News and updates, August 2007

Since June 16, 2000

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News and updates, August 2007	2007-09-02(Sun) 13:02

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News and updates, August 2007

Aug 31, 2007: By Sinkiti Sibata / GGNFS
3·10¹⁴⁸-7 = 2(9)₁₄₇3_<149> = 41 · 293 · 23176583 · C138
C138 = P45 · P93
P45 = 420246714641792212696158791990420325985853003_<45>
P93 = 256398832799819491996337343700283603386076585422635350041027234530711778924253071751054434289_<93>

Number: 29993_148 N=107750767122114335539918675404254523033081059324968763324951362955270960653144758698026016767014068999370645903693836817954006385276819867 ( 138 digits) SNFS difficulty: 148 digits. Divisors found: r1=420246714641792212696158791990420325985853003 (pp45) r2=256398832799819491996337343700283603386076585422635350041027234530711778924253071751054434289 (pp93) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 25.94 hours. Scaled time: 17.71 units (timescale=0.683). Factorization parameters were as follows: name: 29993_148 n: 107750767122114335539918675404254523033081059324968763324951362955270960653144758698026016767014068999370645903693836817954006385276819867 m: 100000000000000000000000000000 c5: 3000 c0: -7 skew: 0.3 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3150001) Primes: RFBsize:114155, AFBsize:114337, largePrimes:2805135 encountered Relations: rels:2752699, finalFF:257378 Max relations in full relation-set: 0 Initial matrix: 228559 x 257378 with sparse part having weight 32600512. Pruned matrix : 220942 x 222148 with weight 25462064. Total sieving time: 23.64 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.99 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 25.94 hours. --------- CPU info (if available) ----------
Aug 30, 2007: By Sinkiti Sibata / GGNFS
3·10¹⁵⁰-7 = 2(9)₁₄₉3_<151> = 83 · 189651047 · C141
C141 = P53 · P89
P53 = 16655019752526043619345197086882937152885261185068417_<53>
P89 = 11443075559040216743203773330203910152796400883206795006697965100458043235549364132362629_<89>

Number: 29993_150 N=190584649465462808903938036705578268690445781961768618815589675746482134493536309892422886710060193892941055624300006842351026644099218988293 ( 141 digits) SNFS difficulty: 150 digits. Divisors found: r1=16655019752526043619345197086882937152885261185068417 (pp53) r2=11443075559040216743203773330203910152796400883206795006697965100458043235549364132362629 (pp89) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 32.25 hours. Scaled time: 22.03 units (timescale=0.683). Factorization parameters were as follows: name: 29993_150 n: 190584649465462808903938036705578268690445781961768618815589675746482134493536309892422886710060193892941055624300006842351026644099218988293 m: 1000000000000000000000000000000 c5: 3 c0: -7 skew: 1.18 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 1750001) Primes: RFBsize:114155, AFBsize:113722, largePrimes:2720694 encountered Relations: rels:2701121, finalFF:257590 Max relations in full relation-set: 0 Initial matrix: 227942 x 257590 with sparse part having weight 18606649. Pruned matrix : 217974 x 219177 with weight 14397030. Total sieving time: 30.84 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.19 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 32.25 hours. --------- CPU info (if available) ----------
Aug 28, 2007 (2nd): By Jo Yeong Uk / GGNFS snfs, GMP-ECM
2·10¹⁷⁰-7 = 1(9)₁₆₉3_<171> = C171
C171 = P50 · P56 · P66
P50 = 12830114637211177323355529618441346334457779697621_<50>
P56 = 21211698624128416961087313467823336589027450130654173021_<56>
P66 = 734892831044394689750114258247584690226884187718469681813063218073_<66>

Number: 19993_170 N=199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 171 digits) SNFS difficulty: 170 digits. Divisors found: r1=12830114637211177323355529618441346334457779697621 (pp50) r2=21211698624128416961087313467823336589027450130654173021 (pp56) r3=734892831044394689750114258247584690226884187718469681813063218073 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 75.19 hours. Scaled time: 161.22 units (timescale=2.144). Factorization parameters were as follows: n: 199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 m: 10000000000000000000000000000000000 c5: 2 c0: -7 skew: 1.28 type: snfs Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [3600000, 7100001) Primes: RFBsize:489319, AFBsize:488568, largePrimes:6562233 encountered Relations: rels:7021806, finalFF:1101502 Max relations in full relation-set: 28 Initial matrix: 977952 x 1101502 with sparse part having weight 56019192. Pruned matrix : 870570 x 875523 with weight 39881257. Total sieving time: 70.10 hours. Total relation processing time: 0.14 hours. Matrix solve time: 4.88 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,7200000,7200000,27,27,49,49,2.6,2.6,100000 total time: 75.19 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
3·10¹³⁷-7 = 2(9)₁₃₆3_<138> = 233 · 701 · 5477 · 21661 · 488603 · C119
C119 = P52 · P67
P52 = 6476427849686591970532300943502577690100886356016287_<52>
P67 = 4892540299472487410211328047955667103685004673915706548024083374513_<67>

Number: 29993_137 N=31686184251217596357918040854365672841886369996089982649246803699536335662325290122709751508408702299412468090548693231 ( 119 digits) SNFS difficulty: 137 digits. Divisors found: r1=6476427849686591970532300943502577690100886356016287 (pp52) r2=4892540299472487410211328047955667103685004673915706548024083374513 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.06 hours. Scaled time: 8.71 units (timescale=2.144). Factorization parameters were as follows: n: 31686184251217596357918040854365672841886369996089982649246803699536335662325290122709751508408702299412468090548693231 m: 1000000000000000000000000000 c5: 300 c0: -7 skew: 0.47 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [700000, 1450001) Primes: RFBsize:107126, AFBsize:107463, largePrimes:1828766 encountered Relations: rels:1902577, finalFF:244082 Max relations in full relation-set: 28 Initial matrix: 214655 x 244082 with sparse part having weight 14922660. Pruned matrix : 203114 x 204251 with weight 10251762. Total sieving time: 3.87 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.14 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000 total time: 4.06 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
3·10¹⁶⁰-7 = 2(9)₁₅₉3_<161> = 127 · 40829 · 1767818010311_<13> · 16453710424472833724720213_<26> · C117
C117 = P42 · P76
P42 = 156576499347676290337540161614647420749481_<42>
P76 = 1270342440851204099715174694929205958381506676212657967303937958146615630937_<76>
3·10¹⁴⁶-7 = 2(9)₁₄₅3_<147> = C147
C147 = P46 · P102
P46 = 1854775915575395694657042218355139211068315081_<46>
P102 = 161744606170893075229127752358828695970725053902533763048339214947771986894331414501673269180172824753_<102>

Number: 29993_146 N=299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 147 digits) SNFS difficulty: 146 digits. Divisors found: r1=1854775915575395694657042218355139211068315081 (pp46) r2=161744606170893075229127752358828695970725053902533763048339214947771986894331414501673269180172824753 (pp102) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.47 hours. Scaled time: 24.54 units (timescale=2.139). Factorization parameters were as follows: n: 299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 m: 100000000000000000000000000000 c5: 30 c0: -7 skew: 0.75 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1650001) Primes: RFBsize:135072, AFBsize:134628, largePrimes:3935573 encountered Relations: rels:4115354, finalFF:442086 Max relations in full relation-set: 28 Initial matrix: 269767 x 442086 with sparse part having weight 44669293. Pruned matrix : 216898 x 218310 with weight 21091258. Total sieving time: 11.13 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.25 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 11.47 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
Aug 28, 2007: By Sinkiti Sibata / GGNFS snfs
3·10¹³³-7 = 2(9)₁₃₂3_<134> = 19 · 23 · 29 · 41 · 4133 · 845895553 · 15285736889_<11> · C106
C106 = P50 · P56
P50 = 63642234051349873089290850183434749198604956677859_<50>
P56 = 16976338245683764819391125937000990768709124738416339799_<56>

Number: 29993_133 N=1080412091966688465073393571002351107257249643609478820582139591078383292048067595486362712519605523810341 ( 106 digits) SNFS difficulty: 133 digits. Divisors found: r1=63642234051349873089290850183434749198604956677859 (pp50) r2=16976338245683764819391125937000990768709124738416339799 (pp56) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 6.23 hours. Scaled time: 4.26 units (timescale=0.683). Factorization parameters were as follows: name: 29993_133 n: 1080412091966688465073393571002351107257249643609478820582139591078383292048067595486362712519605523810341 m: 100000000000000000000000000 c5: 3000 c0: -7 skew: 0.3 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:63898, largePrimes:1485231 encountered Relations: rels:1478487, finalFF:143556 Max relations in full relation-set: 0 Initial matrix: 127916 x 143556 with sparse part having weight 8668341. Pruned matrix : 123225 x 123928 with weight 6769206. Total sieving time: 5.87 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.23 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.23 hours. --------- CPU info (if available) ----------
3·10¹⁴⁰-7 = 2(9)₁₃₉3_<141> = 163 · 257 · 22303 · 277717378709055933498757_<24> · C109
C109 = P38 · P71
P38 = 37093886403445655363232597242736014387_<38>
P71 = 31169644391610806846824618395203670558943768245441618617177544108945299_<71>

Number: 29993_140 N=1156203248298208234556461217638104374790212162863416385692985595553452438217200154827872278873776193460016713 ( 109 digits) SNFS difficulty: 140 digits. Divisors found: r1=37093886403445655363232597242736014387 (pp38) r2=31169644391610806846824618395203670558943768245441618617177544108945299 (pp71) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 11.33 hours. Scaled time: 7.74 units (timescale=0.683). Factorization parameters were as follows: name: 29993_140 n: 1156203248298208234556461217638104374790212162863416385692985595553452438217200154827872278873776193460016713 m: 10000000000000000000000000000 c5: 3 c0: -7 skew: 1.18 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1600001) Primes: RFBsize:78498, AFBsize:63643, largePrimes:1541967 encountered Relations: rels:1525645, finalFF:159967 Max relations in full relation-set: 0 Initial matrix: 142206 x 159967 with sparse part having weight 16090240. Pruned matrix : 137684 x 138459 with weight 12233010. Total sieving time: 10.69 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.48 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 11.33 hours. --------- CPU info (if available) ----------
Aug 27, 2007 (4th): By Jo Yeong Uk / GGNFS snfs
3·10¹²⁸-7 = 2(9)₁₂₇3_<129> = 41 · 59 · 54773 · C121
C121 = P46 · P75
P46 = 7537788328018616405984189140699812345322214029_<46>
P75 = 300382702420089950889070923665817867552296755414839069498484220494663049491_<75>

Number: 29993_128 N=2264221228240843430860612299610477719961224154829802377186244279416764084156061387777267380382909546467657520568921509239 ( 121 digits) SNFS difficulty: 129 digits. Divisors found: r1=7537788328018616405984189140699812345322214029 (pp46) r2=300382702420089950889070923665817867552296755414839069498484220494663049491 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.00 hours. Scaled time: 4.28 units (timescale=2.143). Factorization parameters were as follows: n: 2264221228240843430860612299610477719961224154829802377186244279416764084156061387777267380382909546467657520568921509239 m: 20000000000000000000000000 c5: 375 c0: -28 skew: 0.6 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78556, largePrimes:1541786 encountered Relations: rels:1589228, finalFF:219946 Max relations in full relation-set: 28 Initial matrix: 157121 x 219946 with sparse part having weight 11082418. Pruned matrix : 127164 x 128013 with weight 5146045. Total sieving time: 1.92 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.00 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
Aug 27, 2007 (3rd): By Sinkiti Sibata / GGNFS snfs
3·10¹²⁴-7 = 2(9)₁₂₃3_<125> = 499 · 50123 · 4979165454103_<13> · C105
C105 = P29 · P76
P29 = 32069277584934255341895947641_<29>
P76 = 7511694512964920660213222237541918019312926923461518825741959466812334839383_<76>

Number: 29993_124 N=240894616469499568232342324414062368452631433109656235581566054386083610865203017018054074083650312745503 ( 105 digits) SNFS difficulty: 125 digits. Divisors found: r1=32069277584934255341895947641 (pp29) r2=7511694512964920660213222237541918019312926923461518825741959466812334839383 (pp76) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 3.48 hours. Scaled time: 2.38 units (timescale=0.683). Factorization parameters were as follows: name: 29993_124 n: 240894616469499568232342324414062368452631433109656235581566054386083610865203017018054074083650312745503 m: 10000000000000000000000000 c5: 3 c0: -70 skew: 1.88 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 700001) Primes: RFBsize:49098, AFBsize:63523, largePrimes:2122134 encountered Relations: rels:2121787, finalFF:127648 Max relations in full relation-set: 0 Initial matrix: 112686 x 127648 with sparse part having weight 11268270. Pruned matrix : 108940 x 109567 with weight 8489035. Total sieving time: 3.12 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.23 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.48 hours. --------- CPU info (if available) ----------
Aug 27, 2007 (2nd): By Jo Yeong Uk / GGNFS snfs, GMP-ECM
3·10¹⁰²-7 = 2(9)₁₀₁3_<103> = 5503 · C99
C99 = P43 · P57
P43 = 3539577321355187357058316586614016942558507_<43>
P57 = 154017595180034784335600556931964288371618563510589261333_<57>

Number: 29993_102 N=545157186988915137197892058876976194802834817372342358713429038706160276212974741050336180265309831 ( 99 digits) SNFS difficulty: 102 digits. Divisors found: r1=3539577321355187357058316586614016942558507 (pp43) r2=154017595180034784335600556931964288371618563510589261333 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.35 hours. Scaled time: 0.76 units (timescale=2.144). Factorization parameters were as follows: n: 545157186988915137197892058876976194802834817372342358713429038706160276212974741050336180265309831 m: 100000000000000000000 c5: 300 c0: -7 skew: 0.47 type: snfs Factor base limits: 240000/240000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [120000, 195001) Primes: RFBsize:21221, AFBsize:21254, largePrimes:888627 encountered Relations: rels:745957, finalFF:50115 Max relations in full relation-set: 28 Initial matrix: 42541 x 50115 with sparse part having weight 1437684. Pruned matrix : 37570 x 37846 with weight 922534. Total sieving time: 0.34 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,240000,240000,25,25,43,43,2.1,2.1,15000 total time: 0.35 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
3·10¹⁰⁷-7 = 2(9)₁₀₆3_<108> = 73² · 31957 · C100
C100 = P30 · P34 · P37
P30 = 277589851523296053332037672941_<30>
P34 = 1002459894818158467774433246518331_<34>
P37 = 6330513515041898460559917424038309211_<37>

Number: 29993_107 N=1761609046186588232628906784240055920987324559373280100718000725465837400560765961236391885739829381 ( 100 digits) SNFS difficulty: 107 digits. Divisors found: r1=277589851523296053332037672941 (pp30) r2=1002459894818158467774433246518331 (pp34) r3=6330513515041898460559917424038309211 (pp37) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.45 hours. Scaled time: 0.95 units (timescale=2.129). Factorization parameters were as follows: n: 1761609046186588232628906784240055920987324559373280100718000725465837400560765961236391885739829381 m: 1000000000000000000000 c5: 300 c0: -7 skew: 0.47 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 260001) Primes: RFBsize:30757, AFBsize:30684, largePrimes:962858 encountered Relations: rels:879575, finalFF:80338 Max relations in full relation-set: 28 Initial matrix: 61507 x 80338 with sparse part having weight 3456094. Pruned matrix : 53164 x 53535 with weight 1683537. Total sieving time: 0.42 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,107,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.45 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
3·10¹¹¹-7 = 2(9)₁₁₀3_<112> = 23 · 373003 · C105
C105 = P44 · P62
P44 = 27835335642957025433655367694790412609627019_<44>
P62 = 12562747515193989773402390442014510943362606451247158043351463_<62>

Number: 29993_111 N=349688293683149068972402483299761314427008338550488403811649026252149271675050054965171628762981157978797 ( 105 digits) SNFS difficulty: 111 digits. Divisors found: r1=27835335642957025433655367694790412609627019 (pp44) r2=12562747515193989773402390442014510943362606451247158043351463 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.69 hours. Scaled time: 1.46 units (timescale=2.124). Factorization parameters were as follows: n: 349688293683149068972402483299761314427008338550488403811649026252149271675050054965171628762981157978797 m: 10000000000000000000000 c5: 30 c0: -7 skew: 0.75 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 320001) Primes: RFBsize:30757, AFBsize:30494, largePrimes:1020947 encountered Relations: rels:931251, finalFF:80704 Max relations in full relation-set: 28 Initial matrix: 61318 x 80704 with sparse part having weight 3972837. Pruned matrix : 55579 x 55949 with weight 2017566. Total sieving time: 0.66 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.69 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
3·10¹²⁹-7 = 2(9)₁₂₈3_<130> = C130
C130 = P29 · P48 · P55
P29 = 13634014563100632163485094139_<29>
P48 = 139215960043020963366563162682325387847822463557_<48>
P55 = 1580550856695477889083277991070258583743421455170186591_<55>

Number: 29993_129 N=2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 130 digits) SNFS difficulty: 130 digits. Divisors found: r1=13634014563100632163485094139 (pp29) r2=139215960043020963366563162682325387847822463557 (pp48) r3=1580550856695477889083277991070258583743421455170186591 (pp55) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.83 hours. Scaled time: 6.07 units (timescale=2.146). Factorization parameters were as follows: n: 2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 m: 100000000000000000000000000 c5: 3 c0: -70 skew: 1.88 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 1100001) Primes: RFBsize:78498, AFBsize:78021, largePrimes:1578298 encountered Relations: rels:1600735, finalFF:197381 Max relations in full relation-set: 28 Initial matrix: 156584 x 197381 with sparse part having weight 12021455. Pruned matrix : 141849 x 142695 with weight 6882715. Total sieving time: 2.73 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.83 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
3·10¹¹⁶-7 = 2(9)₁₁₅3_<117> = 5711 · C113
C113 = P43 · P71
P43 = 3219174617934997967729103654362313099113789_<43>
P71 = 16317910987225509303709497983754427492567247926719168101616013003489667_<71>

Number: 29993_116 N=52530204867798984416039222552967956575030642619506216074242689546489231308002101208194711959376641568902118718263 ( 113 digits) SNFS difficulty: 116 digits. Divisors found: r1=3219174617934997967729103654362313099113789 (pp43) r2=16317910987225509303709497983754427492567247926719168101616013003489667 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.83 hours. Scaled time: 1.78 units (timescale=2.145). Factorization parameters were as follows: n: 52530204867798984416039222552967956575030642619506216074242689546489231308002101208194711959376641568902118718263 m: 100000000000000000000000 c5: 30 c0: -7 skew: 0.75 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 420001) Primes: RFBsize:49098, AFBsize:48776, largePrimes:1881701 encountered Relations: rels:1830654, finalFF:116660 Max relations in full relation-set: 28 Initial matrix: 97941 x 116660 with sparse part having weight 9492117. Pruned matrix : 92238 x 92791 with weight 6099665. Total sieving time: 0.77 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.83 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
3·10¹⁴⁹-7 = 2(9)₁₄₈3_<150> = 179 · 521 · 3463 · 5282612227_<10> · 35419352915554933199557_<23> · C109
C109 = P35 · P75
P35 = 21272798033221076607577777047006013_<35>
P75 = 233380215802854007300467394780726271343697166092228509059711875575719508047_<75>
3·10¹²⁶-7 = 2(9)₁₂₅3_<127> = 17 · C126
C126 = P37 · P89
P37 = 1947761627248864935777984869025486217_<37>
P89 = 90601737793013067707297429917950567899839201443202358104654069381901149336940160966925537_<89>

Number: 29993_126 N=176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529 ( 126 digits) SNFS difficulty: 126 digits. Divisors found: r1=1947761627248864935777984869025486217 (pp37) r2=90601737793013067707297429917950567899839201443202358104654069381901149336940160966925537 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.98 hours. Scaled time: 4.25 units (timescale=2.144). Factorization parameters were as follows: n: 176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529 m: 10000000000000000000000000 c5: 30 c0: -7 skew: 0.75 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:77956, largePrimes:1553141 encountered Relations: rels:1599584, finalFF:219775 Max relations in full relation-set: 28 Initial matrix: 156521 x 219775 with sparse part having weight 11340321. Pruned matrix : 126978 x 127824 with weight 5262878. Total sieving time: 1.91 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.98 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
3·10¹⁶⁷-7 = 2(9)₁₆₆3_<168> = C168
C168 = P42 · P126
P42 = 655467036657994741996643867126553366964783_<42>
P126 = 457688919841947776110399176672643492197644369408954631966772160173721908536961345672536829147905758344010973197701056308278871_<126>
Aug 27, 2007: By Sinkiti Sibata / GGNFS gnfs, snfs
3·10¹³¹-7 = 2(9)₁₃₀3_<132> = 67 · 73 · 1019 · 116345861 · 977792987 · 556928995904051921_<18> · C90
C90 = P35 · P56
P35 = 59726562069597109314324525106720499_<35>
P56 = 15906850721045874492067807848099118867247459356850020189_<56>

Number: 29993_131 N=950061506922361956173978053504580512762590466557036500602670856517685312193088447730154311 ( 90 digits) Divisors found: r1=59726562069597109314324525106720499 (pp35) r2=15906850721045874492067807848099118867247459356850020189 (pp56) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 4.36 hours. Scaled time: 2.98 units (timescale=0.683). Factorization parameters were as follows: name: 29993_131 n: 950061506922361956173978053504580512762590466557036500602670856517685312193088447730154311 m: 576763940886060425848 deg: 4 c4: 8585376 c3: 46043290 c2: -8500336392011611 c1: -3690164694860894122 c0: -277517425059888154185 skew: 1635.250 type: gnfs # adj. I(F,S) = 51.668 # E(F1,F2) = 1.698649e-04 # GGNFS version 0.77.1-20060722-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1188125202. # maxskew=2000.0 # These parameters should be manually set: rlim: 700000 alim: 700000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.4 alambda: 2.4 qintsize: 40000 type: gnfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [350000, 710001) Primes: RFBsize:56543, AFBsize:56519, largePrimes:1558747 encountered Relations: rels:1522078, finalFF:127569 Max relations in full relation-set: 0 Initial matrix: 113135 x 127569 with sparse part having weight 11105184. Pruned matrix : 108854 x 109483 with weight 7940686. Polynomial selection time: 0.17 hours. Total sieving time: 3.84 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.22 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,89,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000 total time: 4.36 hours. --------- CPU info (if available) ----------
3·10¹¹⁷-7 = 2(9)₁₁₆3_<118> = 65663146013_<11> · 1115445346207_<13> · C95
C95 = P33 · P63
P33 = 218367804382939724096025924452209_<33>
P63 = 187569691815535808504272490616328250324358050799297959129311747_<63>

Number: 29993_117 N=40959181770543213619060402870043933276823141622498530960829661372304663576743954789636163799123 ( 95 digits) Divisors found: r1=218367804382939724096025924452209 (pp33) r2=187569691815535808504272490616328250324358050799297959129311747 (pp63) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 10.53 hours. Scaled time: 7.19 units (timescale=0.683). Factorization parameters were as follows: name: 29993_117 n: 40959181770543213619060402870043933276823141622498530960829661372304663576743954789636163799123 m: 5448565826898695520624 deg: 4 c4: 46475328 c3: 101344500712 c2: -472255512414059034 c1: -394563556785377973 c0: 235363264286578010957443 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.318 # E(F1,F2) = 3.772756e-05 # GGNFS version 0.77.1-20060722-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1188142345. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1440001) Primes: RFBsize:92938, AFBsize:92847, largePrimes:1898276 encountered Relations: rels:1986717, finalFF:212386 Max relations in full relation-set: 0 Initial matrix: 185859 x 212386 with sparse part having weight 15227931. Pruned matrix : 173280 x 174273 with weight 11148304. Polynomial selection time: 0.17 hours. Total sieving time: 9.50 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.66 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 10.53 hours. --------- CPU info (if available) ----------
3·10¹²²-7 = 2(9)₁₂₁3_<123> = 227 · 541 · 5821 · 2440113394861_<13> · C102
C102 = P47 · P55
P47 = 83874866130091704225931620360708407017715883677_<47>
P55 = 2050494856118000514981197734640153342657783824277403827_<55>

