Since June 16, 2000

STUDIO KAMADA

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News and updates, September 2007

Sep 30, 2007 (4th)

By Jo Yeong Uk / GGNFS
(5·10¹⁶²+7)/3 = 1(6)₁₆₁9_<163> = 26605422918850732566241_<23> · 63779260936918673666795069_<26> · C114
C114 = P56 · P59
P56 = 12345841030073355518195566173708094971913700674342341749_<56>
P59 = 79557003995848246810709883183266502089230667106521497802989_<59>

Number: 16669_162 N=982198124161653180383430896087817726373941018203689950840839374285322703169061071123818762648082907378560911687761 ( 114 digits) Divisors found: r1=12345841030073355518195566173708094971913700674342341749 (pp56) r2=79557003995848246810709883183266502089230667106521497802989 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.98 hours. Scaled time: 53.55 units (timescale=2.144). Factorization parameters were as follows: name: 16669_162 n: 982198124161653180383430896087817726373941018203689950840839374285322703169061071123818762648082907378560911687761 skew: 79581.38 # norm 1.52e+16 c5: 14400 c4: -5104766820 c3: -426663243207224 c2: 28085394149617420745 c1: 790358088000437855793756 c0: -30202005118332397627600032105 # alpha -6.65 Y1: 1156683005687 Y0: -9263415975208444237468 # Murphy_E 5.69e-10 # M 282687440591493322167609652050488048787882302796981977330370789227978501143302103505532468545998949397979264317724 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 3075001) Primes: RFBsize:256726, AFBsize:255796, largePrimes:7643428 encountered Relations: rels:7673917, finalFF:699431 Max relations in full relation-set: 28 Initial matrix: 512600 x 699431 with sparse part having weight 61343989. Pruned matrix : 366077 x 368704 with weight 35631843. Polynomial selection time: 1.18 hours. Total sieving time: 22.62 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.87 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 24.98 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

Sep 30, 2007 (3rd)

By Sinkiti Sibata / GGNFS
(5·10¹⁶⁰+7)/3 = 1(6)₁₅₉9_<161> = 79 · 22979881 · 8218427297_<10> · 120437201921_<12> · 576732416278247_<15> · C116
C116 = P55 · P61
P55 = 4977320437750921565229473834967340708864912661751976709_<55>
P61 = 3231130839822657913824785584822600613852060607675347893277881_<61>

Number: 16669_160 N=16082373566096614517840744716684819770544179685787058568186342091536319780818203204639102366383712317368525176873629 ( 116 digits) SNFS difficulty: 160 digits. Divisors found: r1=4977320437750921565229473834967340708864912661751976709 (pp55) r2=3231130839822657913824785584822600613852060607675347893277881 (pp61) Version: GGNFS-0.77.1-20060513-k8 Total time: 48.41 hours. Scaled time: 96.57 units (timescale=1.995). Factorization parameters were as follows: name: 16669_160 n: 16082373566096614517840744716684819770544179685787058568186342091536319780818203204639102366383712317368525176873629 m: 100000000000000000000000000000000 c5: 5 c0: 7 skew: 1.07 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, 3500001) Primes: RFBsize:283146, AFBsize:282597, largePrimes:5621726 encountered Relations: rels:5644743, finalFF:651649 Max relations in full relation-set: 28 Initial matrix: 565808 x 651649 with sparse part having weight 40725051. Pruned matrix : 498172 x 501065 with weight 27770530. Total sieving time: 45.45 hours. Total relation processing time: 0.15 hours. Matrix solve time: 2.62 hours. Time per square root: 0.19 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: 48.41 hours. --------- CPU info (if available) ----------

Sep 30, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve
(5·10¹⁶⁴+7)/3 = 1(6)₁₆₃9_<165> = 13 · 191 · 111667 · C156
C156 = P59 · P98
P59 = 26302708085062711351718348313317723934590092763062351780943_<59>
P98 = 22853183997916580633609069137995891297392038889869322628145873448439676832765537008398620936667403_<98>

Number: n N=601100627511426222646761161680965546206801796708529971231335989315691212650463737172222577853390145565689747467684178070804876373058548212170868388304701029 ( 156 digits) SNFS difficulty: 165 digits. Divisors found: Linear algebra by Msieve 1.26: Sun Sep 30 03:05:26 2007 commencing square root phase Sun Sep 30 03:05:26 2007 reading relations for dependency 1 Sun Sep 30 03:05:27 2007 read 217366 cycles Sun Sep 30 03:05:27 2007 cycles contain 795544 unique relations Sun Sep 30 03:06:01 2007 read 795544 relations Sun Sep 30 03:06:08 2007 multiplying 1142918 relations Sun Sep 30 03:08:47 2007 multiply complete, coefficients have about 24.09 million bits Sun Sep 30 03:08:48 2007 initial square root is modulo 8296751 Sun Sep 30 03:15:04 2007 prp59 factor: 26302708085062711351718348313317723934590092763062351780943 Sun Sep 30 03:15:04 2007 prp98 factor: 22853183997916580633609069137995891297392038889869322628145873448439676832765537008398620936667403 Sun Sep 30 03:15:04 2007 elapsed time 01:26:28 Version: GGNFS-0.77.1-20051202-athlon Total time: 40.61 hours. Scaled time: 53.77 units (timescale=1.324). Factorization parameters were as follows: name: KA_1_6_163_9 n: 601100627511426222646761161680965546206801796708529971231335989315691212650463737172222577853390145565689747467684178070804876373058548212170868388304701029 skew: 1.70 deg: 5 c5: 1 c0: 14 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 special-q in [100000, 1900000) Primes: RFBsize:250150, AFBsize:250091, largePrimes:7227599 encountered Relations: rels:6752702, finalFF:576673 Max relations in full relation-set: 28 Initial matrix: 500305 x 576673 with sparse part having weight 39570403. Pruned matrix : 436717 x 439282 with weight 24359944. Total sieving time: 40.39 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. 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: 40.61 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(5·10¹⁶³+7)/3 = 1(6)₁₆₂9_<164> = 19 · 932483 · 3338407 · C150
C150 = P36 · P115
P36 = 179096204859467232396164279888334937_<36>
P115 = 1573361650372442894213033131277538811100419125034880034126626043409760465523866973561143332026778461515089011520283_<115>

Number: n N=281783100453132491764192749729106318410556661674307444387519334626303961635821594561083163050656636337622215383852258673518554659375130169219873027171 ( 150 digits) SNFS difficulty: 164 digits. Divisors found: Linear algebra using Msieve 1.26: Sun Sep 30 18:13:20 2007 commencing square root phase Sun Sep 30 18:13:20 2007 reading relations for dependency 1 Sun Sep 30 18:13:21 2007 read 238377 cycles Sun Sep 30 18:13:21 2007 cycles contain 836180 unique relations Sun Sep 30 18:13:57 2007 read 836180 relations Sun Sep 30 18:14:04 2007 multiplying 1175696 relations Sun Sep 30 18:16:39 2007 multiply complete, coefficients have about 28.40 million bits Sun Sep 30 18:16:40 2007 initial square root is modulo 143457841 Sun Sep 30 18:22:25 2007 prp36 factor: 179096204859467232396164279888334937 Sun Sep 30 18:22:25 2007 prp115 factor: 1573361650372442894213033131277538811100419125034880034126626043409760465523866973561143332026778461515089011520283 Sun Sep 30 18:22:25 2007 elapsed time 01:32:22 Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 65.07 hours. Scaled time: 79.39 units (timescale=1.220). Factorization parameters were as follows: name: KA_1_6_162_9 n: 281783100453132491764192749729106318410556661674307444387519334626303961635821594561083163050656636337622215383852258673518554659375130169219873027171 skew: 0.45 deg: 5 c5: 8 c0: 35 m: 500000000000000000000000000000000 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 special-q in [100000, 3100000) Primes: RFBsize:216816, AFBsize:217636, largePrimes:7586330 encountered Relations: rels:7073916, finalFF:488697 Max relations in full relation-set: 28 Initial matrix: 434517 x 488697 with sparse part having weight 43843717. Pruned matrix : 412969 x 415205 with weight 33648580. Total sieving time: 64.61 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.20 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 65.07 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(55·10¹⁵⁸-1)/9 = 6(1)_158<159> = 13 · 23 · 5763827 · 1559789123863_<13> · C138
C138 = P59 · P80
P59 = 15010258650299280272276491101329623983515589707475827317847_<59>
P80 = 15145513101806035552114587951495643112100912817276775268355705388408504954678887_<80>

Number: n N=227338069049605129053211193199122381737271351068558536526884137163254204545481577681925791011163714893896017433744000903964174094369196289 ( 138 digits) SNFS difficulty: 160 digits. Divisors found: Linear algebra using Msieve 1.26: Sun Sep 30 21:00:47 2007 commencing square root phase Sun Sep 30 21:00:47 2007 reading relations for dependency 1 Sun Sep 30 21:00:47 2007 read 187803 cycles Sun Sep 30 21:00:48 2007 cycles contain 698085 unique relations Sun Sep 30 21:01:15 2007 read 698085 relations Sun Sep 30 21:01:20 2007 multiplying 993110 relations Sun Sep 30 21:03:51 2007 multiply complete, coefficients have about 26.43 million bits Sun Sep 30 21:03:52 2007 initial square root is modulo 38909441 Sun Sep 30 21:09:48 2007 prp59 factor: 15010258650299280272276491101329623983515589707475827317847 Sun Sep 30 21:09:48 2007 prp80 factor: 15145513101806035552114587951495643112100912817276775268355705388408504954678887 Sun Sep 30 21:09:48 2007 elapsed time 01:03:31 Version: GGNFS-0.77.1-20051202-athlon Total time: 29.89 hours. Scaled time: 43.28 units (timescale=1.448). Factorization parameters were as follows: name: KA_6_1_158 n: 227338069049605129053211193199122381737271351068558536526884137163254204545481577681925791011163714893896017433744000903964174094369196289 skew: 0.56 deg: 5 c5: 88 c0: -5 m: 50000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1600000) Primes: RFBsize:183072, AFBsize:183537, largePrimes:7075458 encountered Relations: rels:6528000, finalFF:420262 Max relations in full relation-set: 28 Initial matrix: 366675 x 420262 with sparse part having weight 36710081. Pruned matrix : 330856 x 332753 with weight 26194028. Total sieving time: 29.67 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 29.89 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Sep 30, 2007

By Bruce Dodson
(10³³⁹-1)/9 is divisible by 777734075184513369134763199249605543798943174359980119_<54>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 29, 2007 (5th)

By Yousuke Koide
10¹⁰⁷⁵+1 is divisible by 17749774754658825560922224895404476651_<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 29, 2007 (4th)

By suberi / PRIMO
6·10²⁵⁹³+7 is prime!
(55·10²⁹⁶⁹+71)/9 is prime!

Sep 29, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve
(2·10¹⁶⁵-17)/3 = (6)₁₆₄1_<165> = 24310071773347_<14> · C152
C152 = P50 · P102
P50 = 51734164323600805573653584774564809428106146895381_<50>
P102 = 530084446675280350994104791959744914314598013435184675057749458635575389733945696768078005752479641723_<102>

Number: n N=27423475869683962390491718591322401700236139951798106363550172466967761626634044630890142340664811630560708218722793851241742987522268137155303643581463 ( 152 digits) SNFS difficulty: 165 digits. Divisors found: Linear algebra using Msieve 1.26: ... Sat Sep 29 12:41:06 2007 commencing square root phase Sat Sep 29 12:41:06 2007 reading relations for dependency 1 Sat Sep 29 12:41:06 2007 read 242194 cycles Sat Sep 29 12:41:07 2007 cycles contain 838445 unique relations Sat Sep 29 12:41:38 2007 read 838445 relations Sat Sep 29 12:41:44 2007 multiplying 1189934 relations Sat Sep 29 12:44:18 2007 multiply complete, coefficients have about 26.63 million bits Sat Sep 29 12:44:18 2007 initial square root is modulo 44576321 Sat Sep 29 12:50:18 2007 prp50 factor: 51734164323600805573653584774564809428106146895381 Sat Sep 29 12:50:18 2007 prp102 factor: 530084446675280350994104791959744914314598013435184675057749458635575389733945696768078005752479641723 Sat Sep 29 12:50:18 2007 elapsed time 01:33:37 Version: GGNFS-0.77.1-20051202-athlon Total time: 63.87 hours. Scaled time: 92.54 units (timescale=1.449). Factorization parameters were as follows: name: KA_6_164_1 n: 27423475869683962390491718591322401700236139951798106363550172466967761626634044630890142340664811630560708218722793851241742987522268137155303643581463 skew: 1.53 deg: 5 c5: 2 c0: -17 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3300000) Primes: RFBsize:216816, AFBsize:216686, largePrimes:7771552 encountered Relations: rels:7297268, finalFF:503771 Max relations in full relation-set: 28 Initial matrix: 433567 x 503771 with sparse part having weight 49944999. Pruned matrix : 407928 x 410159 with weight 37183923. Total sieving time: 63.60 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 63.87 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

5·10¹⁶⁷-7 = 4(9)₁₆₆3_<168> = 13 · C167
C167 = P47 · P121
P47 = 27166347444900583109731812696436491851217550133_<47>
P121 = 1415778788059272495359858060016860902525618476647398886043545011620987173109239480930954828521246215935467936088821001417_<121>

Number: n N=38461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461 ( 167 digits) SNFS difficulty: 167 digits. Divisors found: Linear algebra by Msieve 1.26: Sat Sep 29 23:21:09 2007 commencing square root phase Sat Sep 29 23:21:09 2007 reading relations for dependency 1 Sat Sep 29 23:21:09 2007 read 257497 cycles Sat Sep 29 23:21:10 2007 cycles contain 895173 unique relations Sat Sep 29 23:22:06 2007 read 895173 relations Sat Sep 29 23:22:16 2007 multiplying 1259610 relations Sat Sep 29 23:29:41 2007 multiply complete, coefficients have about 37.13 milli on bits Sat Sep 29 23:29:43 2007 initial square root is modulo 214451 Sat Sep 29 23:41:15 2007 prp47 factor: 27166347444900583109731812696436491851217550133 Sat Sep 29 23:41:15 2007 prp121 factor: 1415778788059272495359858060016860902525618476647398886043545011620987173109239480930954828521246215935467936088821001417 Sat Sep 29 23:41:15 2007 elapsed time 02:44:57 Version: GGNFS-0.77.1-20051202-athlon Total time: 199.44 hours. Scaled time: 238.33 units (timescale=1.195). Factorization parameters were as follows: name: KA_4_9_166_3 n: 38461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461 type: snfs skew: 1.00 deg: 5 c5: 500 c0: -7 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 special-q in [100000, 3300000) Primes: RFBsize:250150, AFBsize:249951, largePrimes:7696642 encountered Relations: rels:7217894, finalFF:566646 Max relations in full relation-set: 28 Initial matrix: 500167 x 566646 with sparse part having weight 45760093. Pruned matrix : 461435 x 463999 with weight 34043459. Total sieving time: 198.86 hours. Total relation processing time: 0.58 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000 total time: 199.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Sep 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS
(5·10¹⁵⁵+7)/3 = 1(6)₁₅₄9_<156> = 59 · 3975371759544157964120556169_<28> · C126
C126 = P50 · P77
P50 = 12183673828219514815541105378476410328653530357743_<50>
P77 = 58323116951920764556691672750208036680903493856562686440783028131664900724273_<77>

Number: 16669_155 N=710589833587302941718597558350764196066850853049176811985093853269458721857536326881047933687224985740262132968074713493595839 ( 126 digits) SNFS difficulty: 155 digits. Divisors found: r1=12183673828219514815541105378476410328653530357743 (pp50) r2=58323116951920764556691672750208036680903493856562686440783028131664900724273 (pp77) Version: GGNFS-0.77.1-20050930-nocona Total time: 18.11 hours. Scaled time: 38.82 units (timescale=2.143). Factorization parameters were as follows: n: 710589833587302941718597558350764196066850853049176811985093853269458721857536326881047933687224985740262132968074713493595839 m: 10000000000000000000000000000000 c5: 5 c0: 7 skew: 1.07 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2600001) Primes: RFBsize:216816, AFBsize:216351, largePrimes:5702060 encountered Relations: rels:5761249, finalFF:638372 Max relations in full relation-set: 28 Initial matrix: 433232 x 638372 with sparse part having weight 49932713. Pruned matrix : 308816 x 311046 with weight 30557046. Total sieving time: 17.42 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.57 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 18.11 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

Sep 29, 2007

By Sinkiti Sibata / GGNFS
(5·10¹⁵²+7)/3 = 1(6)₁₅₁9_<153> = 13 · 4987 · 377579803 · 3436321013_<10> · 6969202531_<10> · 1361822893003_<13> · C108
C108 = P46 · P62
P46 = 2737389693912651920291775161351885326232522611_<46>
P62 = 76264635966685860724726069046227515943445121318873286926559367_<62>

Number: 16669_152 N=208766028505206032982047684947445945022194314191543387718652600248442907703745958949603148169464391261347237 ( 108 digits) SNFS difficulty: 152 digits. Divisors found: r1=2737389693912651920291775161351885326232522611 (pp46) r2=76264635966685860724726069046227515943445121318873286926559367 (pp62) Version: GGNFS-0.77.1-20060513-k8 Total time: 26.20 hours. Scaled time: 51.28 units (timescale=1.957). Factorization parameters were as follows: name: 16669_152 n: 208766028505206032982047684947445945022194314191543387718652600248442907703745958949603148169464391261347237 m: 1000000000000000000000000000000 c5: 500 c0: 7 skew: 0.43 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176133, largePrimes:5921246 encountered Relations: rels:6179778, finalFF:785801 Max relations in full relation-set: 28 Initial matrix: 352501 x 785801 with sparse part having weight 71297699. Pruned matrix : 226386 x 228212 with weight 33405143. Total sieving time: 24.91 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.02 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 26.20 hours. --------- CPU info (if available) ----------

5·10¹⁶¹-7 = 4(9)₁₆₀3_<162> = 13 · 103 · 58693 · 85201 · 56518060850527_<14> · C136
C136 = P49 · P87
P49 = 4798551110626920975723815067816871876805464439071_<49>
P87 = 275334764005974011025338002993961748286200016743548777673724333243675964471822107503727_<87>

Number: 49993_161 N=1321207937615067776138099496089850613691726498550114845141787036218852281776516361293885682470727693894523974030933270087638528096917617 ( 136 digits) SNFS difficulty: 161 digits. Divisors found: r1=4798551110626920975723815067816871876805464439071 (pp49) r2=275334764005974011025338002993961748286200016743548777673724333243675964471822107503727 (pp87) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 94.90 hours. Scaled time: 64.25 units (timescale=0.677). Factorization parameters were as follows: name: 49993_161 n: 1321207937615067776138099496089850613691726498550114845141787036218852281776516361293885682470727693894523974030933270087638528096917617 m: 100000000000000000000000000000000 c5: 50 c0: -7 skew: 0.67 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4550001) Primes: RFBsize:315948, AFBsize:316881, largePrimes:5844440 encountered Relations: rels:5989509, finalFF:769982 Max relations in full relation-set: 28 Initial matrix: 632894 x 769982 with sparse part having weight 47420540. Pruned matrix : 526978 x 530206 with weight 32469606. Total sieving time: 82.02 hours. Total relation processing time: 0.37 hours. Matrix solve time: 12.29 hours. Time per square root: 0.22 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: 94.90 hours. --------- CPU info (if available) ----------

Sep 28, 2007 (5th)

By Bruce Dodson
10³⁵²+1 is divisible by 196492106862714324563103086902334481596741493532094589569_<57>, cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 28, 2007 (4th)

By Robert Backstrom / GGNFS
(14·10¹⁶⁴-41)/9 = 1(5)₁₆₃1_<165> = 7394276783_<10> · C155
C155 = P33 · P122
P33 = 241913548612846605274086927369517_<33>
P122 = 86962022362460490445785055865229214136443842893085986014021798676035510354833177041605490276301765124099002836589234876341_<122>

Number: n N=21037291424252539446163109033236138674247346680037789377346270695525241546202958190719320217737047557792989848315711277798343615987894452010473997907897297 ( 155 digits) SNFS difficulty: 165 digits. Divisors found: r1=241913548612846605274086927369517 (pp33) r2=86962022362460490445785055865229214136443842893085986014021798676035510354833177041605490276301765124099002836589234876341 (pp122) Version: GGNFS-0.77.1-20051202-athlon Total time: 74.48 hours. Scaled time: 98.54 units (timescale=1.323). Factorization parameters were as follows: name: KA_1_5_163_1 n: 21037291424252539446163109033236138674247346680037789377346270695525241546202958190719320217737047557792989848315711277798343615987894452010473997907897297 skew: 1.96 deg: 5 c5: 7 c0: -205 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, 2800001) Primes: RFBsize:250150, AFBsize:250442, largePrimes:7581353 encountered Relations: rels:7099178, finalFF:586042 Max relations in full relation-set: 48 Initial matrix: 500657 x 586042 with sparse part having weight 50177668. Pruned matrix : 439767 x 442334 with weight 33392103. Total sieving time: 60.70 hours. Total relation processing time: 0.37 hours. Matrix solve time: 13.32 hours. Total square root time: 0.10 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: 74.48 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Sep 28, 2007 (3rd)

By Sinkiti Sibata / GGNFS
(5·10¹³⁸+7)/3 = 1(6)₁₃₇9_<139> = 17 · 3307 · 111476834769978619_<18> · C117
C117 = P58 · P60
P58 = 2207115310302675107711411136506882374916425885644292317671_<58>
P60 = 120491380689937645366860425953951437824016468528431170048099_<60>

Number: 16669_138 N=265938371080269481663171733466742068358255746135570115355624735763817783285646181622002721514196167950503021257657429 ( 117 digits) SNFS difficulty: 139 digits. Divisors found: r1=2207115310302675107711411136506882374916425885644292317671 (pp58) r2=120491380689937645366860425953951437824016468528431170048099 (pp60) Version: GGNFS-0.77.1-20060513-k8 Total time: 9.91 hours. Scaled time: 19.51 units (timescale=1.969). Factorization parameters were as follows: name: 16669_138 n: 265938371080269481663171733466742068358255746135570115355624735763817783285646181622002721514196167950503021257657429 m: 5000000000000000000000000000 c5: 8 c0: 35 skew: 1.34 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, 1675001) Primes: RFBsize:78498, AFBsize:63913, largePrimes:1600904 encountered Relations: rels:1609087, finalFF:168926 Max relations in full relation-set: 28 Initial matrix: 142476 x 168926 with sparse part having weight 16797660. Pruned matrix : 135545 x 136321 with weight 12105787. Total sieving time: 9.60 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.18 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 9.91 hours. --------- CPU info (if available) ----------

(5·10¹³⁹+7)/3 = 1(6)₁₃₈9_<140> = 6871 · 89220757 · C128
C128 = P41 · P87
P41 = 68519056331623047707327877417940217357011_<41>
P87 = 396781599919562194526485294892308063321566863525043969970677953144473101558904885402357_<87>

Number: 16669_139 N=27187100796240000941757996128380631790386988553157290361212166281105529340875250396473903242091659504609700154156408933849874927 ( 128 digits) SNFS difficulty: 140 digits. Divisors found: r1=68519056331623047707327877417940217357011 (pp41) r2=396781599919562194526485294892308063321566863525043969970677953144473101558904885402357 (pp87) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.76 hours. Scaled time: 15.49 units (timescale=1.996). Factorization parameters were as follows: name: 16669_139 n: 27187100796240000941757996128380631790386988553157290361212166281105529340875250396473903242091659504609700154156408933849874927 m: 10000000000000000000000000000 c5: 1 c0: 14 skew: 1.7 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:63623, largePrimes:1550075 encountered Relations: rels:1551224, finalFF:171077 Max relations in full relation-set: 28 Initial matrix: 142185 x 171077 with sparse part having weight 14886101. Pruned matrix : 133835 x 134609 with weight 10106155. Total sieving time: 7.52 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.13 hours. Time per square root: 0.05 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: 7.76 hours. --------- CPU info (if available) ----------

Sep 28, 2007 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM
(5·10¹⁴²+7)/3 = 1(6)₁₄₁9_<143> = 813978461 · C134
C134 = P40 · P94
P40 = 5800307603283903977690274884081525862077_<40>
P94 = 3530082139245880010115509104883085123122514153709233376692762673105064986713732631002976914277_<94>

Number: 16669_142 N=20475562272484586870004004524471890991064770529188077209658090285348062381550740648734029175578721691342968676743237148957761754173329 ( 134 digits) SNFS difficulty: 144 digits. Divisors found: r1=5800307603283903977690274884081525862077 (pp40) r2=3530082139245880010115509104883085123122514153709233376692762673105064986713732631002976914277 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.83 hours. Scaled time: 14.63 units (timescale=2.141). Factorization parameters were as follows: n: 20475562272484586870004004524471890991064770529188077209658090285348062381550740648734029175578721691342968676743237148957761754173329 m: 50000000000000000000000000000 c5: 4 c0: 175 skew: 2.13 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1200001) Primes: RFBsize:114155, AFBsize:114067, largePrimes:3312011 encountered Relations: rels:3363019, finalFF:351333 Max relations in full relation-set: 28 Initial matrix: 228286 x 351333 with sparse part having weight 30146662. Pruned matrix : 184826 x 186031 with weight 13060822. Total sieving time: 6.64 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.12 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.83 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹⁴³+7)/3 = 1(6)₁₄₂9_<144> = 2597673844567493_<16> · C128
C128 = P33 · P96
P33 = 434046091093577317652060703761719_<33>
P96 = 147818325628859156953088758822031349145171816910978388451598502100954879491436158318814376510207_<96>

Number: 16669_143 N=64159966431203876277211145259729258839851155070514316316238539204930112595630101081864207165422843650012653726820231156499365833 ( 128 digits) SNFS difficulty: 145 digits. Divisors found: r1=434046091093577317652060703761719 (pp33) r2=147818325628859156953088758822031349145171816910978388451598502100954879491436158318814376510207 (pp96) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.24 hours. Scaled time: 17.65 units (timescale=2.141). Factorization parameters were as follows: n: 64159966431203876277211145259729258839851155070514316316238539204930112595630101081864207165422843650012653726820231156499365833 m: 100000000000000000000000000000 c5: 1 c0: 140 skew: 2.69 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1300001) Primes: RFBsize:114155, AFBsize:114557, largePrimes:3356219 encountered Relations: rels:3388872, finalFF:326333 Max relations in full relation-set: 28 Initial matrix: 228776 x 326333 with sparse part having weight 29776228. Pruned matrix : 196932 x 198139 with weight 14882362. Total sieving time: 8.02 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.15 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 8.24 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹⁵⁸+7)/3 = 1(6)₁₅₇9_<159> = 13² · 98960718128861_<14> · C142
C142 = P31 · P112
P31 = 2810189725402685724689364943993_<31>
P112 = 3546202774378704117363718958207959078238914256676956218627386149550232256336887900588798661867954338838309183537_<112>

Sep 28, 2007

By Sinkiti Sibata / GGNFS
5·10¹⁷⁹-7 = 4(9)₁₇₈3_<180> = 13 · 157 · 319001 · 740321 · 1275172341197_<13> · 3168934862695211_<16> · 185503352859609293_<18> · C121
C121 = P59 · P62
P59 = 20824276942434306550878491316554921169577070969181605095403_<59>
P62 = 66452449689374424275673726430638274402626958940230091126916841_<62>

Number: 49993_179 N=1383824215834715620070456110706078885338595809203545862722727074810567580733069553796012130255235581892164045691052381923 ( 121 digits) Divisors found: r1=20824276942434306550878491316554921169577070969181605095403 (pp59) r2=66452449689374424275673726430638274402626958940230091126916841 (pp62) Version: GGNFS-0.77.1-20060513-k8 Total time: 84.55 hours. Scaled time: 168.59 units (timescale=1.994). Factorization parameters were as follows: name: 49993_179 n: 1383824215834715620070456110706078885338595809203545862722727074810567580733069553796012130255235581892164045691052381923 skew: 50602.07 # norm 4.41e+16 c5: 37800 c4: 20128544688 c3: 731574065956501 c2: -49160751458878107328 c1: 392457585328640355756184 c0: -30872663122950055012866120 # alpha -5.82 Y1: 2624022091559 Y0: -129633393211373317821743 # Murphy_E 2.81e-10 # M 506787805364640852991178403337491309782409889508448185433954099888929241273787199158859515253510600449456791072798496402 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 4960001) Primes: RFBsize:348513, AFBsize:348699, largePrimes:7743207 encountered Relations: rels:7931207, finalFF:836390 Max relations in full relation-set: 28 Initial matrix: 697293 x 836390 with sparse part having weight 72523171. Pruned matrix : 582401 x 585951 with weight 47666914. Total sieving time: 78.91 hours. Total relation processing time: 0.43 hours. Matrix solve time: 4.74 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 84.55 hours. --------- CPU info (if available) ----------

Sep 27, 2007 (5th)

By suberi / PRIMO
(17·10²⁴⁶⁵-11)/3 is prime!

Sep 27, 2007 (4th)

By Sinkiti Sibata / GGNFS
(5·10¹⁴¹+7)/3 = 1(6)₁₄₀9_<142> = 3643 · 25537 · 51757591 · 63071636252236439379138851123_<29> · C97 = P33 · P65
P33 = 391280500666926357614593359860867_<33>
P65 = 14025661202251856928100285392792838965856556326678840999770191689_<65>

Number: 16669_141 N=5487967737401790843509693098739988690283003641505514417737061993133022559891161126165558959734363 ( 97 digits) Divisors found: r1=391280500666926357614593359860867 (pp33) r2=14025661202251856928100285392792838965856556326678840999770191689 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 13.08 hours. Scaled time: 8.86 units (timescale=0.677). Factorization parameters were as follows: name: 16669_141 n: 5487967737401790843509693098739988690283003641505514417737061993133022559891161126165558959734363 m: 14369675926318849190988 deg: 4 c4: 128713368 c3: 321000566584 c2: 421345394109067688 c1: -1579948430526136245 c0: -274075801134666159754345 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.486 # E(F1,F2) = 1.904845e-05 # GGNFS version 0.77.1-20060513-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1190818402. # 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, 1680001) Primes: RFBsize:92938, AFBsize:92333, largePrimes:1922598 encountered Relations: rels:2011676, finalFF:220756 Max relations in full relation-set: 28 Initial matrix: 185350 x 220756 with sparse part having weight 21582414. Pruned matrix : 170926 x 171916 with weight 14807077. Polynomial selection time: 0.17 hours. Total sieving time: 11.89 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.81 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 13.08 hours. --------- CPU info (if available) ----------

Sep 27, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM, GGNFS
(5·10¹⁸⁷+7)/3 = 1(6)₁₈₆9_<188> = C188
C188 = P30 · P158
P30 = 809800994185580459461342700011_<30>
P158 = 20581188200970768756638678837132189543155931483203808645215586178063428078238759791181233823231551560665801684249575705334754779112834205568013634241048487879_<158>
(5·10¹³²+7)/3 = 1(6)₁₃₁9_<133> = 71 · C131
C131 = P34 · P97
P34 = 2485169554431976453434061661307773_<34>
P97 = 9445704966847322970558865702100853962207830112965205476236509054211032779897889569875889195527943_<97>

Number: 16669_132 N=23474178403755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939 ( 131 digits) SNFS difficulty: 134 digits. Divisors found: r1=2485169554431976453434061661307773 (pp34) r2=9445704966847322970558865702100853962207830112965205476236509054211032779897889569875889195527943 (pp97) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.33 hours. Scaled time: 4.95 units (timescale=2.128). Factorization parameters were as follows: n: 23474178403755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939 m: 500000000000000000000000000 c5: 4 c0: 175 skew: 2.13 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1100001) Primes: RFBsize:107126, AFBsize:106873, largePrimes:2226874 encountered Relations: rels:2343305, finalFF:290382 Max relations in full relation-set: 28 Initial matrix: 214063 x 290382 with sparse part having weight 19190038. Pruned matrix : 176356 x 177490 with weight 8874710. Total sieving time: 2.19 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 2.33 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹³⁵+7)/3 = 1(6)₁₃₄9_<136> = 283 · 92553614341_<11> · C122
C122 = P49 · P74
P49 = 2576769183774005584057447380213481615877532498847_<49>
P74 = 24694111962373273863858692871467284566884745178594644170287579543940440309_<74>

Number: 16669_135 N=63631026725308488187427141159783305023986096327229654593888951415465371751129423611565979517723069748777754256294214823723 ( 122 digits) SNFS difficulty: 135 digits. Divisors found: r1=2576769183774005584057447380213481615877532498847 (pp49) r2=24694111962373273863858692871467284566884745178594644170287579543940440309 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.83 hours. Scaled time: 6.02 units (timescale=2.129). Factorization parameters were as follows: n: 63631026725308488187427141159783305023986096327229654593888951415465371751129423611565979517723069748777754256294214823723 m: 1000000000000000000000000000 c5: 5 c0: 7 skew: 1.07 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1200001) Primes: RFBsize:107126, AFBsize:107203, largePrimes:2285972 encountered Relations: rels:2456639, finalFF:329462 Max relations in full relation-set: 28 Initial matrix: 214394 x 329462 with sparse part having weight 24010778. Pruned matrix : 168264 x 169399 with weight 9837861. Total sieving time: 2.69 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹⁵¹+7)/3 = 1(6)₁₅₀9_<152> = 17701418095831_<14> · 1812077986113440186399161321739_<31> · C108
C108 = P39 · P70
P39 = 194105463026917266409863270055667221771_<39>
P70 = 2676862394581312139459903416519678229802305636596524777765101615813171_<70>
(5·10¹³⁷+7)/3 = 1(6)₁₃₆9_<138> = 293 · 132893 · 1015853 · 512709215972310397_<18> · C106
C106 = P44 · P63
P44 = 33067855423525789757242415631561806102865053_<44>
P63 = 248525526252847290942368984924627161881822914913147146704360297_<63>

Number: 16669_137 N=8218206171184817335096503188675348229821826657900353296819064455753352874913254325905363890559179282000741 ( 106 digits) SNFS difficulty: 139 digits. Divisors found: r1=33067855423525789757242415631561806102865053 (pp44) r2=248525526252847290942368984924627161881822914913147146704360297 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.56 hours. Scaled time: 7.54 units (timescale=2.118). Factorization parameters were as follows: n: 8218206171184817335096503188675348229821826657900353296819064455753352874913254325905363890559179282000741 m: 5000000000000000000000000000 c5: 4 c0: 175 skew: 2.13 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1350001) Primes: RFBsize:107126, AFBsize:106873, largePrimes:2329174 encountered Relations: rels:2479966, finalFF:306952 Max relations in full relation-set: 28 Initial matrix: 214063 x 306952 with sparse part having weight 23622463. Pruned matrix : 181583 x 182717 with weight 11078387. Total sieving time: 3.40 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.56 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

Sep 27, 2007 (2nd)

By Robert Backstrom / GGNFS
2·10¹⁶⁷-7 = 1(9)₁₆₆3_<168> = 23 · C166
C166 = P33 · P134
P33 = 817671420061668453239381786225641_<33>
P134 = 10634653432374120218546314263462036182748850386624188463030773029103326239415114946154180410545538376172609896000131661254182519321751_<134>

Number: n N=8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391 ( 166 digits) SNFS difficulty: 167 digits. Divisors found: r1=817671420061668453239381786225641 (pp33) r2=10634653432374120218546314263462036182748850386624188463030773029103326239415114946154180410545538376172609896000131661254182519321751 (pp134) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 93.38 hours. Scaled time: 121.68 units (timescale=1.303). Factorization parameters were as follows: name: KA_1_9_166_3 n: 8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391 skew: 0.51 deg: 5 c5: 200 c0: -7 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 4100001) Primes: RFBsize:216816, AFBsize:216921, largePrimes:7989364 encountered Relations: rels:7543447, finalFF:491774 Max relations in full relation-set: 28 Initial matrix: 433802 x 491774 with sparse part having weight 54393195. Pruned matrix : 412924 x 415157 with weight 43131647. Total sieving time: 87.10 hours. Total relation processing time: 0.32 hours. Matrix solve time: 5.82 hours. Total square root time: 0.15 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 93.38 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(5·10¹⁴⁸+7)/3 = 1(6)₁₄₇9_<149> = C149
C149 = P47 · P50 · P53
P47 = 18650313335606201329724729364112809673312876463_<47>
P50 = 84145670486626078050750612549722130221630831476553_<50>
P53 = 10620154668476690275768442467100096825061277196932171_<53>

Number: n N=16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 ( 149 digits) SNFS difficulty: 149 digits. Divisors found: r1=18650313335606201329724729364112809673312876463 (pp47) r2=84145670486626078050750612549722130221630831476553 (pp50) r3=10620154668476690275768442467100096825061277196932171 (pp53) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 14.42 hours. Scaled time: 18.77 units (timescale=1.302). Factorization parameters were as follows: name: KA_1_6_147_9 n: 16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 skew: 0.84 deg: 5 c5: 8 c0: 35 m: 500000000000000000000000000000 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, 1700001) Primes: RFBsize:148933, AFBsize:149505, largePrimes:6860845 encountered Relations: rels:6228580, finalFF:338172 Max relations in full relation-set: 28 Initial matrix: 298503 x 338172 with sparse part having weight 28470354. Pruned matrix : 279282 x 280838 with weight 20632016. Total sieving time: 12.23 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.80 hours. Total square root time: 0.19 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 14.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Sep 27, 2007

By Jo Yeong Uk / GGNFS
(5·10¹³¹+7)/3 = 1(6)₁₃₀9_<132> = 502809239 · 2578087651229_<13> · C111
C111 = P40 · P71
P40 = 1302814026384104145222921505524360161093_<40>
P71 = 98688238257748130465524894016056404057253771100584036810592603966756843_<71>

Number: 16669_131 N=128572421041330628945312107304054615470294816718767333011548094860238837956131360269939220155411684012240109399 ( 111 digits) SNFS difficulty: 131 digits. Divisors found: r1=1302814026384104145222921505524360161093 (pp40) r2=98688238257748130465524894016056404057253771100584036810592603966756843 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.83 hours. Scaled time: 6.05 units (timescale=2.139). Factorization parameters were as follows: n: 128572421041330628945312107304054615470294816718767333011548094860238837956131360269939220155411684012240109399 m: 100000000000000000000000000 c5: 50 c0: 7 skew: 0.67 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 1100001) Primes: RFBsize:78498, AFBsize:78386, largePrimes:1577484 encountered Relations: rels:1592551, finalFF:190981 Max relations in full relation-set: 28 Initial matrix: 156949 x 190981 with sparse part having weight 11746680. Pruned matrix : 144889 x 145737 with weight 7156255. 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,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

Sep 26, 2007 (5th)

By JMB / GGNFS
8·10¹⁸¹+3 = 8(0)₁₈₀3_<182> = 17 · 47 · 120077 · 766223541469_<12> · 752719880879203667_<18> · 148057738580234774662331071_<27> · C118
C118 = P45 · P74
P45 = 147863869707137044125193702898663252618158313_<45>
P74 = 66039126656639520936203017529360818061007971819918535640380875386612837009_<74>

Number: N N=9764800819530466924518836952107346921926064836602594080779488507011172569982077589063765484307783295905707377627405817 ( 118 digits) Divisors found: r1=147863869707137044125193702898663252618158313 (pp45) r2=66039126656639520936203017529360818061007971819918535640380875386612837009 (pp74) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 72.97 hours. Scaled time: 134.20 units (timescale=1.839). Factorization parameters were as follows: name: 8*10^181+3 n: 9764800819530466924518836952107346921926064836602594080779488507011172569982077589063765484307783295905707377627405817 skew: 67407.88 # norm 1.60e+16 c5: 12060 c4: 3987625233 c3: -501223287428036 c2: -13966524767850640108 c1: 532227260136176141487706 c0: 11552261902925874836942455365 # alpha -5.61 Y1: 2159113508321 Y0: -60487020326792030157938 # Murphy_E 3.57e-10 # M 5213949619208846846643369347895106390731876475313017475218358403523304199793861470938855378906618354132884471051345753 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 25000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1500000, 1900001) Primes: RFBsize:216816, AFBsize:216818, largePrimes:8168351 encountered Relations: rels:8459764, finalFF:541290 Max relations in full relation-set: 28 Initial matrix: 433714 x 541290 with sparse part having weight 68304122. Pruned matrix : 370334 x 372566 with weight 51046323. Total sieving time: 68.03 hours. Total relation processing time: 0.31 hours. Matrix solve time: 4.39 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,50,50,2.4,2.4,60000 total time: 72.97 hours. --------- CPU info (if available) ----------

Sep 26, 2007 (4th)

By suberi / PRIMO
(52·10²⁴⁸²-43)/9 is prime!

Sep 26, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve
(5·10¹⁰⁹+7)/3 = 1(6)₁₀₈9_<110> = 19² · C107
C107 = P42 · P66
P42 = 153946522305899923004676383646159813796121_<42>
P66 = 299896685009093874497686190587633018428192207232800575636015338349_<66>

Number: 16669_109 N=46168051708217913204062788550323176361957525392428439519852262234533702677746999076638965835641735918744229 ( 107 digits) SNFS difficulty: 110 digits. Divisors found: r1=153946522305899923004676383646159813796121 (pp42) r2=299896685009093874497686190587633018428192207232800575636015338349 (pp66) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.17 hours. Scaled time: 0.79 units (timescale=0.677). Factorization parameters were as follows: name: 16669_109 n: 46168051708217913204062788550323176361957525392428439519852262234533702677746999076638965835641735918744229 m: 10000000000000000000000 c5: 1 c0: 14 skew: 1.7 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, 450001) Primes: RFBsize:49098, AFBsize:63623, largePrimes:1899503 encountered Relations: rels:1884233, finalFF:172922 Max relations in full relation-set: 28 Initial matrix: 112785 x 172922 with sparse part having weight 11280001. Pruned matrix : 87896 x 88523 with weight 3680813. Total sieving time: 1.01 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.17 hours. --------- CPU info (if available) ----------

(5·10¹¹⁵+7)/3 = 1(6)₁₁₄9_<116> = 83 · 1069 · 1180428929_<10> · C102
C102 = P39 · P63
P39 = 296398376609473226797596655124462993281_<39>
P63 = 536880075739627642112309347769656425847569291133442846496928603_<63>

Number: 16669_115 N=159130382883196664131166647978403378748111484644347405870264581612954267174235629404567704102325716443 ( 102 digits) SNFS difficulty: 115 digits. Divisors found: r1=296398376609473226797596655124462993281 (pp39) r2=536880075739627642112309347769656425847569291133442846496928603 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.63 hours. Scaled time: 1.10 units (timescale=0.677). Factorization parameters were as follows: name: 16669_115 n: 159130382883196664131166647978403378748111484644347405870264581612954267174235629404567704102325716443 m: 100000000000000000000000 c5: 5 c0: 7 skew: 1.07 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:64228, largePrimes:2093547 encountered Relations: rels:2213778, finalFF:271300 Max relations in full relation-set: 28 Initial matrix: 113391 x 271300 with sparse part having weight 21663794. Pruned matrix : 76323 x 76953 with weight 4050572. Total sieving time: 1.45 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.63 hours. --------- CPU info (if available) ----------

(5·10¹²⁰+7)/3 = 1(6)₁₁₉9_<121> = 210451967185245864060738227648101_<33> · C88
C88 = P34 · P55
P34 = 2003771457999863638436035664075387_<34>
P55 = 3952278809073709433995319843828553332517951348922169387_<55>

Wed Sep 26 14:24:28 2007 Msieve v. 1.26 Wed Sep 26 14:24:28 2007 random seeds: 5143490f 0701fb59 Wed Sep 26 14:24:28 2007 factoring 7919463471679591443105528414604368703900563230510077999800695379563554517322213551577769 (88 digits) Wed Sep 26 14:24:29 2007 commencing quadratic sieve (88-digit input) Wed Sep 26 14:24:30 2007 using multiplier of 1 Wed Sep 26 14:24:30 2007 using 64kb Pentium 2 sieve core Wed Sep 26 14:24:30 2007 sieve interval: 14 blocks of size 65536 Wed Sep 26 14:24:30 2007 processing polynomials in batches of 8 Wed Sep 26 14:24:30 2007 using a sieve bound of 1527497 (57880 primes) Wed Sep 26 14:24:30 2007 using large prime bound of 122199760 (26 bits) Wed Sep 26 14:24:30 2007 using double large prime bound of 360351695070240 (42-49 bits) Wed Sep 26 14:24:30 2007 using trial factoring cutoff of 49 bits Wed Sep 26 14:24:30 2007 polynomial 'A' values have 11 factors Wed Sep 26 19:19:22 2007 58229 relations (16203 full + 42026 combined from 608880 partial), need 57976 Wed Sep 26 19:19:29 2007 begin with 625083 relations Wed Sep 26 19:19:47 2007 reduce to 139473 relations in 10 passes Wed Sep 26 19:19:48 2007 attempting to read 139473 relations Wed Sep 26 19:19:56 2007 recovered 139473 relations Wed Sep 26 19:19:56 2007 recovered 112269 polynomials Wed Sep 26 19:20:15 2007 attempting to build 58229 cycles Wed Sep 26 19:20:15 2007 found 58229 cycles in 5 passes Wed Sep 26 19:20:17 2007 distribution of cycle lengths: Wed Sep 26 19:20:17 2007 length 1 : 16203 Wed Sep 26 19:20:17 2007 length 2 : 11462 Wed Sep 26 19:20:17 2007 length 3 : 10350 Wed Sep 26 19:20:17 2007 length 4 : 7641 Wed Sep 26 19:20:17 2007 length 5 : 5205 Wed Sep 26 19:20:17 2007 length 6 : 3172 Wed Sep 26 19:20:17 2007 length 7 : 1903 Wed Sep 26 19:20:17 2007 length 9+: 2293 Wed Sep 26 19:20:17 2007 largest cycle: 18 relations Wed Sep 26 19:20:18 2007 matrix is 57880 x 58229 with weight 3346646 (avg 57.47/col) Wed Sep 26 19:20:22 2007 filtering completed in 3 passes Wed Sep 26 19:20:22 2007 matrix is 53415 x 53479 with weight 3096508 (avg 57.90/col) Wed Sep 26 19:20:24 2007 saving the first 48 matrix rows for later Wed Sep 26 19:20:24 2007 matrix is 53367 x 53479 with weight 2483927 (avg 46.45/col) Wed Sep 26 19:20:24 2007 matrix includes 64 packed rows Wed Sep 26 19:20:24 2007 using block size 10922 for processor cache size 256 kB Wed Sep 26 19:20:24 2007 commencing Lanczos iteration Wed Sep 26 19:23:14 2007 lanczos halted after 845 iterations Wed Sep 26 19:23:15 2007 recovered 16 nontrivial dependencies Wed Sep 26 19:23:35 2007 prp34 factor: 2003771457999863638436035664075387 Wed Sep 26 19:23:35 2007 prp55 factor: 3952278809073709433995319843828553332517951348922169387 Wed Sep 26 19:23:35 2007 elapsed time 04:59:07

(5·10¹²¹+7)/3 = 1(6)₁₂₀9_<122> = 79 · 2382356651_<10> · C110
C110 = P39 · P72
P39 = 275708725429269016809228525155998997753_<39>
P72 = 321191741127943587251282728962673310095889920760636481110578718074425937_<72>

Number: 16669_121 N=88555365564793051234214008584940727814733466817154162992301027014493685329128418132245529605674917232827919561 ( 110 digits) SNFS difficulty: 121 digits. Divisors found: r1=275708725429269016809228525155998997753 (pp39) r2=321191741127943587251282728962673310095889920760636481110578718074425937 (pp72) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.59 hours. Scaled time: 1.75 units (timescale=0.677). Factorization parameters were as follows: name: 16669_121 n: 88555365564793051234214008584940727814733466817154162992301027014493685329128418132245529605674917232827919561 m: 1000000000000000000000000 c5: 50 c0: 7 skew: 0.67 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:63963, largePrimes:2104728 encountered Relations: rels:2144770, finalFF:180084 Max relations in full relation-set: 28 Initial matrix: 113126 x 180084 with sparse part having weight 15976568. Pruned matrix : 96531 x 97160 with weight 6113251. Total sieving time: 2.32 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.15 hours. Time per square root: 0.05 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: 2.59 hours. --------- CPU info (if available) ----------

(5·10¹²⁵+7)/3 = 1(6)₁₂₄9_<126> = 4105166921_<10> · 20017012591_<11> · C106
C106 = P33 · P74
P33 = 168513932435459060567620404345611_<33>
P74 = 12036018680677828464748171772279011079478949036231241898241956856646325889_<74>

Number: 16669_125 N=2028236838747666687478534951496303214000516428894914134664497036559678113327291556491062877412232492823179 ( 106 digits) SNFS difficulty: 125 digits. Divisors found: r1=168513932435459060567620404345611 (pp33) r2=12036018680677828464748171772279011079478949036231241898241956856646325889 (pp74) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 3.06 hours. Scaled time: 2.07 units (timescale=0.677). Factorization parameters were as follows: name: 16669_125 n: 2028236838747666687478534951496303214000516428894914134664497036559678113327291556491062877412232492823179 m: 10000000000000000000000000 c5: 5 c0: 7 skew: 1.07 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:64228, largePrimes:2213124 encountered Relations: rels:2360223, finalFF:266542 Max relations in full relation-set: 28 Initial matrix: 113391 x 266542 with sparse part having weight 25504051. Pruned matrix : 85873 x 86503 with weight 6283883. Total sieving time: 2.80 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.13 hours. Time per square root: 0.05 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: 3.06 hours. --------- CPU info (if available) ----------

Sep 26, 2007 (2nd)

By Jo Yeong Uk / GGNFS
(5·10¹¹³+7)/3 = 1(6)₁₁₂9_<114> = 139 · C112
C112 = P56 · P56
P56 = 33323707073076001771345428051913373104674894761352370801_<56>
P56 = 35981614073029109077263780581405124329331786404763064471_<56>

Number: 16669_113 N=1199040767386091127098321342925659472422062350119904076738609112709832134292565947242206235011990407673860911271 ( 112 digits) SNFS difficulty: 115 digits. Divisors found: r1=33323707073076001771345428051913373104674894761352370801 (pp56) r2=35981614073029109077263780581405124329331786404763064471 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.70 hours. Scaled time: 1.50 units (timescale=2.143). Factorization parameters were as follows: n: 1199040767386091127098321342925659472422062350119904076738609112709832134292565947242206235011990407673860911271 m: 100000000000000000000000 c5: 1 c0: 140 skew: 2.69 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, 340001) Primes: RFBsize:30757, AFBsize:30764, largePrimes:1046995 encountered Relations: rels:964799, finalFF:87555 Max relations in full relation-set: 28 Initial matrix: 61585 x 87555 with sparse part having weight 4230236. Pruned matrix : 54927 x 55298 with weight 1881639. Total sieving time: 0.67 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.70 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹¹⁶+7)/3 = 1(6)₁₁₅9_<117> = 13 · C116
C116 = P32 · P84
P32 = 31003216721782548975602081797253_<32>
P84 = 413522020491030430690268175769186538084881606692266956654906116015314098195825309421_<84>

Number: 16669_116 N=12820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513 ( 116 digits) SNFS difficulty: 116 digits. Divisors found: r1=31003216721782548975602081797253 (pp32) r2=413522020491030430690268175769186538084881606692266956654906116015314098195825309421 (pp84) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.84 hours. Scaled time: 1.79 units (timescale=2.139). Factorization parameters were as follows: n: 12820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513 m: 100000000000000000000000 c5: 50 c0: 7 skew: 0.67 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:49041, largePrimes:1943562 encountered Relations: rels:1936531, finalFF:147809 Max relations in full relation-set: 28 Initial matrix: 98204 x 147809 with sparse part having weight 12274062. Pruned matrix : 85193 x 85748 with weight 4983589. Total sieving time: 0.78 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.84 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹¹⁷+7)/3 = 1(6)₁₁₆9_<118> = 337 · 509 · 23677 · C108
C108 = P48 · P60
P48 = 516041832369522017710254534990233044032515687357_<48>
P60 = 795224009016448425092100987054725056223874009925853849747737_<60>

Number: 16669_117 N=410368854757085343761438229042281635409146357321018036623580685567761868529348166730485220151100269610261109 ( 108 digits) SNFS difficulty: 119 digits. Divisors found: r1=516041832369522017710254534990233044032515687357 (pp48) r2=795224009016448425092100987054725056223874009925853849747737 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.79 hours. Scaled time: 1.67 units (timescale=2.113). Factorization parameters were as follows: n: 410368854757085343761438229042281635409146357321018036623580685567761868529348166730485220151100269610261109 m: 500000000000000000000000 c5: 4 c0: 175 skew: 2.13 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:49096, largePrimes:1978458 encountered Relations: rels:2032316, finalFF:203074 Max relations in full relation-set: 28 Initial matrix: 98258 x 203074 with sparse part having weight 16906655. Pruned matrix : 75540 x 76095 with weight 4051422. Total sieving time: 0.74 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,119,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.79 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹¹⁹+7)/3 = 1(6)₁₁₈9_<120> = 179449580749_<12> · C108
C108 = P50 · P59
P50 = 25753449757830406639991914695740623420290006566179_<50>
P59 = 36063750448248243471048952703868375635140956097798086208939_<59>

Number: 16669_119 N=928765985247894944730399218898130893992433011358033499769124983962581877754703244378693651035712215324874081 ( 108 digits) SNFS difficulty: 120 digits. Divisors found: r1=25753449757830406639991914695740623420290006566179 (pp50) r2=36063750448248243471048952703868375635140956097798086208939 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.78 hours. Scaled time: 1.67 units (timescale=2.129). Factorization parameters were as follows: n: 928765985247894944730399218898130893992433011358033499769124983962581877754703244378693651035712215324874081 m: 1000000000000000000000000 c5: 1 c0: 14 skew: 1.7 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:48926, largePrimes:1974603 encountered Relations: rels:2025360, finalFF:198858 Max relations in full relation-set: 28 Initial matrix: 98088 x 198858 with sparse part having weight 16755508. Pruned matrix : 76604 x 77158 with weight 4195384. Total sieving time: 0.73 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.78 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹²⁸+7)/3 = 1(6)₁₂₇9_<129> = 13 · 29 · 41491 · C122
C122 = P33 · P89
P33 = 349983130933154147542494609343249_<33>
P89 = 30444327507033853270702399006913464736680064207497013075681509886136946770149506545458183_<89>

Number: 16669_128 N=10655001060066055465971858309540183216152828175044875135214627202503260377049374912642310058783427748363226684657422856567 ( 122 digits) SNFS difficulty: 130 digits. Divisors found: r1=349983130933154147542494609343249 (pp33) r2=30444327507033853270702399006913464736680064207497013075681509886136946770149506545458183 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.94 hours. Scaled time: 4.16 units (timescale=2.145). Factorization parameters were as follows: n: 10655001060066055465971858309540183216152828175044875135214627202503260377049374912642310058783427748363226684657422856567 m: 100000000000000000000000000 c5: 1 c0: 140 skew: 2.69 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78641, largePrimes:1495828 encountered Relations: rels:1503438, finalFF:186230 Max relations in full relation-set: 28 Initial matrix: 157203 x 186230 with sparse part having weight 9104275. Pruned matrix : 143047 x 143897 with weight 5517984. Total sieving time: 1.86 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 1.94 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).

Sep 26, 2007

The factor table of 166...669 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.

Sep 25, 2007 (3rd)

By Robert Backstrom / GGNFS
3·10¹⁵⁸+7 = 3(0)₁₅₇7_<159> = 89 · 2076619 · 259656955391_<12> · C139
C139 = P45 · P95
P45 = 252655059854571780687683274450095709673880513_<45>
P95 = 24742664377819752522172823349240990874103759568271850621675059742047926996980289580771977958019_<95>

Number: n N=6251359349339630621166108381490606750376571670303750482199645475819777412486638575944263953290323590162412366640843654132109482845536183747 ( 139 digits) SNFS difficulty: 158 digits. Divisors found: r1=252655059854571780687683274450095709673880513 (pp45) r2=24742664377819752522172823349240990874103759568271850621675059742047926996980289580771977958019 (pp95) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.13 hours. Scaled time: 46.40 units (timescale=1.444). Factorization parameters were as follows: name: KA_3_0_157_7 n: 6251359349339630621166108381490606750376571670303750482199645475819777412486638575944263953290323590162412366640843654132109482845536183747 skew: 0.30 deg: 5 c5: 3000 c0: 7 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:183072, AFBsize:183021, largePrimes:7139599 encountered Relations: rels:6634469, finalFF:457174 Max relations in full relation-set: 28 Initial matrix: 366160 x 457174 with sparse part having weight 40338936. Pruned matrix : 305523 x 307417 with weight 25494270. Total sieving time: 28.79 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.99 hours. Total square root time: 0.12 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 32.13 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Sep 25, 2007 (2nd)

By Sinkiti Sibata / GGNFS
5·10¹⁶²-7 = 4(9)₁₆₁3_<163> = 17 · 1163 · 148309339 · 387720132193027_<15> · C136
C136 = P41 · P96
P41 = 32186888333809678325979899492525673198029_<41>
P96 = 136639266967774480350045857113895807555932147258323470751247259644932218298158286602940005007959_<96>

Number: 49993_162 N=4397992827905366561495616972942610757769676397548052455720011518707669668467184795048847173974047956366224189761866099002983083128112811 ( 136 digits) SNFS difficulty: 162 digits. Divisors found: r1=32186888333809678325979899492525673198029 (pp41) r2=136639266967774480350045857113895807555932147258323470751247259644932218298158286602940005007959 (pp96) Version: GGNFS-0.77.1-20060513-k8 Total time: 66.77 hours. Scaled time: 132.61 units (timescale=1.986). Factorization parameters were as follows: name: 49993_162 n: 4397992827905366561495616972942610757769676397548052455720011518707669668467184795048847173974047956366224189761866099002983083128112811 m: 100000000000000000000000000000000 c5: 500 c0: -7 skew: 0.43 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4350001) Primes: RFBsize:315948, AFBsize:315206, largePrimes:5778555 encountered Relations: rels:5922064, finalFF:770316 Max relations in full relation-set: 28 Initial matrix: 631220 x 770316 with sparse part having weight 46730298. Pruned matrix : 518559 x 521779 with weight 31016251. Total sieving time: 63.45 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.94 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 66.77 hours. --------- CPU info (if available) ----------

Sep 25, 2007

By Robert Backstrom / GGNFS, Msieve
(86·10¹⁸²+31)/9 = 9(5)₁₈₁9_<183> = 7 · C183
C183 = P48 · P48 · P87
P48 = 219254706609281472076564248230371923805632108973_<48>
P48 = 667127665052517179233067332728168025449200965073_<48>
P87 = 933254357035504554827120249606468833406095139378559205785196446817284884193061670441653_<87>

Number: n N=136507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937 ( 183 digits) SNFS difficulty: 183 digits. Divisors found: (Completed by MSIEVE 1.26) Tue Sep 25 08:11:44 2007 prp48 factor: 219254706609281472076564248230371923805632108973 Tue Sep 25 08:11:44 2007 prp48 factor: 667127665052517179233067332728168025449200965073 Tue Sep 25 08:11:44 2007 prp87 factor: 933254357035504554827120249606468833406095139378559205785196446817284884193061670441653 Version: GGNFS-0.77.1-20051202-athlon Total time: 760.78 hours. Scaled time: 1004.23 units (timescale=1.320). Factorization parameters were as follows: name: KA_9_5_181_9 n: 136507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937 skew: 0.32 deg: 5 c5: 8600 c0: 31 m: 1000000000000000000000000000000000000 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, 10800000) Primes: RFBsize:283146, AFBsize:283738, largePrimes:9358417 encountered Relations: rels:9011426, finalFF:643650 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 759.81 hours. Total relation processing time: 0.97 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,183,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 760.78 hours. --------- CPU info (if available) ---------- Mem Alloc Error by GGNFS ... [09/24 14:06:36] GGNFS-0.77.1-20051202-athlon : matbuild [09/24 14:07:59] largePrimes: 9358417 , relations: 9011426 [09/24 14:18:34] reduceRelSets dropped relation-set weight from 19495262 to 15297055. [09/24 14:24:25] reduceRelSets dropped relation-set weight from 15297055 to 15246628. [09/24 14:24:25] After removing heavy rel-sets, weight is 13333792. [09/24 14:32:44] Heap stats for matbuild run, after cycle-building [09/24 14:32:44] Max heap usage: 460 MB [09/24 14:32:44] malloc/realloc errors: 0 [09/24 14:32:44] total malloc's : 515 [09/24 14:32:44] total realloc's: 219 [09/24 14:32:44] rels:9011426, initialFF:0, finalFF:643650 [09/24 14:32:52] Memory allocation error (721935180 bytes requested). ... Linear Algebra completed by MSIEVE 1.26 ... Tue Sep 25 07:49:04 2007 reading relations for dependency 2 Tue Sep 25 07:49:04 2007 read 390086 cycles Tue Sep 25 07:49:05 2007 cycles contain 1234166 unique relations Tue Sep 25 07:50:17 2007 read 1234166 relations Tue Sep 25 07:50:29 2007 multiplying 1849254 relations Tue Sep 25 07:56:56 2007 multiply complete, coefficients have about 64.93 million bits Tue Sep 25 07:56:58 2007 initial square root is modulo 2099293891 Tue Sep 25 08:11:44 2007 prp48 factor: 219254706609281472076564248230371923805632108973 Tue Sep 25 08:11:44 2007 prp48 factor: 667127665052517179233067332728168025449200965073 Tue Sep 25 08:11:44 2007 prp87 factor: 933254357035504554827120249606468833406095139378559205785196446817284884193061670441653 Tue Sep 25 08:11:44 2007 elapsed time 05:11:32 Cygwin on AMD 64 3200+

Sep 24, 2007 (4th)

By JMB / GMP-ECM
(16·10²²⁰-61)/9 = 1(7)₂₁₉1_<221> = 13 · 353 · 1877 · 16492937 · 1805034167_<10> · 937019983238111_<15> · C182
C182 = P35 · C148
P35 = 55949358235598934650206505967480781_<35>
C148 = [1322414960079354351709834861520621170706984511895469829631709464819715591749118547779968053941698236864151284187903149814300379387206849149544675063_<148>]

Sep 24, 2007 (3rd)

By Robert Backstrom / GGNFS
5·10¹⁶³-7 = 4(9)₁₆₂3_<164> = 1244029 · C158
C158 = P40 · P119
P40 = 3045777474311016078416962103126374071511_<40>
P119 = 13195970300684442140409379802151398451013119494061176587343764266942527286513791024515689055116238602995731201645467547_<119>

Number: n N=40191989093501839587340809579197912588854439888459191867713694777211785255809952983411158421548050728720954254281853558076218480437353148519849617653607753517 ( 158 digits) SNFS difficulty: 163 digits. Divisors found: r1=3045777474311016078416962103126374071511 (pp40) r2=13195970300684442140409379802151398451013119494061176587343764266942527286513791024515689055116238602995731201645467547 (pp119) Version: GGNFS-0.77.1-20051202-athlon Total time: 63.80 hours. Scaled time: 92.00 units (timescale=1.442). Factorization parameters were as follows: name: KA_4_9_162_3 n: 40191989093501839587340809579197912588854439888459191867713694777211785255809952983411158421548050728720954254281853558076218480437353148519849617653607753517 skew: 0.27 deg: 5 c5: 5000 c0: -7 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, 3000001) Primes: RFBsize:216816, AFBsize:217636, largePrimes:7601696 encountered Relations: rels:7098507, finalFF:494362 Max relations in full relation-set: 28 Initial matrix: 434517 x 494362 with sparse part having weight 44766005. Pruned matrix : 411191 x 413427 with weight 33800123. Total sieving time: 57.42 hours. Total relation processing time: 0.26 hours. Matrix solve time: 6.04 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 63.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Sep 24, 2007 (2nd)

By Sinkiti Sibata / GGNFS
5·10¹⁶⁹-7 = 4(9)₁₆₈3_<170> = 43 · 211 · 1472137 · 2321750736611301907097_<22> · 574482675743693221950617_<24> · C115
C115 = P43 · P72
P43 = 5744494079787571396717760190250240838888041_<43>
P72 = 488569723676345326019989715470508850328546498038944485790862224772950377_<72>

Number: 49993_169 N=2806585885222215377350944994569312431165970817862559316770088936318837708911961250594258617432022173022491551741457 ( 115 digits) Divisors found: r1=5744494079787571396717760190250240838888041 (pp43) r2=488569723676345326019989715470508850328546498038944485790862224772950377 (pp72) Version: GGNFS-0.77.1-20060513-k8 Total time: 48.07 hours. Scaled time: 95.70 units (timescale=1.991). Factorization parameters were as follows: name: 49993_169 n: 2806585885222215377350944994569312431165970817862559316770088936318837708911961250594258617432022173022491551741457 skew: 31373.54 # norm 3.83e+15 c5: 60840 c4: -720780132 c3: 72126305586899 c2: 1666649461314850199 c1: -116989157991344921484511 c0: 162800038608129701576075241 # alpha -6.02 Y1: 896315175217 Y0: -8566391803006571745272 # Murphy_E 5.55e-10 # M 2396840833491453209262727670434957761159698617278948458168476366281194806287209404389368742033257071680380836619726 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3050001) Primes: RFBsize:250150, AFBsize:250437, largePrimes:7884281 encountered Relations: rels:8065906, finalFF:781702 Max relations in full relation-set: 28 Initial matrix: 500667 x 781702 with sparse part having weight 75915276. Pruned matrix : 319011 x 321578 with weight 50104378. Total sieving time: 45.28 hours. Total relation processing time: 0.27 hours. Matrix solve time: 2.18 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 48.07 hours. --------- CPU info (if available) ----------

5·10¹⁵³-7 = 4(9)₁₅₂3_<154> = 1487 · 12703 · 27064010767_<11> · C136
C136 = P50 · P87
P50 = 23985742229316002405160508997718416270586975005491_<50>
P87 = 407762626593054648807646182158981927854290181355167860837282173381501147582605582632029_<87>

Number: 49993_153 N=9780489252209843258748295325322445828861819876619459830498259544007166236469918061045471477958043159769750664560714769953352476507471239 ( 136 digits) SNFS difficulty: 154 digits. Divisors found: r1=23985742229316002405160508997718416270586975005491 (pp50) r2=407762626593054648807646182158981927854290181355167860837282173381501147582605582632029 (pp87) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 41.29 hours. Scaled time: 27.95 units (timescale=0.677). Factorization parameters were as follows: name: 49993_153 n: 9780489252209843258748295325322445828861819876619459830498259544007166236469918061045471477958043159769750664560714769953352476507471239 m: 5000000000000000000000000000000 c5: 8 c0: -35 skew: 1.34 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176798, largePrimes:5470514 encountered Relations: rels:5308781, finalFF:410488 Max relations in full relation-set: 28 Initial matrix: 353165 x 410488 with sparse part having weight 36573902. Pruned matrix : 331184 x 333013 with weight 26077344. Total sieving time: 36.51 hours. Total relation processing time: 0.23 hours. Matrix solve time: 4.39 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 41.29 hours. --------- CPU info (if available) ----------

Sep 24, 2007

By suberi / PRIMO
7·10²⁵⁵⁹+3 is prime!

Sep 23, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM
3·10¹⁶⁹+7 = 3(0)₁₆₈7_<170> = 37 · C168
C168 = P39 · P130
P39 = 321485385345676762706421506544388644469_<39>
P130 = 2522076734340466176982866611144735500345304211081851607078673956180783695480227990278425308960588927381717464690492823021851851119_<130>

Sep 23, 2007 (2nd)

By Sinkiti Sibata / GGNFS
5·10¹⁵⁹-7 = 4(9)₁₅₈3_<160> = 47 · 964644799 · 270706849725621910507211_<24> · C126
C126 = P52 · P75
P52 = 1364391784808783411765902177253121572084574108528241_<52>
P75 = 298583894675727940289845675134760397414301294012470876284306516517828237131_<75>

Number: 49993_159 N=407385412971774246984894055262282656186910895322963362483310889127715264264776948863397719450706989787968437776460909958316571 ( 126 digits) SNFS difficulty: 160 digits. Divisors found: r1=1364391784808783411765902177253121572084574108528241 (pp52) r2=298583894675727940289845675134760397414301294012470876284306516517828237131 (pp75) Version: GGNFS-0.77.1-20060513-k8 Total time: 40.15 hours. Scaled time: 80.17 units (timescale=1.997). Factorization parameters were as follows: name: 49993_159 n: 407385412971774246984894055262282656186910895322963362483310889127715264264776948863397719450706989787968437776460909958316571 m: 100000000000000000000000000000000 c5: 1 c0: -14 skew: 1.7 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, 3300001) Primes: RFBsize:283146, AFBsize:283092, largePrimes:5702766 encountered Relations: rels:5817296, finalFF:727915 Max relations in full relation-set: 28 Initial matrix: 566302 x 727915 with sparse part having weight 43359878. Pruned matrix : 431450 x 434345 with weight 26402153. Total sieving time: 37.67 hours. Total relation processing time: 0.14 hours. Matrix solve time: 2.17 hours. Time per square root: 0.17 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: 40.15 hours. --------- CPU info (if available) ----------

Sep 23, 2007

By Robert Backstrom / GGNFS
4·10¹⁶²+7 = 4(0)₁₆₁7_<163> = 11 · 79 · 1139323553_<10> · C151
C151 = P60 · P92
P60 = 234034230184541159881265925110454036781626436280873469868669_<60>
P92 = 17262900077839710421537401417208645828242546967978794855357928428513665188571039974636777079_<92>

Number: n N=4040109530469872295206417141478966201658930005731568037108063258312773845625926951228352920828858552387046131679020631083739483089980760886171559437851 ( 151 digits) SNFS difficulty: 162 digits. Divisors found: r1=234034230184541159881265925110454036781626436280873469868669 (pp60) r2=17262900077839710421537401417208645828242546967978794855357928428513665188571039974636777079 (pp92) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 39.72 hours. Scaled time: 54.22 units (timescale=1.365). Factorization parameters were as follows: name: KA_4_0_161_7 n: 4040109530469872295206417141478966201658930005731568037108063258312773845625926951228352920828858552387046131679020631083739483089980760886171559437851 skew: 0.45 deg: 5 c5: 400 c0: 7 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, 1800001) Primes: RFBsize:216816, AFBsize:216976, largePrimes:7127302 encountered Relations: rels:6610032, finalFF:494318 Max relations in full relation-set: 28 Initial matrix: 433856 x 494318 with sparse part having weight 36516568. Pruned matrix : 386643 x 388876 with weight 24911065. Total sieving time: 36.27 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.13 hours. Total square root time: 0.11 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 39.72 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Sep 22, 2007

By Sinkiti Sibata / GGNFS
5·10¹⁶⁵-7 = 4(9)₁₆₄3_<166> = 914885729 · 4261399463897_<13> · 6040387634947_<13> · 1491052684691540816159207_<25> · C108
C108 = P33 · P75
P33 = 319197319597996510039273971999701_<33>
P75 = 446101691024302128170720348856355665147674572755074743500867309182182952809_<75>

Number: 49993_165 N=142394464043090857513239492807664605923383657649420029924108397359976327605079156360506333452052514645110109 ( 108 digits) Divisors found: r1=319197319597996510039273971999701 (pp33) r2=446101691024302128170720348856355665147674572755074743500867309182182952809 (pp75) Version: GGNFS-0.77.1-20060513-k8 Total time: 16.02 hours. Scaled time: 31.80 units (timescale=1.985). Factorization parameters were as follows: name: 49993_165 n: 142394464043090857513239492807664605923383657649420029924108397359976327605079156360506333452052514645110109 skew: 13936.08 # norm 1.35e+15 c5: 76800 c4: -4242870768 c3: 25375181134756 c2: 1030238403227851652 c1: 2250557392389371098067 c0: -5950154183708608868842952 # alpha -5.91 Y1: 362384350823 Y0: -284205511495603330335 # Murphy_E 1.34e-09 # M 109003927296022212451091712878426486494476931109986893486521952118176755395827872047646424692080971536718213 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:182559, largePrimes:4445338 encountered Relations: rels:4500132, finalFF:431528 Max relations in full relation-set: 28 Initial matrix: 365712 x 431528 with sparse part having weight 33237805. Pruned matrix : 316128 x 318020 with weight 20984545. Total sieving time: 14.64 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.00 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 16.02 hours. --------- CPU info (if available) ----------

2·10¹⁸⁹-3 = 1(9)₁₈₈7_<190> = 31618164809434211754592287712179187_<35> · 26515433818872756128486451063540368813_<38> · C118
C118 = P57 · P61
P57 = 484578537409999154675042390540664390207331844965054363441_<57>
P61 = 4923006679232260879844150105623901082760825132994000095977307_<61>

Number: 19997_189 N=2385583376282025837302025573831625807718996619292106854661488654167073439506823897959332181406320971559780911666433387 ( 118 digits) Divisors found: r1=484578537409999154675042390540664390207331844965054363441 (pp57) r2=4923006679232260879844150105623901082760825132994000095977307 (pp61) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 89.74 hours. Scaled time: 60.75 units (timescale=0.677). Factorization parameters were as follows: name: 19997_189 n: 2385583376282025837302025573831625807718996619292106854661488654167073439506823897959332181406320971559780911666433387 skew: 144660.76 # norm 2.74e+16 c5: 9120 c4: -1709436956 c3: -853334330700080 c2: 38221101292867669503 c1: 5419411001140512770228250 c0: -113915253989648848942977150816 # alpha -6.21 Y1: 86650737107 Y0: -48252518012964347678477 # Murphy_E 3.65e-10 # M 654987332633075895838719954518597211946085969700968706963931960289336573203282116904651285610709249461397952456672945 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, 4110001) Primes: RFBsize:315948, AFBsize:315530, largePrimes:7677981 encountered Relations: rels:7786564, finalFF:780897 Max relations in full relation-set: 28 Initial matrix: 631557 x 780897 with sparse part having weight 63899163. Pruned matrix : 505956 x 509177 with weight 39093412. Total sieving time: 75.32 hours. Total relation processing time: 0.76 hours. Matrix solve time: 13.18 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 89.74 hours. --------- CPU info (if available) ----------

Sep 21, 2007 (6th)

By Robert Backstrom / GGNFS
5·10¹⁵⁶-7 = 4(9)₁₅₅3_<157> = 2269 · C154
C154 = P57 · P97
P57 = 702447342551455682763805673011418695171148173600333160411_<57>
P97 = 3137052122420974879105045171402526152498877264559652000048811419905235475853470855786187595915127_<97>

Number: n N=2203613926840017628911414720141031291317761128250330542089026002644336712208021154693697664169237549581313353900396650506831203173204054649625385632437197 ( 154 digits) SNFS difficulty: 156 digits. Divisors found: r1=702447342551455682763805673011418695171148173600333160411 (pp57) r2=3137052122420974879105045171402526152498877264559652000048811419905235475853470855786187595915127 (pp97) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.73 hours. Scaled time: 47.30 units (timescale=1.445). Factorization parameters were as follows: name: KA_4_9_155_3 n: 2203613926840017628911414720141031291317761128250330542089026002644336712208021154693697664169237549581313353900396650506831203173204054649625385632437197 skew: 1.00 deg: 5 c5: 50 c0: -7 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, 1600001) Primes: RFBsize:148933, AFBsize:149340, largePrimes:7221415 encountered Relations: rels:6677603, finalFF:340291 Max relations in full relation-set: 28 Initial matrix: 298338 x 340291 with sparse part having weight 35254069. Pruned matrix : 282176 x 283731 with weight 26733037. Total sieving time: 29.31 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.95 hours. Total square root time: 0.24 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 32.73 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Sep 21, 2007 (5th)

By Sinkiti Sibata / GGNFS
3·10¹⁵⁹-7 = 2(9)₁₅₈3_<160> = 2659 · 629501473 · 3776223670753814722104781857341_<31> · C117
C117 = P43 · P75
P43 = 2429003868169712771564765938483840128221281_<43>
P75 = 195398061142744316558324686703766895073805079591953321661587802348156465519_<75>

Number: 29993_159 N=474622646348587991570103845490157192795552107865333169185229129045216764037235466499265469910571227154142957278509839 ( 117 digits) Divisors found: r1=2429003868169712771564765938483840128221281 (pp43) r2=195398061142744316558324686703766895073805079591953321661587802348156465519 (pp75) Version: GGNFS-0.77.1-20060513-k8 Total time: 56.60 hours. Scaled time: 112.69 units (timescale=1.991). Factorization parameters were as follows: name: 29993_159 n: 474622646348587991570103845490157192795552107865333169185229129045216764037235466499265469910571227154142957278509839 skew: 102878.62 # norm 3.14e+16 c5: 34440 c4: -149392696 c3: -462455782301352 c2: -52512162914560500217 c1: 816599221770534738053210 c0: 165609389373825212343298147000 # alpha -6.78 Y1: 2030600269627 Y0: -26782868643055112543701 # Murphy_E 3.95e-10 # M 344120893185492553582171471745909403370088932927055061806908622580423741637740107782212930561733866315489917027001449 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, 3870001) Primes: RFBsize:315948, AFBsize:316176, largePrimes:7649847 encountered Relations: rels:7779364, finalFF:809585 Max relations in full relation-set: 28 Initial matrix: 632210 x 809585 with sparse part having weight 68072410. Pruned matrix : 480081 x 483306 with weight 39163890. Total sieving time: 52.80 hours. Total relation processing time: 0.34 hours. Matrix solve time: 3.04 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 56.60 hours. --------- CPU info (if available) ----------

Sep 21, 2007 (4th)

By suberi / PRIMO
5·10²⁴⁷³+9 is prime!

Sep 21, 2007 (3rd)

By Robert Backstrom / GGNFS
5·10¹⁵⁴-7 = 4(9)₁₅₃3_<155> = 19 · 149 · 147343123 · C144
C144 = P58 · P86
P58 = 2329496337443922537883208273725168308815052824721528210923_<58>
P86 = 51456261798342511671036399891501546912876135404430952940563337964752143215157251247207_<86>

Number: n N=119867173397794507936562028872143053364267557793942124954308317334879039092932793449039649487083341517467372369417965078031872011075677110642061 ( 144 digits) SNFS difficulty: 155 digits. Divisors found: r1=2329496337443922537883208273725168308815052824721528210923 (pp58) r2=51456261798342511671036399891501546912876135404430952940563337964752143215157251247207 (pp86) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 19.32 hours. Scaled time: 26.35 units (timescale=1.364). Factorization parameters were as follows: name: KA_4_9_153_3 n: 119867173397794507936562028872143053364267557793942124954308317334879039092932793449039649487083341517467372369417965078031872011075677110642061 skew: 1.00 deg: 5 c5: 1 c0: -14 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:183072, AFBsize:182621, largePrimes:6422576 encountered Relations: rels:5852822, finalFF:412844 Max relations in full relation-set: 28 Initial matrix: 365757 x 412844 with sparse part having weight 26329532. Pruned matrix : 325573 x 327465 with weight 17263082. Total sieving time: 17.06 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.76 hours. Total square root time: 0.33 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 19.32 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Sep 21, 2007 (2nd)

By Jo Yeong Uk / PRIMO
(14·10²⁰⁰³+1)/3 is prime!

Sep 21, 2007

By Jo Yeong Uk / GGNFS
5·10¹⁵⁰-7 = 4(9)₁₄₉3_<151> = 384637449547853_<15> · 100387217672603863429_<21> · C117
C117 = P31 · P86
P31 = 6154380393511946888616304633963_<31>
P86 = 21040482008161263229987519894156551396567478881186385296972651591714274238026715657003_<86>

Number: 49993_150 N=129491129941068553703812537946480368789816344933526174856540977440519983389852818222234719791591816985068314972592889 ( 117 digits) SNFS difficulty: 150 digits. Divisors found: r1=6154380393511946888616304633963 (pp31) r2=21040482008161263229987519894156551396567478881186385296972651591714274238026715657003 (pp86) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.34 hours. Scaled time: 24.17 units (timescale=2.131). Factorization parameters were as follows: n: 129491129941068553703812537946480368789816344933526174856540977440519983389852818222234719791591816985068314972592889 m: 1000000000000000000000000000000 c5: 5 c0: -7 skew: 1.07 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 1900001) Primes: RFBsize:176302, AFBsize:175868, largePrimes:5272948 encountered Relations: rels:5112371, finalFF:430990 Max relations in full relation-set: 28 Initial matrix: 352235 x 430990 with sparse part having weight 34977477. Pruned matrix : 305477 x 307302 with weight 22005147. Total sieving time: 10.84 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.40 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 11.34 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁵²-7 = 4(9)₁₅₁3_<153> = 4984608868886021_<16> · 5760022922783149935357790511_<28> · C110
C110 = P30 · P30 · P50
P30 = 188518073602970413450229413063_<30>
P30 = 940840568278596734516455337701_<30>
P50 = 98185120607867205620512879136643224913634476404281_<50>

Number: 49993_152 N=17414648247137902210132824181583304066910194155046022301650741655577181114209034000065980412530628852712325803 ( 110 digits) Divisors found: r1=188518073602970413450229413063 (pp30) r2=940840568278596734516455337701 (pp30) r3=98185120607867205620512879136643224913634476404281 (pp50) Version: GGNFS-0.77.1-20050930-nocona Total time: 14.68 hours. Scaled time: 31.13 units (timescale=2.120). Factorization parameters were as follows: name: 49993_152 n: 17414648247137902210132824181583304066910194155046022301650741655577181114209034000065980412530628852712325803 skew: 56517.21 # norm 2.42e+15 c5: 2880 c4: 1175164712 c3: -29239402533387 c2: -938352304661497866 c1: 73927841365309126364192 c0: -902182295668313581002209856 # alpha -6.39 Y1: 72628709197 Y0: -1433186298969104262985 # Murphy_E 1.04e-09 # M 12838353175379424893908978938079702592009453283711586973468906081864813655034909619752608931304311664598306820 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1200000, 1920001) Primes: RFBsize:176302, AFBsize:176892, largePrimes:7434009 encountered Relations: rels:7156751, finalFF:427712 Max relations in full relation-set: 28 Initial matrix: 353274 x 427712 with sparse part having weight 39905520. Pruned matrix : 300831 x 302661 with weight 25640907. Polynomial selection time: 0.78 hours. Total sieving time: 13.25 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.43 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000 total time: 14.68 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 20, 2007 (5th)

By Robert Backstrom / GGNFS
3·10¹⁵⁶-7 = 2(9)₁₅₅3_<157> = 20326576471807_<14> · C144
C144 = P57 · P87
P57 = 755863572447083289435283827464011678816063064420816854967_<57>
P87 = 195260141964162497840754186283403004144880025879973776465137141067044484471377181806897_<87>

Number: n N=147590028461556508171293018028553114061238888148651494440046585451722939356778788070173271532586662801688015902136310673316237331594165849307399 ( 144 digits) SNFS difficulty: 156 digits. Divisors found: r1=755863572447083289435283827464011678816063064420816854967 (pp57) r2=195260141964162497840754186283403004144880025879973776465137141067044484471377181806897 (pp87) Version: GGNFS-0.77.1-20051202-athlon Total time: 45.23 hours. Scaled time: 54.00 units (timescale=1.194). Factorization parameters were as follows: name: KA_2_9_155_3 n: 147590028461556508171293018028553114061238888148651494440046585451722939356778788070173271532586662801688015902136310673316237331594165849307399 type: snfs skew: 1.00 deg: 5 c5: 30 c0: -7 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, 2000001) Primes: RFBsize:148933, AFBsize:148635, largePrimes:6806936 encountered Relations: rels:6172026, finalFF:337910 Max relations in full relation-set: 28 Initial matrix: 297635 x 337910 with sparse part having weight 32569506. Pruned matrix : 284193 x 285745 with weight 24619977. Total sieving time: 41.64 hours. Total relation processing time: 0.30 hours. Matrix solve time: 3.19 hours. Total square root time: 0.10 hours, sqrts: 1. 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: 45.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Sep 20, 2007 (4th)

By Jo Yeong Uk / GGNFS
5·10¹⁴⁹-7 = 4(9)₁₄₈3_<150> = 13 · 67 · 223 · 61166327 · C137
C137 = P58 · P80
P58 = 1863894902146250689138702961366278706980495490732424870829_<58>
P80 = 22579439841623531991161014465575701572092571425255411323896978985792253366291587_<80>

Number: 49993_149 N=42085702814120047318762251527880567894812152207168529855646296135167386162678994579997839545194550841551120722204859676477586031224415623 ( 137 digits) SNFS difficulty: 150 digits. Divisors found: r1=1863894902146250689138702961366278706980495490732424870829 (pp58) r2=22579439841623531991161014465575701572092571425255411323896978985792253366291587 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.20 hours. Scaled time: 19.61 units (timescale=2.132). Factorization parameters were as follows: n: 42085702814120047318762251527880567894812152207168529855646296135167386162678994579997839545194550841551120722204859676477586031224415623 m: 1000000000000000000000000000000 c5: 1 c0: -14 skew: 1.7 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, 1500001) Primes: RFBsize:135072, AFBsize:134923, largePrimes:3682097 encountered Relations: rels:3704501, finalFF:337628 Max relations in full relation-set: 28 Initial matrix: 270059 x 337628 with sparse part having weight 29012768. Pruned matrix : 242332 x 243746 with weight 17407984. Total sieving time: 8.88 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.24 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 9.20 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁴⁸-7 = 4(9)₁₄₇3_<149> = 43 · 4871 · C144
C144 = P47 · P97
P47 = 85730161306764919729693936025764142920932871039_<47>
P97 = 2784516388469492464533403078786154427691160272586017433488469433231396033078317295048722652094979_<97>

Number: 49993_148 N=238717039144820078967596549106482122480938444424286116694437415553847402519897065212720753581949172368025284908786219342764247826481358586413181 ( 144 digits) SNFS difficulty: 150 digits. Divisors found: r1=85730161306764919729693936025764142920932871039 (pp47) r2=2784516388469492464533403078786154427691160272586017433488469433231396033078317295048722652094979 (pp97) Version: GGNFS-0.77.1-20050930-nocona Total time: 12.50 hours. Scaled time: 26.56 units (timescale=2.124). Factorization parameters were as follows: n: 238717039144820078967596549106482122480938444424286116694437415553847402519897065212720753581949172368025284908786219342764247826481358586413181 m: 1000000000000000000000000000000 c5: 1 c0: -140 skew: 2.69 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, 1725001) Primes: RFBsize:135072, AFBsize:135583, largePrimes:3874933 encountered Relations: rels:4005276, finalFF:405690 Max relations in full relation-set: 28 Initial matrix: 270719 x 405690 with sparse part having weight 39826184. Pruned matrix : 229408 x 230825 with weight 20381958. Total sieving time: 12.17 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,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 12.50 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 20, 2007 (3rd)

By Robert Backstrom / GGNFS
3·10¹⁶²-7 = 2(9)₁₆₁3_<163> = 311 · 839 · C158
C158 = P49 · P50 · P60
P49 = 4051197719261188815701375854427236740369079486103_<49>
P50 = 20165397378055339711076080733916793276540156689149_<50>
P60 = 140737126881900958635390331620494185432391996158454693370011_<60>

Number: n N=11497380513473013731704793257936066899424747728309233546290370177327932119465448455326928014900605145461025796289412062285142701654473055888766675992319749817 ( 158 digits) SNFS difficulty: 162 digits. Divisors found: r1=4051197719261188815701375854427236740369079486103 (pp49) r2=20165397378055339711076080733916793276540156689149 (pp50) r3=140737126881900958635390331620494185432391996158454693370011 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 45.25 hours. Scaled time: 65.43 units (timescale=1.446). Factorization parameters were as follows: name: KA_2_9_161_3 n: 11497380513473013731704793257936066899424747728309233546290370177327932119465448455326928014900605145461025796289412062285142701654473055888766675992319749817 skew: 0.47 deg: 5 c5: 300 c0: -7 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2100001) Primes: RFBsize:250150, AFBsize:249771, largePrimes:7357986 encountered Relations: rels:6887181, finalFF:570721 Max relations in full relation-set: 28 Initial matrix: 499987 x 570721 with sparse part having weight 39576388. Pruned matrix : 441715 x 444278 with weight 26543781. Total sieving time: 39.63 hours. Total relation processing time: 0.23 hours. Matrix solve time: 5.09 hours. Total square root time: 0.31 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 45.25 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

5·10¹⁴²-7 = 4(9)₁₄₁3_<143> = 29 · 31 · 1979 · 3277843 · C130
C130 = P46 · P85
P46 = 2223141064464610943664418818229457665011638221_<46>
P85 = 3856642203506996485674317701132711550770098652412611342040704528870940226564907142911_<85>

Number: n N=8573859653563686872153672611065011274732927198251276617077489205709398361640445149078749285697650620290539145986731822988676801331 ( 130 digits) SNFS difficulty: 142 digits. Divisors found: r1=2223141064464610943664418818229457665011638221 (pp46) r2=3856642203506996485674317701132711550770098652412611342040704528870940226564907142911 (pp85) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.11 hours. Scaled time: 22.82 units (timescale=1.194). Factorization parameters were as follows: name: KA_4_9_141_3 n: 8573859653563686872153672611065011274732927198251276617077489205709398361640445149078749285697650620290539145986731822988676801331 type: snfs skew: 1.00 deg: 5 c5: 500 c0: -7 m: 10000000000000000000000000000 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, 900001) Primes: RFBsize:148933, AFBsize:148765, largePrimes:5656958 encountered Relations: rels:5036472, finalFF:365043 Max relations in full relation-set: 28 Initial matrix: 297764 x 365043 with sparse part having weight 18678812. Pruned matrix : 238754 x 240306 with weight 9621800. Total sieving time: 17.82 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.93 hours. Total square root time: 0.10 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 19.11 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

(52·10¹⁸¹-7)/9 = 5(7)_181<182> = 3 · 19 · C181
C181 = P81 · P100
P81 = 401904412375528539331847398345165066791473496316622080484846488508256710720903033_<81>
P100 = 2522105239353325298748130209401148022385513396941975516899451253080021253195404610505390042856114817_<100>

Number: n N=1013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961 ( 181 digits) SNFS difficulty: 182 digits. Divisors found: r1=401904412375528539331847398345165066791473496316622080484846488508256710720903033 (pp81) r2=2522105239353325298748130209401148022385513396941975516899451253080021253195404610505390042856114817 (pp100) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 730.72 hours. Scaled time: 997.43 units (timescale=1.365). Factorization parameters were as follows: name: KA_5_7_181 n: 1013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961 skew: 0.42 deg: 5 c5: 520 c0: -7 m: 1000000000000000000000000000000000000 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, 9700001) Primes: RFBsize:283146, AFBsize:283932, largePrimes:9499562 encountered Relations: rels:9301430, finalFF:638426 Max relations in full relation-set: 28 Initial matrix: 567145 x 638426 with sparse part having weight 92765702. Pruned matrix : 539903 x 542802 with weight 78313454. Total sieving time: 712.95 hours. Total relation processing time: 0.99 hours. Matrix solve time: 16.29 hours. Total square root time: 0.49 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 730.72 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Sep 20, 2007 (2nd)

By Jo Yeong Uk / GGNFS
5·10¹⁴³-7 = 4(9)₁₄₂3_<144> = 13 · 665794015879030348762037_<24> · C119
C119 = P43 · P77
P43 = 2457983453888362366242036666452627350164707_<43>
P77 = 23502161675736277599130693612709951586027071255823077510499322192862480222179_<77>

Number: 49993_143 N=57767924529568957888537801310876296895668866171545711112223603502784417848468335253465142833454489613026092525604436553 ( 119 digits) SNFS difficulty: 145 digits. Divisors found: r1=2457983453888362366242036666452627350164707 (pp43) r2=23502161675736277599130693612709951586027071255823077510499322192862480222179 (pp77) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.30 hours. Scaled time: 17.70 units (timescale=2.132). Factorization parameters were as follows: n: 57767924529568957888537801310876296895668866171545711112223603502784417848468335253465142833454489613026092525604436553 m: 100000000000000000000000000000 c5: 1 c0: -140 skew: 2.69 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1300001) Primes: RFBsize:114155, AFBsize:114557, largePrimes:3355292 encountered Relations: rels:3393674, finalFF:331157 Max relations in full relation-set: 28 Initial matrix: 228776 x 331157 with sparse part having weight 30146465. Pruned matrix : 195268 x 196475 with weight 14800409. Total sieving time: 8.09 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.15 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 8.30 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁴⁶-7 = 4(9)₁₄₅3_<147> = 17 · 14921539 · 248698679 · 471359479252760034787043_<24> · C107
C107 = P47 · P60
P47 = 39419505496131463374918351524556451155850236259_<47>
P60 = 426550611477417551441580681597762746623708391057419314031757_<60>

Number: 49993_146 N=16814414173512297631896560241640536292869348031719843335103615147794108141962215977079516141086042278877063 ( 107 digits) SNFS difficulty: 146 digits. Divisors found: r1=39419505496131463374918351524556451155850236259 (pp47) r2=426550611477417551441580681597762746623708391057419314031757 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.51 hours. Scaled time: 22.53 units (timescale=2.143). Factorization parameters were as follows: n: 16814414173512297631896560241640536292869348031719843335103615147794108141962215977079516141086042278877063 m: 100000000000000000000000000000 c5: 50 c0: -7 skew: 0.67 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, 1575001) Primes: RFBsize:135072, AFBsize:135423, largePrimes:3793573 encountered Relations: rels:3866749, finalFF:362728 Max relations in full relation-set: 28 Initial matrix: 270560 x 362728 with sparse part having weight 34071867. Pruned matrix : 238068 x 239484 with weight 19000621. Total sieving time: 10.19 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.24 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: 10.51 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁴⁷-7 = 4(9)₁₄₆3_<148> = 181 · 1935949243_<10> · C137
C137 = P44 · P93
P44 = 39143694405820216125374984826505126817968351_<44>
P93 = 364531993422512812212311418475269937871127766102122723800434357272554629366883846804656575121_<93>

Number: 49993_147 N=14269128951675306587656103056392781244121178891433426670144019869249655079558182381438140303751595107152717138583707250452128119031995471 ( 137 digits) SNFS difficulty: 149 digits. Divisors found: r1=39143694405820216125374984826505126817968351 (pp44) r2=364531993422512812212311418475269937871127766102122723800434357272554629366883846804656575121 (pp93) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.32 hours. Scaled time: 22.14 units (timescale=2.145). Factorization parameters were as follows: n: 14269128951675306587656103056392781244121178891433426670144019869249655079558182381438140303751595107152717138583707250452128119031995471 m: 500000000000000000000000000000 c5: 4 c0: -175 skew: 2.13 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, 1575001) Primes: RFBsize:135072, AFBsize:134853, largePrimes:3806264 encountered Relations: rels:3951764, finalFF:434720 Max relations in full relation-set: 28 Initial matrix: 269989 x 434720 with sparse part having weight 39919688. Pruned matrix : 213923 x 215336 with weight 18154201. Total sieving time: 10.05 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.19 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 10.32 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 20, 2007

By Sinkiti Sibata / GGNFS
5·10¹⁹⁴-1 = 4(9)_194<195> = C195
C195 = P76 · P120
P76 = 2063673432680440504344308255721789938709506185655504408686729651476059482949_<76>
P120 = 242286396714700023343462981244314581366417767442682354276028410445885393174798778445278457127741012032445076995991310451_<120>

Number: 49999_194 N=499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 ( 195 digits) SNFS difficulty: 195 digits. Divisors found: r1=2063673432680440504344308255721789938709506185655504408686729651476059482949 (pp76) r2=242286396714700023343462981244314581366417767442682354276028410445885393174798778445278457127741012032445076995991310451 (pp120) Version: GGNFS-0.77.1-20060513-k8 Total time: 2170.77 hours. Scaled time: 4335.02 units (timescale=1.997). Factorization parameters were as follows: name: 49999_194 n: 499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 m: 1000000000000000000000000000000000000000 c5: 1 c0: -2 skew: 1.15 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, 30600001) Primes: RFBsize:501962, AFBsize:501936, largePrimes:7672066 encountered Relations: rels:8446002, finalFF:1128792 Max relations in full relation-set: 28 Initial matrix: 1003962 x 1128792 with sparse part having weight 155448349. Pruned matrix : 921781 x 926864 with weight 139585169. Total sieving time: 2144.49 hours. Total relation processing time: 1.59 hours. Matrix solve time: 24.21 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 2170.77 hours. --------- CPU info (if available) ----------

5·10¹³⁰-7 = 4(9)₁₂₉3_<131> = 17 · 160668811253268490388087_<24> · C107
C107 = P49 · P58
P49 = 6467580254270363725519254058868497565332259571617_<49>
P58 = 2830399090682433194863117944409611442158552826222489705151_<58>

Number: 49993_130 N=18305833270602497558634047496818074228604958225953465398543733671509497228985003045752560531079663898299167 ( 107 digits) SNFS difficulty: 130 digits. Divisors found: r1=6467580254270363725519254058868497565332259571617 (pp49) r2=2830399090682433194863117944409611442158552826222489705151 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.74 hours. Scaled time: 7.52 units (timescale=2.010). Factorization parameters were as follows: name: 49993_130 n: 18305833270602497558634047496818074228604958225953465398543733671509497228985003045752560531079663898299167 m: 100000000000000000000000000 c5: 5 c0: -7 skew: 1.07 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:64228, largePrimes:1510813 encountered Relations: rels:1545060, finalFF:204183 Max relations in full relation-set: 28 Initial matrix: 128244 x 204183 with sparse part having weight 12800443. Pruned matrix : 105593 x 106298 with weight 5310169. Total sieving time: 3.62 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 3.74 hours. --------- CPU info (if available) ----------

Sep 19, 2007 (4th)

By Jo Yeong Uk / PRIMO
(5·10²¹⁰⁰+13)/9 is prime!

Sep 19, 2007 (3rd)

By Robert Backstrom / GGNFS
5·10¹²⁵-7 = 4(9)₁₂₄3_<126> = 13 · 2857 · 1574782569067_<13> · 5838950571776281_<16> · C94
C94 = P36 · P58
P36 = 292924442772209379166691899342190629_<36>
P58 = 4998105296856734377409878285199029073331658288276776782731_<58>

Number: n N=1464067208998587059740499172572788768975253189359034678886007716300916068840034369544317227799 ( 94 digits) Divisors found: r1=292924442772209379166691899342190629 (pp36) r2=4998105296856734377409878285199029073331658288276776782731 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.66 hours. Scaled time: 7.97 units (timescale=1.196). Factorization parameters were as follows: name: n n: 1464067208998587059740499172572788768975253189359034678886007716300916068840034369544317227799 m: 2789993933216660492819 deg: 4 c4: 24162840 c3: -41310183912 c2: 305151674828780808 c1: 38958211045003735 c0: -144208424742214707916486 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.410 # E(F1,F2) = 5.603157e-05 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1190129837. # 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 [100000, 880001) Primes: RFBsize:92938, AFBsize:93172, largePrimes:1778839 encountered Relations: rels:1814450, finalFF:217215 Max relations in full relation-set: 28 Initial matrix: 186189 x 217215 with sparse part having weight 13772099. Pruned matrix : 164433 x 165427 with weight 8533423. Total sieving time: 6.03 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.47 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 6.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Sep 19, 2007 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM
5·10¹⁴⁵-7 = 4(9)₁₄₄3_<146> = C146
C146 = P69 · P78
P69 = 348607637797598731797334666578807254587298021398884344017102244986489_<69>
P78 = 143427723832688809873861290555759641653195758704762012607777555925493706059137_<78>

Number: 49993_145 N=49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 146 digits) SNFS difficulty: 145 digits. Divisors found: r1=348607637797598731797334666578807254587298021398884344017102244986489 (pp69) r2=143427723832688809873861290555759641653195758704762012607777555925493706059137 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.30 hours. Scaled time: 17.62 units (timescale=2.122). Factorization parameters were as follows: n: 49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 m: 100000000000000000000000000000 c5: 5 c0: -7 skew: 1.07 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1300001) Primes: RFBsize:114155, AFBsize:114162, largePrimes:3386072 encountered Relations: rels:3436911, finalFF:340015 Max relations in full relation-set: 28 Initial matrix: 228382 x 340015 with sparse part having weight 31556853. Pruned matrix : 193007 x 194212 with weight 15015116. Total sieving time: 8.09 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.14 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 8.30 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹³²-7 = 4(9)₁₃₁3_<133> = 1803259 · 21637095769_<11> · 704898240089_<12> · C105
C105 = P41 · P64
P41 = 66744018120546449161802491041419358230857_<41>
P64 = 2723793341179006978601831413759133998675258378764478782653155571_<64>

Number: 49993_132 N=181796912120275398531617563014368827286582977646429455177241425072313600143265207326873879751902953654347 ( 105 digits) SNFS difficulty: 134 digits. Divisors found: r1=66744018120546449161802491041419358230857 (pp41) r2=2723793341179006978601831413759133998675258378764478782653155571 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.35 hours. Scaled time: 5.04 units (timescale=2.140). Factorization parameters were as follows: n: 181796912120275398531617563014368827286582977646429455177241425072313600143265207326873879751902953654347 m: 500000000000000000000000000 c5: 4 c0: -175 skew: 2.13 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1100001) Primes: RFBsize:107126, AFBsize:106873, largePrimes:2194322 encountered Relations: rels:2272551, finalFF:259727 Max relations in full relation-set: 28 Initial matrix: 214063 x 259727 with sparse part having weight 16899820. Pruned matrix : 189994 x 191128 with weight 9651216. Total sieving time: 2.21 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 2.35 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

3·10¹⁵⁶+7 = 3(0)₁₅₅7_<157> = 1428660435500894737_<19> · C139
C139 = P59 · P80
P59 = 23751015386450850890960912782656510193131256880878674102473_<59>
P80 = 88411764036120295668516229411892223895453769985635566390071101529293788597427807_<80>

Number: 30007_156 N=2099869167965155124756908942201290754204400058585128654740282907304493380080285074505086695930477835539488663926721378385440839832137666711 ( 139 digits) SNFS difficulty: 156 digits. Divisors found: r1=23751015386450850890960912782656510193131256880878674102473 (pp59) r2=88411764036120295668516229411892223895453769985635566390071101529293788597427807 (pp80) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.47 hours. Scaled time: 52.12 units (timescale=2.130). Factorization parameters were as follows: n: 2099869167965155124756908942201290754204400058585128654740282907304493380080285074505086695930477835539488663926721378385440839832137666711 m: 10000000000000000000000000000000 c5: 30 c0: 7 skew: 0.75 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:216451, largePrimes:5637735 encountered Relations: rels:5545407, finalFF:494569 Max relations in full relation-set: 28 Initial matrix: 433334 x 494569 with sparse part having weight 41922437. Pruned matrix : 408265 x 410495 with weight 30955997. Total sieving time: 23.46 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.88 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 24.47 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹³³-7 = 4(9)₁₃₂3_<134> = 401238263593464253441_<21> · C114
C114 = P39 · P75
P39 = 162299914415288288281496198151331987381_<39>
P75 = 767802233705694607885077764652977937099475049390304533874402633274801489333_<75>

Number: 49993_133 N=124614236818301411544359062366169325675748332513461267291694167073654610945066429659024926693632485623021562106873 ( 114 digits) SNFS difficulty: 135 digits. Divisors found: r1=162299914415288288281496198151331987381 (pp39) r2=767802233705694607885077764652977937099475049390304533874402633274801489333 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.90 hours. Scaled time: 6.13 units (timescale=2.113). Factorization parameters were as follows: n: 124614236818301411544359062366169325675748332513461267291694167073654610945066429659024926693632485623021562106873 m: 1000000000000000000000000000 c5: 1 c0: -140 skew: 2.69 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1200001) Primes: RFBsize:107126, AFBsize:107423, largePrimes:2258417 encountered Relations: rels:2365136, finalFF:274865 Max relations in full relation-set: 28 Initial matrix: 214613 x 274865 with sparse part having weight 19811144. Pruned matrix : 188857 x 189994 with weight 10562686. Total sieving time: 2.75 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 2.90 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹³⁶-7 = 4(9)₁₃₅3_<137> = 19 · 139 · 6967 · 304949 · C124
C124 = P56 · P69
P56 = 43352727754257453263558076969496197958853012323126787749_<56>
P69 = 205547477085329019216150576259951986360308957854427429660726601104519_<69>

Number: 49993_136 N=8911043814654741266385357410993071277936469227783606071546576951629885484600301382670236701307968095738801477446099877737731 ( 124 digits) SNFS difficulty: 136 digits. Divisors found: r1=43352727754257453263558076969496197958853012323126787749 (pp56) r2=205547477085329019216150576259951986360308957854427429660726601104519 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.57 hours. Scaled time: 7.58 units (timescale=2.121). Factorization parameters were as follows: n: 8911043814654741266385357410993071277936469227783606071546576951629885484600301382670236701307968095738801477446099877737731 m: 1000000000000000000000000000 c5: 50 c0: -7 skew: 0.67 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1350001) Primes: RFBsize:107126, AFBsize:107448, largePrimes:2286653 encountered Relations: rels:2372902, finalFF:249972 Max relations in full relation-set: 28 Initial matrix: 214639 x 249972 with sparse part having weight 19123445. Pruned matrix : 202249 x 203386 with weight 12879625. Total sieving time: 3.38 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.57 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹³⁷-7 = 4(9)₁₃₆3_<138> = 13 · 673573 · 7297977952249711_<16> · C115
C115 = P34 · P81
P34 = 9394428712264339107505356592635883_<34>
P81 = 832854352226576752484715428137571713119476790537271630219939252608157903031281189_<81>

Number: 49993_137 N=7824190839691669749163653157266934458630643853189079636887156615889238145318912324273611451606146225919988064304887 ( 115 digits) SNFS difficulty: 139 digits. Divisors found: r1=9394428712264339107505356592635883 (pp34) r2=832854352226576752484715428137571713119476790537271630219939252608157903031281189 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.58 hours. Scaled time: 7.64 units (timescale=2.136). Factorization parameters were as follows: n: 7824190839691669749163653157266934458630643853189079636887156615889238145318912324273611451606146225919988064304887 m: 5000000000000000000000000000 c5: 4 c0: -175 skew: 2.13 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1350001) Primes: RFBsize:107126, AFBsize:106873, largePrimes:2324504 encountered Relations: rels:2470570, finalFF:302661 Max relations in full relation-set: 28 Initial matrix: 214063 x 302661 with sparse part having weight 23246989. Pruned matrix : 183090 x 184224 with weight 11133020. Total sieving time: 3.42 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.58 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁵¹-7 = 4(9)₁₅₀3_<152> = 1413677 · 7305622079024944242228091_<25> · C121
C121 = P33 · P89
P33 = 293508139448334928739242445881249_<33>
P89 = 16494625527091676916421984392283134811156918776772753098253796574689797190832398167922951_<89>
5·10¹³⁸-7 = 4(9)₁₃₇3_<139> = 23 · 97 · 76129 · 335507 · C125
C125 = P51 · P75
P51 = 589299164638605947647771819491726255852140418406087_<51>
P75 = 148895954377143576247780304403642128934646012521450079487879648263630397923_<75>

Number: 49993_138 N=87744261532518692236722362187251629645597029515691483213116126366750425844988944265188979806400848045894132573044429215357301 ( 125 digits) SNFS difficulty: 140 digits. Divisors found: r1=589299164638605947647771819491726255852140418406087 (pp51) r2=148895954377143576247780304403642128934646012521450079487879648263630397923 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.39 hours. Scaled time: 11.50 units (timescale=2.133). Factorization parameters were as follows: n: 87744261532518692236722362187251629645597029515691483213116126366750425844988944265188979806400848045894132573044429215357301 m: 10000000000000000000000000000 c5: 1 c0: -140 skew: 2.69 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1050001) Primes: RFBsize:107126, AFBsize:107423, largePrimes:2239474 encountered Relations: rels:2359215, finalFF:276225 Max relations in full relation-set: 28 Initial matrix: 214613 x 276225 with sparse part having weight 22517328. Pruned matrix : 188495 x 189632 with weight 12308616. Total sieving time: 5.22 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.12 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 5.39 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 19, 2007

By Jo Yeong Uk / GGNFS
2·10¹⁵⁶-7 = 1(9)₁₅₅3_<157> = 61 · 379561891 · 591755936832544670700889_<24> · C123
C123 = P58 · P65
P58 = 2996976568019324627915945752938287251955921580343264766897_<58>
P65 = 48707023203560580789797226764686962335766992120048448009260900471_<65>

Number: 19993_156 N=145973807239044599895795366422383396989943956162809260080362174883363753419104691249139419330074996177706630877434132508487 ( 123 digits) SNFS difficulty: 156 digits. Divisors found: r1=2996976568019324627915945752938287251955921580343264766897 (pp58) r2=48707023203560580789797226764686962335766992120048448009260900471 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.84 hours. Scaled time: 35.96 units (timescale=2.135). Factorization parameters were as follows: n: 145973807239044599895795366422383396989943956162809260080362174883363753419104691249139419330074996177706630877434132508487 m: 10000000000000000000000000000000 c5: 20 c0: -7 skew: 0.81 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:215976, largePrimes:5451035 encountered Relations: rels:5348208, finalFF:507344 Max relations in full relation-set: 28 Initial matrix: 432858 x 507344 with sparse part having weight 36913541. Pruned matrix : 378693 x 380921 with weight 24853519. Total sieving time: 15.92 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.80 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 16.84 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 18, 2007 (7th)

By JMB / GGNFS
2·10¹⁷³+3 = 2(0)₁₇₂3_<174> = 31 · 3164590541963_<13> · 1377280097548571230432695973091803101076339_<43> · C118
C118 = P53 · P66
P53 = 10704249832674713026912742559336870309487534796404441_<53>
P66 = 138284106376553420246923079942434034576006381033927871198757392949_<66>

Number: N N=1480227622542794165404399819785920618847153787232185974759390499635827513314206276438905310385107334421379192165686509 ( 118 digits) Divisors found: r1=10704249832674713026912742559336870309487534796404441 (pp53) r2=138284106376553420246923079942434034576006381033927871198757392949 (pp66) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 52.15 hours. Scaled time: 98.15 units (timescale=1.882). Factorization parameters were as follows: name: N n: 1480227622542794165404399819785920618847153787232185974759390499635827513314206276438905310385107334421379192165686509 skew: 33365.99 # norm 5.52e+15 c5: 8400 c4: 2858359922 c3: 69125290698979 c2: 2226394878652247136 c1: -27649659782574825693836 c0: -71117271795651997618937776 # alpha -4.79 Y1: 2892399891821 Y0: -44586966544883642201365 # Murphy_E 3.86e-10 # M 1116241208575494244563539100262926120008752083455990065001830398269407723172354643387959025093684663593340304927476381 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 10000 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, 2430001) Primes: RFBsize:315948, AFBsize:315227, largePrimes:7757737 encountered Relations: rels:7926431, finalFF:820826 Max relations in full relation-set: 28 Initial matrix: 631253 x 820826 with sparse part having weight 71065693. Pruned matrix : 476037 x 479257 with weight 42894052. Total sieving time: 46.30 hours. Total relation processing time: 0.27 hours. Matrix solve time: 5.31 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 52.15 hours. --------- CPU info (if available) ----------

Sep 18, 2007 (6th)

By Sinkiti Sibata / GGNFS, Msieve
5·10¹¹²-7 = 4(9)₁₁₁3_<113> = 31 · 199 · 1726577810038023749_<19> · C91
C91 = P43 · P48
P43 = 6338023959737574815597795059605732175772951_<43>
P48 = 740653709666671254036993453169242903252989973403_<48>

Number: 49993_112 N=4694280957735879835192257868892353847777033806650163825970139352033222478931893194456822253 ( 91 digits) SNFS difficulty: 112 digits. Divisors found: r1=6338023959737574815597795059605732175772951 (pp43) r2=740653709666671254036993453169242903252989973403 (pp48) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.95 hours. Scaled time: 1.32 units (timescale=0.677). Factorization parameters were as follows: name: 49993_112 n: 4694280957735879835192257868892353847777033806650163825970139352033222478931893194456822253 m: 10000000000000000000000 c5: 500 c0: -7 skew: 0.43 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:63743, largePrimes:2287037 encountered Relations: rels:2646059, finalFF:487489 Max relations in full relation-set: 28 Initial matrix: 112907 x 487489 with sparse part having weight 36961708. Pruned matrix : 59914 x 60542 with weight 4878956. Total sieving time: 1.79 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.95 hours. --------- CPU info (if available) ----------

5·10¹²⁴-7 = 4(9)₁₂₃3_<125> = 38611 · 450361 · 2871839245138288177663_<22> · C94
C94 = P32 · P62
P32 = 96307871964544146356044436726531_<32>
P62 = 10396239289011278195567666108316680054766182724101112004334711_<62>

Number: 49993_124 N=1001239682358861648336397232573322011186790460010738716001180000426506650931892738839297917541 ( 94 digits) SNFS difficulty: 125 digits. Divisors found: r1=96307871964544146356044436726531 (pp32) r2=10396239289011278195567666108316680054766182724101112004334711 (pp62) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.52 hours. Scaled time: 1.71 units (timescale=0.677). Factorization parameters were as follows: name: 49993_124 n: 1001239682358861648336397232573322011186790460010738716001180000426506650931892738839297917541 m: 10000000000000000000000000 c5: 1 c0: -14 skew: 1.7 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:63623, largePrimes:2113124 encountered Relations: rels:2175709, finalFF:203620 Max relations in full relation-set: 28 Initial matrix: 112785 x 203620 with sparse part having weight 17991882. Pruned matrix : 92175 x 92802 with weight 5574129. Total sieving time: 2.28 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.13 hours. Time per square root: 0.04 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: 2.52 hours. --------- CPU info (if available) ----------

5·10¹⁰³-7 = 4(9)₁₀₂3_<104> = 1054033 · 11594362361_<11> · C88
C88 = P37 · P51
P37 = 4410131384499304810512717460695947827_<37>
P51 = 927721024511601037911354571948957412235819374408843_<51>

Tue Sep 18 16:15:04 2007 Msieve v. 1.26 Tue Sep 18 16:15:04 2007 random seeds: e103ff01 6e7fc021 Tue Sep 18 16:15:04 2007 factoring 4091371606258460579732267674655946076932554042364590956386352513061582689683113695434161 (88 digits) Tue Sep 18 16:15:05 2007 commencing quadratic sieve (88-digit input) Tue Sep 18 16:15:05 2007 using multiplier of 1 Tue Sep 18 16:15:05 2007 using 64kb Pentium 2 sieve core Tue Sep 18 16:15:05 2007 sieve interval: 14 blocks of size 65536 Tue Sep 18 16:15:05 2007 processing polynomials in batches of 8 Tue Sep 18 16:15:05 2007 using a sieve bound of 1527521 (57818 primes) Tue Sep 18 16:15:05 2007 using large prime bound of 122201680 (26 bits) Tue Sep 18 16:15:05 2007 using double large prime bound of 360361878370480 (42-49 bits) Tue Sep 18 16:15:05 2007 using trial factoring cutoff of 49 bits Tue Sep 18 16:15:05 2007 polynomial 'A' values have 11 factors Tue Sep 18 22:29:06 2007 58366 relations (16041 full + 42325 combined from 613107 partial), need 57914 Tue Sep 18 22:29:16 2007 begin with 629148 relations Tue Sep 18 22:29:19 2007 reduce to 140454 relations in 10 passes Tue Sep 18 22:29:19 2007 attempting to read 140454 relations Tue Sep 18 22:29:28 2007 recovered 140454 relations Tue Sep 18 22:29:28 2007 recovered 115367 polynomials Tue Sep 18 22:29:33 2007 attempting to build 58366 cycles Tue Sep 18 22:29:33 2007 found 58366 cycles in 6 passes Tue Sep 18 22:29:35 2007 distribution of cycle lengths: Tue Sep 18 22:29:35 2007 length 1 : 16041 Tue Sep 18 22:29:35 2007 length 2 : 11360 Tue Sep 18 22:29:35 2007 length 3 : 10344 Tue Sep 18 22:29:35 2007 length 4 : 7623 Tue Sep 18 22:29:35 2007 length 5 : 5353 Tue Sep 18 22:29:35 2007 length 6 : 3379 Tue Sep 18 22:29:35 2007 length 7 : 2011 Tue Sep 18 22:29:35 2007 length 9+: 2255 Tue Sep 18 22:29:35 2007 largest cycle: 16 relations Tue Sep 18 22:29:36 2007 matrix is 57818 x 58366 with weight 3358951 (avg 57.55/col) Tue Sep 18 22:29:39 2007 filtering completed in 3 passes Tue Sep 18 22:29:39 2007 matrix is 53411 x 53475 with weight 3081715 (avg 57.63/col) Tue Sep 18 22:29:41 2007 saving the first 48 matrix rows for later Tue Sep 18 22:29:42 2007 matrix is 53363 x 53475 with weight 2460669 (avg 46.02/col) Tue Sep 18 22:29:42 2007 matrix includes 64 packed rows Tue Sep 18 22:29:42 2007 using block size 10922 for processor cache size 256 kB Tue Sep 18 22:29:42 2007 commencing Lanczos iteration Tue Sep 18 22:32:34 2007 lanczos halted after 845 iterations Tue Sep 18 22:32:35 2007 recovered 14 nontrivial dependencies Tue Sep 18 22:32:48 2007 prp37 factor: 4410131384499304810512717460695947827 Tue Sep 18 22:32:48 2007 prp51 factor: 927721024511601037911354571948957412235819374408843 Tue Sep 18 22:32:48 2007 elapsed time 06:17:44

Sep 18, 2007 (5th)

By Jo Yeong Uk / GMP-ECM
5·10¹⁷⁷-7 = 4(9)₁₇₆3_<178> = C178
C178 = P33 · C146
P33 = 159222322628756092199652384637699_<33>
C146 = [31402631976786545252692940445059838167581831564267435779280007674035294043391904450027457606945967767231885984890715247474553329384690419652493907_<146>]

Sep 18, 2007 (4th)

The factor table of 499...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.

Sep 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS
3·10¹⁵⁴-7 = 2(9)₁₅₃3_<155> = 34019 · 609903171398591373643_<21> · C130
C130 = P43 · P87
P43 = 3638448521596708316295882652136033250258553_<43>
P87 = 397395170759107781009516079528422156485067127226121794287339983126117723660641650772993_<87>

Number: 29993_154 N=1445901871538147156341447649224847712631394873758699363989919101940155761354755440420714445084445119451525115463081130749559659129 ( 130 digits) SNFS difficulty: 155 digits. Divisors found: r1=3638448521596708316295882652136033250258553 (pp43) r2=397395170759107781009516079528422156485067127226121794287339983126117723660641650772993 (pp87) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 57.07 hours. Scaled time: 38.64 units (timescale=0.677). Factorization parameters were as follows: name: 29993_154 n: 1445901871538147156341447649224847712631394873758699363989919101940155761354755440420714445084445119451525115463081130749559659129 m: 10000000000000000000000000000000 c5: 3 c0: -70 skew: 1.88 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2900001) Primes: RFBsize:216816, AFBsize:215951, largePrimes:5611743 encountered Relations: rels:5508735, finalFF:488116 Max relations in full relation-set: 28 Initial matrix: 432832 x 488116 with sparse part having weight 40130555. Pruned matrix : 407641 x 409869 with weight 29858979. Total sieving time: 49.60 hours. Total relation processing time: 0.28 hours. Matrix solve time: 6.99 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 57.07 hours. --------- CPU info (if available) ----------

Sep 18, 2007 (2nd)

By Jo Yeong Uk / PRIMO
(5·10²⁰⁰⁷+1)/3 is prime!

Sep 18, 2007

By Jo Yeong Uk / GGNFS
3·10¹⁷⁹-7 = 2(9)₁₇₈3_<180> = 73 · 3683111 · 16927973 · 584455519 · 482923793970269_<15> · 75814253468842025360202563_<26> · C115
C115 = P42 · P73
P42 = 666955264597468844867283661741291944087841_<42>
P73 = 4618500484221053916134988602864131972644643376658791905760135103112512419_<73>

Number: 29993_179 N=3080333212497190998320588518704248460835256890165010422176507062229667521801892368359086189741076768397158739397379 ( 115 digits) Divisors found: r1=666955264597468844867283661741291944087841 (pp42) r2=4618500484221053916134988602864131972644643376658791905760135103112512419 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 25.35 hours. Scaled time: 54.10 units (timescale=2.134). Factorization parameters were as follows: name: 29993_179 n: 3080333212497190998320588518704248460835256890165010422176507062229667521801892368359086189741076768397158739397379 skew: 64606.11 # norm 5.65e+15 c5: 24480 c4: -1282831244 c3: -285274267141254 c2: 2653256384091794754 c1: 627807025803164651781771 c0: 5959752286338459471323474153 # alpha -5.69 Y1: 974878789993 Y0: -10470265171305626182350 # Murphy_E 5.27e-10 # M 1462313019062199735784145259341739798397661617108705271681928514346601554110168923675620598322111573351965792712109 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 3075001) Primes: RFBsize:256726, AFBsize:257074, largePrimes:7591771 encountered Relations: rels:7548192, finalFF:646497 Max relations in full relation-set: 28 Initial matrix: 513883 x 646497 with sparse part having weight 56504637. Pruned matrix : 406596 x 409229 with weight 33984511. Polynomial selection time: 1.33 hours. Total sieving time: 22.77 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.96 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 25.35 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

3·10¹⁵⁵+7 = 3(0)₁₅₄7_<156> = 307 · 947 · 17011 · 85013863614622230403517_<23> · C123
C123 = P50 · P73
P50 = 81026516161317424585126385687853691355677579362917_<50>
P73 = 8806151149339157734770802696564069152769229056077368044884311562147487877_<73>

Number: 30007_155 N=713531748420933277541673822962652894654142637485514664700401998801446798784016564278662446558305517823810235223089640857209 ( 123 digits) SNFS difficulty: 155 digits. Divisors found: r1=81026516161317424585126385687853691355677579362917 (pp50) r2=8806151149339157734770802696564069152769229056077368044884311562147487877 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.65 hours. Scaled time: 35.65 units (timescale=2.141). Factorization parameters were as follows: n: 713531748420933277541673822962652894654142637485514664700401998801446798784016564278662446558305517823810235223089640857209 m: 10000000000000000000000000000000 c5: 3 c0: 7 skew: 1.18 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:216206, largePrimes:5559375 encountered Relations: rels:5517505, finalFF:555907 Max relations in full relation-set: 28 Initial matrix: 433087 x 555907 with sparse part having weight 41903022. Pruned matrix : 345203 x 347432 with weight 26197869. Total sieving time: 15.98 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.56 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 16.65 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 17, 2007 (2nd)

By Jo Yeong Uk / GGNFS
4·10¹⁷⁷+7 = 4(0)₁₇₆7_<178> = 419 · 173767929557963321729_<21> · 272757861127713014089301_<24> · 55596506082506498754154195877_<29> · C103
C103 = P37 · P67
P37 = 2168624917890105707938720036681408679_<37>
P67 = 1670579402649688089552461215114367735067686171584466742428310437779_<67>

Number: 40007_177 N=3622860119900081675144939418188208681175682968519562762569963159265022505636801426201586907652900083941 ( 103 digits) Divisors found: r1=2168624917890105707938720036681408679 (pp37) r2=1670579402649688089552461215114367735067686171584466742428310437779 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.70 hours. Scaled time: 12.10 units (timescale=2.122). Factorization parameters were as follows: name: 40007_177 n: 3622860119900081675144939418188208681175682968519562762569963159265022505636801426201586907652900083941 skew: 5201.92 # norm 2.88e+14 c5: 538560 c4: 53023360 c3: -50292647881684 c2: -6925540917256562 c1: 749244940025056718037 c0: -1154576317830065586983730 # alpha -6.47 Y1: 58997159591 Y0: -23204032905420498401 # Murphy_E 2.42e-09 # M 1370455034032052557571471097180820566906316879206462490274763309076187559978205487356334531363056920027 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, 1620001) Primes: RFBsize:135072, AFBsize:135194, largePrimes:4450489 encountered Relations: rels:4488383, finalFF:403745 Max relations in full relation-set: 28 Initial matrix: 270349 x 403745 with sparse part having weight 33923516. Pruned matrix : 193755 x 195170 with weight 15534745. Polynomial selection time: 0.35 hours. Total sieving time: 5.06 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.14 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 5.70 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

2·10¹⁵⁵-7 = 1(9)₁₅₄3_<156> = 4339 · 5303 · 1439617218001_<13> · 961207979097509279_<18> · C118
C118 = P35 · P83
P35 = 80965371749079875135193964006734647_<35>
P83 = 77580934154601854923447083339687231799885525920119624203485250965115554274629179933_<83>

Number: 19993_155 N=6281369174468227010565931881995665318163438158792180025253984512757518274749245757587968753964874412460492994748238651 ( 118 digits) SNFS difficulty: 155 digits. Divisors found: r1=80965371749079875135193964006734647 (pp35) r2=77580934154601854923447083339687231799885525920119624203485250965115554274629179933 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.76 hours. Scaled time: 35.87 units (timescale=2.141). Factorization parameters were as follows: n: 6281369174468227010565931881995665318163438158792180025253984512757518274749245757587968753964874412460492994748238651 m: 10000000000000000000000000000000 c5: 2 c0: -7 skew: 1.28 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:216386, largePrimes:5531502 encountered Relations: rels:5461621, finalFF:532447 Max relations in full relation-set: 28 Initial matrix: 433267 x 532447 with sparse part having weight 40040051. Pruned matrix : 362515 x 364745 with weight 25713600. Total sieving time: 15.99 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.65 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 16.76 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 17, 2007

By Jo Yeong Uk / PRIMO
(5·10²⁰⁰²+7)/3 is prime!

Sep 16, 2007 (2nd)

By Jo Yeong Uk / GGNFS
7·10¹⁵³+3 = 7(0)₁₅₂3_<154> = 73 · 131 · 23323831 · 1846251383033_<13> · C131
C131 = P58 · P73
P58 = 2379079812909254428043276041211980572721289410506055623377_<58>
P73 = 7145031581347695270977233930386125972534532154126683920313280001705450711_<73>

Number: 70003_153 N=16998600397783389175759249569289061087069302188459355668140254648218552381501175502221072936905279990154489333515869992693852871047 ( 131 digits) SNFS difficulty: 155 digits. Divisors found: r1=2379079812909254428043276041211980572721289410506055623377 (pp58) r2=7145031581347695270977233930386125972534532154126683920313280001705450711 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.08 hours. Scaled time: 42.73 units (timescale=2.128). Factorization parameters were as follows: n: 16998600397783389175759249569289061087069302188459355668140254648218552381501175502221072936905279990154489333515869992693852871047 m: 10000000000000000000000000000000 c5: 7 c0: 300 skew: 2.12 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:216676, largePrimes:5675578 encountered Relations: rels:5689109, finalFF:598690 Max relations in full relation-set: 28 Initial matrix: 433559 x 598690 with sparse part having weight 47345346. Pruned matrix : 332263 x 334494 with weight 29525513. Total sieving time: 19.32 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.62 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 20.08 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

2·10¹⁶³-7 = 1(9)₁₆₂3_<164> = 13 · 201757487 · 164834767007237_<15> · 129162229318541414865248023_<27> · C114
C114 = P49 · P66
P49 = 2870602702071050972528733922531425863733789921251_<49>
P66 = 124766945602396491462945015979925208408928505160969226719559459403_<66>

Number: 19993_163 N=358156331175391198893339808547858557746935279886252689505085670398402621508842992831589269212432640565739501473153 ( 114 digits) Divisors found: r1=2870602702071050972528733922531425863733789921251 (pp49) r2=124766945602396491462945015979925208408928505160969226719559459403 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 21.80 hours. Scaled time: 46.41 units (timescale=2.129). Factorization parameters were as follows: name: 19993_163 n: 358156331175391198893339808547858557746935279886252689505085670398402621508842992831589269212432640565739501473153 skew: 45628.38 # norm 6.02e+15 c5: 51840 c4: -3683687742 c3: -219889653043975 c2: 9456954518204852587 c1: 291767181530166543087243 c0: -21035126965595459418314492 # alpha -5.76 Y1: 58235380021 Y0: -5859783753033214798315 # Murphy_E 5.80e-10 # M 44894003223997302383774582468193933612947797133112838301158642168226836618277433846086123864581870351008011079287 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 2925001) Primes: RFBsize:256726, AFBsize:257368, largePrimes:7412290 encountered Relations: rels:7272447, finalFF:595178 Max relations in full relation-set: 28 Initial matrix: 514169 x 595178 with sparse part having weight 46315095. Pruned matrix : 446792 x 449426 with weight 29929625. Total sieving time: 20.50 hours. Total relation processing time: 0.14 hours. Matrix solve time: 1.01 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 21.80 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 16, 2007

By Jo Yeong Uk / GMP-ECM
(73·10¹⁹²-1)/9 = 8(1)_192<193> = C193
C193 = P41 · C153
P41 = 73256271947274662782040893968743123700881_<41>
C153 = [110722411822280385931003784443497819857603220976577157566466357414344260125670777720438670653233237078832661859484778212857408425370362300763453787759831_<153>]

Sep 15, 2007 (3rd)

By Jo Yeong Uk / GGNFS
2·10¹⁸⁰-3 = 1(9)₁₇₉7_<181> = 2593 · 51067720369_<11> · 2039081640448510323571_<22> · 112032125257256292325042410655727_<33> · C113
C113 = P39 · P74
P39 = 905172686450661562749851540460137766673_<39>
P74 = 73041953120006531682243304867114152425466458123310047541535943923877620801_<74>

Number: 19997_180 N=66115580929239593359723808855458909629091457719484972084609617544199525101235044807799431332453896293536909365073 ( 113 digits) Divisors found: r1=905172686450661562749851540460137766673 (pp39) r2=73041953120006531682243304867114152425466458123310047541535943923877620801 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 19.07 hours. Scaled time: 40.84 units (timescale=2.142). Factorization parameters were as follows: name: 19997_180 n: 66115580929239593359723808855458909629091457719484972084609617544199525101235044807799431332453896293536909365073 skew: 50900.26 # norm 4.78e+15 c5: 35640 c4: 2092026780 c3: -257421258914871 c2: -3597313150952401664 c1: 336073469633725578681108 c0: 880253753751683250101584592 # alpha -6.29 Y1: 891128745329 Y0: -4504765787799004324305 # Murphy_E 6.77e-10 # M 31447131488392542736505992818019557460517464114991795498415980855609373894140662627343843911601067913431897504545 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 70000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1400000, 2310001) Primes: RFBsize:203362, AFBsize:203921, largePrimes:7460034 encountered Relations: rels:7203107, finalFF:459537 Max relations in full relation-set: 28 Initial matrix: 407366 x 459537 with sparse part having weight 41639635. Pruned matrix : 368891 x 370991 with weight 29954447. Polynomial selection time: 1.04 hours. Total sieving time: 17.05 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.71 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000 total time: 19.07 hours. --------- CPU info (if available) ----------

3·10¹⁵³+7 = 3(0)₁₅₂7_<154> = 31 · 1960320883_<10> · 234995429723777_<15> · C129
C129 = P59 · P71
P59 = 12766708087797880775647643713694004841381361147278295433889_<59>
P71 = 16454854639373394037106403236176282020045812281709905847229481803749603_<71>

Number: 30007_153 N=210074325808026790448996368590420356086009745382036315917389148054666342924659655032019177558676920733305767288001767113996496067 ( 129 digits) SNFS difficulty: 155 digits. Divisors found: r1=12766708087797880775647643713694004841381361147278295433889 (pp59) r2=16454854639373394037106403236176282020045812281709905847229481803749603 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.75 hours. Scaled time: 35.43 units (timescale=2.116). Factorization parameters were as follows: n: 210074325808026790448996368590420356086009745382036315917389148054666342924659655032019177558676920733305767288001767113996496067 m: 10000000000000000000000000000000 c5: 3 c0: 700 skew: 2.98 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:216741, largePrimes:5443893 encountered Relations: rels:5315927, finalFF:487026 Max relations in full relation-set: 28 Initial matrix: 433623 x 487026 with sparse part having weight 35101675. Pruned matrix : 395950 x 398182 with weight 25217603. Total sieving time: 15.90 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.73 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 16.75 hours. --------- CPU info (if available) ----------

Sep 15, 2007 (2nd)

By Sinkiti Sibata / GGNFS
4·10¹⁵³+7 = 4(0)₁₅₂7_<154> = 15122759 · 24745976488388042357_<20> · C128
C128 = P63 · P65
P63 = 309312185819485412279995450362993507710825827912972995314067713_<63>
P65 = 34556307836253073852792654157706035652442377990012162822070317853_<65>

Number: 40007_153 N=10688687110682450660439951947485525140658610226471628564203051191314620050655242128626856748244492908709436441566630388274780189 ( 128 digits) SNFS difficulty: 153 digits. Divisors found: r1=309312185819485412279995450362993507710825827912972995314067713 (pp63) r2=34556307836253073852792654157706035652442377990012162822070317853 (pp65) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 34.45 hours. Scaled time: 22.81 units (timescale=0.662). Factorization parameters were as follows: name: 40007_153 n: 10688687110682450660439951947485525140658610226471628564203051191314620050655242128626856748244492908709436441566630388274780189 m: 2000000000000000000000000000000 c5: 125 c0: 7 skew: 0.56 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176043, largePrimes:5482109 encountered Relations: rels:5371718, finalFF:399515 Max relations in full relation-set: 0 Initial matrix: 352410 x 399515 with sparse part having weight 26957995. Pruned matrix : 325683 x 327509 with weight 20456304. Total sieving time: 30.73 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.36 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 34.45 hours. --------- CPU info (if available) ----------

Sep 15, 2007

By Jo Yeong Uk / PRIMO
(25·10²⁰¹⁸-7)/9 is prime!

Sep 14, 2007 (4th)

By Jo Yeong Uk / GGNFS
4·10¹⁵⁴+7 = 4(0)₁₅₃7_<155> = 11 · 342802429 · 25012593481129_<14> · 9378914296479408781_<19> · C113
C113 = P37 · P76
P37 = 4999642122681669494026196348160121217_<37>
P76 = 9044263464946840747038283509739191493041103507550062570873462979319591737141_<76>

Number: 40007_154 N=45218080587979093989708475325381839456130749535604419753028667196019088987174074624391266950271169021962161020597 ( 113 digits) Divisors found: r1=4999642122681669494026196348160121217 (pp37) r2=9044263464946840747038283509739191493041103507550062570873462979319591737141 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 19.99 hours. Scaled time: 42.53 units (timescale=2.127). Factorization parameters were as follows: name: 40007_154 n: 45218080587979093989708475325381839456130749535604419753028667196019088987174074624391266950271169021962161020597 skew: 31283.77 # norm 1.65e+16 c5: 68040 c4: 13966398846 c3: -414229534697503 c2: 932493901125242698 c1: 180032739590643387395624 c0: 35538889773243182429407920 # alpha -6.92 Y1: 836403879509 Y0: -3668643396033347782541 # Murphy_E 6.56e-10 # M 28071116392022513803667070326716114062434066061004312341816282378150721023164556206800033729572617394388783406386 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 70000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1400000, 2380001) Primes: RFBsize:203362, AFBsize:203919, largePrimes:7534644 encountered Relations: rels:7339518, finalFF:490981 Max relations in full relation-set: 28 Initial matrix: 407361 x 490981 with sparse part having weight 46092839. Pruned matrix : 345308 x 347408 with weight 30104251. Polynomial selection time: 1.07 hours. Total sieving time: 18.05 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.61 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000 total time: 19.99 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

Sep 14, 2007 (3rd)

By Alban Nonymous
10¹²³¹+1 is divisible by 8500614695927155829161050714503_<31>
10¹³¹³+1 is divisible by 34620946390749763175836315244453_<32>
10¹³⁴⁵+1 is divisible by 21044037584000626448961059324881_<32>
10¹³⁵⁴+1 is divisible by 36764627737869172094680667009_<29>
10¹³⁹¹+1 is divisible by 155490403648623445664788291934117_<33>
10¹⁴⁰⁵+1 is divisible by 83260647980205591593475319975561_<32>
10¹⁴³⁹+1 is divisible by 75673683062427966236317236967_<29>
10¹⁴⁵⁹+1 is divisible by 794157316664184535777113799277_<30>
10¹⁵⁷⁴+1 is divisible by 31760068204068839447245615309_<29>
10¹⁵⁹⁴+1 is divisible by 4281518523436324087802519357629_<31>
10¹⁶¹²+1 is divisible by 144685957475846477676841682164313_<33>
10¹⁶⁶¹+1 is divisible by 260721284044113991032016909263383_<33>
10¹⁶⁸⁷+1 is divisible by 135355988585304270436638671970733_<33>
10¹⁷²⁷+1 is divisible by 197450481378401142788807346609757_<33>
10¹⁷⁶¹+1 is divisible by 221356639156600314082995856870369_<33>
10¹⁸⁴⁴+1 is divisible by 9125072483779648050066911421569_<31>
10¹⁸⁵⁴+1 is divisible by 122708016673764191207130969289_<30>
Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Sep 14, 2007 (2nd)

By Jo Yeong Uk / GGNFS
3·10¹⁶²+7 = 3(0)₁₆₁7_<163> = C163
C163 = P49 · P55 · P60
P49 = 3733216672222512252402080024047876262175838601063_<49>
P55 = 1801107624738145935914817354265795383914325232132040341_<55>
P60 = 446167973934504101158694839309139582095409259666991720176029_<60>

Number: 30007_162 N=3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 ( 163 digits) SNFS difficulty: 162 digits. Divisors found: r1=3733216672222512252402080024047876262175838601063 (pp49) r2=1801107624738145935914817354265795383914325232132040341 (pp55) r3=446167973934504101158694839309139582095409259666991720176029 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 43.21 hours. Scaled time: 91.29 units (timescale=2.113). Factorization parameters were as follows: n: 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 m: 100000000000000000000000000000000 c5: 300 c0: 7 skew: 0.47 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 4800001) Primes: RFBsize:348513, AFBsize:348181, largePrimes:5776537 encountered Relations: rels:5923973, finalFF:791467 Max relations in full relation-set: 28 Initial matrix: 696760 x 791467 with sparse part having weight 43570598. Pruned matrix : 617703 x 621250 with weight 30629496. Total sieving time: 41.23 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.80 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 43.21 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

Sep 14, 2007

By Sinkiti Sibata / GGNFS
4·10¹⁴⁹+7 = 4(0)₁₄₈7_<150> = 19 · 37² · 79 · 156593 · 156967 · 6118218475309117_<16> · C118
C118 = P45 · P73
P45 = 458151166462975414839515281092455846471073253_<45>
P73 = 2825279191259063103973675923003172457201413683427285242607338783549973213_<73>

Number: 40007_149 N=1294404957058911574763733833658886023194297370404618272196308663603704846302793844151119322689824792125201967510771889 ( 118 digits) SNFS difficulty: 150 digits. Divisors found: r1=458151166462975414839515281092455846471073253 (pp45) r2=2825279191259063103973675923003172457201413683427285242607338783549973213 (pp73) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 26.65 hours. Scaled time: 18.20 units (timescale=0.683). Factorization parameters were as follows: name: 40007_149 n: 1294404957058911574763733833658886023194297370404618272196308663603704846302793844151119322689824792125201967510771889 m: 1000000000000000000000000000000 c5: 2 c0: 35 skew: 1.77 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, 1550001) Primes: RFBsize:114155, AFBsize:113967, largePrimes:2700927 encountered Relations: rels:2700881, finalFF:256445 Max relations in full relation-set: 0 Initial matrix: 228187 x 256445 with sparse part having weight 13732659. Pruned matrix : 217172 x 218376 with weight 10745713. Total sieving time: 25.50 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.94 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: 26.65 hours. --------- CPU info (if available) ----------

Sep 13, 2007 (2nd)

By Robert Backstrom / GGNFS
4·10¹⁶¹+7 = 4(0)₁₆₀7_<162> = 37 · C161
C161 = P60 · P101
P60 = 135634950176910695018973466825893607656590609530685636796371_<60>
P101 = 79705199852324998153571878460082630852438535935125517735082254432468091835256979745543882602791947641_<101>

Number: n N=10810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811 ( 161 digits) SNFS difficulty: 161 digits. Divisors found: r1=135634950176910695018973466825893607656590609530685636796371 (pp60) r2=79705199852324998153571878460082630852438535935125517735082254432468091835256979745543882602791947641 (pp101) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.22 hours. Scaled time: 51.03 units (timescale=1.449). Factorization parameters were as follows: name: KA_4_0_160_7 n: 10810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811 skew: 0.71 deg: 5 c5: 40 c0: 7 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:250150, AFBsize:249831, largePrimes:7163858 encountered Relations: rels:6733578, finalFF:603451 Max relations in full relation-set: 28 Initial matrix: 500047 x 603451 with sparse part having weight 36708271. Pruned matrix : 409178 x 411742 with weight 20824560. Total sieving time: 31.18 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.64 hours. Total square root time: 0.20 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 35.22 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Sep 13, 2007

By Jo Yeong Uk / GMP-ECM, GGNFS
4·10¹⁵⁹+7 = 4(0)₁₅₈7_<160> = 1759 · 665251 · 380206966797325875839_<21> · C130
C130 = P35 · P96
P35 = 38552289465776278156018648781010077_<35>
P96 = 233205275767539960164870481835449750381744466297103083038069953484504186782020869825210096921041_<96>
2·10¹⁵²-7 = 1(9)₁₅₁3_<153> = 43 · 204334865038223_<15> · 16693847621802210188347_<23> · C115
C115 = P54 · P61
P54 = 327984025003795812551523975755537204514529776773084171_<54>
P61 = 4157286246714744149068820102379243249246807718475885348533501_<61>

Number: 19993_152 N=1363523476290425092172349444739152306924486329874070738366011303585880390988622988895824915088159406187843686312671 ( 115 digits) SNFS difficulty: 152 digits. Divisors found: r1=327984025003795812551523975755537204514529776773084171 (pp54) r2=4157286246714744149068820102379243249246807718475885348533501 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 15.90 hours. Scaled time: 33.88 units (timescale=2.131). Factorization parameters were as follows: n: 1363523476290425092172349444739152306924486329874070738366011303585880390988622988895824915088159406187843686312671 m: 2000000000000000000000000000000 c5: 25 c0: -28 skew: 1.02 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2200001) Primes: RFBsize:176302, AFBsize:176668, largePrimes:5516420 encountered Relations: rels:5423681, finalFF:472836 Max relations in full relation-set: 28 Initial matrix: 353034 x 472836 with sparse part having weight 41918739. Pruned matrix : 303636 x 305465 with weight 23920078. Total sieving time: 15.34 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.44 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 15.90 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹⁶⁰+7 = 4(0)₁₅₉7_<161> = 11 · 1136957848708636651_<19> · C142
C142 = P35 · P108
P35 = 25817512708582211180172834678179339_<35>
P108 = 123882095407939278236523043249249576804371883991910405477004505369234945547803086828965151030213745119507133_<108>

Sep 12, 2007 (8th)

By Yousuke Koide
10¹³⁸³+1 is divisible by 19106661240397987951762164436636893943_<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 12, 2007 (7th)

By suberi / GMP-ECM
2·10¹⁸⁹-3 = 1(9)₁₈₈7_<190> = 26515433818872756128486451063540368813_<38> · C152
C152 = P35 · C118
P35 = 31618164809434211754592287712179187_<35>
C118 = [2385583376282025837302025573831625807718996619292106854661488654167073439506823897959332181406320971559780911666433387_<118>]

Sep 12, 2007 (6th)

By Sinkiti Sibata / GGNFS
4·10¹⁴⁴+7 = 4(0)₁₄₃7_<145> = 11 · 179 · 18849577301_<11> · 752837899459199_<15> · C117
C117 = P35 · P82
P35 = 48338648874827112317609973195674549_<35>
P82 = 2961533694098241796253566194687162650499134657877589080508209090117714412844440753_<82>

Number: 40007_144 N=143156537369984557247257807124511565476769024965337464560184628079260630402615596072010099193813141404565420500495397 ( 117 digits) SNFS difficulty: 145 digits. Divisors found: r1=48338648874827112317609973195674549 (pp35) r2=2961533694098241796253566194687162650499134657877589080508209090117714412844440753 (pp82) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 13.12 hours. Scaled time: 8.96 units (timescale=0.683). Factorization parameters were as follows: name: 40007_144 n: 143156537369984557247257807124511565476769024965337464560184628079260630402615596072010099193813141404565420500495397 m: 100000000000000000000000000000 c5: 2 c0: 35 skew: 1.77 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, 1850001) Primes: RFBsize:100021, AFBsize:99918, largePrimes:2650465 encountered Relations: rels:2603751, finalFF:227166 Max relations in full relation-set: 0 Initial matrix: 200004 x 227166 with sparse part having weight 17999391. Pruned matrix : 191344 x 192408 with weight 13832480. Total sieving time: 12.00 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.91 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 13.12 hours. --------- CPU info (if available) ----------

Sep 12, 2007 (5th)

By Jo Yeong Uk / PRIMO
(8·10²⁰⁹⁰-53)/9 is prime!

Sep 12, 2007 (4th)

By Robert Backstrom / GGNFS
4·10¹⁴⁸+7 = 4(0)₁₄₇7_<149> = 11 · 23 · 2447 · C143
C143 = P66 · P78
P66 = 245114463615524143538086032433891970756683404064249115073005692163_<66>
P78 = 263594632206945158216136499659187321494630614449650644664224883579346714068479_<78>

Number: n N=64610856885336727557015043022754328523593462027391772776538505647796527489496697577577448226512742068613499469383337829172124938013959175630077 ( 143 digits) SNFS difficulty: 148 digits. Divisors found: r1=245114463615524143538086032433891970756683404064249115073005692163 (pp66) r2=263594632206945158216136499659187321494630614449650644664224883579346714068479 (pp78) Version: GGNFS-0.77.1-20051202-athlon Total time: 11.66 hours. Scaled time: 8.43 units (timescale=0.723). Factorization parameters were as follows: name: KA_4_0_147_7 n: 64610856885336727557015043022754328523593462027391772776538505647796527489496697577577448226512742068613499469383337829172124938013959175630077 skew: 0.56 deg: 5 c5: 125 c0: 7 m: 200000000000000000000000000000 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, 1200001) Primes: RFBsize:148933, AFBsize:148595, largePrimes:6600171 encountered Relations: rels:5970160, finalFF:355083 Max relations in full relation-set: 28 Initial matrix: 297593 x 355083 with sparse part having weight 26405611. Pruned matrix : 257089 x 258640 with weight 16503342. Total sieving time: 7.87 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.09 hours. Total square root time: 0.47 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 11.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Sep 12, 2007 (3rd)

By Jo Yeong Uk / GGNFS
4·10¹⁵⁷+7 = 4(0)₁₅₆7_<158> = 17 · 19875157 · 1469183047_<10> · 42169567669_<11> · 46007753657_<11> · 292957231827292399177_<21> · C99
C99 = P40 · P59
P40 = 8814970410242325051502600691310445528441_<40>
P59 = 16083084130339877401016180137996623124776743395012266452129_<59>

Number: 40007_157 N=141771910714383936723190602488517820827004390019966573920874057536635436839306793283547283634500889 ( 99 digits) Divisors found: r1=8814970410242325051502600691310445528441 (pp40) r2=16083084130339877401016180137996623124776743395012266452129 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.05 hours. Scaled time: 6.54 units (timescale=2.142). Factorization parameters were as follows: name: 40007_157 n: 141771910714383936723190602488517820827004390019966573920874057536635436839306793283547283634500889 skew: 4008.53 # norm 3.45e+13 c5: 21960 c4: -71874162 c3: -4406460702773 c2: 2450429555282521 c1: 12809475412520706169 c0: 5116825832921210112837 # alpha -5.07 Y1: 14932061617 Y0: -5780858056141522292 # Murphy_E 4.14e-09 # M 88781377175097529873633494690642072436766223929986758768355796430593531738087159338827855254497350 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, 1050001) Primes: RFBsize:100021, AFBsize:99853, largePrimes:3742855 encountered Relations: rels:3574058, finalFF:242656 Max relations in full relation-set: 28 Initial matrix: 199952 x 242656 with sparse part having weight 17822918. Pruned matrix : 173035 x 174098 with weight 10123182. Polynomial selection time: 0.23 hours. Total sieving time: 2.58 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.14 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1300000,1300000,26,26,48,48,2.5,2.5,50000 total time: 3.05 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹⁸⁴-1 = 2(9)_184<185> = C185
C185 = P62 · P124
P62 = 10073641022189321360228001328707180659381468877455557544719139_<62>
P124 = 2978069194040036330503581914737461793403041082476154833888528931755723356899703483852214198475678536123147506448805613562741_<124>

Number: 29999_184 N=29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 ( 185 digits) SNFS difficulty: 185 digits. Divisors found: r1=10073641022189321360228001328707180659381468877455557544719139 (pp62) r2=2978069194040036330503581914737461793403041082476154833888528931755723356899703483852214198475678536123147506448805613562741 (pp124) Version: GGNFS-0.77.1-20050930-nocona Total time: 343.63 hours. Scaled time: 729.87 units (timescale=2.124). Factorization parameters were as follows: n: 29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 m: 10000000000000000000000000000000000000 c5: 3 c0: -10 skew: 1.27 type: snfs Factor base limits: 11000000/11000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [5500000, 11100001) Primes: RFBsize:726517, AFBsize:727028, largePrimes:11282043 encountered Relations: rels:11683743, finalFF:1645813 Max relations in full relation-set: 28 Initial matrix: 1453610 x 1645813 with sparse part having weight 94399149. Pruned matrix : 1285739 x 1293071 with weight 69947957. Total sieving time: 331.30 hours. Total relation processing time: 0.39 hours. Matrix solve time: 11.81 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,50,50,2.6,2.6,100000 total time: 343.63 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

Sep 12, 2007 (2nd)

By Sinkiti Sibata / GGNFS
4·10¹⁴³+7 = 4(0)₁₄₂7_<144> = 37 · 43 · 2953 · 85208610560597464386908162003_<29> · C108
C108 = P31 · P78
P31 = 1000749795659211467211625369787_<31>
P78 = 998429423289612292605918747746093298336322693193270765403387192272005415284169_<78>

Number: 40007_143 N=999178041337223852488855483773425882364042283838812522867286562602400394959670087123679083063501766312002003 ( 108 digits) SNFS difficulty: 143 digits. Divisors found: r1=1000749795659211467211625369787 (pp31) r2=998429423289612292605918747746093298336322693193270765403387192272005415284169 (pp78) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 12.96 hours. Scaled time: 8.85 units (timescale=0.683). Factorization parameters were as follows: name: 40007_143 n: 999178041337223852488855483773425882364042283838812522867286562602400394959670087123679083063501766312002003 m: 20000000000000000000000000000 c5: 125 c0: 7 skew: 0.56 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, 1850001) Primes: RFBsize:100021, AFBsize:99858, largePrimes:2670610 encountered Relations: rels:2631232, finalFF:227950 Max relations in full relation-set: 0 Initial matrix: 199944 x 227950 with sparse part having weight 17712373. Pruned matrix : 190831 x 191894 with weight 13565004. Total sieving time: 11.85 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.90 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 12.96 hours. --------- CPU info (if available) ----------

Sep 12, 2007

By Robert Backstrom / GGNFS
5·10¹⁸²-3 = 4(9)₁₈₁7_<183> = 7² · C182
C182 = P47 · P135
P47 = 29770834642130994832881614532449420836505709773_<47>
P135 = 342754301493868147025468004954466202887529212100972680571593317530253611454746160580734860582053102922819500742588146493363342762650561_<135>

Number: n N=10204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653 ( 182 digits) SNFS difficulty: 182 digits. Divisors found: r1=29770834642130994832881614532449420836505709773 (pp47) r2=342754301493868147025468004954466202887529212100972680571593317530253611454746160580734860582053102922819500742588146493363342762650561 (pp135) Version: GGNFS-0.77.1-20051202-athlon Total time: 526.30 hours. Scaled time: 759.46 units (timescale=1.443). Factorization parameters were as follows: name: KA_4_9_181_7 n: 10204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653 skew: 1.36 deg: 5 c5: 500 c0: -3 m: 1000000000000000000000000000000000000 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, 7900001) Primes: RFBsize:283146, AFBsize:282917, largePrimes:9091651 encountered Relations: rels:8782511, finalFF:640766 Max relations in full relation-set: 28 Initial matrix: 566129 x 640766 with sparse part having weight 83377454. Pruned matrix : 535642 x 538536 with weight 69043920. Total sieving time: 508.12 hours. Total relation processing time: 0.68 hours. Matrix solve time: 17.38 hours. Total square root time: 0.12 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 526.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Sep 11, 2007 (4th)

By Sinkiti Sibata / GGNFS
4·10¹³⁹+7 = 4(0)₁₃₈7_<140> = 47 · 59 · 61 · 7229 · 8623 · 10837 · C123
C123 = P50 · P74
P50 = 31986300717986806917050274578788541806841309083879_<50>
P74 = 10943861459545403346659982155635581621711169730625226161155822473142568559_<74>

Number: 40007_139 N=350053643661005279748843704503251430769753790262193682777340431379729126555588061839938125103056209629639011990529239160361 ( 123 digits) SNFS difficulty: 140 digits. Divisors found: r1=31986300717986806917050274578788541806841309083879 (pp50) r2=10943861459545403346659982155635581621711169730625226161155822473142568559 (pp74) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 8.92 hours. Scaled time: 6.09 units (timescale=0.683). Factorization parameters were as follows: name: 40007_139 n: 350053643661005279748843704503251430769753790262193682777340431379729126555588061839938125103056209629639011990529239160361 m: 10000000000000000000000000000 c5: 2 c0: 35 skew: 1.77 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, 1300001) Primes: RFBsize:78498, AFBsize:63938, largePrimes:1494045 encountered Relations: rels:1474401, finalFF:159762 Max relations in full relation-set: 0 Initial matrix: 142501 x 159762 with sparse part having weight 13322206. Pruned matrix : 137478 x 138254 with weight 9904526. Total sieving time: 8.38 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.40 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: 8.92 hours. --------- CPU info (if available) ----------

Sep 11, 2007 (3rd)

By Robert Backstrom / GGNFS
3·10¹⁵¹+7 = 3(0)₁₅₀7_<152> = 37 · 73 · 1244863 · 20628811590269_<14> · C129
C129 = P64 · P66
P64 = 1197832543309205649377891301884244716228803440401897936550987217_<64>
P66 = 361081131072503212385537651948543045335365693158346674560705560593_<66>

Number: n N=432514729573541165878814502602851075559541863386033196591231623575925857266862190179793058170814822307811485963457490435561939681 ( 129 digits) SNFS difficulty: 151 digits. Divisors found: r1=1197832543309205649377891301884244716228803440401897936550987217 (pp64) r2=361081131072503212385537651948543045335365693158346674560705560593 (pp66) Version: GGNFS-0.77.1-20051202-athlon Total time: 27.46 hours. Scaled time: 32.81 units (timescale=1.195). Factorization parameters were as follows: name: KA_3_0_150_7 n: 432514729573541165878814502602851075559541863386033196591231623575925857266862190179793058170814822307811485963457490435561939681 type: snfs skew: 1.00 deg: 5 c5: 30 c0: 7 m: 1000000000000000000000000000000 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, 1150001) Primes: RFBsize:148933, AFBsize:148635, largePrimes:6069369 encountered Relations: rels:5430747, finalFF:346854 Max relations in full relation-set: 28 Initial matrix: 297635 x 346854 with sparse part having weight 25044237. Pruned matrix : 262468 x 264020 with weight 16394510. Total sieving time: 25.39 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.78 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 27.46 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Sep 11, 2007 (2nd)

By Sinkiti Sibata / GGNFS
4·10¹⁴⁰+7 = 4(0)₁₃₉7_<141> = 11 · 37 · 84263 · 21289799939_<11> · 339012053851_<12> · 5722935804716380853_<19> · C93
C93 = P39 · P55
P39 = 246523695335114998234346215684034044871_<39>
P55 = 1145419047714673326600757462103639786711752383269528461_<55>

Number: 40007_140 N=282372936349849676344049794975421655211442692035412953083742345621409096950554935978685573531 ( 93 digits) SNFS difficulty: 140 digits. Divisors found: r1=246523695335114998234346215684034044871 (pp39) r2=1145419047714673326600757462103639786711752383269528461 (pp55) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 8.01 hours. Scaled time: 5.47 units (timescale=0.683). Factorization parameters were as follows: n: 282372936349849676344049794975421655211442692035412953083742345621409096950554935978685573531 m: 10000000000000000000000000000 c5: 4 c0: 7 skew: 1.12 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, 1350001) Primes: RFBsize:100021, AFBsize:100128, largePrimes:2522999 encountered Relations: rels:2447285, finalFF:225591 Max relations in full relation-set: 0 Initial matrix: 200213 x 225591 with sparse part having weight 13214244. Pruned matrix : 190912 x 191977 with weight 9721443. Total sieving time: 7.15 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.69 hours. Time per square root: 0.07 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: 8.01 hours. --------- CPU info (if available) ----------

Sep 11, 2007

By Jo Yeong Uk / GGNFS
4·10¹³²+7 = 4(0)₁₃₁7_<133> = 11 · 1383665436911_<13> · 15993881312447791_<17> · C104
C104 = P42 · P63
P42 = 105178237608324529255932346205701327687403_<42>
P63 = 156227130243012416024084470042988923198135605773570637061345279_<63>

Number: 40007_132 N=16431694225566222948609513601281972899576566543250776087667169652945304700613585557818414923365161820437 ( 104 digits) SNFS difficulty: 132 digits. Divisors found: r1=105178237608324529255932346205701327687403 (pp42) r2=156227130243012416024084470042988923198135605773570637061345279 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.47 hours. Scaled time: 5.23 units (timescale=2.118). Factorization parameters were as follows: n: 16431694225566222948609513601281972899576566543250776087667169652945304700613585557818414923365161820437 m: 200000000000000000000000000 c5: 25 c0: 14 skew: 0.89 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 1000001) Primes: RFBsize:78498, AFBsize:78371, largePrimes:1569406 encountered Relations: rels:1611834, finalFF:216226 Max relations in full relation-set: 28 Initial matrix: 156933 x 216226 with sparse part having weight 10703211. Pruned matrix : 133627 x 134475 with weight 5265424. Total sieving time: 2.38 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 2.47 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹³³+7 = 4(0)₁₃₂7_<134> = 103 · 139 · 581182594323229533763_<21> · C109
C109 = P35 · P75
P35 = 26266897688914103600761963556264623_<35>
P75 = 183014957204357914443774593629154442488846573682381077826399652046581216079_<75>

Number: 40007_133 N=4807235156427862477801484912313373050636771228697485220905861647175509857379509740170422840569881678066473217 ( 109 digits) SNFS difficulty: 135 digits. Divisors found: r1=26266897688914103600761963556264623 (pp35) r2=183014957204357914443774593629154442488846573682381077826399652046581216079 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.48 hours. Scaled time: 5.32 units (timescale=2.144). Factorization parameters were as follows: n: 4807235156427862477801484912313373050636771228697485220905861647175509857379509740170422840569881678066473217 m: 1000000000000000000000000000 c5: 1 c0: 175 skew: 2.81 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1100001) Primes: RFBsize:107126, AFBsize:107108, largePrimes:2183290 encountered Relations: rels:2279537, finalFF:274333 Max relations in full relation-set: 28 Initial matrix: 214298 x 274333 with sparse part having weight 17720307. Pruned matrix : 182909 x 184044 with weight 9107441. Total sieving time: 2.27 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.16 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 2.48 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

Sep 10, 2007 (4th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve
4·10¹⁴²+7 = 4(0)₁₄₁7_<143> = 11 · 128425333 · 330484919 · 1110686627_<10> · C116
C116 = P31 · P86
P31 = 2229599509718725418315923215401_<31>
P86 = 34597646459065868838026205405922156262284783213861761567480768713986485734911023224453_<86>
4·10¹⁰⁵+7 = 4(0)₁₀₄7_<106> = C106
C106 = P37 · P70
P37 = 1043329248228030997017608973380352553_<37>
P70 = 3833880826012994445256424591562881885990352920890139603449554354425519_<70>

Number: 40007_105 N=4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 ( 106 digits) SNFS difficulty: 105 digits. Divisors found: r1=1043329248228030997017608973380352553 (pp37) r2=3833880826012994445256424591562881885990352920890139603449554354425519 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.37 hours. Scaled time: 0.79 units (timescale=2.144). Factorization parameters were as follows: n: 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 m: 1000000000000000000000 c5: 4 c0: 7 skew: 1.12 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, 240001) Primes: RFBsize:30757, AFBsize:30779, largePrimes:1084096 encountered Relations: rels:1048724, finalFF:128939 Max relations in full relation-set: 28 Initial matrix: 61600 x 128939 with sparse part having weight 5037821. Pruned matrix : 40561 x 40933 with weight 1175515. Total sieving time: 0.35 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,105,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.37 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹¹⁷+7 = 4(0)₁₁₆7_<118> = 3372533359686783953_<19> · C100
C100 = P46 · P54
P46 = 7571231308415109663829195119389645559083504639_<46>
P54 = 156652461213639440290493125833595279391925366872158121_<54>

Number: 40007_117 N=1186052018880990557463388064411320977047917277971455374837039249136844921468320398869036762045023319 ( 100 digits) SNFS difficulty: 117 digits. Divisors found: r1=7571231308415109663829195119389645559083504639 (pp46) r2=156652461213639440290493125833595279391925366872158121 (pp54) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.85 hours. Scaled time: 1.81 units (timescale=2.142). Factorization parameters were as follows: n: 1186052018880990557463388064411320977047917277971455374837039249136844921468320398869036762045023319 m: 200000000000000000000000 c5: 25 c0: 14 skew: 0.89 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:49126, largePrimes:2081921 encountered Relations: rels:2247563, finalFF:299949 Max relations in full relation-set: 28 Initial matrix: 98288 x 299949 with sparse part having weight 25856697. Pruned matrix : 64697 x 65252 with weight 4307300. Total sieving time: 0.80 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.85 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹³⁰+7 = 4(0)₁₂₉7_<131> = 11 · 1444520412397380043861_<22> · C109
C109 = P36 · P73
P36 = 408504680191109431162215803581538597_<36>
P73 = 6162353197057531640657105318413959662898339394094871838459411864184198861_<73>

Number: 40007_130 N=2517350121988647718566832619749419527856760925822505300539585253388798073057602635805421866091633938194938017 ( 109 digits) SNFS difficulty: 130 digits. Divisors found: r1=408504680191109431162215803581538597 (pp36) r2=6162353197057531640657105318413959662898339394094871838459411864184198861 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.80 hours. Scaled time: 3.85 units (timescale=2.143). Factorization parameters were as follows: n: 2517350121988647718566832619749419527856760925822505300539585253388798073057602635805421866091633938194938017 m: 100000000000000000000000000 c5: 4 c0: 7 skew: 1.12 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 850001) Primes: RFBsize:78498, AFBsize:78491, largePrimes:1505533 encountered Relations: rels:1534239, finalFF:204166 Max relations in full relation-set: 28 Initial matrix: 157053 x 204166 with sparse part having weight 9603809. Pruned matrix : 132553 x 133402 with weight 4860764. Total sieving time: 1.72 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 1.80 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹²⁷+7 = 4(0)₁₂₆7_<128> = 606497 · 2268865117_<10> · 211856473010664580779859_<24> · C90
C90 = P39 · P51
P39 = 377275926509092007527238672431385514979_<39>
P51 = 363682014571282571218438761205122109617347029045963_<51>

Mon Sep 10 22:32:35 2007 Mon Sep 10 22:32:35 2007 Mon Sep 10 22:32:35 2007 Msieve v. 1.25 Mon Sep 10 22:32:35 2007 random seeds: 1cdda497 27465ce9 Mon Sep 10 22:32:35 2007 factoring 137208469002073731963742143203405569527855447772540937594569482584938095837884419815979777 (90 digits) Mon Sep 10 22:32:35 2007 commencing quadratic sieve (89-digit input) Mon Sep 10 22:32:35 2007 using multiplier of 1 Mon Sep 10 22:32:35 2007 using 32kb Intel Core sieve core Mon Sep 10 22:32:35 2007 sieve interval: 35 blocks of size 32768 Mon Sep 10 22:32:35 2007 processing polynomials in batches of 6 Mon Sep 10 22:32:35 2007 using a sieve bound of 1565341 (59667 primes) Mon Sep 10 22:32:35 2007 using large prime bound of 125227280 (26 bits) Mon Sep 10 22:32:35 2007 using double large prime bound of 376580721415840 (42-49 bits) Mon Sep 10 22:32:35 2007 using trial factoring cutoff of 49 bits Mon Sep 10 22:32:35 2007 polynomial 'A' values have 11 factors Mon Sep 10 23:20:35 2007 59861 relations (16019 full + 43842 combined from 631769 partial), need 59763 Mon Sep 10 23:20:36 2007 begin with 647788 relations Mon Sep 10 23:20:36 2007 reduce to 145237 relations in 10 passes Mon Sep 10 23:20:36 2007 attempting to read 145237 relations Mon Sep 10 23:20:37 2007 recovered 145237 relations Mon Sep 10 23:20:37 2007 recovered 120863 polynomials Mon Sep 10 23:20:37 2007 attempting to build 59861 cycles Mon Sep 10 23:20:37 2007 found 59861 cycles in 6 passes Mon Sep 10 23:20:38 2007 distribution of cycle lengths: Mon Sep 10 23:20:38 2007 length 1 : 16019 Mon Sep 10 23:20:38 2007 length 2 : 11430 Mon Sep 10 23:20:38 2007 length 3 : 10659 Mon Sep 10 23:20:38 2007 length 4 : 7965 Mon Sep 10 23:20:38 2007 length 5 : 5631 Mon Sep 10 23:20:38 2007 length 6 : 3573 Mon Sep 10 23:20:38 2007 length 7 : 2094 Mon Sep 10 23:20:38 2007 length 9+: 2490 Mon Sep 10 23:20:38 2007 largest cycle: 18 relations Mon Sep 10 23:20:38 2007 matrix is 59667 x 59861 with weight 3591214 (avg 59.99/col) Mon Sep 10 23:20:38 2007 filtering completed in 3 passes Mon Sep 10 23:20:38 2007 matrix is 55719 x 55783 with weight 3372987 (avg 60.47/col) Mon Sep 10 23:20:39 2007 saving the first 48 matrix rows for later Mon Sep 10 23:20:39 2007 matrix is 55671 x 55783 with weight 2801744 (avg 50.23/col) Mon Sep 10 23:20:39 2007 matrix includes 64 packed rows Mon Sep 10 23:20:39 2007 using block size 22313 for processor cache size 4096 kB Mon Sep 10 23:20:39 2007 commencing Lanczos iteration Mon Sep 10 23:20:58 2007 lanczos halted after 882 iterations Mon Sep 10 23:20:58 2007 recovered 14 nontrivial dependencies Mon Sep 10 23:20:58 2007 prp39 factor: 377275926509092007527238672431385514979 Mon Sep 10 23:20:58 2007 prp51 factor: 363682014571282571218438761205122109617347029045963 Mon Sep 10 23:20:58 2007 elapsed time 00:48:23

Sep 10, 2007 (3rd)

By suberi / GMP-ECM
2·10¹⁸⁰-3 = 1(9)₁₇₉7_<181> = 2593 · 51067720369_<11> · 2039081640448510323571_<22> · C145
C145 = P33 · C113
P33 = 112032125257256292325042410655727_<33>
C113 = [66115580929239593359723808855458909629091457719484972084609617544199525101235044807799431332453896293536909365073_<113>]

Sep 10, 2007 (2nd)

By Sinkiti Sibata / GGNFS, Msieve
3·10¹⁶⁰+7 = 3(0)₁₅₉7_<161> = 19 · 37 · 5987 · 190783 · 2301583954628587_<16> · 30214589326193078803_<20> · C114
C114 = P39 · P76
P39 = 168821492926505124753835321037510889107_<39>
P76 = 3182333894509189879957908738033612846872644789961813377047250471481774358607_<76>

Number: 30007_160 N=537246359061660705186390632240506481498326672090893936382168433356729665263223577193112313073083261784303227993949 ( 114 digits) SNFS difficulty: 160 digits. Divisors found: r1=168821492926505124753835321037510889107 (pp39) r2=3182333894509189879957908738033612846872644789961813377047250471481774358607 (pp76) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 62.61 hours. Scaled time: 42.82 units (timescale=0.684). Factorization parameters were as follows: name: 30007_160 n: 537246359061660705186390632240506481498326672090893936382168433356729665263223577193112313073083261784303227993949 m: 100000000000000000000000000000000 c5: 3 c0: 7 skew: 1.18 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, 3500001) Primes: RFBsize:283146, AFBsize:282807, largePrimes:5650728 encountered Relations: rels:5709851, finalFF:639843 Max relations in full relation-set: 0 Initial matrix: 566018 x 639843 with sparse part having weight 34788105. Pruned matrix : 505676 x 508570 with weight 25305535. Total sieving time: 53.13 hours. Total relation processing time: 0.27 hours. Matrix solve time: 9.00 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: 62.61 hours. --------- CPU info (if available) ----------

4·10¹⁰²+7 = 4(0)₁₀₁7_<103> = 11² · C101
C101 = P46 · P56
P46 = 2585280752085942635036731470745668477195362783_<46>
P56 = 12786948269736886765489577885313149519498166924858577249_<56>

Number: 40007_102 N=33057851239669421487603305785123966942148760330578512396694214876033057851239669421487603305785123967 ( 101 digits) SNFS difficulty: 102 digits. Divisors found: r1=2585280752085942635036731470745668477195362783 (pp46) r2=12786948269736886765489577885313149519498166924858577249 (pp56) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 0.61 hours. Scaled time: 0.42 units (timescale=0.683). Factorization parameters were as follows: name: 40007_102 n: 33057851239669421487603305785123966942148760330578512396694214876033057851239669421487603305785123967 m: 200000000000000000000 c5: 25 c0: 14 skew: 0.89 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 290001) Primes: RFBsize:37706, AFBsize:41617, largePrimes:1013476 encountered Relations: rels:951414, finalFF:91482 Max relations in full relation-set: 0 Initial matrix: 79387 x 91482 with sparse part having weight 2362982. Pruned matrix : 65477 x 65937 with weight 1513258. Total sieving time: 0.53 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 0.61 hours. --------- CPU info (if available) ----------

4·10¹³⁶+7 = 4(0)₁₃₅7_<137> = 11 · 79 · 113 · 151 · 967 · 8035637264791904171821_<22> · 151132305869278356285433_<24> · C82
C82 = P41 · P42
P41 = 13843131922546324190310604226546490969103_<41>
P42 = 165938194222088675576956806070665609433217_<42>

Mon Sep 10 12:56:10 2007 Mon Sep 10 12:56:10 2007 Mon Sep 10 12:56:10 2007 Msieve v. 1.26 Mon Sep 10 12:56:10 2007 random seeds: ae13a040 ea7e6816 Mon Sep 10 12:56:10 2007 factoring 2297104313605487751994058909995621445226670899397396722147182347374454856888894351 (82 digits) Mon Sep 10 12:56:11 2007 commencing quadratic sieve (82-digit input) Mon Sep 10 12:56:11 2007 using multiplier of 1 Mon Sep 10 12:56:11 2007 using 64kb Pentium 2 sieve core Mon Sep 10 12:56:11 2007 sieve interval: 6 blocks of size 65536 Mon Sep 10 12:56:11 2007 processing polynomials in batches of 17 Mon Sep 10 12:56:11 2007 using a sieve bound of 1338397 (51471 primes) Mon Sep 10 12:56:11 2007 using large prime bound of 125809318 (26 bits) Mon Sep 10 12:56:11 2007 using trial factoring cutoff of 27 bits Mon Sep 10 12:56:11 2007 polynomial 'A' values have 10 factors Mon Sep 10 14:47:10 2007 51608 relations (26063 full + 25545 combined from 276098 partial), need 51567 Mon Sep 10 14:47:12 2007 begin with 302161 relations Mon Sep 10 14:47:12 2007 reduce to 73959 relations in 2 passes Mon Sep 10 14:47:12 2007 attempting to read 73959 relations Mon Sep 10 14:47:15 2007 recovered 73959 relations Mon Sep 10 14:47:15 2007 recovered 65324 polynomials Mon Sep 10 14:47:15 2007 attempting to build 51608 cycles Mon Sep 10 14:47:15 2007 found 51608 cycles in 1 passes Mon Sep 10 14:47:15 2007 distribution of cycle lengths: Mon Sep 10 14:47:15 2007 length 1 : 26063 Mon Sep 10 14:47:15 2007 length 2 : 25545 Mon Sep 10 14:47:15 2007 largest cycle: 2 relations Mon Sep 10 14:47:16 2007 matrix is 51471 x 51608 with weight 1602662 (avg 31.05/col) Mon Sep 10 14:47:19 2007 filtering completed in 4 passes Mon Sep 10 14:47:19 2007 matrix is 44265 x 44329 with weight 1349414 (avg 30.44/col) Mon Sep 10 14:47:21 2007 saving the first 48 matrix rows for later Mon Sep 10 14:47:21 2007 matrix is 44217 x 44329 with weight 1066574 (avg 24.06/col) Mon Sep 10 14:47:21 2007 matrix includes 64 packed rows Mon Sep 10 14:47:21 2007 commencing Lanczos iteration Mon Sep 10 14:50:30 2007 lanczos halted after 700 iterations Mon Sep 10 14:50:31 2007 recovered 5 nontrivial dependencies Mon Sep 10 14:50:32 2007 prp41 factor: 13843131922546324190310604226546490969103 Mon Sep 10 14:50:32 2007 prp42 factor: 165938194222088675576956806070665609433217 Mon Sep 10 14:50:32 2007 elapsed time 01:54:22

4·10¹²⁰+7 = 4(0)₁₁₉7_<121> = 11 · 1250831 · 51158077863472778717_<20> · C94
C94 = P41 · P54
P41 = 16163441146585422712119803589901420539893_<41>
P54 = 351577137058775393064141868807182275859318715677825467_<54>

Number: 40007_120 N=5682696363334512849721537896612724909471809965504303562702985349408048099863665858911364855031 ( 94 digits) SNFS difficulty: 120 digits. Divisors found: r1=16163441146585422712119803589901420539893 (pp41) r2=351577137058775393064141868807182275859318715677825467 (pp54) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.14 hours. Scaled time: 1.46 units (timescale=0.683). Factorization parameters were as follows: name: 40007_120 n: 5682696363334512849721537896612724909471809965504303562702985349408048099863665858911364855031 m: 1000000000000000000000000 c5: 4 c0: 7 skew: 1.12 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63998, largePrimes:2233386 encountered Relations: rels:2497504, finalFF:145478 Max relations in full relation-set: 0 Initial matrix: 113160 x 145478 with sparse part having weight 5118153. Pruned matrix : 93207 x 93836 with weight 3055007. Total sieving time: 1.96 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.08 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.14 hours. --------- CPU info (if available) ----------

4·10¹⁰⁶+7 = 4(0)₁₀₅7_<107> = 11 · 11887 · 96607700155906921_<17> · C85
C85 = P35 · P50
P35 = 64819024777953578883539736640240237_<35>
P50 = 48851826656369687093848975611401730998510732736463_<50>

Mon Sep 10 12:52:04 2007 Msieve v. 1.26 Mon Sep 10 12:52:04 2007 random seeds: d51dc9a3 8d7922ad Mon Sep 10 12:52:04 2007 factoring 3166527762487519882929791626294636973417702535337351459863375266451834768004729661731 (85 digits) Mon Sep 10 12:52:05 2007 commencing quadratic sieve (85-digit input) Mon Sep 10 12:52:06 2007 using multiplier of 1 Mon Sep 10 12:52:06 2007 using 64kb Pentium 2 sieve core Mon Sep 10 12:52:06 2007 sieve interval: 6 blocks of size 65536 Mon Sep 10 12:52:06 2007 processing polynomials in batches of 17 Mon Sep 10 12:52:06 2007 using a sieve bound of 1426129 (54070 primes) Mon Sep 10 12:52:06 2007 using large prime bound of 116942578 (26 bits) Mon Sep 10 12:52:06 2007 using trial factoring cutoff of 27 bits Mon Sep 10 12:52:06 2007 polynomial 'A' values have 11 factors Mon Sep 10 16:46:56 2007 Mon Sep 10 16:46:56 2007 Mon Sep 10 16:46:56 2007 Msieve v. 1.26 Mon Sep 10 16:46:57 2007 random seeds: 2317f812 12a05399 Mon Sep 10 16:46:57 2007 factoring 3166527762487519882929791626294636973417702535337351459863375266451834768004729661731 (85 digits) Mon Sep 10 16:46:57 2007 commencing quadratic sieve (85-digit input) Mon Sep 10 16:46:58 2007 using multiplier of 1 Mon Sep 10 16:46:58 2007 using 64kb Pentium 2 sieve core Mon Sep 10 16:46:58 2007 sieve interval: 6 blocks of size 65536 Mon Sep 10 16:46:58 2007 processing polynomials in batches of 17 Mon Sep 10 16:46:58 2007 using a sieve bound of 1426129 (54070 primes) Mon Sep 10 16:46:58 2007 using large prime bound of 116942578 (26 bits) Mon Sep 10 16:46:58 2007 using trial factoring cutoff of 27 bits Mon Sep 10 16:46:58 2007 polynomial 'A' values have 11 factors Mon Sep 10 16:47:01 2007 restarting with 21856 full and 243609 partial relations Mon Sep 10 17:26:58 2007 54200 relations (26099 full + 28101 combined from 290676 partial), need 54166 Mon Sep 10 17:27:01 2007 begin with 316775 relations Mon Sep 10 17:27:01 2007 reduce to 78679 relations in 2 passes Mon Sep 10 17:27:01 2007 attempting to read 78679 relations Mon Sep 10 17:27:05 2007 recovered 78679 relations Mon Sep 10 17:27:05 2007 recovered 75104 polynomials Mon Sep 10 17:27:06 2007 attempting to build 54200 cycles Mon Sep 10 17:27:06 2007 found 54200 cycles in 1 passes Mon Sep 10 17:27:06 2007 distribution of cycle lengths: Mon Sep 10 17:27:06 2007 length 1 : 26099 Mon Sep 10 17:27:06 2007 length 2 : 28101 Mon Sep 10 17:27:06 2007 largest cycle: 2 relations Mon Sep 10 17:27:06 2007 matrix is 54070 x 54200 with weight 1761587 (avg 32.50/col) Mon Sep 10 17:27:08 2007 filtering completed in 3 passes Mon Sep 10 17:27:08 2007 matrix is 42387 x 42451 with weight 1482165 (avg 34.91/col) Mon Sep 10 17:27:10 2007 saving the first 48 matrix rows for later Mon Sep 10 17:27:10 2007 matrix is 42339 x 42451 with weight 1055687 (avg 24.87/col) Mon Sep 10 17:27:10 2007 matrix includes 64 packed rows Mon Sep 10 17:27:10 2007 commencing Lanczos iteration Mon Sep 10 17:29:38 2007 lanczos halted after 670 iterations Mon Sep 10 17:29:39 2007 recovered 17 nontrivial dependencies Mon Sep 10 17:29:40 2007 prp35 factor: 64819024777953578883539736640240237 Mon Sep 10 17:29:40 2007 prp50 factor: 48851826656369687093848975611401730998510732736463 Mon Sep 10 17:29:40 2007 elapsed time 00:42:43

4·10¹²³+7 = 4(0)₁₂₂7_<124> = 67 · 79 · 1459 · 2333 · 19949 · 33829 · 46451 · C100
C100 = P45 · P55
P45 = 893003465557677469001745507020861686789619767_<45>
P55 = 7931029477391238937468273562091619341494204808802031281_<55>

Number: 40007_123 N=7082436808750471977331869139572712189502812999808595720773130522724928764839469912722939255229931527 ( 100 digits) SNFS difficulty: 123 digits. Divisors found: r1=893003465557677469001745507020861686789619767 (pp45) r2=7931029477391238937468273562091619341494204808802031281 (pp55) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.59 hours. Scaled time: 1.77 units (timescale=0.683). Factorization parameters were as follows: name: 40007_123 n: 7082436808750471977331869139572712189502812999808595720773130522724928764839469912722939255229931527 m: 2000000000000000000000000 c5: 125 c0: 7 skew: 0.56 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:63758, largePrimes:2177651 encountered Relations: rels:2321280, finalFF:137515 Max relations in full relation-set: 0 Initial matrix: 112921 x 137515 with sparse part having weight 6377289. Pruned matrix : 100907 x 101535 with weight 4197773. Total sieving time: 2.36 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.12 hours. Time per square root: 0.04 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: 2.59 hours. --------- CPU info (if available) ----------

4·10¹²⁴+7 = 4(0)₁₂₃7_<125> = 11³ · 29 · 709 · 1801 · 2531 · 260722306516963_<15> · C97
C97 = P47 · P50
P47 = 67816150798627989304720548529530399180885482189_<47>
P50 = 18135123580998002481347196781299085919725495181681_<50>

Number: 40007_124 N=1229854275520714967260471838947950713893193162791736456300050444358471249630604163174163844579709 ( 97 digits) SNFS difficulty: 125 digits. Divisors found: r1=67816150798627989304720548529530399180885482189 (pp47) r2=18135123580998002481347196781299085919725495181681 (pp50) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.58 hours. Scaled time: 1.76 units (timescale=0.683). Factorization parameters were as follows: name: 40007_124 n: 1229854275520714967260471838947950713893193162791736456300050444358471249630604163174163844579709 m: 10000000000000000000000000 c5: 2 c0: 35 skew: 1.77 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:63938, largePrimes:2187471 encountered Relations: rels:2353021, finalFF:136777 Max relations in full relation-set: 0 Initial matrix: 113101 x 136777 with sparse part having weight 5875625. Pruned matrix : 100625 x 101254 with weight 3925534. Total sieving time: 2.35 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Time per square root: 0.04 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: 2.58 hours. --------- CPU info (if available) ----------

Sep 10, 2007

The factor table of 400...007 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.

Sep 9, 2007 (3rd)

By Robert Backstrom / GGNFS
3·10¹⁴⁴+7 = 3(0)₁₄₃7_<145> = 23 · 459383 · 128248879471_<12> · 1352119565902402853_<19> · C109
C109 = P42 · P67
P42 = 412360496428279684134266762455314955302583_<42>
P67 = 3970752049300281989132003305040428926587105565745390502436467127587_<67>

Number: n N=1637381286243073167428156705928812402202347963241767077546317363263128053960163775922772278248987696451657221 ( 109 digits) SNFS difficulty: 145 digits. Divisors found: r1=412360496428279684134266762455314955302583 (pp42) r2=3970752049300281989132003305040428926587105565745390502436467127587 (pp67) Version: GGNFS-0.77.1-20051202-athlon Total time: 13.30 hours. Scaled time: 15.91 units (timescale=1.196). Factorization parameters were as follows: name: KA_3_0_143_7 n: 1637381286243073167428156705928812402202347963241767077546317363263128053960163775922772278248987696451657221 type: snfs skew: 1.00 deg: 5 c5: 3 c0: 70 m: 100000000000000000000000000000 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, 1600001) Primes: RFBsize:148933, AFBsize:148155, largePrimes:6391676 encountered Relations: rels:5742559, finalFF:361324 Max relations in full relation-set: 28 Initial matrix: 297153 x 361324 with sparse part having weight 25349389. Pruned matrix : 259545 x 261094 with weight 15462821. Total sieving time: 11.30 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.71 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 13.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Sep 9, 2007 (2nd)

By Yousuke Koide
10⁹¹¹+1 is divisible by 12555609937128249776670687863910703_<35>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 9, 2007

By Robert Backstrom / GGNFS
(16·10¹⁸¹-61)/9 = 1(7)₁₈₀1_<182> = 11 · C181
C181 = P84 · P97
P84 = 875423954337579283724570530051042761164622675183831303860786988601476587061520145977_<84>
P97 = 1846147353123941432037361969644146179225690892776532016346590270070332318078159872250761970493993_<97>

Number: n N=1616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161 ( 181 digits) SNFS difficulty: 182 digits. Divisors found: r1=875423954337579283724570530051042761164622675183831303860786988601476587061520145977 (pp84) r2=1846147353123941432037361969644146179225690892776532016346590270070332318078159872250761970493993 (pp97) Version: GGNFS-0.77.1-20051202-athlon Total time: 455.66 hours. Scaled time: 540.87 units (timescale=1.187). Factorization parameters were as follows: name: KA_1_7_180_1 n: 1616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161 type: snfs skew: 1.65 deg: 5 c5: 5 c0: -61 m: 2000000000000000000000000000000000000 rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 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, 5400001) Primes: RFBsize:283146, AFBsize:283778, largePrimes:8451586 encountered Relations: rels:8040019, finalFF:636287 Max relations in full relation-set: 28 Initial matrix: 566989 x 636287 with sparse part having weight 69987297. Pruned matrix : 537909 x 540807 with weight 56556721. Total sieving time: 440.13 hours. Total relation processing time: 0.50 hours. Matrix solve time: 14.43 hours. Total square root time: 0.60 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.6,2.6,100000 total time: 455.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+

Sep 7, 2007 (5th)

GMP-ECM 6.1.3 has been released.

Sep 7, 2007 (4th)

By Sinkiti Sibata / GGNFS
3·10¹⁴⁰+7 = 3(0)₁₃₉7_<141> = 886591 · 21345509 · C128
C128 = P57 · P71
P57 = 870020740547606992047908247418054629224598409723907992361_<57>
P71 = 18220563960260903608607526139448840316782587407515464316476336274810173_<71>

Number: 30007_140 N=15852268549901230174324386508028804607528286278559127718419294725472196231167351989448701028316117068813288359277306912809088453 ( 128 digits) SNFS difficulty: 140 digits. Divisors found: r1=870020740547606992047908247418054629224598409723907992361 (pp57) r2=18220563960260903608607526139448840316782587407515464316476336274810173 (pp71) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 12.05 hours. Scaled time: 8.18 units (timescale=0.679). Factorization parameters were as follows: name: 30007_140 n: 15852268549901230174324386508028804607528286278559127718419294725472196231167351989448701028316117068813288359277306912809088453 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, 1675001) Primes: RFBsize:78498, AFBsize:63643, largePrimes:1566102 encountered Relations: rels:1559976, finalFF:160050 Max relations in full relation-set: 0 Initial matrix: 142206 x 160050 with sparse part having weight 15608362. Pruned matrix : 137606 x 138381 with weight 12130130. Total sieving time: 11.40 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.49 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: 12.05 hours. --------- CPU info (if available) ----------

Sep 7, 2007 (3rd)

By Shaopu Lin
10⁶¹⁰+1 is divisible by 27186363592392725942593454290345801336551729326489701011779461_<62>, cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 7, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM
3·10¹⁷¹+7 = 3(0)₁₇₀7_<172> = C172
C172 = P44 · C128
P44 = 31620332097111024989233352721851562907652707_<44>
C128 = [94875663885708949340722098875716958576811202800602452263648706419261724778781975587671373398601569684090092604704674588003973901_<128>]

Sep 7, 2007

By Sinkiti Sibata / GGNFS
3·10¹³⁸+7 = 3(0)₁₃₇7_<139> = 31 · 30347 · C133
C133 = P35 · P40 · P59
P35 = 27582727203473715137972750799973321_<35>
P40 = 9338357328303256578758498008894337760073_<40>
P59 = 12380440690635148293553334360514326357608119969517531812347_<59>

Number: 30007_138 N=3188921262345111436853512649919160845999551425075763454324549272553911371374329396432872675940758346735660749800426677664901775910251 ( 133 digits) SNFS difficulty: 138 digits. Divisors found: r1=27582727203473715137972750799973321 (pp35) r2=9338357328303256578758498008894337760073 (pp40) r3=12380440690635148293553334360514326357608119969517531812347 (pp59) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 11.09 hours. Scaled time: 7.53 units (timescale=0.679). Factorization parameters were as follows: name: 30007_138 n: 3188921262345111436853512649919160845999551425075763454324549272553911371374329396432872675940758346735660749800426677664901775910251 m: 1000000000000000000000000000 c5: 3000 c0: 7 skew: 0.3 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, 1525001) Primes: RFBsize:78498, AFBsize:63898, largePrimes:1530665 encountered Relations: rels:1508359, finalFF:159826 Max relations in full relation-set: 0 Initial matrix: 142463 x 159826 with sparse part having weight 16585980. Pruned matrix : 138060 x 138836 with weight 12364485. Total sieving time: 10.41 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.52 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 11.09 hours. --------- CPU info (if available) ----------

Sep 6, 2007

By JMB / GGNFS
3·10¹⁷⁴+7 = 3(0)₁₇₃7_<175> = 2131 · 2539 · 388785044783_<12> · 372247744413533552867_<21> · 3918018457203894704610101_<25> · C111
C111 = P41 · P71
P41 = 83101205384307732797112639371594904845329_<41>
P71 = 11766835380003014836384610732539311187782328395943642994305646727529367_<71>

Number: N N=977838203636969263622248987068537357449295333609103753437784788553386921946103919242214810477100330081440276743 ( 111 digits) Divisors found: r1=83101205384307732797112639371594904845329 (pp41) r2=11766835380003014836384610732539311187782328395943642994305646727529367 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 48.39 hours. Scaled time: 43.21 units (timescale=0.893). Factorization parameters were as follows: name: N n: 977838203636969263622248987068537357449295333609103753437784788553386921946103919242214810477100330081440276743 skew: 37355.45 # norm 3.46e+15 c5: 34020 c4: -62247927 c3: 40964358765630 c2: -919130756124140464 c1: -117696980178055287871024 c0: -943686829374413022658503360 # alpha -6.74 Y1: 512727852197 Y0: -1957521676766462803349 # Murphy_E 8.69e-10 # M 429058690311523254003492787243369289356028090221678835208754814859752251708490910300982484190538642312749052680 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 10000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1600000, 1900001) Relations: rels:7170449, finalFF:547721 Initial matrix: 460925 x 547721 with sparse part having weight 44666784. Pruned matrix : 422725 x 425093 with weight 25906024. Total sieving time: 40.38 hours. Total relation processing time: 0.41 hours. Matrix solve time: 7.33 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,10000 total time: 48.39 hours. --------- CPU info (if available) ----------

Sep 5, 2007 (3rd)

By Sinkiti Sibata / GGNFS
3·10¹⁵²+7 = 3(0)₁₅₁7_<153> = 8347351 · 7811046197_<10> · 858719673857_<12> · 250559653015574120385408539_<27> · C98
C98 = P39 · P59
P39 = 577938539278524803843369748270872920429_<39>
P59 = 37001485905141343750684997572615954124281964070904019247443_<59>

Number: 30007_152 N=21384584715152312399410371055118338529381577034286595544703207108885189504169973874072912200713047 ( 98 digits) SNFS difficulty: 152 digits. Divisors found: r1=577938539278524803843369748270872920429 (pp39) r2=37001485905141343750684997572615954124281964070904019247443 (pp59) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 36.57 hours. Scaled time: 24.97 units (timescale=0.683). Factorization parameters were as follows: name: 30007_152 n: 21384584715152312399410371055118338529381577034286595544703207108885189504169973874072912200713047 m: 1000000000000000000000000000000 c5: 300 c0: 7 skew: 0.47 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 4000000 ) Primes: RFBsize:176302, AFBsize:176433, largePrimes:5580476 encountered Relations: rels:5520272, finalFF:399263 Max relations in full relation-set: 0 Initial matrix: 352801 x 399263 with sparse part having weight 25768097. Pruned matrix : 328424 x 330252 with weight 19913239. Total sieving time: 33.78 hours. Total relation processing time: 0.24 hours. Matrix solve time: 2.40 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 36.57 hours. --------- CPU info (if available) ----------

Sep 5, 2007 (2nd)

By Jo Yeong Uk / GGNFS
3·10¹³³+7 = 3(0)₁₃₂7_<134> = 37 · 29581 · C128
C128 = P38 · P90
P38 = 71206879090633339569010774993897538969_<38>
P90 = 384932630573456592303493441248187029453637827755687637553671267379325800269120529793395199_<90>

Number: 30007_133 N=27409851283283553997863858923322768358433143261242378919266110368507177269558527798614340651459072066894655718562956316920009831 ( 128 digits) SNFS difficulty: 134 digits. Divisors found: r1=71206879090633339569010774993897538969 (pp38) r2=384932630573456592303493441248187029453637827755687637553671267379325800269120529793395199 (pp90) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.83 hours. Scaled time: 6.02 units (timescale=2.128). Factorization parameters were as follows: n: 27409851283283553997863858923322768358433143261242378919266110368507177269558527798614340651459072066894655718562956316920009831 m: 200000000000000000000000000 c5: 375 c0: 28 skew: 0.6 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, 1200001) Primes: RFBsize:107126, AFBsize:107333, largePrimes:1824277 encountered Relations: rels:1912873, finalFF:260803 Max relations in full relation-set: 28 Initial matrix: 214526 x 260803 with sparse part having weight 13896029. Pruned matrix : 187120 x 188256 with weight 7957202. Total sieving time: 2.68 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407685) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130) Total of 4 processors activated (19246.11 BogoMIPS).

3·10¹³⁶+7 = 3(0)₁₃₅7_<137> = 37 · C135
C135 = P46 · P90
P46 = 6556535936327394866605979149660371778651962509_<46>
P90 = 123664511059628497811157288760274150729201758246527989892496823924203364385516946923141479_<90>

Number: 30007_136 N=810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811 ( 135 digits) SNFS difficulty: 136 digits. Divisors found: r1=6556535936327394866605979149660371778651962509 (pp46) r2=123664511059628497811157288760274150729201758246527989892496823924203364385516946923141479 (pp90) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.25 hours. Scaled time: 9.13 units (timescale=2.146). Factorization parameters were as follows: n: 810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811 m: 1000000000000000000000000000 c5: 30 c0: 7 skew: 0.75 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, 1500001) Primes: RFBsize:107126, AFBsize:106593, largePrimes:1867694 encountered Relations: rels:1959724, finalFF:256837 Max relations in full relation-set: 28 Initial matrix: 213786 x 256837 with sparse part having weight 17263562. Pruned matrix : 196794 x 197926 with weight 10886320. