417437569 · 3210493232143522115233150147270451_<34> · C98
C98 = P46 · P53
P46 = 2111007970395248522288822270407200076593257339_<46>
P53 = 43610401448779057354383384061999544768111674794916639_<53>

Wed Jun 06 13:02:36 2007 Wed Jun 06 13:02:36 2007 Wed Jun 06 13:02:36 2007 Msieve v. 1.22 Wed Jun 06 13:02:36 2007 random seeds: 1e082aa8 9c72287f Wed Jun 06 13:02:36 2007 factoring 92061905050509083573242674474131090797477960189592323155314191961704503438069174058130179979963621 (98 digits) Wed Jun 06 13:02:37 2007 commencing quadratic sieve (98-digit input) Wed Jun 06 13:02:37 2007 using multiplier of 5 Wed Jun 06 13:02:37 2007 using 64kb Opteron sieve core Wed Jun 06 13:02:37 2007 sieve interval: 18 blocks of size 65536 Wed Jun 06 13:02:37 2007 processing polynomials in batches of 6 Wed Jun 06 13:02:37 2007 using a sieve bound of 2542703 (92941 primes) Wed Jun 06 13:02:37 2007 using large prime bound of 381405450 (28 bits) Wed Jun 06 13:02:37 2007 using double large prime bound of 2795737419206850 (43-52 bits) Wed Jun 06 13:02:37 2007 using trial factoring cutoff of 52 bits Wed Jun 06 13:02:37 2007 polynomial 'A' values have 13 factors Wed Jun 06 21:05:02 2007 93287 relations (22735 full + 70552 combined from 1389878 partial), need 93037 Wed Jun 06 21:05:26 2007 begin with 1412613 relations Wed Jun 06 21:05:28 2007 reduce to 242711 relations in 10 passes Wed Jun 06 21:05:28 2007 attempting to read 242711 relations Wed Jun 06 21:05:33 2007 recovered 242711 relations Wed Jun 06 21:05:33 2007 recovered 229853 polynomials Wed Jun 06 21:05:34 2007 attempting to build 93287 cycles Wed Jun 06 21:05:34 2007 found 93287 cycles in 6 passes Wed Jun 06 21:05:34 2007 distribution of cycle lengths: Wed Jun 06 21:05:34 2007 length 1 : 22735 Wed Jun 06 21:05:34 2007 length 2 : 16342 Wed Jun 06 21:05:34 2007 length 3 : 15825 Wed Jun 06 21:05:34 2007 length 4 : 12688 Wed Jun 06 21:05:34 2007 length 5 : 9623 Wed Jun 06 21:05:34 2007 length 6 : 6425 Wed Jun 06 21:05:34 2007 length 7 : 4104 Wed Jun 06 21:05:34 2007 length 9+: 5545 Wed Jun 06 21:05:34 2007 largest cycle: 20 relations Wed Jun 06 21:05:34 2007 matrix is 92941 x 93287 with weight 6011165 (avg 64.44/col) Wed Jun 06 21:05:35 2007 filtering completed in 3 passes Wed Jun 06 21:05:35 2007 matrix is 91290 x 91354 with weight 5815830 (avg 63.66/col) Wed Jun 06 21:05:36 2007 saving the first 48 matrix rows for later Wed Jun 06 21:05:36 2007 matrix is 91242 x 91354 with weight 4375853 (avg 47.90/col) Wed Jun 06 21:05:36 2007 matrix includes 64 packed rows Wed Jun 06 21:05:36 2007 using block size 10922 for processor cache size 256 kB Wed Jun 06 21:05:36 2007 commencing Lanczos iteration Wed Jun 06 21:07:07 2007 lanczos halted after 1445 iterations Wed Jun 06 21:07:07 2007 recovered 15 nontrivial dependencies Wed Jun 06 21:07:08 2007 prp46 factor: 2111007970395248522288822270407200076593257339 Wed Jun 06 21:07:08 2007 prp53 factor: 43610401448779057354383384061999544768111674794916639 Wed Jun 06 21:07:08 2007 elapsed time 08:04:32

4·10¹⁶¹+3 = 4(0)₁₆₀3_<162> = 93187 · 34563163 · 1429384127_<10> · 174991800857_<12> · 5565980346411937268388128381439563107_<37> · C92
C92 = P39 · P54
P39 = 700131433832122433345260550981903682611_<39>
P54 = 127409931013861119158868865095362078118650478133953821_<54>

Wed Jun 06 13:03:32 2007 Wed Jun 06 13:03:32 2007 Wed Jun 06 13:03:32 2007 Msieve v. 1.22 Wed Jun 06 13:03:32 2007 random seeds: 42a4d6dc 17b79130 Wed Jun 06 13:03:32 2007 factoring 89203697685186390047288507359292435046300468270991492132748857979599129994346738197714706631 (92 digits) Wed Jun 06 13:03:33 2007 commencing quadratic sieve (92-digit input) Wed Jun 06 13:03:33 2007 using multiplier of 31 Wed Jun 06 13:03:33 2007 using 64kb Pentium 4 sieve core Wed Jun 06 13:03:33 2007 sieve interval: 18 blocks of size 65536 Wed Jun 06 13:03:33 2007 processing polynomials in batches of 6 Wed Jun 06 13:03:33 2007 using a sieve bound of 1854623 (69412 primes) Wed Jun 06 13:03:33 2007 using large prime bound of 209572399 (27 bits) Wed Jun 06 13:03:33 2007 using double large prime bound of 951483630575481 (42-50 bits) Wed Jun 06 13:03:33 2007 using trial factoring cutoff of 50 bits Wed Jun 06 13:03:33 2007 polynomial 'A' values have 12 factors Wed Jun 06 17:47:55 2007 69664 relations (17315 full + 52349 combined from 897404 partial), need 69508 Wed Jun 06 17:47:58 2007 begin with 914719 relations Wed Jun 06 17:47:59 2007 reduce to 178248 relations in 10 passes Wed Jun 06 17:47:59 2007 attempting to read 178248 relations Wed Jun 06 17:48:03 2007 recovered 178248 relations Wed Jun 06 17:48:03 2007 recovered 161681 polynomials Wed Jun 06 17:48:03 2007 attempting to build 69664 cycles Wed Jun 06 17:48:03 2007 found 69664 cycles in 6 passes Wed Jun 06 17:48:03 2007 distribution of cycle lengths: Wed Jun 06 17:48:03 2007 length 1 : 17315 Wed Jun 06 17:48:03 2007 length 2 : 12552 Wed Jun 06 17:48:03 2007 length 3 : 12009 Wed Jun 06 17:48:03 2007 length 4 : 9448 Wed Jun 06 17:48:03 2007 length 5 : 6958 Wed Jun 06 17:48:03 2007 length 6 : 4647 Wed Jun 06 17:48:03 2007 length 7 : 2820 Wed Jun 06 17:48:03 2007 length 9+: 3915 Wed Jun 06 17:48:03 2007 largest cycle: 19 relations Wed Jun 06 17:48:04 2007 matrix is 69412 x 69664 with weight 4316925 (avg 61.97/col) Wed Jun 06 17:48:05 2007 filtering completed in 3 passes Wed Jun 06 17:48:05 2007 matrix is 68116 x 68180 with weight 4166475 (avg 61.11/col) Wed Jun 06 17:48:05 2007 saving the first 48 matrix rows for later Wed Jun 06 17:48:05 2007 matrix is 68068 x 68180 with weight 3190313 (avg 46.79/col) Wed Jun 06 17:48:05 2007 matrix includes 64 packed rows Wed Jun 06 17:48:05 2007 using block size 21845 for processor cache size 512 kB Wed Jun 06 17:48:06 2007 commencing Lanczos iteration Wed Jun 06 17:49:11 2007 lanczos halted after 1078 iterations Wed Jun 06 17:49:11 2007 recovered 17 nontrivial dependencies Wed Jun 06 17:49:13 2007 prp39 factor: 700131433832122433345260550981903682611 Wed Jun 06 17:49:13 2007 prp54 factor: 127409931013861119158868865095362078118650478133953821 Wed Jun 06 17:49:13 2007 elapsed time 04:45:41

Jun 6, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(16·10¹⁶⁰-7)/9 = 1(7)_160<161> = 19 · 23603 · C155
C155 = P56 · P100
P56 = 16770759996905604146905291574126233673996019246169099349_<56>
P100 = 2363762954520662154675832128367503145931432005400900847902652199986102917164639275903970666869960389_<100>

Number: n N=39642101199842521752983625582336272547374169157305556113022603678341017706887790307159388253004809330164938394935919782226117058665106749984452863435686761 ( 155 digits) SNFS difficulty: 161 digits. Divisors found: r1=16770759996905604146905291574126233673996019246169099349 (pp56) r2=2363762954520662154675832128367503145931432005400900847902652199986102917164639275903970666869960389 (pp100) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 31.87 hours. Scaled time: 43.51 units (timescale=1.365). Factorization parameters were as follows: name: KA_1_7_160 n: 39642101199842521752983625582336272547374169157305556113022603678341017706887790307159388253004809330164938394935919782226117058665106749984452863435686761 skew: 1.70 deg: 5 c5: 1 c0: -14 m: 200000000000000000000000000000000 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, 1400001) Primes: RFBsize:250150, AFBsize:250091, largePrimes:7003207 encountered Relations: rels:6534990, finalFF:569860 Max relations in full relation-set: 28 Initial matrix: 500305 x 569860 with sparse part having weight 31858690. Pruned matrix : 436112 x 438677 with weight 19800703. Total sieving time: 28.59 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.98 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 31.87 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 6, 2007

By suberi / GMP-ECM 6.1.2 B1=5000000
4·10¹⁵⁹+3 = 4(0)₁₅₈3_<160> = 17 · 29 · 409 · 4108499 · 39134819 · 417437569 · C132
C132 = P34 · C98
P34 = 3210493232143522115233150147270451_<34>
C98 = [92061905050509083573242674474131090797477960189592323155314191961704503438069174058130179979963621_<98>]
4·10¹⁷⁰+3 = 4(0)₁₆₉3_<171> = 13 · 2332022449008725190543961_<25> · C146
C146 = P31 · C115
P31 = 9091674957193157331925985427613_<31>
C115 = [1451242577945435488202684730983697729965218073649465682642517742785018455031453318180555507115689620266670700586067_<115>]
4·10¹⁶¹+3 = 4(0)₁₆₀3_<162> = 93187 · 34563163 · 1429384127_<10> · 174991800857_<12> · C129
C129 = P37 · C92
P37 = 5565980346411937268388128381439563107_<37>
C92 = [89203697685186390047288507359292435046300468270991492132748857979599129994346738197714706631_<92>]

Jun 5, 2007 (5th)

By suberi / GMP-ECM 6.1.2 B1=5000000
4·10¹⁶⁵+3 = 4(0)₁₆₄3_<166> = 47 · 2239 · 64301 · 5622060993572083_<16> · C141
C141 = P32 · P109
P32 = 17162193244336712083651773667387_<32>
P109 = 6126634498248786631325750859569676596678356085694049608225501662771812141931771359526911934006293383097455871_<109>

Jun 5, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(46·10¹⁶⁰-1)/9 = 5(1)_160<161> = 3 · 16361 · C157
C157 = P56 · P101
P56 = 63188612413904730140907248034497209619568206489435363729_<56>
P101 = 16479552118993128813473617476831373281686860448323688740205309001943172664096989506162049716810356373_<101>

Number: n N=1041320031601799219915471978304323515496426687674166434633398755396188315936497587985883322354198217531754601615857040342096267773182387203535055133368194917 ( 157 digits) SNFS difficulty: 161 digits. Divisors found: r1=63188612413904730140907248034497209619568206489435363729 (pp56) r2=16479552118993128813473617476831373281686860448323688740205309001943172664096989506162049716810356373 (pp101) Version: GGNFS-0.77.1-20051202-athlon Total time: 42.51 hours. Scaled time: 61.64 units (timescale=1.450). Factorization parameters were as follows: name: KA_5_1_160 n: 1041320031601799219915471978304323515496426687674166434633398755396188315936497587985883322354198217531754601615857040342096267773182387203535055133368194917 skew: 0.46 deg: 5 c5: 46 c0: -1 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:250556, largePrimes:7300603 encountered Relations: rels:6822189, finalFF:562929 Max relations in full relation-set: 28 Initial matrix: 500772 x 562929 with sparse part having weight 39004994. Pruned matrix : 449144 x 451711 with weight 26733692. Total sieving time: 37.13 hours. Total relation processing time: 0.22 hours. Matrix solve time: 5.08 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 42.51 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 5, 2007 (3rd)

By Torbjorn Granlund / GMP-ECM P-1 B1=100000000 / May 25, 2007
10⁹²⁶+1 = 1(0)₉₂₅1_<927> = 101 · 62969 · 118529 · 15103061 · C907
C907 = P29 · C879
P29 = 35034118330919297779082305261_<29>
By Yousuke Koide / GMP-ECM B1=1000000 / May 26, 2007
10¹⁰⁵⁵+1 = 1(0)₁₀₅₄1_<1056> = 11 · 9091 · 14771 · 177196221721_<12> · 8708337574089530396491_<22> · 2708591227536778275869251_<25> · 9376657450882829279982731_<25> · 2764617069785703725933625413_<28> · P183 · C754
C754 = P32 · C722
P32 = 19178509602144721723538217992641_<32>
By Yousuke Koide / GMP-ECM B1=1000000 / May 26, 2007
(10¹¹⁴⁹-1)/9 = (1)_1149<1149> = 3 · 37 · 34471 · 852559 · 145364587 · 1628675880394909638591813700831880313095925587_<46> · 23181229247696012268805890210990826546682789683_<47> · C285 · C752
C752 = P33 · P719
P33 = 347266658845989451344982160757667_<33>
By Yousuke Koide / GMP-ECM B1=5000000 / May 29, 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> · 234065099292222402013296307835793151_<36> · 5440907236518498609451112390256369995629321_<43> · 8414640003465161203119978906558054839526493_<43> · P143 · C232
C232 = P35 · P198
P35 = 41766848698222033158540558591648271_<35>
By Yousuke Koide / GMP-ECM B1=1250000 / May 30, 2007
(10⁷⁸⁷-1)/9 = (1)_787<787> = 26759 · 213141637 · 1074022836653095912870566750079013_<34> · C741
C741 = P40 · C702
P40 = 1629242936815583422402932260494746089387_<40>
By Yousuke Koide / GMP-ECM B1=1250000 / May 31, 2007
(10⁸⁵³-1)/9 = (1)_853<853> = 5119 · 13649 · 34505557 · 872209561 · 258392363336333_<15> · C814
C814 = P32 · C782
P32 = 87440115231123175885662305449333_<32>
By Yousuke Koide / GMP-ECM B1=1000000 / Jun 2, 2007
(10¹³¹¹-1)/9 = (1)_1311<1311> = 3 · 37 · 277 · 21319 · 23599 · 81283 · 10749631 · 9021705647077_<13> · 203864078068831_<15> · 1111111111111111111_<19> · 11111111111111111111111_<23> · 2152970896196020817900437_<25> · 3931123022305129377976519_<25> · 1595352086329224644348978893_<28> · C363 · C780
C780 = P33 · C747
P33 = 933052229529582992021083478515963_<33>
By Yousuke Koide / GMP-ECM B1=1000000 / Jun 2, 2007
(10¹⁴⁰⁷-1)/9 = (1)_1407<1407> = 3 · 37 · 43 · 239 · 1609 · 1933 · 4649 · 493121 · 10838689 · 1695022306115797_<16> · 2046166739518832881_<19> · 25877379396467255119_<20> · 79863595778924342083_<20> · 28213380943176667001263153660999177245677_<41> · 184976479633092931103313037835504355363361_<42> · 1479324487468932812154772125499257696540643946328553680234277466780839_<70> · C396 · C758
C758 = P35 · C723
P35 = 39184667823173817016379582631270559_<35>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 5, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
9·10¹⁷⁴+1 = 9(0)₁₇₃1_<175> = C175
C175 = P64 · P112
P64 = 6701858154129508946109631584557125937056799890919240999671909373_<64>
P112 = 1342911143897373658594292493986198100072281134132513257099614367422167831910468286290583725850693432647730948437_<112>

Number: 90001_174 N=9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 ( 175 digits) SNFS difficulty: 175 digits. Divisors found: r1=6701858154129508946109631584557125937056799890919240999671909373 (pp64) r2=1342911143897373658594292493986198100072281134132513257099614367422167831910468286290583725850693432647730948437 (pp112) Version: GGNFS-0.77.1-20050930-nocona Total time: 173.62 hours. Scaled time: 162.16 units (timescale=0.934). Factorization parameters were as follows: n: 9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 m: 100000000000000000000000000000000000 c5: 9 c0: 10 skew: 1.02 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, 7200001) Primes: RFBsize:602489, AFBsize:602235, largePrimes:10103196 encountered Relations: rels:10291943, finalFF:1454570 Max relations in full relation-set: 28 Initial matrix: 1204788 x 1454570 with sparse part having weight 67687049. Pruned matrix : 966267 x 972354 with weight 40422034. Total sieving time: 167.46 hours. Total relation processing time: 0.29 hours. Matrix solve time: 5.78 hours. Time per square root: 0.09 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: 173.62 hours. --------- CPU info (if available) ----------

Jun 5, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
8·10¹⁶⁰-1 = 7(9)_160<161> = 939359 · C155
C155 = P40 · P55 · P61
P40 = 7430283334715190763428010216563200237119_<40>
P55 = 8371325514886127521657093908547021699702744768728781303_<55>
P61 = 1369174436449288928232717093121729013383869942151960421280473_<61>

Number: n N=85164457890966073673643410027476183227072929518959205160114503613634403886054213564781941728348799553738240651337773950108531456024799890137849320653764961 ( 155 digits) SNFS difficulty: 160 digits. Divisors found: r1=7430283334715190763428010216563200237119 (pp40) r2=8371325514886127521657093908547021699702744768728781303 (pp55) r3=1369174436449288928232717093121729013383869942151960421280473 (pp61) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 37.67 hours. Scaled time: 51.49 units (timescale=1.367). Factorization parameters were as follows: name: KA_7_9_160 n: 85164457890966073673643410027476183227072929518959205160114503613634403886054213564781941728348799553738240651337773950108531456024799890137849320653764961 skew: 0.66 deg: 5 c5: 8 c0: -1 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, 1500001) Primes: RFBsize:250150, AFBsize:249851, largePrimes:7325544 encountered Relations: rels:6965044, finalFF:662712 Max relations in full relation-set: 28 Initial matrix: 500066 x 662712 with sparse part having weight 42447996. Pruned matrix : 358049 x 360613 with weight 22237841. Total sieving time: 34.43 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.83 hours. Total square root time: 0.20 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: 37.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 4, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(14·10¹⁷⁰-41)/9 = 1(5)₁₆₉1_<171> = 89 · C169
C169 = P47 · P122
P47 = 23562871960702446576109209737209512980072163311_<47>
P122 = 74176663773255644917317906830538807621668868770340406914332112105118853831007147436387613726854741316452945435326628021369_<122>

Number: n N=1747815230961298377028714107365792759051186017478152309612983770287141073657927590511860174781523096129837702871410736579275905118601747815230961298377028714107365792759 ( 169 digits) SNFS difficulty: 171 digits. Divisors found: r1=23562871960702446576109209737209512980072163311 (pp47) r2=74176663773255644917317906830538807621668868770340406914332112105118853831007147436387613726854741316452945435326628021369 (pp122) Version: GGNFS-0.77.1-20051202-athlon Total time: 101.58 hours. Scaled time: 134.39 units (timescale=1.323). Factorization parameters were as follows: name: KA_1_5_169_1 n: 1747815230961298377028714107365792759051186017478152309612983770287141073657927590511860174781523096129837702871410736579275905118601747815230961298377028714107365792759 skew: 1.24 deg: 5 c5: 14 c0: -41 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, 4000001) Primes: RFBsize:348513, AFBsize:349737, largePrimes:8140106 encountered Relations: rels:7766379, finalFF:797968 Max relations in full relation-set: 48 Initial matrix: 698316 x 797968 with sparse part having weight 47933037. Pruned matrix : 612389 x 615944 with weight 31910090. Total sieving time: 91.84 hours. Total relation processing time: 0.33 hours. Matrix solve time: 9.19 hours. Total square root time: 0.22 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000 total time: 101.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 3, 2007 (2nd)

By Robert Backstrom / GMP-ECM 5.0 B1=1175000, GGNFS-0.77.1-20051202-athlon
4·10¹⁵⁹-3 = 3(9)₁₅₈7_<160> = 7 · 80177 · C154
C154 = P37 · P118
P37 = 6869025736566408403013738614059587089_<37>
P118 = 1037569042972137310167842357523279974289448792553913560988035736213951007069294488349444811458102522621741991129070107_<118>
(55·10¹⁵⁹-1)/9 = 6(1)_159<160> = 3 · 7 · 2879 · C154
C154 = P46(1033...) · P46(5512...) · P65
P46(1033...) = 1033119730398606727874017412985081979328287301_<46>
P46(5512...) = 5512969028825793796895660458496810276891422129_<46>
P65 = 17746920835907189395385191131490589648783353079850430487298717601_<65>

Number: n N=101078600557586316530394335187666205380689576590931227957973355680893020246962588053244531188261650227610630528310278223442516599862900661789164741578774229 ( 156 digits) SNFS difficulty: 161 digits. Divisors found: r1=1033119730398606727874017412985081979328287301 (pp46) r2=5512969028825793796895660458496810276891422129 (pp46) r3=17746920835907189395385191131490589648783353079850430487298717601 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.00 hours. Scaled time: 42.05 units (timescale=1.450). Factorization parameters were as follows: name: KA_6_1_159 n: 101078600557586316530394335187666205380689576590931227957973355680893020246962588053244531188261650227610630528310278223442516599862900661789164741578774229 skew: 0.71 deg: 5 c5: 11 c0: -2 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, 1400001) Primes: RFBsize:250150, AFBsize:250187, largePrimes:6962438 encountered Relations: rels:6492622, finalFF:567417 Max relations in full relation-set: 28 Initial matrix: 500404 x 567417 with sparse part having weight 32876452. Pruned matrix : 437769 x 440335 with weight 20727804. Total sieving time: 24.93 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.75 hours. Total square root time: 0.13 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 29.00 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 3, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8
(82·10¹⁶⁴-1)/9 = 9(1)_164<165> = 23 · 29 · C163
C163 = P56 · P108
P56 = 11722798638770736454179599031506665643455103982980173427_<56>
P108 = 116523683202366287222326406187442967335215483093587034853875156598506211825703054134781180379470982769675879_<108>

Number: 91111_164 N=1365983674829252040646343494919207063135099117108112610361485923704814259536898217557887722805264034649341995668832250541395968682325503914709312010661335998667333 ( 163 digits) SNFS difficulty: 166 digits. Divisors found: r1=11722798638770736454179599031506665643455103982980173427 (pp56) r2=116523683202366287222326406187442967335215483093587034853875156598506211825703054134781180379470982769675879 (pp108) Version: GGNFS-0.77.1-20060513-k8 Total time: 94.93 hours. Scaled time: 190.15 units (timescale=2.003). Factorization parameters were as follows: name: 91111_164 n: 1365983674829252040646343494919207063135099117108112610361485923704814259536898217557887722805264034649341995668832250541395968682325503914709312010661335998667333 m: 1000000000000000000000000000000000 c5: 41 c0: -5 skew: 1 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5400001) Primes: RFBsize:348513, AFBsize:348787, largePrimes:5848756 encountered Relations: rels:6000231, finalFF:794384 Max relations in full relation-set: 28 Initial matrix: 697365 x 794384 with sparse part having weight 49085999. Pruned matrix : 622750 x 626300 with weight 35785753. Total sieving time: 90.29 hours. Total relation processing time: 0.20 hours. Matrix solve time: 4.20 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 94.93 hours. --------- CPU info (if available) ----------

Jun 2, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(8·10¹⁵⁷-17)/9 = (8)₁₅₆7_<157> = 7 · C129
8739994595235952825155053837_<28> · C129
C129 = P64 · P66
P64 = 1097338309267008237239239772614316948193823367920986887082646889_<64>
P66 = 132402971590214069443001363228800248580081550757875671603997677837_<66>

Number: n N=145290852986733231960131889761460491703794538807068334652232282714626655166495302127159129035785015114582751752183571455452299093 ( 129 digits) SNFS difficulty: 157 digits. Divisors found: r1=1097338309267008237239239772614316948193823367920986887082646889 (pp64) r2=132402971590214069443001363228800248580081550757875671603997677837 (pp66) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 33.76 hours. Scaled time: 46.21 units (timescale=1.369). Factorization parameters were as follows: name: KA_8_156_7 n: 145290852986733231960131889761460491703794538807068334652232282714626655166495302127159129035785015114582751752183571455452299093 skew: 0.93 deg: 5 c5: 25 c0: -17 m: 20000000000000000000000000000000 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, 1400001) Primes: RFBsize:250150, AFBsize:250611, largePrimes:7095641 encountered Relations: rels:6625206, finalFF:569684 Max relations in full relation-set: 28 Initial matrix: 500825 x 569684 with sparse part having weight 34217548. Pruned matrix : 439147 x 441715 with weight 21728785. Total sieving time: 30.25 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.08 hours. Total square root time: 0.22 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 33.76 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(4·10¹⁵⁸-13)/9 = (4)₁₅₇3_<158> = 131 · 173 · 100467687810755071_<18> · C137
C137 = P53 · P84
P53 = 24842867387305405261100498732839983321474852653757937_<53>
P84 = 785727502087926126786887826591860692223274703506416827388958712572751463133189766243_<84>

Number: n N=19519724136929079694548208428483677843768554481542628710715214750048789472954415174850519785238780109629364396557689211568718844535920691 ( 137 digits) SNFS difficulty: 158 digits. Divisors found: r1=24842867387305405261100498732839983321474852653757937 (pp53) r2=785727502087926126786887826591860692223274703506416827388958712572751463133189766243 (pp84) Version: GGNFS-0.77.1-20051202-athlon Total time: 27.07 hours. Scaled time: 39.06 units (timescale=1.443). Factorization parameters were as follows: name: KA_4_157_3 n: 19519724136929079694548208428483677843768554481542628710715214750048789472954415174850519785238780109629364396557689211568718844535920691 skew: 0.64 deg: 5 c5: 125 c0: -13 m: 20000000000000000000000000000000 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 sp