Number: 29993_122 N=171984981557338943720876089963265461754031849148782559859775844954175603505748020782384283778686631879 ( 102 digits) SNFS difficulty: 122 digits. Divisors found: r1=83874866130091704225931620360708407017715883677 (pp47) r2=2050494856118000514981197734640153342657783824277403827 (pp55) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.62 hours. Scaled time: 1.79 units (timescale=0.683). Factorization parameters were as follows: name: 29993_122 n: 171984981557338943720876089963265461754031849148782559859775844954175603505748020782384283778686631879 m: 1000000000000000000000000 c5: 300 c0: -7 skew: 0.47 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 600001) Primes: RFBsize:49098, AFBsize:64153, largePrimes:2107885 encountered Relations: rels:2154235, finalFF:132169 Max relations in full relation-set: 0 Initial matrix: 113317 x 132169 with sparse part having weight 7558650. Pruned matrix : 105278 x 105908 with weight 5324836. Total sieving time: 2.35 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.15 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.62 hours. --------- CPU info (if available) ----------
3·10¹²³-7 = 2(9)₁₂₂3_<124> = 41 · 73 · 25229 · 80436896303091941_<17> · C99
C99 = P47 · P53
P47 = 25717660438571745381489038333885826323571075209_<47>
P53 = 19205593766110280619993552722286434599284651570080801_<53>

Number: 29993_123 N=493922938997974498580414521518774754063241395387693330419187722978244874523656899408600794577962409 ( 99 digits) SNFS difficulty: 123 digits. Divisors found: r1=25717660438571745381489038333885826323571075209 (pp47) r2=19205593766110280619993552722286434599284651570080801 (pp53) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.60 hours. Scaled time: 1.78 units (timescale=0.683). Factorization parameters were as follows: name: 29993_123 n: 493922938997974498580414521518774754063241395387693330419187722978244874523656899408600794577962409 m: 1000000000000000000000000 c5: 3000 c0: -7 skew: 0.3 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 600001) Primes: RFBsize:49098, AFBsize:63898, largePrimes:2059050 encountered Relations: rels:2063041, finalFF:130571 Max relations in full relation-set: 0 Initial matrix: 113063 x 130571 with sparse part having weight 8675304. Pruned matrix : 106089 x 106718 with weight 6142343. Total sieving time: 2.31 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.17 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.60 hours. --------- CPU info (if available) ----------
Aug 26, 2007 (2nd): By Sinkiti Sibata / Msieve v. 1.26, GGNFS
3·10¹⁰⁹-7 = 2(9)₁₀₈3_<110> = 83 · 56809 · 16216515547_<11> · 1243071210473_<13> · C81
C81 = P37 · P45
P37 = 2248059687775148500471809593908702163_<37>
P45 = 140399198593424783364159287344550310097264723_<45>

Sun Aug 26 13:50:58 2007 Msieve v. 1.26 Sun Aug 26 13:50:58 2007 random seeds: 1451f000 cc105488 Sun Aug 26 13:50:58 2007 factoring 315625778553815587004811754086956831579675851159971598797911152419592933173695849 (81 digits) Sun Aug 26 13:50:59 2007 commencing quadratic sieve (81-digit input) Sun Aug 26 13:50:59 2007 using multiplier of 41 Sun Aug 26 13:50:59 2007 using 64kb Pentium 2 sieve core Sun Aug 26 13:50:59 2007 sieve interval: 6 blocks of size 65536 Sun Aug 26 13:50:59 2007 processing polynomials in batches of 17 Sun Aug 26 13:50:59 2007 using a sieve bound of 1317713 (50343 primes) Sun Aug 26 13:50:59 2007 using large prime bound of 129135874 (26 bits) Sun Aug 26 13:50:59 2007 using trial factoring cutoff of 27 bits Sun Aug 26 13:50:59 2007 polynomial 'A' values have 10 factors Sun Aug 26 15:12:14 2007 50617 relations (26609 full + 24008 combined from 267360 partial), need 50439 Sun Aug 26 15:12:16 2007 begin with 293969 relations Sun Aug 26 15:12:16 2007 reduce to 71642 relations in 2 passes Sun Aug 26 15:12:16 2007 attempting to read 71642 relations Sun Aug 26 15:12:19 2007 recovered 71642 relations Sun Aug 26 15:12:19 2007 recovered 60192 polynomials Sun Aug 26 15:12:19 2007 attempting to build 50617 cycles Sun Aug 26 15:12:19 2007 found 50617 cycles in 1 passes Sun Aug 26 15:12:19 2007 distribution of cycle lengths: Sun Aug 26 15:12:19 2007 length 1 : 26609 Sun Aug 26 15:12:19 2007 length 2 : 24008 Sun Aug 26 15:12:19 2007 largest cycle: 2 relations Sun Aug 26 15:12:19 2007 matrix is 50343 x 50617 with weight 1561449 (avg 30.85/col) Sun Aug 26 15:12:22 2007 filtering completed in 4 passes Sun Aug 26 15:12:22 2007 matrix is 42140 x 42204 with weight 1269497 (avg 30.08/col) Sun Aug 26 15:12:24 2007 saving the first 48 matrix rows for later Sun Aug 26 15:12:24 2007 matrix is 42092 x 42204 with weight 1011189 (avg 23.96/col) Sun Aug 26 15:12:24 2007 matrix includes 64 packed rows Sun Aug 26 15:12:24 2007 commencing Lanczos iteration Sun Aug 26 15:15:12 2007 lanczos halted after 667 iterations Sun Aug 26 15:15:13 2007 recovered 13 nontrivial dependencies Sun Aug 26 15:15:13 2007 prp37 factor: 2248059687775148500471809593908702163 Sun Aug 26 15:15:13 2007 prp45 factor: 140399198593424783364159287344550310097264723 Sun Aug 26 15:15:13 2007 elapsed time 01:24:15
3·10¹⁰¹-7 = 2(9)₁₀₀3_<102> = 61 · 270538861909140599_<18> · C83
C83 = P34 · P50
P34 = 1503944237661379360868402573256481_<34>
P50 = 12087320199218433786007971497669328028718661880027_<50>

Number: 29993_101 N=18178655562382559504603600172348702425295980655038020769681684834586255227122204987 ( 83 digits) Divisors found: r1=1503944237661379360868402573256481 (pp34) r2=12087320199218433786007971497669328028718661880027 (pp50) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.70 hours. Scaled time: 1.84 units (timescale=0.683). Factorization parameters were as follows: name: 29993_101 n: 18178655562382559504603600172348702425295980655038020769681684834586255227122204987 m: 13520163201302496320 deg: 4 c4: 544044 c3: 1525702999 c2: -2090212604885881 c1: -5785762335682389 c0: 1219195069438556895867 skew: 1379.250 type: gnfs # adj. I(F,S) = 47.935 # E(F1,F2) = 1.453982e-03 # GGNFS version 0.77.1-20060722-pentium4 polyselect. # Options were: # lcd=1, enumLCD=12, maxS1=56.00000000, seed=1188103115. # maxskew=1500.0 # These parameters should be manually set: rlim: 550000 alim: 550000 lpbr: 24 lpba: 24 mfbr: 40 mfba: 40 rlambda: 1.9 alambda: 1.9 qintsize: 10000 type: gnfs Factor base limits: 550000/550000 Large primes per side: 3 Large prime bits: 24/24 Max factor residue bits: 40/40 Sieved algebraic special-q in [275000, 555001) Primes: RFBsize:45322, AFBsize:45360, largePrimes:833800 encountered Relations: rels:815718, finalFF:104325 Max relations in full relation-set: 0 Initial matrix: 90757 x 104325 with sparse part having weight 2839349. Pruned matrix : 78966 x 79483 with weight 2017468. Polynomial selection time: 0.10 hours. Total sieving time: 2.49 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.05 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: gnfs,82,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,550000,550000,24,24,40,40,1.9,1.9,10000 total time: 2.70 hours. --------- CPU info (if available) ----------
3·10¹¹⁹-7 = 2(9)₁₁₈3_<120> = 78368605499_<11> · 53095903456340370936693577_<26> · C83
C83 = P39 · P45
P39 = 188290868464416554619696945024940247957_<39>
P45 = 382903082208360177830892669855412560821185463_<45>

Number: 29993_119 N=72097153886714024932882352086117787528471155467902080177717553304923243985903849091 ( 83 digits) Divisors found: r1=188290868464416554619696945024940247957 (pp39) r2=382903082208360177830892669855412560821185463 (pp45) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.71 hours. Scaled time: 1.85 units (timescale=0.683). Factorization parameters were as follows: name: 29993_119 n: 72097153886714024932882352086117787528471155467902080177717553304923243985903849091 m: 15077363100825086328 deg: 4 c4: 1395136 c3: 4169473474 c2: -4457287606760667 c1: -10940135386059515 c0: 222330235747687799275 skew: 1379.250 type: gnfs # adj. I(F,S) = 48.893 # E(F1,F2) = 1.238494e-03 # GGNFS version 0.77.1-20060722-pentium4 polyselect. # Options were: # lcd=1, enumLCD=2, maxS1=56.00000000, seed=1188114582. # maxskew=1500.0 # These parameters should be manually set: rlim: 550000 alim: 550000 lpbr: 24 lpba: 24 mfbr: 40 mfba: 40 rlambda: 1.9 alambda: 1.9 qintsize: 10000 type: gnfs Factor base limits: 550000/550000 Large primes per side: 3 Large prime bits: 24/24 Max factor residue bits: 40/40 Sieved algebraic special-q in [275000, 555001) Primes: RFBsize:45322, AFBsize:45273, largePrimes:832054 encountered Relations: rels:813824, finalFF:104604 Max relations in full relation-set: 0 Initial matrix: 90669 x 104604 with sparse part having weight 2856065. Pruned matrix : 78768 x 79285 with weight 2014929. Polynomial selection time: 0.14 hours. Total sieving time: 2.45 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.05 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: gnfs,82,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,550000,550000,24,24,40,40,1.9,1.9,10000 total time: 2.71 hours. --------- CPU info (if available) ----------
Aug 26, 2007: The factor table of 299...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Aug 25, 2007 (3rd): By Yousuke Koide
(10¹¹²⁷-1)/9 is divisible by 241553587165443690259691154554887409_<36>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Aug 25, 2007 (2nd): By Sinkiti Sibata / GGNFS gnfs
2·10¹⁶¹-7 = 1(9)₁₆₀3_<162> = 31 · 313 · 142448923 · 17325841849_<11> · 15585783388091791295501248633_<29> · C111
C111 = P36 · P76
P36 = 266553003634306871217586370997016387_<36>
P76 = 2010287774860919418202526881731198334032989116402867831616415928274528790943_<76>

Number: 19993_161 N=535848244558505326981889880448516590560696883242115262678313109743369334051689534371625931132298086183468182941 ( 111 digits) Divisors found: r1=266553003634306871217586370997016387 (pp36) r2=2010287774860919418202526881731198334032989116402867831616415928274528790943 (pp76) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 40.17 hours. Scaled time: 27.43 units (timescale=0.683). Factorization parameters were as follows: name: 19993_161 n: 535848244558505326981889880448516590560696883242115262678313109743369334051689534371625931132298086183468182941 skew: 38462.86 # norm 1.20e+15 c5: 14400 c4: 1189258772 c3: -61157220101536 c2: -1665797028207107129 c1: 35529798518665248099674 c0: 456489891463513885112956704 # alpha -6.23 Y1: 579357828269 Y0: -2061265089212221663831 # Murphy_E 1.01e-09 # M 180678419163438711842001077111863466249073647594527557717463130782957750173637314545849972614753799691397384718 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2300001) Primes: RFBsize:230209, AFBsize:229517, largePrimes:7279052 encountered Relations: rels:6986811, finalFF:516183 Max relations in full relation-set: 0 Initial matrix: 459803 x 516183 with sparse part having weight 43767277. Pruned matrix : 413366 x 415729 with weight 29134753. Polynomial selection time: 2.18 hours. Total sieving time: 30.39 hours. Total relation processing time: 0.32 hours. Matrix solve time: 6.89 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 40.17 hours. --------- CPU info (if available) ----------
Aug 25, 2007: By Jo Yeong Uk / GGNFS
10¹⁸²-3 = (9)₁₈₁7_<182> = C182
C182 = P62 · P121
P62 = 65534081280247754710444002932518609571718586565539736236949437_<62>
P121 = 1525923581233455345160090558666254929382951100902891094757531494547444044927553100912619162340394581853825038559214658881_<121>

Number: 99997_182 N=99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 182 digits) SNFS difficulty: 182 digits. Divisors found: r1=65534081280247754710444002932518609571718586565539736236949437 (pp62) r2=1525923581233455345160090558666254929382951100902891094757531494547444044927553100912619162340394581853825038559214658881 (pp121) Version: GGNFS-0.77.1-20050930-nocona Total time: 266.82 hours. Scaled time: 572.61 units (timescale=2.146). Factorization parameters were as follows: n: 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 1000000000000000000000000000000000000 c5: 100 c0: -3 skew: 0.5 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, 9300001) Primes: RFBsize:664579, AFBsize:665255, largePrimes:11054485 encountered Relations: rels:11325581, finalFF:1493802 Max relations in full relation-set: 28 Initial matrix: 1329898 x 1493802 with sparse part having weight 90406090. Pruned matrix : 1184081 x 1190794 with weight 65471125. Total sieving time: 254.23 hours. Total relation processing time: 0.34 hours. Matrix solve time: 12.13 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000 total time: 266.82 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
Aug 24, 2007: By Jo Yeong Uk / GGNFS gnfs
2·10¹⁶⁵-7 = 1(9)₁₆₄3_<166> = 59797 · 246613 · 23678089 · 41577973901_<11> · 34612991488332463201_<20> · 336810499334585532769_<21> · C98
C98 = P46 · P52
P46 = 8373248538781344557355140845393442753439917323_<46>
P52 = 1411256395841790563687916889769452582264264863948791_<52>

Number: 19993_165 N=11816800554328099620625661265085248289285152349800401170173394776530045681226710459572934345806493 ( 98 digits) Divisors found: r1=8373248538781344557355140845393442753439917323 (pp46) r2=1411256395841790563687916889769452582264264863948791 (pp52) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.74 hours. Scaled time: 5.88 units (timescale=2.144). Factorization parameters were as follows: name: 19993_165 n: 11816800554328099620625661265085248289285152349800401170173394776530045681226710459572934345806493 skew: 1237.28 # norm 1.21e+13 c5: 113220 c4: 480980685 c3: 2430122298256 c2: -1110451066817246 c1: -1086725127653307920 c0: 201867094610748041685 # alpha -5.21 Y1: 14369106697 Y0: -2533455370402983104 # Murphy_E 4.96e-09 # M 9593727833258514037579465404153082108432528258843425541809868831355743798983219962802223254495886 type: gnfs rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [650000, 1000001) Primes: RFBsize:100021, AFBsize:100606, largePrimes:3733014 encountered Relations: rels:3561953, finalFF:244813 Max relations in full relation-set: 28 Initial matrix: 200709 x 244813 with sparse part having weight 18256185. Pruned matrix : 171699 x 172766 with weight 10219484. Polynomial selection time: 0.20 hours. Total sieving time: 2.33 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.10 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1300000,1300000,26,26,48,48,2.5,2.5,50000 total time: 2.74 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
Aug 23, 2007 (2nd): By Yousuke Koide
(10¹⁰⁰⁷-1)/9 is divisible by 172358178102983968116191222304067_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Aug 23, 2007: By Sinkiti Sibata / GGNFS
2·10¹⁶⁰-7 = 1(9)₁₅₉3_<161> = 9778720056013703211871_<22> · 3697455345403613029511363255055491_<34> · C105
C105 = P35 · P70
P35 = 88983955588580213717636993253398599_<35>
P70 = 6216319634016996326346051640131835569522780364047133332828651637579787_<70>

Number: 19993_160 N=553152710237787609065609048212168477170736374711112981864333893174433466742570138896896172282264776518413 ( 105 digits) SNFS difficulty: 160 digits. Divisors found: r1=88983955588580213717636993253398599 (pp35) r2=6216319634016996326346051640131835569522780364047133332828651637579787 (pp70) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 66.09 hours. Scaled time: 45.14 units (timescale=0.683). Factorization parameters were as follows: name: 19993_160 n: 553152710237787609065609048212168477170736374711112981864333893174433466742570138896896172282264776518413 m: 100000000000000000000000000000000 c5: 2 c0: -7 skew: 1.28 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:282562, largePrimes:5694547 encountered Relations: rels:5775416, finalFF:641262 Max relations in full relation-set: 0 Initial matrix: 565773 x 641262 with sparse part having weight 34681631. Pruned matrix : 504212 x 507104 with weight 25688162. Total sieving time: 56.46 hours. Total relation processing time: 0.27 hours. Matrix solve time: 9.15 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 66.09 hours. --------- CPU info (if available) ----------
Aug 20, 2007 (2nd): By Robert Backstrom / GGNFS
2·10¹⁴⁸-7 = 1(9)₁₄₇3_<149> = 727 · 55259 · 689461 · 71275313 · C128
C128 = P48 · P80
P48 = 116574430973904193855146706732208499099941411897_<48>
P80 = 86904130976575581951526367276706846060506184025707483584177277127705512595780481_<80>

Number: n N=10130799617875939439341399345302520071267999743485898743887114293281557156798471710018762477085932643315539431360437715813782457 ( 128 digits) SNFS difficulty: 148 digits. Divisors found: r1=116574430973904193855146706732208499099941411897 (pp48) r2=86904130976575581951526367276706846060506184025707483584177277127705512595780481 (pp80) Version: GGNFS-0.77.1-20051202-athlon Total time: 17.29 hours. Scaled time: 20.70 units (timescale=1.197). Factorization parameters were as follows: name: KA_1_9_147_3 n: 10130799617875939439341399345302520071267999743485898743887114293281557156798471710018762477085932643315539431360437715813782457 type: snfs skew: 1.00 deg: 5 c5: 125 c0: -14 m: 200000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:148933, AFBsize:149045, largePrimes:6657395 encountered Relations: rels:5980839, finalFF:339775 Max relations in full relation-set: 28 Initial matrix: 298043 x 339775 with sparse part having weight 27123958. Pruned matrix : 283441 x 284995 with weight 19686152. Total sieving time: 14.52 hours. Total relation processing time: 0.27 hours. Matrix solve time: 2.42 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 17.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
2·10¹⁵³-7 = 1(9)₁₅₂3_<154> = 449 · 677 · C148
C148 = P46 · P103
P46 = 3762028438491263860353713420746250519837842493_<46>
P103 = 1748931950489219682449972965472311190393808085080580038420592920946818270596715052250792592387757778537_<103>

Number: n N=6579531734726439519299411460886328719984998667644823717895997341869179170518434203037769801923197126060538271491217970017073884851615110552581972741 ( 148 digits) SNFS difficulty: 153 digits. Divisors found: r1=3762028438491263860353713420746250519837842493 (pp46) r2=1748931950489219682449972965472311190393808085080580038420592920946818270596715052250792592387757778537 (pp103) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 26.79 hours. Scaled time: 36.59 units (timescale=1.366). Factorization parameters were as follows: name: KA_1_9_152_3 n: 6579531734726439519299411460886328719984998667644823717895997341869179170518434203037769801923197126060538271491217970017073884851615110552581972741 skew: 1.00 deg: 5 c5: 125 c0: -14 m: 2000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:203362, AFBsize:204052, largePrimes:6864428 encountered Relations: rels:6333807, finalFF:471535 Max relations in full relation-set: 28 Initial matrix: 407479 x 471535 with sparse part having weight 32214453. Pruned matrix : 354626 x 356727 with weight 20521709. Total sieving time: 23.94 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.55 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 26.79 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(17·10¹⁶⁴-71)/9 = 1(8)₁₆₃1_<165> = 216583463554531_<15> · C150
C150 = P43 · P47 · P61
P43 = 5393696868579157005523711065632147602089029_<43>
P47 = 38447484784957009504048982784105217220178467777_<47>
P61 = 4205587262171089272039659014159109528298565349557528731191647_<61>

Number: n N=872129782158233792110440795362543649954023480251741539294763244976946979043259196816200705125877018942721308771218136883684994106138959566906294693851 ( 150 digits) SNFS difficulty: 166 digits. Divisors found: r1=5393696868579157005523711065632147602089029 (pp43) r2=38447484784957009504048982784105217220178467777 (pp47) r3=4205587262171089272039659014159109528298565349557528731191647 (pp61) Version: GGNFS-0.77.1-20051202-athlon Total time: 96.76 hours. Scaled time: 140.39 units (timescale=1.451). Factorization parameters were as follows: name: KA_1_8_163_1 n: 872129782158233792110440795362543649954023480251741539294763244976946979043259196816200705125877018942721308771218136883684994106138959566906294693851 skew: 1.00 deg: 5 c5: 17 c0: -710 m: 1000000000000000000000000000000000 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, 4400001) Primes: RFBsize:250150, AFBsize:249432, largePrimes:8074559 encountered Relations: rels:7600831, finalFF:561306 Max relations in full relation-set: 28 Initial matrix: 499647 x 561306 with sparse part having weight 54689824. Pruned matrix : 472890 x 475452 with weight 43077382. Total sieving time: 87.19 hours. Total relation processing time: 0.31 hours. Matrix solve time: 9.05 hours. Total square root time: 0.20 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 96.76 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
3·10¹⁶⁰+1 = 3(0)₁₅₉1_<161> = 12697 · 44454007667553277_<17> · C140
C140 = P59 · P82
P59 = 29275289584766911761299359521184239465004060018132044373477_<59>
P82 = 1815549170260446417865866950799703327121370197342878399772057644753731002595701977_<82>

Number: n N=53150727714757855596028755975143659660511735972840980625776628679939604228946393189742287388651544032546054205292253547945196114285975264029 ( 140 digits) SNFS difficulty: 160 digits. Divisors found: r1=29275289584766911761299359521184239465004060018132044373477 (pp59) r2=1815549170260446417865866950799703327121370197342878399772057644753731002595701977 (pp82) Version: GGNFS-0.77.1-20051202-athlon Total time: 31.82 hours. Scaled time: 41.46 units (timescale=1.303). Factorization parameters were as follows: name: KA_3_0_159_1 n: 53150727714757855596028755975143659660511735972840980625776628679939604228946393189742287388651544032546054205292253547945196114285975264029 skew: 1.00 deg: 5 c5: 3 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, 1300001) Primes: RFBsize:250150, AFBsize:249986, largePrimes:7004434 encountered Relations: rels:6536240, finalFF:574940 Max relations in full relation-set: 48 Initial matrix: 500201 x 574940 with sparse part having weight 35481689. Pruned matrix : 432298 x 434863 with weight 21149842. Total sieving time: 27.52 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.95 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: 31.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Aug 20, 2007: By Sinkiti Sibata / GGNFS
2·10¹⁵⁰-7 = 1(9)₁₄₉3_<151> = 11952940053651615413333135761471_<32> · C120
C120 = P55 · P65
P55 = 5135103254216728139255928526842762174060283210192549973_<55>
P65 = 32584125786762908430335253253731098461829476256546485262340435371_<65>

Number: 19993_150 N=167322850363413418158164834583548112090064493980285945977571771138046552314385841614896291617004196921469969657494294983 ( 120 digits) SNFS difficulty: 150 digits. Divisors found: r1=5135103254216728139255928526842762174060283210192549973 (pp55) r2=32584125786762908430335253253731098461829476256546485262340435371 (pp65) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 32.39 hours. Scaled time: 22.12 units (timescale=0.683). Factorization parameters were as follows: name: 19993_150 n: 167322850363413418158164834583548112090064493980285945977571771138046552314385841614896291617004196921469969657494294983 m: 1000000000000000000000000000000 c5: 2 c0: -7 skew: 1.28 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 1750001) Primes: RFBsize:114155, AFBsize:113917, largePrimes:2699817 encountered Relations: rels:2662344, finalFF:256787 Max relations in full relation-set: 0 Initial matrix: 228137 x 256787 with sparse part having weight 20597364. Pruned matrix : 219117 x 220321 with weight 15817334. Total sieving time: 30.89 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.28 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 32.39 hours. --------- CPU info (if available) ----------
2·10¹⁵⁴-7 = 1(9)₁₅₃3_<155> = 67² · 229 · 55049 · 50009407956250793_<17> · 61602475925415368717517641_<26> · C102
C102 = P39 · P63
P39 = 351490277394110695323131847836679690401_<39>
P63 = 326386567160734215007637212280611893892518870849999885489152869_<63>

Number: 19993_154 N=114721705029038009684258993602678013088151782796643426876986034777151039743560427927268917878680910469 ( 102 digits) Divisors found: r1=351490277394110695323131847836679690401 (pp39) r2=326386567160734215007637212280611893892518870849999885489152869 (pp63) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 12.31 hours. Scaled time: 8.41 units (timescale=0.683). Factorization parameters were as follows: name: 19993_154 n: 114721705029038009684258993602678013088151782796643426876986034777151039743560427927268917878680910469 skew: 6838.50 # norm 1.98e+14 c5: 57420 c4: 806981968 c3: -8759452266381 c2: 58156300282939815 c1: 72656612070836578217 c0: -291819258638452880648082 # alpha -6.34 Y1: 18567356473 Y0: -18201837623511379385 # Murphy_E 2.96e-09 # M 87987576487836068557265036980859895901729801322279531052036278029304020648302296853134444042946255226 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1750001) Primes: RFBsize:169511, AFBsize:170137, largePrimes:4352283 encountered Relations: rels:4419667, finalFF:389432 Max relations in full relation-set: 0 Initial matrix: 339732 x 389432 with sparse part having weight 18830906. Pruned matrix : 292135 x 293897 with weight 12311149. Polynomial selection time: 0.73 hours. Total sieving time: 9.40 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.79 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 12.31 hours. --------- CPU info (if available) ----------
Aug 19, 2007 (3rd): By Bruce Dodson
10⁶¹⁰+1 is divisible by 30177150878514090521547663054628235944221777770161_<50>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Aug 19, 2007 (2nd): By Robert Backstrom / GGNFS
7·10¹⁵⁶+3 = 7(0)₁₅₅3_<157> = 131869366750590330739_<21> · C137
C137 = P34 · P104
P34 = 1122763019112328991917896688146547_<34>
P104 = 47278753694379635584088304024046021007264290269515393607169408994420953596008025338686045504887530367691_<104>

Number: n N=53082836237769857722135010860503485221907656970354532121622796129493381197886353182035304221918803574861216603875564877388744020202012977 ( 137 digits) SNFS difficulty: 156 digits. Divisors found: r1=1122763019112328991917896688146547 (pp34) r2=47278753694379635584088304024046021007264290269515393607169408994420953596008025338686045504887530367691 (pp104) Version: GGNFS-0.77.1-20051202-athlon Total time: 48.61 hours. Scaled time: 58.14 units (timescale=1.196). Factorization parameters were as follows: name: KA_7_0_155_3 n: 53082836237769857722135010860503485221907656970354532121622796129493381197886353182035304221918803574861216603875564877388744020202012977 type: snfs skew: 1.00 deg: 5 c5: 70 c0: 3 m: 10000000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2100001) Primes: RFBsize:148933, AFBsize:148155, largePrimes:7023899 encountered Relations: rels:6408331, finalFF:334175 Max relations in full relation-set: 28 Initial matrix: 297155 x 334175 with sparse part having weight 35120249. Pruned matrix : 287404 x 288953 with weight 27659186. Total sieving time: 44.44 hours. Total relation processing time: 0.30 hours. Matrix solve time: 3.56 hours. Total square root time: 0.31 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 48.61 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
(2·10¹⁶⁵-11)/9 = (2)₁₆₄1_<165> = 13 · 724499 · C158
C158 = P39 · P119
P39 = 454131008520969815015609614546162302581_<39>
P119 = 51954741289049915090131599165962689609766478375843775620784761410878644041216476959039033357173188712948113263437198543_<119>

Number: n N=23594259059042309260736063257529815799737497351986812979857828781015700528356860525711000314829995754331053620631660076849097123797295916236038996732938339483 ( 158 digits) SNFS difficulty: 165 digits. Divisors found: r1=454131008520969815015609614546162302581 (pp39) r2=51954741289049915090131599165962689609766478375843775620784761410878644041216476959039033357173188712948113263437198543 (pp119) Version: GGNFS-0.77.1-20051202-athlon Total time: 49.52 hours. Scaled time: 65.56 units (timescale=1.324). Factorization parameters were as follows: name: KA_2_164_1 n: 23594259059042309260736063257529815799737497351986812979857828781015700528356860525711000314829995754331053620631660076849097123797295916236038996732938339483 skew: 1.00 deg: 5 c5: 2 c0: -11 m: 1000000000000000000000000000000000 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, 2100001) Primes: RFBsize:250150, AFBsize:250187, largePrimes:7289192 encountered Relations: rels:6812467, finalFF:578182 Max relations in full relation-set: 48 Initial matrix: 500404 x 578182 with sparse part having weight 42208298. Pruned matrix : 436256 x 438822 with weight 26433646. Total sieving time: 44.02 hours. Total relation processing time: 0.24 hours. Matrix solve time: 5.18 hours. Total square root time: 0.08 hours, sqrts: 1. 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: 49.52 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
2·10¹³⁴-7 = 1(9)₁₃₃3_<135> = 2857 · 27927023 · C124
C124 = P50 · P74
P50 = 53144573565322907925832295743438999653609663807679_<50>
P74 = 47166775363319527326178169171770117349576735102560712103900237618601981697_<74>

Number: n N=2506658163134994748187870797893663432529551237390369677630812454096726037917263172448982542288494354114405110663168086051263 ( 124 digits) SNFS difficulty: 135 digits. Divisors found: r1=53144573565322907925832295743438999653609663807679 (pp50) r2=47166775363319527326178169171770117349576735102560712103900237618601981697 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.42 hours. Scaled time: 5.81 units (timescale=1.315). Factorization parameters were as follows: name: KA_1_9_133_3 n: 2506658163134994748187870797893663432529551237390369677630812454096726037917263172448982542288494354114405110663168086051263 skew: 1.00 deg: 5 c5: 1 c0: -35 m: 1000000000000000000000000000 type: snfs rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 550001) Primes: RFBsize:92938, AFBsize:93179, largePrimes:5793654 encountered Relations: rels:5159522, finalFF:291661 Max relations in full relation-set: 48 Initial matrix: 186181 x 291661 with sparse part having weight 28321965. Pruned matrix : 147755 x 148749 with weight 9548185. Total sieving time: 3.69 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.57 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000 total time: 4.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
2·10¹⁴⁶-7 = 1(9)₁₄₅3_<147> = 31² · 47 · C142
C142 = P42 · P43 · P58
P42 = 435789728193384491010265428807562407041323_<42>
P43 = 7824864009218661541825600129317326360954459_<43>
P58 = 1298538893538002080810765152446905474596595362243224337247_<58>

Number: n N=4428011601390395642836584231850687448801115858923550379701994819226426373237097881196448734695684902694445059446055748666061505081143312595479 ( 142 digits) SNFS difficulty: 146 digits. Divisors found: r1=435789728193384491010265428807562407041323 (pp42) r2=7824864009218661541825600129317326360954459 (pp43) r3=1298538893538002080810765152446905474596595362243224337247 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.67 hours. Scaled time: 10.36 units (timescale=1.195). Factorization parameters were as follows: name: KA_1_9_145_3 n: 4428011601390395642836584231850687448801115858923550379701994819226426373237097881196448734695684902694445059446055748666061505081143312595479 type: snfs skew: 1.00 deg: 5 c5: 20 c0: -7 m: 100000000000000000000000000000 rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1050001) Primes: RFBsize:135072, AFBsize:134113, largePrimes:5640095 encountered Relations: rels:4976824, finalFF:312780 Max relations in full relation-set: 28 Initial matrix: 269251 x 312780 with sparse part having weight 17817889. Pruned matrix : 235514 x 236924 with weight 10920385. Total sieving time: 7.28 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.10 hours. Total square root time: 0.11 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.3,2.3,100000 total time: 8.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
2·10¹⁵⁷-7 = 1(9)₁₅₆3_<158> = 13 · 19 · C155
C155 = P50 · P106
P50 = 34394983393086726911525485365768764383612514728573_<50>
P106 = 2354170635689371043056236203816500880637102917069176450408667904943221662630923232028232978839918295665403_<106>

Number: n N=80971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919 ( 155 digits) SNFS difficulty: 157 digits. Divisors found: r1=34394983393086726911525485365768764383612514728573 (pp50) r2=2354170635689371043056236203816500880637102917069176450408667904943221662630923232028232978839918295665403 (pp106) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 31.86 hours. Scaled time: 43.52 units (timescale=1.366). Factorization parameters were as follows: name: KA_1_9_156_3 n: 80971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919 skew: 1.00 deg: 5 c5: 200 c0: -7 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216921, largePrimes:6966596 encountered Relations: rels:6455257, finalFF:502554 Max relations in full relation-set: 28 Initial matrix: 433802 x 502554 with sparse part having weight 33690650. Pruned matrix : 377727 x 379960 with weight 21241570. Total sieving time: 28.24 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.20 hours. Total square root time: 0.21 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 31.86 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
2·10¹³⁸-7 = 1(9)₁₃₇3_<139> = 658279 · C133
C133 = P44 · P90
P44 = 20210881938782879485293912186383278080876647_<44>
P90 = 150326217455104768578918165545438708371606106048971235069662906160218582347415312161469961_<90>

Number: n N=3038225433288924604916760218691466688136793061908400541411772212086364596166670970819363825976523632076976479577808193790171036900767 ( 133 digits) SNFS difficulty: 138 digits. Divisors found: r1=20210881938782879485293912186383278080876647 (pp44) r2=150326217455104768578918165545438708371606106048971235069662906160218582347415312161469961 (pp90) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.57 hours. Scaled time: 8.62 units (timescale=1.311). Factorization parameters were as follows: name: KA_1_9_137_3 n: 3038225433288924604916760218691466688136793061908400541411772212086364596166670970819363825976523632076976479577808193790171036900767 skew: 1.00 deg: 5 c5: 125 c0: -14 m: 2000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 750001) Primes: RFBsize:114155, AFBsize:114067, largePrimes:6195557 encountered Relations: rels:5510791, finalFF:295473 Max relations in full relation-set: 48 Initial matrix: 228287 x 295473 with sparse part having weight 28469908. Pruned matrix : 197360 x 198565 with weight 13852233. Total sieving time: 5.39 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.94 hours. Total square root time: 0.08 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000 total time: 6.57 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Aug 19, 2007: By JMB / GMP-ECM
2·10¹⁶⁰-7 = 1(9)₁₅₉3_<161> = 9778720056013703211871_<22> · C139
C139 = P34 · C105
P34 = 3697455345403613029511363255055491_<34>
C105 = [553152710237787609065609048212168477170736374711112981864333893174433466742570138896896172282264776518413_<105>]
Aug 18, 2007 (3rd): By JMB / GMP-ECM
2·10¹⁵⁸-7 = 1(9)₁₅₇3_<159> = 953 · 25057 · C151
C151 = P31 · C121
P31 = 2414090848213589432916932990633_<31>
C121 = [3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601_<121>]
2·10¹³⁷-7 = 1(9)₁₃₆3_<138> = 748003 · 33310522579_<11> · C121
C121 = P28 · P94
P28 = 2390131300820543368485406409_<28>
P94 = 3358330630726815585866665148198037542537791667019952702420547131059345414855706436951109119321_<94>
Aug 18, 2007 (2nd): By Sinkiti Sibata / GGNFS
2·10¹¹³-7 = 1(9)₁₁₂3_<114> = 433 · 193594939 · 6438265937_<10> · C93
C93 = P42 · P52
P42 = 103768776474506761548880707440030104142231_<42>
P52 = 3571186177883878701163022523856197962069162111081437_<52>

Number: 19993_113 N=370577620241680351107960936083701744464801655582601702548670887408021026411042271800671865947 ( 93 digits) SNFS difficulty: 113 digits. Divisors found: r1=103768776474506761548880707440030104142231 (pp42) r2=3571186177883878701163022523856197962069162111081437 (pp52) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 1.84 hours. Scaled time: 1.26 units (timescale=0.683). Factorization parameters were as follows: name: 19993_113 n: 370577620241680351107960936083701744464801655582601702548670887408021026411042271800671865947 m: 20000000000000000000000 c5: 125 c0: -14 skew: 0.65 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:63823, largePrimes:1971406 encountered Relations: rels:1935298, finalFF:127077 Max relations in full relation-set: 0 Initial matrix: 112986 x 127077 with sparse part having weight 7926145. Pruned matrix : 106103 x 106731 with weight 5732448. Total sieving time: 1.58 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.16 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.84 hours. --------- CPU info (if available) ----------
2·10¹²¹-7 = 1(9)₁₂₀3_<122> = 13 · 19² · 29 · 67 · 449 · 105683783 · 560286053 · C95
C95 = P32 · P63
P32 = 84709044758553106779503153611219_<32>
P63 = 973895486213706256874024049169829152280917871863189669742989003_<63>

Number: 19993_121 N=82497756331829683462558669352925498586702592066075493931163282676698334873528872233466454424657 ( 95 digits) SNFS difficulty: 121 digits. Divisors found: r1=84709044758553106779503153611219 (pp32) r2=973895486213706256874024049169829152280917871863189669742989003 (pp63) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.15 hours. Scaled time: 1.46 units (timescale=0.677). Factorization parameters were as follows: name: 19993_121 n: 82497756331829683462558669352925498586702592066075493931163282676698334873528872233466454424657 m: 1000000000000000000000000 c5: 20 c0: -7 skew: 0.81 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63823, largePrimes:2192336 encountered Relations: rels:2389469, finalFF:130435 Max relations in full relation-set: 0 Initial matrix: 112987 x 130435 with sparse part having weight 4525679. Pruned matrix : 99255 x 99883 with weight 3222049. Total sieving time: 1.95 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.10 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.15 hours. --------- CPU info (if available) ----------
2·10¹³¹-7 = 1(9)₁₃₀3_<132> = 31 · 43 · 547 · 17191 · C122
C122 = P39 · P83
P39 = 336512056301210231838855734796868432039_<39>
P83 = 47414453712323773154974881733917128690695953514154501437581484178811965886517575607_<83>

Number: 19993_131 N=15955535317132624037259941748282345796884680309287211931921457057513056386029490246875124343730473568510897621965723672673 ( 122 digits) SNFS difficulty: 131 digits. Divisors found: r1=336512056301210231838855734796868432039 (pp39) r2=47414453712323773154974881733917128690695953514154501437581484178811965886517575607 (pp83) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 4.50 hours. Scaled time: 3.07 units (timescale=0.683). Factorization parameters were as follows: name: 19993_131 n: 15955535317132624037259941748282345796884680309287211931921457057513056386029490246875124343730473568510897621965723672673 m: 100000000000000000000000000 c5: 20 c0: -7 skew: 0.81 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 850001) Primes: RFBsize:63951, AFBsize:63823, largePrimes:1471860 encountered Relations: rels:1489112, finalFF:145656 Max relations in full relation-set: 0 Initial matrix: 127840 x 145656 with sparse part having weight 5859360. Pruned matrix : 120924 x 121627 with weight 4468738. Total sieving time: 4.22 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.17 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.50 hours. --------- CPU info (if available) ----------
Aug 18, 2007: By Robert Backstrom / GGNFS, Msieve
2·10¹⁰³-7 = 1(9)₁₀₂3_<104> = 13 · 19 · 109 · 27271 · 45843061261_<11> · C84
C84 = P37 · P48
P37 = 1499785301098546070559433483576047617_<37>
P48 = 396189332056518295199839376172030596884900883633_<48>

Sat Aug 18 00:41:33 2007 Msieve v. 1.25 Sat Aug 18 00:41:33 2007 random seeds: 45574060 fe00702c Sat Aug 18 00:41:33 2007 factoring 594198936670417142250034428006910675032083389876682398379113331137221661036983952561 (84 digits) Sat Aug 18 00:41:34 2007 commencing quadratic sieve (84-digit input) Sat Aug 18 00:41:34 2007 using multiplier of 1 Sat Aug 18 00:41:34 2007 using 64kb Opteron sieve core Sat Aug 18 00:41:34 2007 sieve interval: 6 blocks of size 65536 Sat Aug 18 00:41:34 2007 processing polynomials in batches of 17 Sat Aug 18 00:41:34 2007 using a sieve bound of 1409171 (53774 primes) Sat Aug 18 00:41:34 2007 using large prime bound of 119779535 (26 bits) Sat Aug 18 00:41:34 2007 using trial factoring cutoff of 27 bits Sat Aug 18 00:41:34 2007 polynomial 'A' values have 11 factors Sat Aug 18 01:03:48 2007 54036 relations (27875 full + 26161 combined from 277827 partial), need 53870 Sat Aug 18 01:03:49 2007 begin with 305702 relations Sat Aug 18 01:03:49 2007 reduce to 76900 relations in 2 passes Sat Aug 18 01:03:49 2007 attempting to read 76900 relations Sat Aug 18 01:03:49 2007 recovered 76900 relations Sat Aug 18 01:03:49 2007 recovered 69605 polynomials Sat Aug 18 01:03:50 2007 attempting to build 54036 cycles Sat Aug 18 01:03:50 2007 found 54036 cycles in 1 passes Sat Aug 18 01:03:50 2007 distribution of cycle lengths: Sat Aug 18 01:03:50 2007 length 1 : 27875 Sat Aug 18 01:03:50 2007 length 2 : 26161 Sat Aug 18 01:03:50 2007 largest cycle: 2 relations Sat Aug 18 01:03:50 2007 matrix is 53774 x 54036 with weight 1726315 (avg 31.95/col) Sat Aug 18 01:03:50 2007 filtering completed in 4 passes Sat Aug 18 01:03:50 2007 matrix is 46254 x 46318 with weight 1449783 (avg 31.30/col) Sat Aug 18 01:03:51 2007 saving the first 48 matrix rows for later Sat Aug 18 01:03:51 2007 matrix is 46206 x 46318 with weight 1037966 (avg 22.41/col) Sat Aug 18 01:03:51 2007 matrix includes 64 packed rows Sat Aug 18 01:03:51 2007 commencing Lanczos iteration Sat Aug 18 01:04:42 2007 lanczos halted after 732 iterations Sat Aug 18 01:04:42 2007 recovered 9 nontrivial dependencies Sat Aug 18 01:04:42 2007 prp37 factor: 1499785301098546070559433483576047617 Sat Aug 18 01:04:42 2007 prp48 factor: 396189332056518295199839376172030596884900883633 Sat Aug 18 01:04:42 2007 elapsed time 00:23:09
2·10¹⁰¹-7 = 1(9)₁₀₀3_<102> = 23 · 31 · C99
C99 = P32 · P67
P32 = 40817008110892419885360745295659_<32>
P67 = 6872255508630705731993785461808742826606432539570772235049035346579_<67>

Number: n N=280504908835904628330995792426367461430575035063113604488078541374474053295932678821879382889200561 ( 99 digits) SNFS difficulty: 101 digits. Divisors found: r1=40817008110892419885360745295659 (pp32) r2=6872255508630705731993785461808742826606432539570772235049035346579 (pp67) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.58 hours. Scaled time: 0.69 units (timescale=1.195). Factorization parameters were as follows: name: KA_1_9_100_3 n: 280504908835904628330995792426367461430575035063113604488078541374474053295932678821879382889200561 type: snfs skew: 1.00 deg: 5 c5: 20 c0: -7 m: 100000000000000000000 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 150001) Primes: RFBsize:41538, AFBsize:41592, largePrimes:3289182 encountered Relations: rels:2767321, finalFF:227176 Max relations in full relation-set: 28 Initial matrix: 83196 x 227176 with sparse part having weight 6114936. Pruned matrix : 41906 x 42385 with weight 1147122. Total sieving time: 0.50 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.01 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,101,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.2,2.2,20000 total time: 0.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
2·10¹⁰⁷-7 = 1(9)₁₀₆3_<108> = C108
C108 = P53 · P55
P53 = 82054863816299707259814398629080646350578566200027409_<53>
P55 = 2437393601039298755451892933667568529233231518271465577_<55>

Number: n N=199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 108 digits) SNFS difficulty: 107 digits. Divisors found: r1=82054863816299707259814398629080646350578566200027409 (pp53) r2=2437393601039298755451892933667568529233231518271465577 (pp55) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.81 hours. Scaled time: 1.07 units (timescale=1.324). Factorization parameters were as follows: name: KA_1_9_106_3 n: 199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 skew: 1.00 deg: 5 c5: 200 c0: -7 m: 1000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 150001) Primes: RFBsize:49098, AFBsize:49236, largePrimes:3580731 encountered Relations: rels:2988128, finalFF:136292 Max relations in full relation-set: 48 Initial matrix: 98399 x 136292 with sparse part having weight 7847627. Pruned matrix : 78677 x 79232 with weight 2761136. Total sieving time: 0.70 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.04 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,107,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 0.81 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
2·10¹¹⁶-7 = 1(9)₁₁₅3_<117> = 31 · 15287 · 57388723099_<11> · 7056481988900947_<16> · C85
C85 = P38 · P47
P38 = 53770152002195367607766769002285035703_<38>
P47 = 19381615468650712446069311543584612837099830391_<47>

Sat Aug 18 01:11:25 2007 Msieve v. 1.25 Sat Aug 18 01:11:25 2007 random seeds: 8c7476f8 0ac7e520 Sat Aug 18 01:11:25 2007 factoring 1042152409797449813919505804291041079610830022103112436355806625120281914418679449873 (85 digits) Sat Aug 18 01:11:25 2007 commencing quadratic sieve (84-digit input) Sat Aug 18 01:11:25 2007 using multiplier of 23 Sat Aug 18 01:11:25 2007 using 64kb Opteron sieve core Sat Aug 18 01:11:25 2007 sieve interval: 6 blocks of size 65536 Sat Aug 18 01:11:25 2007 processing polynomials in batches of 17 Sat Aug 18 01:11:25 2007 using a sieve bound of 1412767 (54118 primes) Sat Aug 18 01:11:25 2007 using large prime bound of 118672428 (26 bits) Sat Aug 18 01:11:25 2007 using double large prime bound of 341845303975812 (41-49 bits) Sat Aug 18 01:11:25 2007 using trial factoring cutoff of 49 bits Sat Aug 18 01:11:25 2007 polynomial 'A' values have 11 factors Sat Aug 18 01:41:18 2007 54532 relations (16323 full + 38209 combined from 574167 partial), need 54214 Sat Aug 18 01:41:18 2007 begin with 590490 relations Sat Aug 18 01:41:19 2007 reduce to 127649 relations in 9 passes Sat Aug 18 01:41:19 2007 attempting to read 127649 relations Sat Aug 18 01:41:20 2007 recovered 127649 relations Sat Aug 18 01:41:20 2007 recovered 105145 polynomials Sat Aug 18 01:41:20 2007 attempting to build 54532 cycles Sat Aug 18 01:41:20 2007 found 54532 cycles in 6 passes Sat Aug 18 01:41:21 2007 distribution of cycle lengths: Sat Aug 18 01:41:21 2007 length 1 : 16323 Sat Aug 18 01:41:21 2007 length 2 : 10945 Sat Aug 18 01:41:21 2007 length 3 : 9517 Sat Aug 18 01:41:21 2007 length 4 : 6903 Sat Aug 18 01:41:21 2007 length 5 : 4676 Sat Aug 18 01:41:21 2007 length 6 : 2756 Sat Aug 18 01:41:21 2007 length 7 : 1628 Sat Aug 18 01:41:21 2007 length 9+: 1784 Sat Aug 18 01:41:21 2007 largest cycle: 20 relations Sat Aug 18 01:41:21 2007 matrix is 54118 x 54532 with weight 2861941 (avg 52.48/col) Sat Aug 18 01:41:21 2007 filtering completed in 3 passes Sat Aug 18 01:41:21 2007 matrix is 49283 x 49347 with weight 2589053 (avg 52.47/col) Sat Aug 18 01:41:22 2007 saving the first 48 matrix rows for later Sat Aug 18 01:41:22 2007 matrix is 49235 x 49347 with weight 1923717 (avg 38.98/col) Sat Aug 18 01:41:22 2007 matrix includes 64 packed rows Sat Aug 18 01:41:22 2007 commencing Lanczos iteration Sat Aug 18 01:42:37 2007 lanczos halted after 780 iterations Sat Aug 18 01:42:37 2007 recovered 16 nontrivial dependencies Sat Aug 18 01:42:37 2007 prp38 factor: 53770152002195367607766769002285035703 Sat Aug 18 01:42:37 2007 prp47 factor: 19381615468650712446069311543584612837099830391 Sat Aug 18 01:42:37 2007 elapsed time 00:31:12
7·10¹⁵⁷+3 = 7(0)₁₅₆3_<158> = 229 · 20670690483852242291_<20> · C137
C137 = P54 · P83
P54 = 289487332555897025292304347439098723403965940378647989_<54>
P83 = 51083189905954193522289990799875185494212136099456609629347350039925026063426710793_<83>

Number: n N=14787936384321003708141216422843185879204009734434037034013241495186860920918712525674496781342997140195863042629969015291500910654045277 ( 137 digits) SNFS difficulty: 157 digits. Divisors found: r1=289487332555897025292304347439098723403965940378647989 (pp54) r2=51083189905954193522289990799875185494212136099456609629347350039925026063426710793 (pp83) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 31.10 hours. Scaled time: 42.45 units (timescale=1.365). Factorization parameters were as follows: name: KA_7_0_156_3 n: 14787936384321003708141216422843185879204009734434037034013241495186860920918712525674496781342997140195863042629969015291500910654045277 skew: 1.00 deg: 5 c5: 700 c0: 3 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:216816, AFBsize:216741, largePrimes:6935490 encountered Relations: rels:6416479, finalFF:495576 Max relations in full relation-set: 28 Initial matrix: 433624 x 495576 with sparse part having weight 32902854. Pruned matrix : 382603 x 384835 with weight 21351181. Total sieving time: 28.05 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.62 hours. Total square root time: 0.22 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 31.10 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
2·10¹²⁹-7 = 1(9)₁₂₈3_<130> = 83639 · 3574169 · 129553992197347_<15> · 261030882891310001_<18> · C87
C87 = P31 · P57
P31 = 1486751042568008988903546205849_<31>
P57 = 133065397594874242418254943012440252718810034095919697541_<57>

Sat Aug 18 01:57:43 2007 Msieve v. 1.25 Sat Aug 18 01:57:43 2007 random seeds: cba2d240 7c081f2e Sat Aug 18 01:57:43 2007 factoring 197835118603905915720214023895293099346240518843919779049358943033088066153354205117309 (87 digits) Sat Aug 18 01:57:43 2007 commencing quadratic sieve (86-digit input) Sat Aug 18 01:57:43 2007 using multiplier of 11 Sat Aug 18 01:57:43 2007 using 64kb Opteron sieve core Sat Aug 18 01:57:43 2007 sieve interval: 10 blocks of size 65536 Sat Aug 18 01:57:43 2007 processing polynomials in batches of 11 Sat Aug 18 01:57:43 2007 using a sieve bound of 1477219 (56333 primes) Sat Aug 18 01:57:43 2007 using large prime bound of 118177520 (26 bits) Sat Aug 18 01:57:43 2007 using double large prime bound of 339283405529280 (41-49 bits) Sat Aug 18 01:57:43 2007 using trial factoring cutoff of 49 bits Sat Aug 18 01:57:43 2007 polynomial 'A' values have 11 factors Sat Aug 18 02:41:39 2007 56816 relations (15831 full + 40985 combined from 595388 partial), need 56429 Sat Aug 18 02:41:40 2007 begin with 611219 relations Sat Aug 18 02:41:41 2007 reduce to 136446 relations in 10 passes Sat Aug 18 02:41:41 2007 attempting to read 136446 relations Sat Aug 18 02:41:42 2007 recovered 136446 relations Sat Aug 18 02:41:42 2007 recovered 114684 polynomials Sat Aug 18 02:41:42 2007 attempting to build 56816 cycles Sat Aug 18 02:41:42 2007 found 56816 cycles in 5 passes Sat Aug 18 02:41:43 2007 distribution of cycle lengths: Sat Aug 18 02:41:43 2007 length 1 : 15831 Sat Aug 18 02:41:43 2007 length 2 : 11249 Sat Aug 18 02:41:43 2007 length 3 : 9985 Sat Aug 18 02:41:43 2007 length 4 : 7344 Sat Aug 18 02:41:43 2007 length 5 : 5110 Sat Aug 18 02:41:43 2007 length 6 : 3192 Sat Aug 18 02:41:43 2007 length 7 : 1864 Sat Aug 18 02:41:43 2007 length 9+: 2241 Sat Aug 18 02:41:43 2007 largest cycle: 22 relations Sat Aug 18 02:41:43 2007 matrix is 56333 x 56816 with weight 3281518 (avg 57.76/col) Sat Aug 18 02:41:44 2007 filtering completed in 3 passes Sat Aug 18 02:41:44 2007 matrix is 51901 x 51965 with weight 3009122 (avg 57.91/col) Sat Aug 18 02:41:44 2007 saving the first 48 matrix rows for later Sat Aug 18 02:41:44 2007 matrix is 51853 x 51965 with weight 2376073 (avg 45.72/col) Sat Aug 18 02:41:44 2007 matrix includes 64 packed rows Sat Aug 18 02:41:44 2007 using block size 20786 for processor cache size 512 kB Sat Aug 18 02:41:45 2007 commencing Lanczos iteration Sat Aug 18 02:42:09 2007 lanczos halted after 821 iterations Sat Aug 18 02:42:09 2007 recovered 18 nontrivial dependencies Sat Aug 18 02:42:10 2007 prp31 factor: 1486751042568008988903546205849 Sat Aug 18 02:42:10 2007 prp57 factor: 133065397594874242418254943012440252718810034095919697541 Sat Aug 18 02:42:10 2007 elapsed time 00:44:27
2·10¹⁰⁵-7 = 1(9)₁₀₄3_<106> = 249871 · 19798132157_<11> · C90
C90 = P40 · P51
P40 = 3163117297741861192762916686673115456869_<40>
P51 = 127812881122780074917861322196995275825625504898951_<51>

Sat Aug 18 02:48:52 2007 Msieve v. 1.25 Sat Aug 18 02:48:52 2007 random seeds: 17aa9510 0f4a9a94 Sat Aug 18 02:48:52 2007 factoring 404287135153689852139853507001355860700950742482453612994941638390577044704142200043844419 (90 digits) Sat Aug 18 02:48:52 2007 commencing quadratic sieve (90-digit input) Sat Aug 18 02:48:52 2007 using multiplier of 35 Sat Aug 18 02:48:52 2007 using 64kb Opteron sieve core Sat Aug 18 02:48:52 2007 sieve interval: 18 blocks of size 65536 Sat Aug 18 02:48:52 2007 processing polynomials in batches of 6 Sat Aug 18 02:48:52 2007 using a sieve bound of 1584941 (59865 primes) Sat Aug 18 02:48:52 2007 using large prime bound of 126795280 (26 bits) Sat Aug 18 02:48:52 2007 using double large prime bound of 385110612518640 (42-49 bits) Sat Aug 18 02:48:52 2007 using trial factoring cutoff of 49 bits Sat Aug 18 02:48:52 2007 polynomial 'A' values have 12 factors Sat Aug 18 04:06:48 2007 60026 relations (16158 full + 43868 combined from 635630 partial), need 59961 Sat Aug 18 04:06:48 2007 begin with 651788 relations Sat Aug 18 04:06:49 2007 reduce to 145703 relations in 10 passes Sat Aug 18 04:06:49 2007 attempting to read 145703 relations Sat Aug 18 04:06:51 2007 recovered 145703 relations Sat Aug 18 04:06:51 2007 recovered 125654 polynomials Sat Aug 18 04:06:51 2007 attempting to build 60026 cycles Sat Aug 18 04:06:51 2007 found 60026 cycles in 5 passes Sat Aug 18 04:06:51 2007 distribution of cycle lengths: Sat Aug 18 04:06:51 2007 length 1 : 16158 Sat Aug 18 04:06:51 2007 length 2 : 11640 Sat Aug 18 04:06:51 2007 length 3 : 10601 Sat Aug 18 04:06:51 2007 length 4 : 8002 Sat Aug 18 04:06:51 2007 length 5 : 5438 Sat Aug 18 04:06:51 2007 length 6 : 3507 Sat Aug 18 04:06:51 2007 length 7 : 2180 Sat Aug 18 04:06:51 2007 length 9+: 2500 Sat Aug 18 04:06:51 2007 largest cycle: 19 relations Sat Aug 18 04:06:51 2007 matrix is 59865 x 60026 with weight 3621110 (avg 60.33/col) Sat Aug 18 04:06:52 2007 filtering completed in 3 passes Sat Aug 18 04:06:52 2007 matrix is 55875 x 55939 with weight 3404274 (avg 60.86/col) Sat Aug 18 04:06:53 2007 saving the first 48 matrix rows for later Sat Aug 18 04:06:53 2007 matrix is 55827 x 55939 with weight 2670443 (avg 47.74/col) Sat Aug 18 04:06:53 2007 matrix includes 64 packed rows Sat Aug 18 04:06:53 2007 using block size 21845 for processor cache size 512 kB Sat Aug 18 04:06:53 2007 commencing Lanczos iteration Sat Aug 18 04:07:22 2007 lanczos halted after 884 iterations Sat Aug 18 04:07:22 2007 recovered 17 nontrivial dependencies Sat Aug 18 04:07:23 2007 prp40 factor: 3163117297741861192762916686673115456869 Sat Aug 18 04:07:23 2007 prp51 factor: 127812881122780074917861322196995275825625504898951 Sat Aug 18 04:07:23 2007 elapsed time 01:18:31
2·10¹¹⁸-7 = 1(9)₁₁₇3_<119> = 7603 · 15467 · 36691 · 560783 · 44963591969_<11> · C90
C90 = P39 · P51
P39 = 228255834357666971162546058313791223921_<39>
P51 = 805381494221740368380247875416367103097200384770669_<51>

Sat Aug 18 06:06:11 2007 Msieve v. 1.25 Sat Aug 18 06:06:11 2007 random seeds: 5f6a4b80 2ab61692 Sat Aug 18 06:06:11 2007 factoring 183833024939807888384756175161493723771813679252307301971496985010466178538582354411973149 (90 digits) Sat Aug 18 06:06:11 2007 commencing quadratic sieve (89-digit input) Sat Aug 18 06:06:11 2007 using multiplier of 5 Sat Aug 18 06:06:11 2007 using 64kb Opteron sieve core Sat Aug 18 06:06:11 2007 sieve interval: 18 blocks of size 65536 Sat Aug 18 06:06:11 2007 processing polynomials in batches of 6 Sat Aug 18 06:06:11 2007 using a sieve bound of 1575227 (59526 primes) Sat Aug 18 06:06:11 2007 using large prime bound of 126018160 (26 bits) Sat Aug 18 06:06:11 2007 using double large prime bound of 380872498093920 (42-49 bits) Sat Aug 18 06:06:11 2007 using trial factoring cutoff of 49 bits Sat Aug 18 06:06:11 2007 polynomial 'A' values have 11 factors Sat Aug 18 07:19:05 2007 59934 relations (15603 full + 44331 combined from 637765 partial), need 59622 Sat Aug 18 07:19:06 2007 begin with 653368 relations Sat Aug 18 07:19:07 2007 reduce to 146935 relations in 11 passes Sat Aug 18 07:19:07 2007 attempting to read 146935 relations Sat Aug 18 07:19:08 2007 recovered 146935 relations Sat Aug 18 07:19:08 2007 recovered 124808 polynomials Sat Aug 18 07:19:09 2007 attempting to build 59934 cycles Sat Aug 18 07:19:09 2007 found 59934 cycles in 6 passes Sat Aug 18 07:19:09 2007 distribution of cycle lengths: Sat Aug 18 07:19:09 2007 length 1 : 15603 Sat Aug 18 07:19:09 2007 length 2 : 11295 Sat Aug 18 07:19:09 2007 length 3 : 10597 Sat Aug 18 07:19:09 2007 length 4 : 8235 Sat Aug 18 07:19:09 2007 length 5 : 5780 Sat Aug 18 07:19:09 2007 length 6 : 3694 Sat Aug 18 07:19:09 2007 length 7 : 2249 Sat Aug 18 07:19:09 2007 length 9+: 2481 Sat Aug 18 07:19:09 2007 largest cycle: 18 relations Sat Aug 18 07:19:09 2007 matrix is 59526 x 59934 with weight 3646667 (avg 60.84/col) Sat Aug 18 07:19:10 2007 filtering completed in 3 passes Sat Aug 18 07:19:10 2007 matrix is 55752 x 55815 with weight 3412104 (avg 61.13/col) Sat Aug 18 07:19:11 2007 saving the first 48 matrix rows for later Sat Aug 18 07:19:11 2007 matrix is 55704 x 55815 with weight 2806624 (avg 50.28/col) Sat Aug 18 07:19:11 2007 matrix includes 64 packed rows Sat Aug 18 07:19:11 2007 using block size 21845 for processor cache size 512 kB Sat Aug 18 07:19:11 2007 commencing Lanczos iteration Sat Aug 18 07:19:45 2007 lanczos halted after 883 iterations Sat Aug 18 07:19:45 2007 recovered 18 nontrivial dependencies Sat Aug 18 07:19:46 2007 prp39 factor: 228255834357666971162546058313791223921 Sat Aug 18 07:19:46 2007 prp51 factor: 805381494221740368380247875416367103097200384770669 Sat Aug 18 07:19:46 2007 elapsed time 01:13:35
Aug 17, 2007 (2nd): The factor table of 199...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Aug 17, 2007: By Sinkiti Sibata / GGNFS
8·10¹⁴⁷+3 = 8(0)₁₄₆3_<148> = 31466053047841_<14> · 446393418652404001_<18> · C117
C117 = P55 · P63
P55 = 2323850000470988610164769082031528440943605820371041061_<55>
P63 = 245087883633789932212635585467307279310123198991773916587660103_<63>

Number: 80003_147 N=569547478497816335653236580096415110037272527469806007281214758971851303247684071335941951908761857655410364124489283 ( 117 digits) SNFS difficulty: 147 digits. Divisors found: r1=2323850000470988610164769082031528440943605820371041061 (pp55) r2=245087883633789932212635585467307279310123198991773916587660103 (pp63) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 18.83 hours. Scaled time: 12.86 units (timescale=0.683). Factorization parameters were as follows: name: 80003_147 n: 569547478497816335653236580096415110037272527469806007281214758971851303247684071335941951908761857655410364124489283 m: 200000000000000000000000000000 c5: 25 c0: 3 skew: 0.65 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 2450001) Primes: RFBsize:114155, AFBsize:114287, largePrimes:2708471 encountered Relations: rels:2648929, finalFF:256730 Max relations in full relation-set: 0 Initial matrix: 228506 x 256730 with sparse part having weight 24970341. Pruned matrix : 219964 x 221170 with weight 19140475. Total sieving time: 17.03 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.55 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 18.83 hours. --------- CPU info (if available) ----------
Aug 16, 2007 (2nd): By Sinkiti Sibata / GGNFS
8·10¹⁶¹+3 = 8(0)₁₆₀3_<162> = 19 · 23 · 31 · 129126249073062336423461145334519_<33> · C126
C126 = P52 · P75
P52 = 2631015527810085421291051911982281677569752486170207_<52>
P75 = 173823667706511661436246647779256732900511330139840852735400152888111969953_<75>
Aug 16, 2007: By Robert Backstrom / GGNFS
(7·10¹⁶⁴-43)/9 = (7)₁₆₃3_<164> = 23 · 711289786791481_<15> · C148
C148 = P52 · P96
P52 = 6711531394644396265684065465544051167200478004582667_<52>
P96 = 708368916114260301416021742929112249942005710589804708659563255988563220760762909875017169699513_<96>

Number: n N=4754240219491080788312230946104229406177747980744173052452025549226149029482922498597241709937906716835807695523262461778588861036905275229358141171 ( 148 digits) SNFS difficulty: 165 digits. Divisors found: r1=6711531394644396265684065465544051167200478004582667 (pp52) r2=708368916114260301416021742929112249942005710589804708659563255988563220760762909875017169699513 (pp96) Version: GGNFS-0.77.1-20051202-athlon Total time: 68.29 hours. Scaled time: 98.61 units (timescale=1.444). Factorization parameters were as follows: name: KA_7_163_3 n: 4754240219491080788312230946104229406177747980744173052452025549226149029482922498597241709937906716835807695523262461778588861036905275229358141171 skew: 1.00 deg: 5 c5: 7 c0: -430 m: 1000000000000000000000000000000000 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, 3100001) Primes: RFBsize:250150, AFBsize:249976, largePrimes:7609891 encountered Relations: rels:7117769, finalFF:563963 Max relations in full relation-set: 28 Initial matrix: 500191 x 563963 with sparse part having weight 43297342. Pruned matrix : 456543 x 459107 with weight 32040185. Total sieving time: 61.30 hours. Total relation processing time: 0.26 hours. Matrix solve time: 6.64 hours. Total square root time: 0.09 hours, sqrts: 1. 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: 68.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
8·10¹⁴⁸+3 = 8(0)₁₄₇3_<149> = 7 · 11 · 29 · 317 · 509 · 13229 · C137
C137 = P43 · P95
P43 = 1633127480251888041774589540737718105895353_<43>
P95 = 10277254618113551226936717541671467485926625997768564715394439356053800695383219974495822267431_<95>

Number: n N=16784066938386863809673549107097123019053594081024750091689098181846065843165170875752881062581853809077533297118793759110758492866148143 ( 137 digits) SNFS difficulty: 150 digits. Divisors found: r1=1633127480251888041774589540737718105895353 (pp43) r2=10277254618113551226936717541671467485926625997768564715394439356053800695383219974495822267431 (pp95) Version: GGNFS-0.77.1-20051202-athlon Total time: 17.86 hours. Scaled time: 21.39 units (timescale=1.198). Factorization parameters were as follows: name: KA_8_0_147_3 n: 16784066938386863809673549107097123019053594081024750091689098181846065843165170875752881062581853809077533297118793759110758492866148143 type: snfs skew: 1.00 deg: 5 c5: 2 c0: 75 m: 1000000000000000000000000000000 rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:135072, AFBsize:134848, largePrimes:5661412 encountered Relations: rels:5066697, finalFF:360387 Max relations in full relation-set: 28 Initial matrix: 269985 x 360387 with sparse part having weight 21720490. Pruned matrix : 199413 x 200826 with weight 10892762. Total sieving time: 16.73 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.86 hours. Total square root time: 0.10 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.3,2.3,100000 total time: 17.86 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
7·10¹⁶³-3 = 6(9)₁₆₂7_<164> = 521 · 8929 · 20049478817_<11> · C147
C147 = P32 · P116
P32 = 18834724717582733339854276484953_<32>
P116 = 39846954049113870438326350054437585548327057756753553930562437288636637623138186710621577302650844411531338277069533_<116>

Number: n N=750506410349228396108340941035609903362273370421470668905748757604180204449969666910202490334397310209946975430176004793022692543599630852809236949 ( 147 digits) SNFS difficulty: 163 digits. Divisors found: r1=18834724717582733339854276484953 (pp32) r2=39846954049113870438326350054437585548327057756753553930562437288636637623138186710621577302650844411531338277069533 (pp116) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 69.78 hours. Scaled time: 94.62 units (timescale=1.356). Factorization parameters were as follows: name: KA_6_9_162_7 n: 750506410349228396108340941035609903362273370421470668905748757604180204449969666910202490334397310209946975430176004793022692543599630852809236949 skew: 1.00 deg: 5 c5: 7000 c0: -3 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2900001) Primes: RFBsize:250150, AFBsize:249771, largePrimes:7592845 encountered Relations: rels:7109288, finalFF:566068 Max relations in full relation-set: 28 Initial matrix: 499988 x 566068 with sparse part having weight 44087913. Pruned matrix : 452753 x 455316 with weight 32088899. Total sieving time: 64.59 hours. Total relation processing time: 0.30 hours. Matrix solve time: 4.73 hours. Total square root time: 0.15 hours, sqrts: 1. 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: 69.78 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(83·10¹⁶³+61)/9 = 9(2)₁₆₂9_<164> = 3² · 11 · 405948153112321_<15> · C148
C148 = P45 · P103
P45 = 266614931935353132585870319448121552669271271_<45>
P103 = 8606872108912684768820232718493204401373246518359328695784136236316614714942900588215155616801419951681_<103>

Number: n N=2294720621494044723501193022587510995379466046473791605416061226154482486212075390007842580455013701527981276373027895660286461909530014578301456551 ( 148 digits) SNFS difficulty: 164 digits. Divisors found: r1=266614931935353132585870319448121552669271271 (pp45) r2=8606872108912684768820232718493204401373246518359328695784136236316614714942900588215155616801419951681 (pp103) Version: GGNFS-0.77.1-20051202-athlon Total time: 89.26 hours. Scaled time: 117.91 units (timescale=1.321). Factorization parameters were as follows: name: KA_9_2_162_9 n: 2294720621494044723501193022587510995379466046473791605416061226154482486212075390007842580455013701527981276373027895660286461909530014578301456551 skew: 1.00 deg: 5 c5: 83000 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, 3500001) Primes: RFBsize:250150, AFBsize:249877, largePrimes:7740802 encountered Relations: rels:7222735, finalFF:569028 Max relations in full relation-set: 48 Initial matrix: 500094 x 569028 with sparse part having weight 54550980. Pruned matrix : 469886 x 472450 with weight 38556850. Total sieving time: 80.47 hours. Total relation processing time: 0.32 hours. Matrix solve time: 8.13 hours. Total square root time: 0.34 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 89.26 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Aug 15, 2007 (2nd): By Robert Backstrom / GGNFS
(2·10¹⁶⁴+1)/3 = (6)₁₆₃7_<164> = 593 · 90617845494707_<14> · C148
C148 = P69 · P79
P69 = 905685704538199081405478788593241373745603366270356038442638975449577_<69>
P79 = 1369817790937139389142693698471450846149527260439060627521041224566510416295921_<79>

Number: n N=1240624391073862584177081105224640061651512320190878112287750695849877675218001116528687519332352510520546136007485011619473977733985821548046275417 ( 148 digits) SNFS difficulty: 165 digits. Divisors found: r1=905685704538199081405478788593241373745603366270356038442638975449577 (pp69) r2=1369817790937139389142693698471450846149527260439060627521041224566510416295921 (pp79) Version: GGNFS-0.77.1-20051202-athlon Total time: 51.41 hours. Scaled time: 61.53 units (timescale=1.197). Factorization parameters were as follows: name: KA_6_163_7 n: 1240624391073862584177081105224640061651512320190878112287750695849877675218001116528687519332352510520546136007485011619473977733985821548046275417 type: snfs skew: 1.00 deg: 5 c5: 1 c0: 5 m: 1000000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:250150, AFBsize:249616, largePrimes:7240131 encountered Relations: rels:6756925, finalFF:561200 Max relations in full relation-set: 28 Initial matrix: 499830 x 561200 with sparse part having weight 36079230. Pruned matrix : 447952 x 450515 with weight 24495508. Total sieving time: 45.60 hours. Total relation processing time: 0.33 hours. Matrix solve time: 5.25 hours. Total square root time: 0.23 hours, sqrts: 2. 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: 51.41 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Aug 15, 2007: By JMB / MSieve, GMP-ECM
8·10¹⁶⁵+3 = 8(0)₁₆₄3_<166> = 17 · 83 · 2221 · 12653 · 1033040033209816345546009288939_<31> · 19558081525904346337653953996359_<32> · C94
C94 = P44 · P51
P44 = 31235192130845769254279459512560137999028121_<44>
P51 = 319693142674609372256180538787347658839023974155301_<51>
8·10¹⁷²+3 = 8(0)₁₇₁3_<173> = 7 · 11² · 53 · 261587 · 13420331 · C156
C156 = P35 · C122
P35 = 14742878852145643127878371424312249_<35>
C122 = [34432537221857307847885115428554920425568029885965301615634596789076443254421769772956443274804876835533993545735639636561_<122>]
Aug 14, 2007 (2nd): By JMB / GMP-ECM
8·10¹⁷⁰+3 = 8(0)₁₆₉3_<171> = 11 · 73 · 25087 · 32666806785659_<14> · C151
C151 = P33 · P118
P33 = 518810619846876503372769619770433_<33>
P118 = 2343204381484500438488187466170885890773141731069741607646382933532921328434754372068190854059489563670232771599467309_<118>
8·10¹⁶⁵+3 = 8(0)₁₆₄3_<166> = 17 · 83 · 2221 · 12653 · 19558081525904346337653953996359_<32> · C125
C125 = P31 · C94
P31 = 1033040033209816345546009288939_<31>
C94 = [9985676734355312445998651932324904435324205513572694026740373190359859585183702210559920219421_<94>]
Aug 14, 2007: By Sinkiti Sibata / GGNFS
8·10¹⁸⁹+3 = 8(0)₁₈₈3_<190> = 619 · 1847 · 2087 · 17854618292333_<14> · 66686803592942902296799_<23> · 921080685636059212526826174467963_<33> · C112
C112 = P47 · P66
P47 = 17588503812768618802899470677477549249528890421_<47>
P66 = 173817279856071866628575928062476489118502849448260284689789701413_<66>

Number: 80003_189 N=3057185889473590067108879535881711047802061887351934101508239518685119755420999299188104236165875118418785864873 ( 112 digits) Divisors found: r1=17588503812768618802899470677477549249528890421 (pp47) r2=173817279856071866628575928062476489118502849448260284689789701413 (pp66) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 44.29 hours. Scaled time: 30.21 units (timescale=0.682). Factorization parameters were as follows: name: 80003_189 n: 3057185889473590067108879535881711047802061887351934101508239518685119755420999299188104236165875118418785864873 skew: 42151.48 # norm 8.84e+15 c5: 37440 c4: -298371218 c3: -300194331630874 c2: -2696942357896617447 c1: -27789569306702796022486 c0: 469893487864104658111591365 # alpha -6.89 Y1: 204062775301 Y0: -2412110836924559280358 # Murphy_E 8.26e-10 # M 1005760143397642380352074720913871517578447049436816287197307383505060650599072483745071851791769646797691653031 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2550001) Primes: RFBsize:250150, AFBsize:250023, largePrimes:7400988 encountered Relations: rels:7270904, finalFF:564212 Max relations in full relation-set: 0 Initial matrix: 500263 x 564212 with sparse part having weight 39359534. Pruned matrix : 442161 x 444726 with weight 27121752. Polynomial selection time: 1.87 hours. Total sieving time: 34.72 hours. Total relation processing time: 0.37 hours. Matrix solve time: 7.00 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 44.29 hours. --------- CPU info (if available) ----------
Aug 13, 2007 (2nd): By Jo Yeong Uk / GGNFS
7·10¹⁷⁹-3 = 6(9)₁₇₈7_<180> = C180
C180 = P74 · P106
P74 = 83251080449638728944649575376467201073537285846278352308844383882413696253_<74>
P106 = 8408299282355291944507594847871979982320198163187651997979672667927349257101780731688554079997824589461249_<106>

Number: 69997_179 N=699999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 180 digits) SNFS difficulty: 180 digits. Divisors found: r1=83251080449638728944649575376467201073537285846278352308844383882413696253 (pp74) r2=8408299282355291944507594847871979982320198163187651997979672667927349257101780731688554079997824589461249 (pp106) Version: GGNFS-0.77.1-20050930-nocona Total time: 259.62 hours. Scaled time: 556.63 units (timescale=2.144). Factorization parameters were as follows: n: 699999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 1000000000000000000000000000000000000 c5: 7 c0: -30 skew: 1.34 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, 9200001) Primes: RFBsize:664579, AFBsize:664690, largePrimes:11188054 encountered Relations: rels:11548928, finalFF:1569648 Max relations in full relation-set: 28 Initial matrix: 1329334 x 1569648 with sparse part having weight 96955888. Pruned matrix : 1111881 x 1118591 with weight 66486936. Total sieving time: 248.05 hours. Total relation processing time: 0.34 hours. Matrix solve time: 11.11 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000 total time: 259.62 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
Aug 13, 2007: By Robert Backstrom / GGNFS
(5·10¹⁶³-41)/9 = (5)₁₆₂1_<163> = 6197 · 16253 · 7766599 · C148
C148 = P41 · P108
P41 = 44413093788181068954686083501992838352239_<41>
P108 = 159908133455531109958414064342395777100821881761406305592132607285851371898166471209881193256579918516686151_<108>

Number: n N=7102014928653478112505380375170028150587599569829032560645158534704706517857033098640933711918896001508344830631819199337896740041018214185551142089 ( 148 digits) SNFS difficulty: 164 digits. Divisors found: r1=44413093788181068954686083501992838352239 (pp41) r2=159908133455531109958414064342395777100821881761406305592132607285851371898166471209881193256579918516686151 (pp108) Version: GGNFS-0.77.1-20051202-athlon Total time: 69.01 hours. Scaled time: 91.16 units (timescale=1.321). Factorization parameters were as follows: name: KA_5_162_1 n: 7102014928653478112505380375170028150587599569829032560645158534704706517857033098640933711918896001508344830631819199337896740041018214185551142089 skew: 1.91 deg: 5 c5: 8 c0: -205 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, 2900001) Primes: RFBsize:250150, AFBsize:250182, largePrimes:7611933 encountered Relations: rels:7124868, finalFF:583205 Max relations in full relation-set: 48 Initial matrix: 500397 x 583205 with sparse part having weight 50754245. Pruned matrix : 443931 x 446496 with weight 33952521. Total sieving time: 61.81 hours. Total relation processing time: 0.26 hours. Matrix solve time: 6.84 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 69.01 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁵⁰+3 = 8(0)₁₄₉3_<151> = 11² · 333847094812043_<15> · C135
C135 = P63 · P73
P63 = 123915190735934296426572399348483454050629019309155367871597523_<63>
P73 = 1598204928807240823149342852972588765245266509250337333568977262671359787_<73>

Number: n N=198041868588259539803544224019989437375283062870153485808447332705304657558186289935035160659072536263589755720823920126704382391007601 ( 135 digits) SNFS difficulty: 150 digits. Divisors found: r1=123915190735934296426572399348483454050629019309155367871597523 (pp63) r2=1598204928807240823149342852972588765245266509250337333568977262671359787 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 16.97 hours. Scaled time: 20.32 units (timescale=1.197). Factorization parameters were as follows: name: KA_8_0_149_3 n: 198041868588259539803544224019989437375283062870153485808447332705304657558186289935035160659072536263589755720823920126704382391007601 type: snfs skew: 1.00 deg: 5 c5: 8 c0: 3 m: 1000000000000000000000000000000 rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:135072, AFBsize:135053, largePrimes:5515066 encountered Relations: rels:4864048, finalFF:313876 Max relations in full relation-set: 28 Initial matrix: 270190 x 313876 with sparse part having weight 18476130. Pruned matrix : 235766 x 237180 with weight 11424414. Total sieving time: 15.58 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.12 hours. Total square root time: 0.10 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.3,2.3,100000 total time: 16.97 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
8·10¹⁵⁹+3 = 8(0)₁₅₈3_<160> = 53 · 1249 · 15803 · C151
C151 = P63 · P89
P63 = 153231313845746405825884701365885833226325571486615400562069271_<63>
P89 = 49907361884479263130985185256128895476821348429200465525031812515377456758530477125109523_<89>

Number: n N=7647370632133883748883439676346985948647594574867711170484935573163178215153995040284393630963460365084651885728655779192405179039901887446685387767733 ( 151 digits) SNFS difficulty: 160 digits. Divisors found: r1=153231313845746405825884701365885833226325571486615400562069271 (pp63) r2=49907361884479263130985185256128895476821348429200465525031812515377456758530477125109523 (pp89) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.43 hours. Scaled time: 42.61 units (timescale=1.448). Factorization parameters were as follows: name: KA_8_0_158_3 n: 7647370632133883748883439676346985948647594574867711170484935573163178215153995040284393630963460365084651885728655779192405179039901887446685387767733 skew: 1.00 deg: 5 c5: 4 c0: 15 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:216816, AFBsize:216826, largePrimes:7196792 encountered Relations: rels:6799215, finalFF:597924 Max relations in full relation-set: 28 Initial matrix: 433706 x 597924 with sparse part having weight 41582443. Pruned matrix : 302044 x 304276 with weight 22428346. Total sieving time: 26.46 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.67 hours. Total square root time: 0.11 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 29.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
8·10¹⁶³+3 = 8(0)₁₆₂3_<164> = C164
C164 = P45 · P52 · P69
P45 = 263814841588028840292075635769021187187588777_<45>
P52 = 2946574066938041203271903376456481181720414869700453_<52>
P69 = 102913749296606783576701454837580698830029182185894558528664578737263_<69>

Number: n N=80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 164 digits) SNFS difficulty: 165 digits. Divisors found: r1=263814841588028840292075635769021187187588777 (pp45) r2=2946574066938041203271903376456481181720414869700453 (pp52) r3=102913749296606783576701454837580698830029182185894558528664578737263 (pp69) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 62.05 hours. Scaled time: 84.20 units (timescale=1.357). Factorization parameters were as follows: name: KA_8_0_162_3 n: 80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 skew: 1.00 deg: 5 c5: 2 c0: 75 m: 1000000000000000000000000000000000 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, 2500001) Primes: RFBsize:250150, AFBsize:249511, largePrimes:7415037 encountered Relations: rels:6927576, finalFF:563657 Max relations in full relation-set: 28 Initial matrix: 499726 x 563657 with sparse part having weight 39806187. Pruned matrix : 449061 x 451623 with weight 27825880. Total sieving time: 57.09 hours. Total relation processing time: 0.27 hours. Matrix solve time: 4.42 hours. Total square root time: 0.28 hours, sqrts: 2. 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: 62.05 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Aug 12, 2007 (4th): By Jo Yeong Uk / GGNFS gnfs
8·10¹⁷⁶+3 = 8(0)₁₇₅3_<177> = 11 · 29 · 31 · 97 · 62483 · 122288966750943559327954013_<27> · 13203393905721557635469906716094551_<35> · C106
C106 = P43 · P64
P43 = 4919037198222532817308550055704182012037503_<43>
P64 = 1680548460217191645379213872474567141004274448100352481467434493_<64>

Number: 80003_176 N=8266680389223966046190855264388717362005347788894913038658978035326508882118999267460085367871413111790979 ( 106 digits) Divisors found: r1=4919037198222532817308550055704182012037503 (pp43) r2=1680548460217191645379213872474567141004274448100352481467434493 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.56 hours. Scaled time: 22.54 units (timescale=2.135). Factorization parameters were as follows: name: 80003_176 n: 8266680389223966046190855264388717362005347788894913038658978035326508882118999267460085367871413111790979 skew: 8767.65 # norm 5.59e+14 c5: 116160 c4: 400128896 c3: 21447396988402 c2: 200361732810880499 c1: -1755467344504781210762 c0: 512626880120314573894360 # alpha -5.94 Y1: 2910066641 Y0: -148065849568313383617 # Murphy_E 1.51e-09 # M 3579913611478992133536848804092742505729175910292785985960854211602842315010438921637008484004440532117018 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1440001) Primes: RFBsize:135072, AFBsize:135363, largePrimes:4572261 encountered Relations: rels:4637401, finalFF:384253 Max relations in full relation-set: 28 Initial matrix: 270519 x 384253 with sparse part having weight 37006164. Pruned matrix : 210066 x 211482 with weight 18180369. Polynomial selection time: 0.48 hours. Total sieving time: 9.69 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.22 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 10.56 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.10 BogoMIPS).
Aug 12, 2007 (3rd): By Robert Backstrom / GGNFS
7·10¹⁶¹+3 = 7(0)₁₆₀3_<162> = 29 · 37 · 73 · 1403225401_<10> · C148
C148 = P40 · P109
P40 = 3753845625711756879793515975255349607797_<40>
P109 = 1696569329960212414283207012646965391569808922194244639849139334297461697448507406571284397297756255793527431_<109>

Number: n N=6368659357987869688073561004013094128236058980958992215610258085707689898194797495537752585473375498765201263898209639690325753644190663517010979507 ( 148 digits) SNFS difficulty: 161 digits. Divisors found: r1=3753845625711756879793515975255349607797 (pp40) r2=1696569329960212414283207012646965391569808922194244639849139334297461697448507406571284397297756255793527431 (pp109) Version: GGNFS-0.77.1-20051202-athlon Total time: 52.92 hours. Scaled time: 76.63 units (timescale=1.448). Factorization parameters were as follows: name: KA_7_0_160_3 n: 6368659357987869688073561004013094128236058980958992215610258085707689898194797495537752585473375498765201263898209639690325753644190663517010979507 skew: 0.53 deg: 5 c5: 70 c0: 3 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2400001) Primes: RFBsize:250150, AFBsize:249361, largePrimes:7501056 encountered Relations: rels:7035914, finalFF:574163 Max relations in full relation-set: 28 Initial matrix: 499578 x 574163 with sparse part having weight 42428847. Pruned matrix : 441215 x 443776 with weight 29106337. Total sieving time: 46.77 hours. Total relation processing time: 0.24 hours. Matrix solve time: 5.57 hours. Total square root time: 0.34 hours, sqrts: 4. 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: 52.92 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(8·10¹⁶⁴-71)/9 = (8)₁₆₃1_<164> = 3⁴ · 499 · C160
C160 = P79 · P81
P79 = 6702863948665376016824925578772117152858124361875429504392949157960651371083473_<79>
P81 = 328096432855899090449878151867788591711321056497892958204836930069357451062128363_<81>

Number: n N=2199185751475516190130604143815752217741381253590857984831116279197627078574157918030849078128822803357057049627375464234367225534745760382218483606444713844699 ( 160 digits) SNFS difficulty: 165 digits. Divisors found: r1=6702863948665376016824925578772117152858124361875429504392949157960651371083473 (pp79) r2=328096432855899090449878151867788591711321056497892958204836930069357451062128363 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 92.52 hours. Scaled time: 110.83 units (timescale=1.198). Factorization parameters were as follows: name: KA_8_163_1 n: 2199185751475516190130604143815752217741381253590857984831116279197627078574157918030849078128822803357057049627375464234367225534745760382218483606444713844699 type: snfs skew: 2.45 deg: 5 c5: 4 c0: -355 m: 1000000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3600001) Primes: RFBsize:250150, AFBsize:250837, largePrimes:7783343 encountered Relations: rels:7291842, finalFF:562621 Max relations in full relation-set: 28 Initial matrix: 501051 x 562621 with sparse part having weight 46426453. Pruned matrix : 472306 x 474875 with weight 35341023. Total sieving time: 83.37 hours. Total relation processing time: 0.36 hours. Matrix solve time: 8.48 hours. Total square root time: 0.30 hours, sqrts: 2. 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: 92.52 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Aug 12, 2007 (2nd): By Sinkiti Sibata / GGNFS
8·10¹⁴²+3 = 8(0)₁₄₁3_<143> = 7 · 11 · 2052821 · 555623953052671_<15> · 66874197333983887_<17> · C104
C104 = P43 · P61
P43 = 7352063485952674581275466674908134761977993_<43>
P61 = 1852675630827404483230700868124109595424698262269677635106219_<61>

Number: 80003_142 N=13620988856720497819323489328579752204608642469675042020812530924002228230975710728961746240569095438467 ( 104 digits) SNFS difficulty: 142 digits. Divisors found: r1=7352063485952674581275466674908134761977993 (pp43) r2=1852675630827404483230700868124109595424698262269677635106219 (pp61) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 10.17 hours. Scaled time: 6.93 units (timescale=0.682). Factorization parameters were as follows: name: 80003_142 n: 13620988856720497819323489328579752204608642469675042020812530924002228230975710728961746240569095438467 m: 20000000000000000000000000000 c5: 25 c0: 3 skew: 0.65 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1550001) Primes: RFBsize:100021, AFBsize:100163, largePrimes:2522518 encountered Relations: rels:2425661, finalFF:224441 Max relations in full relation-set: 0 Initial matrix: 200248 x 224441 with sparse part having weight 19391779. Pruned matrix : 193093 x 194158 with weight 13708815. Total sieving time: 9.05 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.93 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 10.17 hours. --------- CPU info (if available) ----------
Aug 12, 2007: By Jo Yeong Uk / GMP-ECM
8·10¹⁶⁹+3 = 8(0)₁₆₈3_<170> = C170
C170 = P37 · P134
P37 = 1224246060187948513536044665977519421_<37>
P134 = 65346340577741579518249257770472291479731205704109850662463019782005485937532123816920926149530479698626097812995924318713137169466943_<134>
Aug 11, 2007 (3rd): By Sinkiti Sibata / GGNFS gnfs
10¹⁷⁷+9 = 1(0)₁₇₆9_<178> = 33223 · 58440312251_<11> · 744650270536087_<15> · 1299108566054859101828202487_<28> · C120
C120 = P29 · P43 · P49
P29 = 47281281988259427195595389853_<29>
P43 = 6045096991231523085796053943692409216016933_<43>
P49 = 1862766037506329182860674793008889448818081551293_<49>

Number: 10009_177 N=532415668670779658238030449477892100777113679642064502418427003147194580334216529773302144542970825544807513606040387757 ( 120 digits) Divisors found: r1=47281281988259427195595389853 (pp29) r2=6045096991231523085796053943692409216016933 (pp43) r3=1862766037506329182860674793008889448818081551293 (pp49) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 103.73 hours. Scaled time: 70.75 units (timescale=0.682). Factorization parameters were as follows: name: 10009_177 n: 532415668670779658238030449477892100777113679642064502418427003147194580334216529773302144542970825544807513606040387757 skew: 48264.27 # norm 2.43e+16 c5: 75600 c4: 16297075446 c3: -73949054544926 c2: -41520893798791949092 c1: 676986651332945360199391 c0: -51146483475813285206452764 # alpha -5.94 Y1: 12936640435517 Y0: -93227321831539954601855 # Murphy_E 3.10e-10 # M 480158086077406144788789117762923709702782058085914313143143829119151924171861230494781642332247911106356265369031255073 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4170001) Primes: RFBsize:315948, AFBsize:316216, largePrimes:7549833 encountered Relations: rels:7503324, finalFF:708238 Max relations in full relation-set: 0 Initial matrix: 632249 x 708238 with sparse part having weight 69993656. Pruned matrix : 571237 x 574462 with weight 47768804. Polynomial selection time: 5.21 hours. Total sieving time: 78.11 hours. Total relation processing time: 0.69 hours. Matrix solve time: 19.22 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 103.73 hours. --------- CPU info (if available) ----------
(2·10¹⁹³-11)/9 = (2)₁₉₂1_<193> = 23 · 181 · 277 · 3511 · 281650732446817_<15> · 54780711280843190885242223364871889_<35> · 35938228281219889499007772234416370507_<38> · C96
C96 = P42 · P55
P42 = 679822382825034769795684390738450884934873_<42>
P55 = 1456061780748313525137900176910207059850883947091570327_<55>

Number: 22221_193 N=989863389328781839230043303989307230434755222530043430476647889044550036356250295190656694313471 ( 96 digits) Divisors found: r1=679822382825034769795684390738450884934873 (pp42) r2=1456061780748313525137900176910207059850883947091570327 (pp55) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 12.06 hours. Scaled time: 8.22 units (timescale=0.682). Factorization parameters were as follows: name: 22221_193 n: 989863389328781839230043303989307230434755222530043430476647889044550036356250295190656694313471 m: 9969085082195574864923 deg: 4 c4: 100219920 c3: 489291912 c2: -3426064493939695 c1: 7273856613595100453 c0: -1638550796927040570617 skew: 1635.250 type: gnfs # adj. I(F,S) = 51.150 # E(F1,F2) = 2.262164e-05 # GGNFS version 0.77.1-20060722-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1186765353. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1620001) Primes: RFBsize:92938, AFBsize:92821, largePrimes:1911630 encountered Relations: rels:1990482, finalFF:208813 Max relations in full relation-set: 0 Initial matrix: 185833 x 208813 with sparse part having weight 19174383. Pruned matrix : 176230 x 177223 with weight 14578587. Polynomial selection time: 0.17 hours. Total sieving time: 10.85 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.84 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 12.06 hours. --------- CPU info (if available) ----------
Aug 11, 2007 (2nd): By JMB / GMP-ECM
8·10¹⁷⁶+3 = 8(0)₁₇₅3_<177> = 11 · 29 · 31 · 97 · 62483 · 122288966750943559327954013_<27> · C141
C141 = P35 · C106
P35 = 13203393905721557635469906716094551_<35>
C106 = [8266680389223966046190855264388717362005347788894913038658978035326508882118999267460085367871413111790979_<106>]
8·10¹⁷⁵+3 = 8(0)₁₇₄3_<176> = 2311 · 8719 · 10144789 · 189170845637_<12> · C151
C151 = P35 · P116
P35 = 64291971599470835512165635997396471_<35>
P116 = 32178766751417498825847425179242872864738948414927779187900762406084025362150026649375978793241187540045915304472389_<116>
8·10¹⁸⁹+3 = 8(0)₁₈₈3_<190> = 619 · 1847 · 2087 · 17854618292333_<14> · 66686803592942902296799_<23> · C145
C145 = P33 · C112
P33 = 921080685636059212526826174467963_<33>
C112 = [3057185889473590067108879535881711047802061887351934101508239518685119755420999299188104236165875118418785864873_<112>]
Aug 11, 2007: By Robert Backstrom / GGNFS
8·10¹⁴⁵+3 = 8(0)₁₄₄3_<146> = 11766775508491_<14> · 605396612359960159_<18> · C116
C116 = P50 · P66
P50 = 51046027337556414770008979411652470215926317473591_<50>
P66 = 220004003518038430086171786263037474229055943495226606880307715457_<66>

Number: n N=11230330377953647351813832317701470309443467192544987569991922681053152302088521038361975470850797594365793139996087 ( 116 digits) SNFS difficulty: 145 digits. Divisors found: r1=51046027337556414770008979411652470215926317473591 (pp50) r2=220004003518038430086171786263037474229055943495226606880307715457 (pp66) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 7.75 hours. Scaled time: 9.76 units (timescale=1.260). Factorization parameters were as follows: name: KA_8_0_144_3 n: 11230330377953647351813832317701470309443467192544987569991922681053152302088521038361975470850797594365793139996087 skew: 1.00 deg: 5 c5: 8 c0: 3 m: 100000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:148933, AFBsize:149135, largePrimes:6365962 encountered Relations: rels:5765123, finalFF:372600 Max relations in full relation-set: 28 Initial matrix: 298133 x 372600 with sparse part having weight 24992928. Pruned matrix : 240431 x 241985 with weight 13737511. Total sieving time: 6.21 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.30 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 7.75 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁵³+3 = 8(0)₁₅₂3_<154> = 151 · 347 · 2843 · C146
C146 = P73 · P74
P73 = 1902048496423825078608398414836733249964757502655492013897910231644363411_<73>
P74 = 28234826233775491249880369404044758618051858710202572340818371819411450863_<74>

Number: n N=53704008784740644981520484142176234524761914856979746560176003073910054820985037452269471329883311728322482583806733611354063944463717843541573693 ( 146 digits) SNFS difficulty: 153 digits. Divisors found: r1=1902048496423825078608398414836733249964757502655492013897910231644363411 (pp73) r2=28234826233775491249880369404044758618051858710202572340818371819411450863 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.88 hours. Scaled time: 32.17 units (timescale=1.197). Factorization parameters were as follows: name: KA_8_0_152_3 n: 53704008784740644981520484142176234524761914856979746560176003073910054820985037452269471329883311728322482583806733611354063944463717843541573693 type: snfs skew: 1.00 deg: 5 c5: 250 c0: 3 m: 2000000000000000000000000000000 rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1200000) Primes: RFBsize:135072, AFBsize:134848, largePrimes:5889592 encountered Relations: rels:5236925, finalFF:309112 Max relations in full relation-set: 28 Initial matrix: 269986 x 309112 with sparse part having weight 23758236. Pruned matrix : 245541 x 246954 with weight 16261877. Total sieving time: 24.71 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.63 hours. Total square root time: 0.34 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.3,2.3,100000 total time: 26.88 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Aug 10, 2007 (2nd): By Robert Backstrom / GGNFS
8·10¹³⁸+3 = 8(0)₁₃₇3_<139> = 11 · 73 · 114702851 · C128
C128 = P37 · P45 · P48
P37 = 1670593388520748238821421178145481837_<37>
P45 = 104636458414847985111598726280566932595983083_<45>
P48 = 496874190989597803112505558533083407730421846981_<48>

Number: n N=86856080845160518253064258730936858983574839513012302022899381995276333715215501484147076660404979494712817786900486579971431051 ( 128 digits) SNFS difficulty: 138 digits. Divisors found: r1=1670593388520748238821421178145481837 (pp37) r2=104636458414847985111598726280566932595983083 (pp45) r3=496874190989597803112505558533083407730421846981 (pp48) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 5.54 hours. Scaled time: 7.56 units (timescale=1.364). Factorization parameters were as follows: name: KA_8_0_137_3 n: 86856080845160518253064258730936858983574839513012302022899381995276333715215501484147076660404979494712817786900486579971431051 skew: 1.00 deg: 5 c5: 250 c0: 3 m: 2000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 550001) Primes: RFBsize:114155, AFBsize:113962, largePrimes:5547105 encountered Relations: rels:4879377, finalFF:259041 Max relations in full relation-set: 28 Initial matrix: 228183 x 259041 with sparse part having weight 16762861. Pruned matrix : 205241 x 206445 with weight 11006091. Total sieving time: 4.58 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.70 hours. Total square root time: 0.11 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000 total time: 5.54 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁴⁴+3 = 8(0)₁₄₃3_<145> = 11 · 683 · C142
C142 = P51 · P91
P51 = 393806677683834962330167370796793978219439105832001_<51>
P91 = 2703918032157216794192284740946405968077357310935054868472060871084932805552853385839924731_<91>

Number: n N=1064820976973246372953547184879542126979901504059629974710501796885398642353254359110874484227339278583788100625582323971782244110208971116731 ( 142 digits) SNFS difficulty: 145 digits. Divisors found: r1=393806677683834962330167370796793978219439105832001 (pp51) r2=2703918032157216794192284740946405968077357310935054868472060871084932805552853385839924731 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.79 hours. Scaled time: 8.99 units (timescale=1.324). Factorization parameters were as follows: name: KA_8_0_143_3 n: 1064820976973246372953547184879542126979901504059629974710501796885398642353254359110874484227339278583788100625582323971782244110208971116731 skew: 1.00 deg: 5 c5: 4 c0: 15 m: 100000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 850001) Primes: RFBsize:114155, AFBsize:113727, largePrimes:6267824 encountered Relations: rels:5579150, finalFF:297337 Max relations in full relation-set: 48 Initial matrix: 227946 x 297337 with sparse part having weight 29469240. Pruned matrix : 198102 x 199305 with weight 14244835. Total sieving time: 5.61 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.99 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 6.79 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁵⁴+3 = 8(0)₁₅₃3_<155> = 7² · 11 · 73 · C151
C151 = P70 · P81
P70 = 6763250917489964555182738767583283902011275699423252245547421266789261_<70>
P81 = 300623454884502196692218573721100636698457518684754797248879483662802680386190709_<81>

Number: n N=2033191857066612448217144890334714209469591074287747477571352326733931430604620428495183876788573461763285638041019645716318906142780898162502859176049 ( 151 digits) SNFS difficulty: 155 digits. Divisors found: r1=6763250917489964555182738767583283902011275699423252245547421266789261 (pp70) r2=300623454884502196692218573721100636698457518684754797248879483662802680386190709 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 17.23 hours. Scaled time: 24.95 units (timescale=1.448). Factorization parameters were as follows: name: KA_8_0_153_3 n: 2033191857066612448217144890334714209469591074287747477571352326733931430604620428495183876788573461763285638041019645716318906142780898162502859176049 skew: 1.00 deg: 5 c5: 4 c0: 15 m: 10000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 850001) Primes: RFBsize:148933, AFBsize:148725, largePrimes:6495234 encountered Relations: rels:5901096, finalFF:356866 Max relations in full relation-set: 28 Initial matrix: 297722 x 356866 with sparse part having weight 28838481. Pruned matrix : 256532 x 258084 with weight 18263570. Total sieving time: 15.26 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.67 hours. Total square root time: 0.14 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 17.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(10¹⁶⁵+11)/3 = (3)₁₆₄7_<165> = 17 · 5623 · 36251 · 40841 · C151
C151 = P39 · P112
P39 = 251375332502629231539468126698454636637_<39>
P112 = 9369636094184618241793486374540111317162701410154625358284353734039880944057232414047815901279320321000606011721_<112>

Number: n N=2355295388604294669648572183314730221423189911340492129466961410071358157729919347954433141504960864116536706486551542372736924805270377019388818022277 ( 151 digits) SNFS difficulty: 165 digits. Divisors found: r1=251375332502629231539468126698454636637 (pp39) r2=9369636094184618241793486374540111317162701410154625358284353734039880944057232414047815901279320321000606011721 (pp112) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 48.70 hours. Scaled time: 66.62 units (timescale=1.368). Factorization parameters were as follows: name: KA_3_164_7 n: 2355295388604294669648572183314730221423189911340492129466961410071358157729919347954433141504960864116536706486551542372736924805270377019388818022277 skew: 1.62 deg: 5 c5: 1 c0: 11 m: 1000000000000000000000000000000000 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, 2000001) Primes: RFBsize:250150, AFBsize:249887, largePrimes:7439713 encountered Relations: rels:7043065, finalFF:634459 Max relations in full relation-set: 28 Initial matrix: 500101 x 634459 with sparse part having weight 42656542. Pruned matrix : 388359 x 390923 with weight 24700758. Total sieving time: 45.21 hours. Total relation processing time: 0.25 hours. Matrix solve time: 3.12 hours. Total square root time: 0.11 hours, sqrts: 1. 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: 48.70 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Aug 10, 2007: By JMB / GMP-ECM
8·10¹⁶⁵+3 = 8(0)₁₆₄3_<166> = 17 · 83 · 2221 · 12653 · C156
C156 = P32 · C125
P32 = 19558081525904346337653953996359_<32>
C125 = [10315603825280902403145997952176939809173663207855210896021945321896591973517956833167339304970176688502856732303629068284319_<125>]
8·10¹⁹⁷+3 = 8(0)₁₉₆3_<198> = 17 · 19 · 49701979 · 780808607 · C179
C179 = P29 · C151
P29 = 26076920319273076996675767301_<29>
C151 = [2447444719548378339619829614249789627085695960053062447396841606685367979050190055438702256834046939845645421862753151405036735916578790278144353058537_<151>]
8·10¹⁷⁷+3 = 8(0)₁₇₆3_<178> = 385193 · C173
C173 = P34 · P139
P34 = 2734184657326888957539301452070127_<34>
P139 = 7595979059565388610562921211099574234745355573365762780772087213624892584821367744840306376847974198287155385422756473803526652906088908773_<139>
Aug 9, 2007 (4th): By JMB / GMP-ECM B1=3000000
(2·10¹⁹³-11)/9 = (2)₁₉₂1_<193> = 23 · 181 · 277 · 3511 · 281650732446817_<15> · 54780711280843190885242223364871889_<35> · C134
C134 = P38 · C96
P38 = 35938228281219889499007772234416370507_<38>
C96 = [989863389328781839230043303989307230434755222530043430476647889044550036356250295190656694313471_<96>]
Aug 9, 2007 (3rd): By Robert Backstrom / Msieve, GGNFS
8·10¹¹⁶+3 = 8(0)₁₁₅3_<117> = 11 · 31 · 501077 · 30244611063283188190841459_<26> · C84
C84 = P35 · P49
P35 = 47772235073471907793622686848045341_<35>
P49 = 3240466788618869376438883648133185467425146712141_<49>

Thu Aug 09 14:29:32 2007 Msieve v. 1.25 Thu Aug 09 14:29:32 2007 random seeds: 96c33e48 849923a9 Thu Aug 09 14:29:32 2007 factoring 154804341173679230387244001472705605593917034967797099265321043659212166198643185081 (84 digits) Thu Aug 09 14:29:32 2007 commencing quadratic sieve (83-digit input) Thu Aug 09 14:29:32 2007 using multiplier of 1 Thu Aug 09 14:29:32 2007 using 64kb Opteron sieve core Thu Aug 09 14:29:32 2007 sieve interval: 6 blocks of size 65536 Thu Aug 09 14:29:32 2007 processing polynomials in batches of 17 Thu Aug 09 14:29:32 2007 using a sieve bound of 1392701 (52970 primes) Thu Aug 09 14:29:32 2007 using large prime bound of 121164987 (26 bits) Thu Aug 09 14:29:32 2007 using trial factoring cutoff of 27 bits Thu Aug 09 14:29:32 2007 polynomial 'A' values have 11 factors Thu Aug 09 14:55:43 2007 53067 relations (26868 full + 26199 combined from 280831 partial), need 53066 Thu Aug 09 14:55:44 2007 begin with 307699 relations Thu Aug 09 14:55:44 2007 reduce to 75934 relations in 2 passes Thu Aug 09 14:55:44 2007 attempting to read 75934 relations Thu Aug 09 14:55:45 2007 recovered 75934 relations Thu Aug 09 14:55:45 2007 recovered 69763 polynomials Thu Aug 09 14:55:45 2007 attempting to build 53067 cycles Thu Aug 09 14:55:45 2007 found 53067 cycles in 1 passes Thu Aug 09 14:55:45 2007 distribution of cycle lengths: Thu Aug 09 14:55:45 2007 length 1 : 26868 Thu Aug 09 14:55:45 2007 length 2 : 26199 Thu Aug 09 14:55:45 2007 largest cycle: 2 relations Thu Aug 09 14:55:45 2007 matrix is 52970 x 53067 with weight 1684778 (avg 31.75/col) Thu Aug 09 14:55:45 2007 filtering completed in 4 passes Thu Aug 09 14:55:45 2007 matrix is 46050 x 46114 with weight 1439023 (avg 31.21/col) Thu Aug 09 14:55:46 2007 saving the first 48 matrix rows for later Thu Aug 09 14:55:46 2007 matrix is 46002 x 46114 with weight 1048370 (avg 22.73/col) Thu Aug 09 14:55:46 2007 matrix includes 64 packed rows Thu Aug 09 14:55:46 2007 commencing Lanczos iteration Thu Aug 09 14:56:38 2007 lanczos halted after 729 iterations Thu Aug 09 14:56:38 2007 recovered 9 nontrivial dependencies Thu Aug 09 14:56:38 2007 prp35 factor: 47772235073471907793622686848045341 Thu Aug 09 14:56:38 2007 prp49 factor: 3240466788618869376438883648133185467425146712141 Thu Aug 09 14:56:38 2007 elapsed time 00:27:06
8·10¹⁰²+3 = 8(0)₁₀₁3_<103> = 11 · 59 · 2909 · 250321394839_<12> · C86
C86 = P32 · P54
P32 = 73893077891192132187902179374341_<32>
P54 = 229086681980295270219691452305688749689507823847518717_<54>

Thu Aug 09 14:31:54 2007 Msieve v. 1.25 Thu Aug 09 14:31:54 2007 random seeds: e58a55a8 3980cc5c Thu Aug 09 14:31:54 2007 factoring 16927920035404719454950678067803074038183144629096960489580783099151622954488347040497 (86 digits) Thu Aug 09 14:31:55 2007 commencing quadratic sieve (85-digit input) Thu Aug 09 14:31:55 2007 using multiplier of 1 Thu Aug 09 14:31:55 2007 using 64kb Opteron sieve core Thu Aug 09 14:31:55 2007 sieve interval: 7 blocks of size 65536 Thu Aug 09 14:31:55 2007 processing polynomials in batches of 15 Thu Aug 09 14:31:55 2007 using a sieve bound of 1449953 (55333 primes) Thu Aug 09 14:31:55 2007 using large prime bound of 115996240 (26 bits) Thu Aug 09 14:31:55 2007 using double large prime bound of 328094552866320 (41-49 bits) Thu Aug 09 14:31:55 2007 using trial factoring cutoff of 49 bits Thu Aug 09 14:31:55 2007 polynomial 'A' values have 11 factors Thu Aug 09 15:12:48 2007 55692 relations (15689 full + 40003 combined from 580417 partial), need 55429 Thu Aug 09 15:12:49 2007 begin with 596106 relations Thu Aug 09 15:12:50 2007 reduce to 132442 relations in 9 passes Thu Aug 09 15:12:50 2007 attempting to read 132442 relations Thu Aug 09 15:12:51 2007 recovered 132442 relations Thu Aug 09 15:12:51 2007 recovered 111632 polynomials Thu Aug 09 15:12:51 2007 attempting to build 55692 cycles Thu Aug 09 15:12:52 2007 found 55691 cycles in 4 passes Thu Aug 09 15:12:52 2007 distribution of cycle lengths: Thu Aug 09 15:12:52 2007 length 1 : 15689 Thu Aug 09 15:12:52 2007 length 2 : 11064 Thu Aug 09 15:12:52 2007 length 3 : 9749 Thu Aug 09 15:12:52 2007 length 4 : 7447 Thu Aug 09 15:12:52 2007 length 5 : 4954 Thu Aug 09 15:12:52 2007 length 6 : 3059 Thu Aug 09 15:12:52 2007 length 7 : 1772 Thu Aug 09 15:12:52 2007 length 9+: 1957 Thu Aug 09 15:12:52 2007 largest cycle: 16 relations Thu Aug 09 15:12:52 2007 matrix is 55333 x 55691 with weight 2873455 (avg 51.60/col) Thu Aug 09 15:12:52 2007 filtering completed in 3 passes Thu Aug 09 15:12:52 2007 matrix is 50648 x 50712 with weight 2633663 (avg 51.93/col) Thu Aug 09 15:12:53 2007 saving the first 48 matrix rows for later Thu Aug 09 15:12:53 2007 matrix is 50600 x 50712 with weight 1927165 (avg 38.00/col) Thu Aug 09 15:12:53 2007 matrix includes 64 packed rows Thu Aug 09 15:12:53 2007 using block size 20284 for processor cache size 512 kB Thu Aug 09 15:12:53 2007 commencing Lanczos iteration Thu Aug 09 15:13:14 2007 lanczos halted after 801 iterations Thu Aug 09 15:13:14 2007 recovered 16 nontrivial dependencies Thu Aug 09 15:13:14 2007 prp32 factor: 73893077891192132187902179374341 Thu Aug 09 15:13:14 2007 prp54 factor: 229086681980295270219691452305688749689507823847518717 Thu Aug 09 15:13:14 2007 elapsed time 00:41:20
8·10¹⁰⁷+3 = 8(0)₁₀₆3_<108> = 19² · 53 · C104
C104 = P52(4311...) · P52(9698...)
P52(4311...) = 4311041529493168981918983158515670589329095421550917_<52>
P52(9698...) = 9698949742404051679952742591797529833940595342191923_<52>

Number: n N=41812575131970940260283280196519103120263419223331416923639784665238070349657659541106987926618930643391 ( 104 digits) SNFS difficulty: 107 digits. Divisors found: r1=4311041529493168981918983158515670589329095421550917 (pp52) r2=9698949742404051679952742591797529833940595342191923 (pp52) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.82 hours. Scaled time: 0.98 units (timescale=1.196). Factorization parameters were as follows: name: KA_8_0_106_3 n: 41812575131970940260283280196519103120263419223331416923639784665238070349657659541106987926618930643391 type: snfs skew: 2.45 deg: 5 c5: 25 c0: 3 m: 2000000000000000000000 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 150001) Primes: RFBsize:41538, AFBsize:41527, largePrimes:3147623 encountered Relations: rels:2766724, finalFF:215667 Max relations in full relation-set: 28 Initial matrix: 83129 x 215667 with sparse part having weight 9858859. Pruned matrix : 43285 x 43764 with weight 1396638. Total sieving time: 0.71 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.01 hours. Total square root time: 0.03 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,107,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.4,2.4,50000 total time: 0.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
8·10¹⁰⁸+3 = 8(0)₁₀₇3_<109> = 11 · 5527 · C105
C105 = P31 · P74
P31 = 9958256083822556593072164658877_<31>
P74 = 13213703178894954610665804924839486965167161792188153823634168464500913387_<74>

Number: n N=131585440071056137638370314324719969735348783657088343174827705314406960869779758869681069789627777686399 ( 105 digits) SNFS difficulty: 108 digits. Divisors found: r1=9958256083822556593072164658877 (pp31) r2=13213703178894954610665804924839486965167161792188153823634168464500913387 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.96 hours. Scaled time: 1.27 units (timescale=1.318). Factorization parameters were as follows: name: KA_8_0_107_3 n: 131585440071056137638370314324719969735348783657088343174827705314406960869779758869681069789627777686399 skew: 1.91 deg: 5 c5: 250 c0: 3 m: 2000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 150001) Primes: RFBsize:49098, AFBsize:48961, largePrimes:3846138 encountered Relations: rels:3291694, finalFF:187322 Max relations in full relation-set: 48 Initial matrix: 98125 x 187322 with sparse part having weight 11179634. Pruned matrix : 63307 x 63861 with weight 2245348. Total sieving time: 0.84 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.02 hours. Total square root time: 0.03 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,108,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 0.96 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹¹⁷+3 = 8(0)₁₁₆3_<118> = 17 · 23 · 95569 · 3626149 · C104
C104 = P42 · P62
P42 = 743563094142647141671434594596447952314537_<42>
P62 = 79402233062151798302517520827673963545042250342272076178284489_<62>

Number: n N=59040570097529187032128911277836039384013278371200389290158971364162462588485899647445468362305596316593 ( 104 digits) SNFS difficulty: 117 digits. Divisors found: r1=743563094142647141671434594596447952314537 (pp42) r2=79402233062151798302517520827673963545042250342272076178284489 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.14 hours. Scaled time: 1.64 units (timescale=1.443). Factorization parameters were as follows: name: KA_8_0_116_3 n: 59040570097529187032128911277836039384013278371200389290158971364162462588485899647445468362305596316593 skew: 1.00 deg: 5 c5: 25 c0: 3 m: 200000000000000000000000 type: snfs rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:63951, AFBsize:63918, largePrimes:4177926 encountered Relations: rels:3612878, finalFF:208283 Max relations in full relation-set: 28 Initial matrix: 127933 x 208283 with sparse part having weight 10962041. Pruned matrix : 86287 x 86990 with weight 3088440. Total sieving time: 1.00 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.05 hours. Total square root time: 0.02 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000 total time: 1.14 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
8·10¹²⁶+3 = 8(0)₁₂₅3_<127> = 11 · 103 · 227 · 60103 · C117
C117 = P43 · P75
P43 = 2949429481414692226044768697960391260971797_<43>
P75 = 175468859339115509595120669476348065354330998690902949927637469395852909063_<75>

Number: n N=517533026804995032345061488216330006916176164718700807307201581209237696213471414277684828267532924867161658848696211 ( 117 digits) SNFS difficulty: 126 digits. Divisors found: r1=2949429481414692226044768697960391260971797 (pp43) r2=175468859339115509595120669476348065354330998690902949927637469395852909063 (pp75) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 2.10 hours. Scaled time: 2.86 units (timescale=1.363). Factorization parameters were as follows: name: KA_8_0_125_3 n: 517533026804995032345061488216330006916176164718700807307201581209237696213471414277684828267532924867161658848696211 skew: 1.00 deg: 5 c5: 80 c0: 3 m: 10000000000000000000000000 type: snfs rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 250001) Primes: RFBsize:63951, AFBsize:63988, largePrimes:4577180 encountered Relations: rels:3968605, finalFF:202139 Max relations in full relation-set: 28 Initial matrix: 128005 x 202139 with sparse part having weight 13983078. Pruned matrix : 98139 x 98843 with weight 4654958. Total sieving time: 1.87 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.11 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000 total time: 2.10 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹³⁰+3 = 8(0)₁₂₉3_<131> = 7 · 11 · 73 · 1301 · 1879 · 3920377 · 125920165279_<12> · C104
C104 = P47 · P57
P47 = 15660751854468820254646065544043536489389591847_<47>
P57 = 753072171293408570603918263199513415256851689104201069517_<57>

Number: n N=11793676403132109337177444136713268893806641945749404632686412140850069050669393720927990575945503427899 ( 104 digits) SNFS difficulty: 130 digits. Divisors found: r1=15660751854468820254646065544043536489389591847 (pp47) r2=753072171293408570603918263199513415256851689104201069517 (pp57) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.27 hours. Scaled time: 2.96 units (timescale=1.305). Factorization parameters were as follows: name: KA_8_0_129_3 n: 11793676403132109337177444136713268893806641945749404632686412140850069050669393720927990575945503427899 skew: 1.00 deg: 5 c5: 8 c0: 3 m: 100000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 300001) Primes: RFBsize:78498, AFBsize:78246, largePrimes:4755487 encountered Relations: rels:4123226, finalFF:215781 Max relations in full relation-set: 48 Initial matrix: 156809 x 215781 with sparse part having weight 16140594. Pruned matrix : 127889 x 128737 with weight 6317106. Total sieving time: 1.93 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.20 hours. Total square root time: 0.04 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 2.27 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹²⁹+3 = 8(0)₁₂₈3_<130> = 4373 · 82883 · C122
C122 = P46 · P76
P46 = 9383621683393851037733688168129743757022677767_<46>
P76 = 2352201687843988988161223366148433683159763965903221828415227547320810905051_<76>

Number: n N=22072170761768469666239173783026516686523849108802583384253601362287757765121417259381934136261701937246009840562805701117 ( 122 digits) SNFS difficulty: 130 digits. Divisors found: r1=9383621683393851037733688168129743757022677767 (pp46) r2=2352201687843988988161223366148433683159763965903221828415227547320810905051 (pp76) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.89 hours. Scaled time: 3.46 units (timescale=1.195). Factorization parameters were as follows: name: KA_8_0_128_3 n: 22072170761768469666239173783026516686523849108802583384253601362287757765121417259381934136261701937246009840562805701117 type: snfs skew: 1.00 deg: 5 c5: 4 c0: 15 m: 100000000000000000000000000 rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 450001) Primes: RFBsize:78498, AFBsize:78411, largePrimes:3620998 encountered Relations: rels:2967951, finalFF:178355 Max relations in full relation-set: 28 Initial matrix: 156973 x 178355 with sparse part having weight 5919463. Pruned matrix : 130863 x 131711 with weight 3517685. Total sieving time: 2.62 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.16 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.2,2.2,50000 total time: 2.89 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
8·10¹³¹+3 = 8(0)₁₃₀3_<132> = 31 · 18556133 · C124
C124 = P30 · P94
P30 = 140515311157889484872449865329_<30>
P94 = 9897309858587474462533808559524778559507284816320764852168510088136599686173598612238548962409_<94>

Number: n N=1390723574405466150002891922752752766517296638572619177330924811028871850790561074961733849709228297345315740432104733417561 ( 124 digits) SNFS difficulty: 131 digits. Divisors found: r1=140515311157889484872449865329 (pp30) r2=9897309858587474462533808559524778559507284816320764852168510088136599686173598612238548962409 (pp94) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.46 hours. Scaled time: 3.56 units (timescale=1.446). Factorization parameters were as follows: name: KA_8_0_130_3 n: 1390723574405466150002891922752752766517296638572619177330924811028871850790561074961733849709228297345315740432104733417561 skew: 1.00 deg: 5 c5: 80 c0: 3 m: 100000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 350001) Primes: RFBsize:78498, AFBsize:78611, largePrimes:4642958 encountered Relations: rels:3975934, finalFF:178377 Max relations in full relation-set: 28 Initial matrix: 157175 x 178377 with sparse part having weight 11167450. Pruned matrix : 144022 x 144871 with weight 7345153. Total sieving time: 2.06 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.26 hours. Total square root time: 0.05 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 2.46 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
8·10¹³²+3 = 8(0)₁₃₁3_<133> = 11 · 10091 · 41507 · 72923 · C119
C119 = P59 · P60
P59 = 59137933926855043059088194258782854822196623669244767645811_<59>
P60 = 402634584408763303069783264206996096355933083613814946383593_<60>

Number: n N=23810977449432183899061928385609941180131057745684131742392932620719752663657136531720801972378829641765634246765578923 ( 119 digits) SNFS difficulty: 132 digits. Divisors found: r1=59137933926855043059088194258782854822196623669244767645811 (pp59) r2=402634584408763303069783264206996096355933083613814946383593 (pp60) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 2.77 hours. Scaled time: 3.78 units (timescale=1.364). Factorization parameters were as follows: name: KA_8_0_131_3 n: 23810977449432183899061928385609941180131057745684131742392932620719752663657136531720801972378829641765634246765578923 skew: 1.00 deg: 5 c5: 25 c0: 3 m: 200000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 350001) Primes: RFBsize:78498, AFBsize:78411, largePrimes:4990879 encountered Relations: rels:4353452, finalFF:209067 Max relations in full relation-set: 28 Initial matrix: 156973 x 209067 with sparse part having weight 14999686. Pruned matrix : 132523 x 133371 with weight 7082557. Total sieving time: 2.37 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.26 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 2.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹³⁴+3 = 8(0)₁₃₃3_<135> = 11 · 149 · 43405903 · 643534253 · C116
C116 = P53 · P63
P53 = 99025999314875960050767509377639719951680928982163689_<53>
P63 = 176457993407320655445898143590093815879839497274040644855506527_<63>

Number: n N=17473929134257721901626949367676531901183471917932969856802783667946806325413661744285936035329994212640218521898103 ( 116 digits) SNFS difficulty: 135 digits. Divisors found: r1=99025999314875960050767509377639719951680928982163689 (pp53) r2=176457993407320655445898143590093815879839497274040644855506527 (pp63) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.16 hours. Scaled time: 4.11 units (timescale=1.301). Factorization parameters were as follows: name: KA_8_0_133_3 n: 17473929134257721901626949367676531901183471917932969856802783667946806325413661744285936035329994212640218521898103 skew: 1.00 deg: 5 c5: 4 c0: 15 m: 1000000000000000000000000000 type: snfs rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 400001) Primes: RFBsize:92938, AFBsize:92529, largePrimes:4943597 encountered Relations: rels:4272145, finalFF:210944 Max relations in full relation-set: 48 Initial matrix: 185531 x 210944 with sparse part having weight 15009718. Pruned matrix : 169069 x 170060 with weight 9148254. Total sieving time: 2.53 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.44 hours. Total square root time: 0.09 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000 total time: 3.16 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹³⁶+3 = 8(0)₁₃₅3_<137> = 7 · 11 · 525529 · 3285647117_<10> · C120
C120 = P54 · P67
P54 = 143530513309195232999340064204983398299225538897530547_<54>
P67 = 4192155846886791687644896239201840126733252957278980362790474381809_<67>

Number: n N=601702280575805267699515045826589007810490254765282153660216860433071030113676661720770461574543961771608356536518619523 ( 120 digits) SNFS difficulty: 137 digits. Divisors found: r1=143530513309195232999340064204983398299225538897530547 (pp54) r2=4192155846886791687644896239201840126733252957278980362790474381809 (pp67) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.95 hours. Scaled time: 4.27 units (timescale=1.446). Factorization parameters were as follows: name: KA_8_0_135_3 n: 601702280575805267699515045826589007810490254765282153660216860433071030113676661720770461574543961771608356536518619523 skew: 1.00 deg: 5 c5: 5 c0: 6 m: 2000000000000000000000000000 type: snfs rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 450001) Primes: RFBsize:92938, AFBsize:93119, largePrimes:5260301 encountered Relations: rels:4633571, finalFF:246993 Max relations in full relation-set: 28 Initial matrix: 186122 x 246993 with sparse part having weight 17116585. Pruned matrix : 152676 x 153670 with weight 8112545. Total sieving time: 2.48 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.34 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000 total time: 2.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
8·10¹³⁵+3 = 8(0)₁₃₄3_<136> = 47 · 107 · 167 · 445141 · 64394703446581_<14> · C111
C111 = P42 · P69
P42 = 671518907669361327306106053768429944141723_<42>
P69 = 494864033010832382214144161118931762517426636975925163439107088158187_<69>

Number: n N=332310554892288926436831772045323636037576637237580462259403763467341105224779770796417611307390273406570736201 ( 111 digits) SNFS difficulty: 135 digits. Divisors found: r1=671518907669361327306106053768429944141723 (pp42) r2=494864033010832382214144161118931762517426636975925163439107088158187 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.65 hours. Scaled time: 2.39 units (timescale=0.654). Factorization parameters were as follows: name: KA_8_0_134_3 n: 332310554892288926436831772045323636037576637237580462259403763467341105224779770796417611307390273406570736201 type: snfs skew: 1.00 deg: 5 c5: 8 c0: 3 m: 1000000000000000000000000000 rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 550001) Primes: RFBsize:92938, AFBsize:92739, largePrimes:4242280 encountered Relations: rels:3637701, finalFF:220619 Max relations in full relation-set: 28 Initial matrix: 185742 x 220619 with sparse part having weight 11033317. Pruned matrix : 156303 x 157295 with weight 6162049. Total sieving time: 3.16 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.34 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.3,2.3,75000 total time: 3.65 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Aug 9, 2007 (2nd): The factor table of 800...003 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Aug 9, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(8·10¹⁶⁴-17)/9 = (8)₁₆₃7_<164> = 3 · 151 · 48781123 · C154
C154 = P69 · P86
P69 = 122357220642452584209664973630349681033155453532931520441153082441941_<69>
P86 = 32875160220972597758764681161227086029639996457194993224995199129738972707239023844853_<86>

Number: n N=4022513232813524398211303045208836597289264340939797746512434565865799965289774544812734306459747688749162392566060216989979878271103883598312223964179673 ( 154 digits) SNFS difficulty: 165 digits. Divisors found: r1=122357220642452584209664973630349681033155453532931520441153082441941 (pp69) r2=32875160220972597758764681161227086029639996457194993224995199129738972707239023844853 (pp86) Version: GGNFS-0.77.1-20051202-athlon Total time: 65.65 hours. Scaled time: 86.53 units (timescale=1.318). Factorization parameters were as follows: name: KA_8_163_7 n: 4022513232813524398211303045208836597289264340939797746512434565865799965289774544812734306459747688749162392566060216989979878271103883598312223964179673 skew: 1.84 deg: 5 c5: 4 c0: -85 m: 1000000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2700000) Primes: RFBsize:283146, AFBsize:283447, largePrimes:7572788 encountered Relations: rels:7122775, finalFF:638638 Max relations in full relation-set: 28 Initial matrix: 566657 x 638638 with sparse part having weight 44039280. Pruned matrix : 507869 x 510766 with weight 29149793. Total sieving time: 58.05 hours. Total relation processing time: 0.26 hours. Matrix solve time: 7.07 hours. Total square root time: 0.27 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 65.65 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Aug 8, 2007: By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(7·10¹⁶⁴+11)/9 = (7)₁₆₃9_<164> = 511123815986207_<15> · C150
C150 = P42 · P108
P42 = 395215337436906000005934571501636192952207_<42>
P108 = 385030933976339826493877379968305215655393397579526887571960054940570793779333975437642428406825564469725571_<108>

Number: n N=152170130495106219796450999003009138605715611628956873355664530278848244167737884492518709827802444530255770541483818513470450546436825988489608785197 ( 150 digits) SNFS difficulty: 165 digits. Divisors found: r1=395215337436906000005934571501636192952207 (pp42) r2=385030933976339826493877379968305215655393397579526887571960054940570793779333975437642428406825564469725571 (pp108) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 86.65 hours. Scaled time: 117.85 units (timescale=1.360). Factorization parameters were as follows: name: KA_7_163_9 n: 152170130495106219796450999003009138605715611628956873355664530278848244167737884492518709827802444530255770541483818513470450546436825988489608785197 skew: 1.73 deg: 5 c5: 7 c0: 110 m: 1000000000000000000000000000000000 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, 3800001) Primes: RFBsize:250150, AFBsize:250327, largePrimes:7881745 encountered Relations: rels:7397798, finalFF:565193 Max relations in full relation-set: 28 Initial matrix: 500542 x 565193 with sparse part having weight 50214723. Pruned matrix : 471840 x 474406 with weight 38505738. Total sieving time: 79.17 hours. Total relation processing time: 0.31 hours. Matrix solve time: 6.00 hours. Total square root time: 1.18 hours, sqrts: 7. 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: 86.65 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁶⁴-3 = 6(9)₁₆₃7_<165> = 47 · 193 · 1621 · 2267 · C155
C155 = P42 · P113
P42 = 610889581248729734327409484516692590832461_<42>
P113 = 34375230566759292489277721179939552331809978623383280776559465068189748526644096155791768378027428880241905345241_<113>

Number: n N=20999470206256118682944798667139458618641061580335085268363922120761568297261969524524443030033995145039545360363662467592334735070279038086473229794668101 ( 155 digits) SNFS difficulty: 165 digits. Divisors found: r1=610889581248729734327409484516692590832461 (pp42) r2=34375230566759292489277721179939552331809978623383280776559465068189748526644096155791768378027428880241905345241 (pp113) Version: GGNFS-0.77.1-20051202-athlon Total time: 71.77 hours. Scaled time: 103.50 units (timescale=1.442). Factorization parameters were as follows: name: KA_6_9_163_7 n: 20999470206256118682944798667139458618641061580335085268363922120761568297261969524524443030033995145039545360363662467592334735070279038086473229794668101 skew: 1.34 deg: 5 c5: 7 c0: -30 m: 1000000000000000000000000000000000 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, 3400001) Primes: RFBsize:250150, AFBsize:249671, largePrimes:7747415 encountered Relations: rels:7257732, finalFF:563161 Max relations in full relation-set: 28 Initial matrix: 499886 x 563161 with sparse part having weight 46183744. Pruned matrix : 466798 x 469361 with weight 34859573. Total sieving time: 64.19 hours. Total relation processing time: 0.26 hours. Matrix solve time: 7.23 hours. Total square root time: 0.09 hours, sqrts: 1. 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: 71.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Aug 7, 2007: By JMB / GMP-ECM B1=3000000
(2·10¹⁹³-11)/9 = (2)₁₉₂1_<193> = 23 · 181 · 277 · 3511 · 281650732446817_<15> · C169
C169 = P35 · C134
P35 = 54780711280843190885242223364871889_<35>
C134 = [35573936452919801666661978767493840314935627092380374712790703051952660053016745490719105773995659310348247513610333155438457937199797_<134>]
Aug 6, 2007 (2nd): By JMB / GMP-ECM B1=1000000
(2·10²⁰⁰-11)/9 = (2)₁₉₉1_<200> = 3 · 7 · 14001880603763633983098127_<26> · C173
C173 = P36 · C138
P36 = 249790641645802510176227421442280099_<36>
C138 = [302555921974370475370998169294219199252084902441380482697802372630541007145563557322381282854361483076742218761588448860732153113329663037_<138>]
Aug 6, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(8·10¹⁶³-53)/9 = (8)₁₆₂3_<163> = 3 · 2087570567_<10> · C154
C154 = P40 · P114
P40 = 1901722501401858363651894167934894678547_<40>
P114 = 746342052674360387307334925536045196341796871193013347158150552642871903024652042586940759722677149467693386559389_<114>

Number: n N=1419335475313282170337747898973401727867416787047928791267999786357863016835187523010791214591292406817576559060081327043811957980610368972960789479727783 ( 154 digits) SNFS difficulty: 163 digits. Divisors found: r1=1901722501401858363651894167934894678547 (pp40) r2=746342052674360387307334925536045196341796871193013347158150552642871903024652042586940759722677149467693386559389 (pp114) Version: GGNFS-0.77.1-20051202-athlon Total time: 67.10 hours. Scaled time: 88.83 units (timescale=1.324). Factorization parameters were as follows: name: KA_8_162_3 n: 1419335475313282170337747898973401727867416787047928791267999786357863016835187523010791214591292406817576559060081327043811957980610368972960789479727783 skew: 0.73 deg: 5 c5: 250 c0: -53 m: 200000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2700001) Primes: RFBsize:283146, AFBsize:283257, largePrimes:7662329 encountered Relations: rels:7226501, finalFF:653830 Max relations in full relation-set: 48 Initial matrix: 566469 x 653828 with sparse part having weight 45553298. Pruned matrix : 494193 x 497089 with weight 29199532. Total sieving time: 59.93 hours. Total relation processing time: 0.27 hours. Matrix solve time: 6.79 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 67.10 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁴³+3 = 7(0)₁₄₂3_<144> = 37 · 107 · 181 · 42929 · 55778925763273769417_<20> · C114
C114 = P50 · P64
P50 = 99615388886871440186141889727022388487187792018971_<50>
P64 = 4095308385474807274359199791739966295408609792078800566560390219_<64>

Number: n N=407955737430738536692939991644316206131841159102557048096582503950767590461218943000918208625655443001223610844649 ( 114 digits) SNFS difficulty: 143 digits. Divisors found: r1=99615388886871440186141889727022388487187792018971 (pp50) r2=4095308385474807274359199791739966295408609792078800566560390219 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.69 hours. Scaled time: 11.45 units (timescale=1.318). Factorization parameters were as follows: name: KA_7_0_142_3 n: 407955737430738536692939991644316206131841159102557048096582503950767590461218943000918208625655443001223610844649 skew: 0.21 deg: 5 c5: 7000 c0: 3 m: 10000000000000000000000000000 type: snfs rlim: 1300000 alim: 1300000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:100021, AFBsize:100188, largePrimes:6536058 encountered Relations: rels:5813023, finalFF:258829 Max relations in full relation-set: 48 Initial matrix: 200276 x 258829 with sparse part having weight 33020205. Pruned matrix : 185384 x 186449 with weight 17965451. Total sieving time: 7.28 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.13 hours. Total square root time: 0.09 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,28,28,48,48,2.5,2.5,100000 total time: 8.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(5·10¹⁶⁴+31)/9 = (5)₁₆₃9_<164> = 17 · 51907 · 20894983 · C151
C151 = P38 · P113
P38 = 32744384953346829276967265860867079327_<38>
P113 = 92018210830867189627110800207659209711575697364865394156667931972180333326904385340235396502563540887671080754821_<113>

Number: n N=3013079718164143841497655666928758205678816669159984408897339155449092269654212483918172491212764027974836353746129082075124381070656207009312844685467 ( 151 digits) SNFS difficulty: 165 digits. Divisors found: r1=32744384953346829276967265860867079327 (pp38) r2=92018210830867189627110800207659209711575697364865394156667931972180333326904385340235396502563540887671080754821 (pp113) Version: GGNFS-0.77.1-20051202-athlon Total time: 54.24 hours. Scaled time: 64.65 units (timescale=1.192). Factorization parameters were as follows: name: KA_5_163_9 n: 3013079718164143841497655666928758205678816669159984408897339155449092269654212483918172491212764027974836353746129082075124381070656207009312844685467 type: snfs skew: 2.28 deg: 5 c5: 1 c0: 62 m: 1000000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2100001) Primes: RFBsize:250150, AFBsize:250072, largePrimes:7300517 encountered Relations: rels:6821415, finalFF:564991 Max relations in full relation-set: 28 Initial matrix: 500286 x 564991 with sparse part having weight 37801274. Pruned matrix : 447562 x 450127 with weight 25647572. Total sieving time: 48.36 hours. Total relation processing time: 0.33 hours. Matrix solve time: 5.42 hours. Total square root time: 0.12 hours, sqrts: 1. 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: 54.24 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Aug 5, 2007 (6th): By Yousuke Koide
(10¹²⁶⁵-1)/9 is divisible by 937659362930322328142805649502351_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Aug 5, 2007 (5th): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs
7·10¹⁶⁴+3 = 7(0)₁₆₃3_<165> = 19 · 23 · 37 · 337 · 929 · 269413 · 347533 · 3469921837_<10> · 10858699084919331104580583379_<29> · 329805675824054241199035943707983_<33> · 118849963103897079083614037915925391439183742364207872856583449031842800979_<75> ( C107 = P33 · P75
P33 = 329805675824054241199035943707983_<33>
P75 = 118849963103897079083614037915925391439183742364207872856583449031842800979_<75>

Number: 70003_164 N=39197392403144687459815035426745024063531397479986412229829216553848174308140333001931690855527749962515357 ( 107 digits) Divisors found: r1=329805675824054241199035943707983 (pp33) r2=118849963103897079083614037915925391439183742364207872856583449031842800979 (pp75) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 19.99 hours. Scaled time: 13.63 units (timescale=0.682). Factorization parameters were as follows: name: 70003_164 n: 39197392403144687459815035426745024063531397479986412229829216553848174308140333001931690855527749962515357 skew: 20910.15 # norm 1.06e+15 c5: 9720 c4: 2125480070 c3: -30292207723211 c2: -241365060444554346 c1: 6224386460235202586792 c0: 9860520441272134662836800 # alpha -6.80 Y1: 174301888739 Y0: -331977164050768224741 # Murphy_E 1.59e-09 # M 19494045783360941309357024716550423366184593205803102929257298699651293357014392618726071159638485253850725 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2300001) Primes: RFBsize:183072, AFBsize:182671, largePrimes:4488141 encountered Relations: rels:4624312, finalFF:419683 Max relations in full relation-set: 0 Initial matrix: 365820 x 419683 with sparse part having weight 23910189. Pruned matrix : 319973 x 321866 with weight 16314933. Polynomial selection time: 1.16 hours. Total sieving time: 15.72 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.66 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 19.99 hours. --------- CPU info (if available) ----------
Aug 5, 2007 (4th): By JMB / GMP-ECM B1=3000000
(2·10¹⁷⁴-11)/9 = (2)₁₇₃1_<174> = 14519 · 48049681 · C162
C162 = P39 · C123
P39 = 498348657919234104075045395918906731471_<39>
C123 = [639185595393241060368558509801103716904374062098782041091490513631206214345337531118525083250572654266352921615626524660709_<123>]
Aug 5, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(5·10¹⁶⁴-17)/3 = 1(6)₁₆₃1_<165> = 7 · 89 · 397 · 5894957 · C153
C153 = P45 · P108
P45 = 161298457539788941817796286115085431869711519_<45>
P108 = 708694953619147226673103188232021943957327776601583178016851560378815912464731109927271144169197806764708557_<108>

Number: n N=114311402885000712403892487530808345971552888111341690651388701164490192899870173759027180390972569507303387784542444950170703623051519404536221700768083 ( 153 digits) SNFS difficulty: 165 digits. Divisors found: r1=161298457539788941817796286115085431869711519 (pp45) r2=708694953619147226673103188232021943957327776601583178016851560378815912464731109927271144169197806764708557 (pp108) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.28 hours. Scaled time: 57.93 units (timescale=1.438). Factorization parameters were as follows: name: KA_1_6_163_1 n: 114311402885000712403892487530808345971552888111341690651388701164490192899870173759027180390972569507303387784542444950170703623051519404536221700768083 skew: 2.02 deg: 5 c5: 1 c0: -34 m: 1000000000000000000000000000000000 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:249831, largePrimes:7181141 encountered Relations: rels:6707182, finalFF:566395 Max relations in full relation-set: 28 Initial matrix: 500045 x 566395 with sparse part having weight 35400182. Pruned matrix : 443290 x 445854 with weight 23187095. Total sieving time: 35.22 hours. Total relation processing time: 0.20 hours. Matrix solve time: 4.79 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 40.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Aug 5, 2007 (2nd): By JMB / GMP-ECM B1=1000000
(2·10¹⁷³-11)/9 = (2)₁₇₂1_<173> = 3 · 4780584353_<10> · C163
C163 = P32 · P131
P32 = 37913745669376504562053041209773_<32>
P131 = 40868486384377850363075248339637631162815021698805356262193295482622750962455291582666552767183399762886016728604351667010921652203_<131>
(2·10¹⁹⁶-11)/9 = (2)₁₉₅1_<196> = 165443 · 247462843 · C182
C182 = P33 · C150
P33 = 258199423348160658302432304492257_<33>
C150 = [210219899230871720367863640427655425071639482317984140098945614468521925473775770678828557000890931928428063480054499871330273471885150271347346444797_<150>]
Aug 5, 2007: By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8
(14·10¹⁹⁰-41)/9 = 1(5)₁₈₉1_<191> = C191
C191 = P41 · P150
P41 = 35979232514979028691658608275491778123813_<41>
P150 = 432348176106296870587027279656162097057836779149603113487443591832639183538536761174932277931864748203116574693057107906194995991781437958621511650227_<150>

Number: 15551_190 N=15555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551 ( 191 digits) SNFS difficulty: 191 digits. Divisors found: r1=35979232514979028691658608275491778123813 (pp41) r2=432348176106296870587027279656162097057836779149603113487443591832639183538536761174932277931864748203116574693057107906194995991781437958621511650227 (pp150) Version: GGNFS-0.77.1-20060513-k8 Total time: 1349.01 hours. Scaled time: 2702.07 units (timescale=2.003). Factorization parameters were as follows: name: 15551_190 n: 15555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551 m: 100000000000000000000000000000000000000 c5: 14 c0: -41 skew: 1.24 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, 19800001) Primes: RFBsize:501962, AFBsize:502607, largePrimes:7128971 encountered Relations: rels:7710294, finalFF:1147825 Max relations in full relation-set: 28 Initial matrix: 1004635 x 1147825 with sparse part having weight 130586785. Pruned matrix : 900542 x 905629 with weight 111974876. Total sieving time: 1328.99 hours. Total relation processing time: 0.88 hours. Matrix solve time: 18.70 hours. Time per square root: 0.44 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1349.01 hours. --------- CPU info (if available) ----------
Aug 4, 2007 (4th): By JMB / GMP-ECM B1=1000000
(2·10¹⁸⁴-11)/9 = (2)₁₈₃1_<184> = 1326093162203393_<16> · 5817057857572301_<16> · C136
C136 = P34 · P102
P34 = 1754676921979215318291368793294107_<34>
P102 = 698512124268376321562816716178278625864224388509844952931589370471677010602977158625180855254980820277_<102>
Aug 4, 2007 (3rd): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
7·10¹⁴⁷+3 = 7(0)₁₄₆3_<148> = 31 · 151451 · 7030015143559119037524563_<25> · C117
C117 = P32 · P85
P32 = 49184959607580348859573544470471_<32>
P85 = 4311968914702968224249026994416631354378899830941813009414303440243079537179314918331_<85>

Number: 70003_147 N=212084016898807566754857352490161533118634629504259292309654861162435026120974930470578532991845919966137704006103901 ( 117 digits) SNFS difficulty: 147 digits. Divisors found: r1=49184959607580348859573544470471 (pp32) r2=4311968914702968224249026994416631354378899830941813009414303440243079537179314918331 (pp85) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 22.87 hours. Scaled time: 15.60 units (timescale=0.682). Factorization parameters were as follows: name: 70003_147 n: 212084016898807566754857352490161533118634629504259292309654861162435026120974930470578532991845919966137704006103901 m: 100000000000000000000000000000 c5: 700 c0: 3 skew: 0.34 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 2850001) Primes: RFBsize:114155, AFBsize:114337, largePrimes:2762094 encountered Relations: rels:2702598, finalFF:256255 Max relations in full relation-set: 0 Initial matrix: 228559 x 256255 with sparse part having weight 29944652. Pruned matrix : 220754 x 221960 with weight 23313853. Total sieving time: 20.76 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.83 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 22.87 hours. --------- CPU info (if available) ----------
Aug 4, 2007 (2nd): By JMB / GMP-ECM B1=1000000
(2·10¹⁸²-11)/9 = (2)₁₈₁1_<182> = 3 · 7³ · 15590527644441643987_<20> · C160
C160 = P28 · P132
P28 = 3859810844261017292702989709_<28>
P132 = 358876710814360315317023330251097074583196051792006020792471873976522644363636948726993210189326153704314907059958585059249644910303_<132>
(2·10¹⁸⁰-11)/9 = (2)₁₇₉1_<180> = 29 · 2699 · 27799 · C171
C171 = P32 · P139
P32 = 64863739486980795803630431431379_<32>
P139 = 1574546342648474722022271751727776130594766428709953635443779531729815050710283278155800017708651481579996117040508836655706483328393873031_<139>
Aug 4, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
7·10¹⁵²+3 = 7(0)₁₅₁3_<153> = 37 · 505533211217_<12> · C140
C140 = P39 · P101
P39 = 710664466259752258736962985632455239789_<39>
P101 = 52660141650353797139373582732951853429418586057828085008415146466989469864283870303119649117935460563_<101>

Number: n N=37423691459111630694213075267719021502276516612327799793244021635177923501617996604911113655109015687913454442940049105499674605998317941207 ( 140 digits) SNFS difficulty: 152 digits. Divisors found: r1=710664466259752258736962985632455239789 (pp39) r2=52660141650353797139373582732951853429418586057828085008415146466989469864283870303119649117935460563 (pp101) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.23 hours. Scaled time: 31.40 units (timescale=1.197). Factorization parameters were as follows: name: KA_7_0_151_3 n: 37423691459111630694213075267719021502276516612327799793244021635177923501617996604911113655109015687913454442940049105499674605998317941207 type: snfs skew: 0.34 deg: 5 c5: 700 c0: 3 m: 1000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:216816, AFBsize:216741, largePrimes:6016357 encountered Relations: rels:5499110, finalFF:498155 Max relations in full relation-set: 28 Initial matrix: 433624 x 498155 with sparse part having weight 22030485. Pruned matrix : 366825 x 369057 with weight 12772769. Total sieving time: 23.88 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.02 hours. Total square root time: 0.14 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 26.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
7·10¹⁵⁰+3 = 7(0)₁₄₉3_<151> = 71 · 89 · 191 · 5813 · 69387272384806722377_<20> · C122
C122 = P52 · P70
P52 = 2860432727051506986615284475786112947115219635815431_<52>
P70 = 5026948551624322877511681422548970043126094617265313823362275760438297_<70>

Number: n N=14379248154270385139813463545958394801202417801191544982206419087617630689229379296085630002943418668516430905971555961007 ( 122 digits) SNFS difficulty: 150 digits. Divisors found: r1=2860432727051506986615284475786112947115219635815431 (pp52) r2=5026948551624322877511681422548970043126094617265313823362275760438297 (pp70) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 14.95 hours. Scaled time: 20.40 units (timescale=1.365). Factorization parameters were as follows: name: KA_7_0_149_3 n: 14379248154270385139813463545958394801202417801191544982206419087617630689229379296085630002943418668516430905971555961007 skew: 0.84 deg: 5 c5: 7 c0: 3 m: 1000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:148933, AFBsize:148270, largePrimes:5983637 encountered Relations: rels:5373975, finalFF:333157 Max relations in full relation-set: 28 Initial matrix: 297268 x 333157 with sparse part having weight 22706688. Pruned matrix : 269197 x 270747 with weight 15488628. Total sieving time: 13.19 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.53 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 14.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Aug 3, 2007 (4th): By Yousuke Koide
(10¹¹³⁵-1)/9 is divisible by 19556724483255900086046136607479201_<35>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Aug 3, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
7·10¹⁵⁸+3 = 7(0)₁₅₇3_<159> = 37 · C158
C158 = P52 · P106
P52 = 4683555637807654711165402911872475397796795663167619_<52>
P106 = 4039435074966837668459019948543510692643700803297645131234240674842966427190365006893589626840507633222701_<106>

Number: n N=18918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918919 ( 158 digits) SNFS difficulty: 158 digits. Divisors found: r1=4683555637807654711165402911872475397796795663167619 (pp52) r2=4039435074966837668459019948543510692643700803297645131234240674842966427190365006893589626840507633222701 (pp106) Version: GGNFS-0.77.1-20051202-athlon Total time: 38.49 hours. Scaled time: 51.00 units (timescale=1.325). Factorization parameters were as follows: name: KA_7_0_157_3 n: 18918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918919 skew: 0.21 deg: 5 c5: 7000 c0: 3 m: 10000000000000000000000000000000 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:249771, largePrimes:7165440 encountered Relations: rels:6701601, finalFF:585929 Max relations in full relation-set: 48 Initial matrix: 499988 x 585929 with sparse part having weight 38496719. Pruned matrix : 424349 x 426912 with weight 22476047. Total sieving time: 34.02 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.17 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 38.49 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁴⁸+3 = 7(0)₁₄₇3_<149> = 541 · 94793 · C142
C142 = P37 · P48 · P58
P37 = 1248139200509574640907510234705365019_<37>
P48 = 668778149760661722591247508440960905084930985277_<48>
P58 = 1635232116045943944454517876533152037422559560020696414537_<58>

Number: n N=1364974401952552982797637104512560523696218862959553488013662535779635256610215160329990751518441398909225555838538581966703087433649813048231 ( 142 digits) SNFS difficulty: 148 digits. Divisors found: r1=1248139200509574640907510234705365019 (pp37) r2=668778149760661722591247508440960905084930985277 (pp48) r3=1635232116045943944454517876533152037422559560020696414537 (pp58) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 16.09 hours. Scaled time: 21.91 units (timescale=1.362). Factorization parameters were as follows: name: KA_7_0_147_3 n: 1364974401952552982797637104512560523696218862959553488013662535779635256610215160329990751518441398909225555838538581966703087433649813048231 skew: 0.21 deg: 5 c5: 7000 c0: 3 m: 100000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:114155, AFBsize:114347, largePrimes:7377130 encountered Relations: rels:6857385, finalFF:270003 Max relations in full relation-set: 28 Initial matrix: 228569 x 270003 with sparse part having weight 30080076. Pruned matrix : 218314 x 219520 with weight 22382143. Total sieving time: 14.03 hours. Total relation processing time: 0.24 hours. Matrix solve time: 1.64 hours. Total square root time: 0.17 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 16.09 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁶⁵+3 = 7(0)₁₆₄3_<166> = C166
C166 = P36 · P49 · P83
P36 = 152833588533830632515504625196129899_<36>
P49 = 2783607568442084600657258901797095301845534239737_<49>
P83 = 16453989692271955709439095429034688807841041398306296314589415102129894839413356881_<83>

Number: n N=7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 166 digits) SNFS difficulty: 165 digits. Divisors found: r1=152833588533830632515504625196129899 (pp36) r2=2783607568442084600657258901797095301845534239737 (pp49) r3=16453989692271955709439095429034688807841041398306296314589415102129894839413356881 (pp83) Version: GGNFS-0.77.1-20051202-athlon Total time: 52.97 hours. Scaled time: 76.80 units (timescale=1.450). Factorization parameters were as follows: name: KA_7_0_164_3 n: 7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 skew: 0.84 deg: 5 c5: 7 c0: 3 m: 1000000000000000000000000000000000 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:249766, largePrimes:7413466 encountered Relations: rels:6928393, finalFF:560270 Max relations in full relation-set: 28 Initial matrix: 499981 x 560270 with sparse part having weight 40280814. Pruned matrix : 452422 x 454985 with weight 28649122. Total sieving time: 46.55 hours. Total relation processing time: 0.23 hours. Matrix solve time: 5.70 hours. Total square root time: 0.49 hours, sqrts: 6. 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: 52.97 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Aug 3, 2007 (2nd): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
7·10¹³⁸+3 = 7(0)₁₃₇3_<139> = 17 · 8243 · 68483 · 259690877 · 416873729 · 472302839 · C104
C104 = P32 · P72
P32 = 39500434691109480414761661938549_<32>
P72 = 361158125739483496643032610400546386075176007047634753673066706124874797_<72>

Number: 70003_138 N=14265902958935973680620930474842135188483839358780870437646100498699296745754482441030588187552932849553 ( 104 digits) SNFS difficulty: 138 digits. Divisors found: r1=39500434691109480414761661938549 (pp32) r2=361158125739483496643032610400546386075176007047634753673066706124874797 (pp72) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 12.90 hours. Scaled time: 8.80 units (timescale=0.682). Factorization parameters were as follows: name: 70003_138 n: 14265902958935973680620930474842135188483839358780870437646100498699296745754482441030588187552932849553 m: 1000000000000000000000000000 c5: 7000 c0: 3 skew: 0.21 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1750001) Primes: RFBsize:78498, AFBsize:64153, largePrimes:1565292 encountered Relations: rels:1549696, finalFF:159894 Max relations in full relation-set: 0 Initial matrix: 142718 x 159894 with sparse part having weight 17823941. Pruned matrix : 138506 x 139283 with weight 13759036. Total sieving time: 12.18 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.54 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 12.90 hours. --------- CPU info (if available) ----------
7·10¹⁰⁸+3 = 7(0)₁₀₇3_<109> = 15932731 · C102
C102 = P35 · P68
P35 = 21135103243411643094225839323775893_<35>
P68 = 20787556496228678876263628963578198111397575572164064323810422220341_<68>

Number: 70003_108 N=439347152726045522264827040637289363637658854593101458877326178418502138773321409870034208196950039513 ( 102 digits) SNFS difficulty: 108 digits. Divisors found: r1=21135103243411643094225839323775893 (pp35) r2=20787556496228678876263628963578198111397575572164064323810422220341 (pp68) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 1.97 hours. Scaled time: 1.30 units (timescale=0.661). Factorization parameters were as follows: name: 70003_108 n: 439347152726045522264827040637289363637658854593101458877326178418502138773321409870034208196950039513 m: 1000000000000000000000 c5: 7000 c0: 3 skew: 0.21 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:64153, largePrimes:2383720 encountered Relations: rels:2939110, finalFF:154239 Max relations in full relation-set: 0 Initial matrix: 113318 x 154239 with sparse part having weight 3864688. Pruned matrix : 79599 x 80229 with weight 1974973. Total sieving time: 1.80 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,108,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.97 hours. --------- CPU info (if available) ----------
Aug 3, 2007: By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000
7·10¹⁸⁰+3 = 7(0)₁₇₉3_<181> = C181
C181 = P37 · C145
P37 = 1661635052382325894228860798388965059_<37>
C145 = [4212718063430313817949556918391010227926614475612398920219025346271127082558521092818662843579474726787185571200372160360259201106912513664366017_<145>]
Aug 2, 2007 (4th): By Robert Backstrom / GMP-ECM 5.0 B1=536000, GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
(10¹⁶⁴+11)/3 = (3)₁₆₃7_<164> = 37 · 8419 · 279007 · C153
C153 = P31 · P48 · P75
P31 = 4161801207038325803680462744351_<31>
P48 = 154736176694355509814594114434265558831989783897_<48>
P75 = 595563698951275492246179266439849085291671641089578658213681985453227855151_<75>

Number: n N=92155249753668515805069774853618530650531992960849125594638260650099015648789979128441694079227557758205130066181308303447 ( 122 digits) SNFS difficulty: 165 digits. Divisors found: r1=154736176694355509814594114434265558831989783897 (pp48) r2=595563698951275492246179266439849085291671641089578658213681985453227855151 (pp75) Version: GGNFS-0.77.1-20051202-athlon Total time: 96.22 hours. Scaled time: 115.08 units (timescale=1.196). Factorization parameters were as follows: name: KA_3_163_7 n: 92155249753668515805069774853618530650531992960849125594638260650099015648789979128441694079227557758205130066181308303447 # n: 383531829659736005765621077922788434765907478295374100321404205450489861931970595643574521924764095540194512505080222201006312737689809245844169493077897 type: snfs skew: 0.43 deg: 5 c5: 1 c0: 110 m: 1000000000000000000000000000000000 rlim: 3600000 alim: 3600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3600000/3600000 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:256726, AFBsize:257022, largePrimes:7802543 encountered Relations: rels:7325962, finalFF:593422 Max relations in full relation-set: 28 Initial matrix: 513812 x 593422 with sparse part having weight 45665185. Pruned matrix : 470389 x 473022 with weight 33187299. Total sieving time: 88.29 hours. Total relation processing time: 0.36 hours. Matrix solve time: 7.43 hours. Total square root time: 0.14 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.5,2.5,100000 total time: 96.22 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
7·10¹³⁵+3 = 7(0)₁₃₄3_<136> = 75019561 · 127203697 · C120
C120 = P48 · P73
P48 = 498282829674007715259141593888416290550964085919_<48>
P73 = 1472135771787141323267702134218700861789671776680188265909145553844113061_<73>

Number: n N=733539978030426032474138343766645879888898534474528389024587518339851243854978692112465545639290426570208439273154088059 ( 120 digits) SNFS difficulty: 135 digits. Divisors found: r1=498282829674007715259141593888416290550964085919 (pp48) r2=1472135771787141323267702134218700861789671776680188265909145553844113061 (pp73) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 3.62 hours. Scaled time: 4.92 units (timescale=1.358). Factorization parameters were as follows: name: KA_7_0_134_3 n: 733539978030426032474138343766645879888898534474528389024587518339851243854978692112465545639290426570208439273154088059 skew: 0.84 deg: 5 c5: 7 c0: 3 m: 1000000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 550001) Primes: RFBsize:78498, AFBsize:78031, largePrimes:5443174 encountered Relations: rels:4746285, finalFF:189754 Max relations in full relation-set: 28 Initial matrix: 156594 x 189754 with sparse part having weight 15131695. Pruned matrix : 142669 x 143515 with weight 9259290. Total sieving time: 3.03 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.43 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,75000 total time: 3.62 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹³²+3 = 7(0)₁₃₁3_<133> = 31 · 1897144835436283709_<19> · C114
C114 = P49 · P65
P49 = 1514672391291856973675707124754820474913203927051_<49>
P65 = 78580927206153670651740539814203277361304443804223185859614493507_<65>

Number: n N=119024360921276121842517421424303849703442150179435383100670930768158762553946642889669912459689870973548741157857 ( 114 digits) SNFS difficulty: 132 digits. Divisors found: r1=1514672391291856973675707124754820474913203927051 (pp49) r2=78580927206153670651740539814203277361304443804223185859614493507 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.29 hours. Scaled time: 5.12 units (timescale=1.193). Factorization parameters were as follows: name: KA_7_0_131_3 n: 119024360921276121842517421424303849703442150179435383100670930768158762553946642889669912459689870973548741157857 type: snfs skew: 0.34 deg: 5 c5: 700 c0: 3 m: 100000000000000000000000000 rlim: 900000 alim: 900000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:71274, AFBsize:71340, largePrimes:3740700 encountered Relations: rels:3055228, finalFF:161685 Max relations in full relation-set: 28 Initial matrix: 142681 x 161685 with sparse part having weight 7259713. Pruned matrix : 128325 x 129102 with weight 4802914. Total sieving time: 3.74 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.40 hours. Total square root time: 0.05 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,900000,900000,28,28,48,48,2.2,2.2,50000 total time: 4.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Aug 2, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
9·10¹⁶³+1 = 9(0)₁₆₂1_<164> = 7² · 13 · 179 · 470008183 · C151
C151 = P36 · P45 · P71
P36 = 259481291797001816650176355670832013_<36>
P45 = 580459551785892461725007555092462668798367841_<45>
P71 = 11149788091046450752175493549254706615173820321550790352125382027235333_<71>

Number: n N=1679363179430100904238066369647856492488978635545047894559404239979036929530217645752206682742665314434231355893232990238004850731203395449127465734689 ( 151 digits) SNFS difficulty: 163 digits. Divisors found: r1=259481291797001816650176355670832013 (pp36) r2=580459551785892461725007555092462668798367841 (pp45) r3=11149788091046450752175493549254706615173820321550790352125382027235333 (pp71) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 66.05 hours. Scaled time: 47.23 units (timescale=0.715). Factorization parameters were as follows: name: KA_9_0_162_1 n: 1679363179430100904238066369647856492488978635545047894559404239979036929530217645752206682742665314434231355893232990238004850731203395449127465734689 skew: 0.16 deg: 5 c5: 9000 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, 2700001) Primes: RFBsize:250150, AFBsize:250001, largePrimes:7541796 encountered Relations: rels:7066191, finalFF:569227 Max relations in full relation-set: 28 Initial matrix: 500218 x 569227 with sparse part having weight 42649432. Pruned matrix : 448769 x 451334 with weight 30222203. Total sieving time: 59.53 hours. Total relation processing time: 0.30 hours. Matrix solve time: 4.98 hours. Total square root time: 1.25 hours, sqrts: 6. 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: 66.05 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹²⁷+3 = 7(0)₁₂₆3_<128> = 277 · 683 · C123
C123 = P60 · P64
P60 = 101758248455110600982078958785140824830321627783059244018899_<60>
P64 = 3636034073135055601486854090198041730366400527898690994554262567_<64>

Number: n N=369996458605324777605700059727999746288142670634438213234244757943031116702168707813796639375023124778662832798600356253733 ( 123 digits) SNFS difficulty: 127 digits. Divisors found: r1=101758248455110600982078958785140824830321627783059244018899 (pp60) r2=3636034073135055601486854090198041730366400527898690994554262567 (pp64) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 2.70 hours. Scaled time: 3.67 units (timescale=1.358). Factorization parameters were as follows: name: KA_7_0_126_3 n: 369996458605324777605700059727999746288142670634438213234244757943031116702168707813796639375023124778662832798600356253733 skew: 0.34 deg: 5 c5: 700 c0: 3 m: 10000000000000000000000000 type: snfs rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 400001) Primes: RFBsize:63951, AFBsize:63898, largePrimes:4621659 encountered Relations: rels:3934593, finalFF:151818 Max relations in full relation-set: 28 Initial matrix: 127916 x 151818 with sparse part having weight 11015888. Pruned matrix : 117329 x 118032 with weight 6729113. Total sieving time: 2.34 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.20 hours. Total square root time: 0.07 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000 total time: 2.70 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹²⁵+3 = 7(0)₁₂₄3_<126> = 37 · 499 · C122
C122 = P53 · P70
P53 = 13699452564493006814819701274146501315424887911148777_<53>
P70 = 2767531402418291140749455418859878737861230939330176281407585478703253_<70>

Number: n N=37913665168174186210258354546931701240318474787412663164166170178194226290418675188214266370578995829496831500839516871581 ( 122 digits) SNFS difficulty: 125 digits. Divisors found: r1=13699452564493006814819701274146501315424887911148777 (pp53) r2=2767531402418291140749455418859878737861230939330176281407585478703253 (pp70) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 2.02 hours. Scaled time: 2.73 units (timescale=1.352). Factorization parameters were as follows: name: KA_7_0_124_3 n: 37913665168174186210258354546931701240318474787412663164166170178194226290418675188214266370578995829496831500839516871581 skew: 0.84 deg: 5 c5: 7 c0: 3 m: 10000000000000000000000000 type: snfs rlim: 700000 alim: 700000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 300001) Primes: RFBsize:56543, AFBsize:56283, largePrimes:5007709 encountered Relations: rels:4440675, finalFF:243454 Max relations in full relation-set: 28 Initial matrix: 112891 x 243454 with sparse part having weight 20075677. Pruned matrix : 80668 x 81296 with weight 4508727. Total sieving time: 1.76 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.08 hours. Total square root time: 0.08 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,700000,700000,28,28,48,48,2.5,2.5,50000 total time: 2.02 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Aug 2, 2007 (2nd): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
7·10¹³⁷+3 = 7(0)₁₃₆3_<138> = 37² · 73 · 373 · 521 · 18719 · 249341 · 960331 · 1467499879_<10> · C103
C103 = P30 · P74
P30 = 139631923964055191736784404269_<30>
P74 = 39243261185324721562992298947369650901900632234898044840233858916987494957_<74>

Number: 70003_137 N=5479612061930819937675113993646705222614196918682242006504828855291692670246697931177796783015886771433 ( 103 digits) SNFS difficulty: 137 digits. Divisors found: r1=139631923964055191736784404269 (pp30) r2=39243261185324721562992298947369650901900632234898044840233858916987494957 (pp74) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 9.59 hours. Scaled time: 6.54 units (timescale=0.682). Factorization parameters were as follows: name: 70003_137 n: 5479612061930819937675113993646705222614196918682242006504828855291692670246697931177796783015886771433 m: 1000000000000000000000000000 c5: 700 c0: 3 skew: 0.34 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1375001) Primes: RFBsize:78498, AFBsize:63898, largePrimes:1539023 encountered Relations: rels:1533849, finalFF:161515 Max relations in full relation-set: 0 Initial matrix: 142463 x 161515 with sparse part having weight 13047221. Pruned matrix : 136623 x 137399 with weight 9876416. Total sieving time: 9.04 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.40 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 9.59 hours. --------- CPU info (if available) ----------
7·10¹⁴⁰+3 = 7(0)₁₃₉3_<141> = 37 · 8930917 · 113901888018295570523922817_<27> · C107
C107 = P33 · P74
P33 = 278323359075849334609317178348129_<33>
P74 = 66822032691525636457754568132542380413223137289570793768530446299737118299_<74>

Number: 70003_140 N=18598132598981632690429372380577188394736092833600211994959614409569142544257818749339461669680023478312571 ( 107 digits) SNFS difficulty: 140 digits. Divisors found: r1=278323359075849334609317178348129 (pp33) r2=66822032691525636457754568132542380413223137289570793768530446299737118299 (pp74) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 9.94 hours. Scaled time: 6.78 units (timescale=0.682). Factorization parameters were as follows: name: 70003_140 n: 18598132598981632690429372380577188394736092833600211994959614409569142544257818749339461669680023478312571 m: 10000000000000000000000000000 c5: 7 c0: 3 skew: 0.84 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1550001) Primes: RFBsize:100021, AFBsize:99538, largePrimes:2645025 encountered Relations: rels:2617239, finalFF:224213 Max relations in full relation-set: 0 Initial matrix: 199624 x 224213 with sparse part having weight 12939835. Pruned matrix : 190257 x 191319 with weight 10105839. Total sieving time: 9.03 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.72 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 9.94 hours. --------- CPU info (if available) ----------
Aug 2, 2007: By Yousuke Koide
10⁹²⁶+1 is divisible by 222918345451775051784679332634923849829_<39>
10¹⁶⁵⁹+1 is divisible by154527628727094706891588937475019_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Aug 1, 2007 (2nd): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(43·10¹⁶⁰-7)/9 = 4(7)₁₆₀_<161> = 5007179 · 7008751163_<10> · 4421264001211142317908244507_<28> · C117
C117 = P59 · P59
P59 = 10962690224883063587814306144466516475374288984362790602653_<59>
P59 = 28088503235042124615343896925550058586948441134278026650631_<59>

Number: 47777_160 N=307925559846392608191890342655880287652240774038193999902100985083530393790025178760683643373658220133542015572724043 ( 117 digits) SNFS difficulty: 161 digits. Divisors found: r1=10962690224883063587814306144466516475374288984362790602653 (pp59) r2=28088503235042124615343896925550058586948441134278026650631 (pp59) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 92.60 hours. Scaled time: 63.15 units (timescale=0.682). Factorization parameters were as follows: name: 47777_160 n: 307925559846392608191890342655880287652240774038193999902100985083530393790025178760683643373658220133542015572724043 m: 100000000000000000000000000000000 c5: 43 c0: -7 skew: 0.7 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, 4450001) Primes: RFBsize:315948, AFBsize:316331, largePrimes:5787779 encountered Relations: rels:5898099, finalFF:709902 Max relations in full relation-set: 0 Initial matrix: 632346 x 709902 with sparse part having weight 39393248. Pruned matrix : 573683 x 576908 with weight 30096165. Total sieving time: 78.88 hours. Total relation processing time: 0.34 hours. Matrix solve time: 13.14 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 92.60 hours. --------- CPU info (if available) ----------
Aug 1, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
7·10¹²⁰+3 = 7(0)₁₁₉3_<121> = 23 · 366479 · 490913 · C109
C109 = P30 · P79
P30 = 787073943986243214424803305243_<30>
P79 = 2149319812250807291486495152588101029793779750183550066121886943689304730180801_<79>

Number: n N=1691673621516014680304576988516586290004567558148171765518815439071657240016879833070443049183852561781239643 ( 109 digits) SNFS difficulty: 120 digits. Divisors found: r1=787073943986243214424803305243 (pp30) r2=2149319812250807291486495152588101029793779750183550066121886943689304730180801 (pp79) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.62 hours. Scaled time: 2.35 units (timescale=1.448). Factorization parameters were as follows: name: KA_7_0_119_3 n: 1691673621516014680304576988516586290004567558148171765518815439071657240016879833070443049183852561781239643 skew: 0.34 deg: 5 c5: 7 c0: 3 m: 1000000000000000000000000 type: snfs rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 250001) Primes: RFBsize:63951, AFBsize:63643, largePrimes:4609625 encountered Relations: rels:4046821, finalFF:240563 Max relations in full relation-set: 28 Initial matrix: 127659 x 240563 with sparse part having weight 15790458. Pruned matrix : 84816 x 85518 with weight 3791952. Total sieving time: 1.46 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.06 hours. Total square root time: 0.03 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000 total time: 1.62 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
7·10¹⁴⁵+3 = 7(0)₁₄₄3_<146> = 73 · 28793 · 63545947 · 288853667 · 53326121669_<11> · 1531658044549_<13> · C101
C101 = P44 · P57
P44 = 54389898345654421049856493544427544048520119_<44>
P57 = 408415728230237921555405467245794348472339374239159426157_<57>

Number: n N=22213689941209063158208924297571722939004404285708946735588677498261543842008297054574418225109352683 ( 101 digits) Divisors found: r1=54389898345654421049856493544427544048520119 (pp44) r2=408415728230237921555405467245794348472339374239159426157 (pp57) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.98 hours. Scaled time: 8.61 units (timescale=1.440). Factorization parameters were as follows: name: n n: 22213689941209063158208924297571722939004404285708946735588677498261543842008297054574418225109352683 skew: 9797.27 # norm 1.17e+14 c5: 52860 c4: 698483228 c3: -14911543473265 c2: -55584912348479370 c1: 671780603124125519596 c0: 65049529035605759990224 # alpha -6.39 Y1: 18029502491 Y0: -13325918615022094611 # Murphy_E 3.27e-09 # M 11752346036422637204237551646785296678119824290663937408764580117521053325165969638739266765025892067 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:135072, AFBsize:135185, largePrimes:3524807 encountered Relations: rels:3561278, finalFF:435975 Max relations in full relation-set: 28 Initial matrix: 270338 x 435975 with sparse part having weight 24359364. Pruned matrix : 135847 x 137262 with weight 7808751. Total sieving time: 5.46 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.28 hours. Total square root time: 0.10 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 5.98 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
7·10¹⁶⁶-3 = 6(9)₁₆₅7_<167> = 67 · 173 · C163
C163 = P42 · P49 · P74
P42 = 153583387324042801184481984693585153371533_<42>
P49 = 2067097285247959280399851585395695989586036741113_<49>
P74 = 19022691978446235710973810593733140748567297663247313327626391472876229823_<74>

Number: n N=6039168320248468639461651281166422224139418514364593218876714692433784833060132861703045466310068156328185661288931067207316021050815287723233543266327322922957467 ( 163 digits) SNFS difficulty: 166 digits. Divisors found: r1=153583387324042801184481984693585153371533 (pp42) r2=2067097285247959280399851585395695989586036741113 (pp49) r3=19022691978446235710973810593733140748567297663247313327626391472876229823 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 97.45 hours. Scaled time: 128.92 units (timescale=1.323). Factorization parameters were as follows: name: KA_6_9_165_7 n: 6039168320248468639461651281166422224139418514364593218876714692433784833060132861703045466310068156328185661288931067207316021050815287723233543266327322922957467 skew: 0.53 deg: 5 c5: 70 c0: -3 m: 1000000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 4000001) Primes: RFBsize:283146, AFBsize:281947, largePrimes:7979224 encountered Relations: rels:7489789, finalFF:636155 Max relations in full relation-set: 48 Initial matrix: 565160 x 636155 with sparse part having weight 53405311. Pruned matrix : 527962 x 530851 with weight 38879892. Total sieving time: 87.02 hours. Total relation processing time: 0.32 hours. Matrix solve time: 9.88 hours. Total square root time: 0.23 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 97.45 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

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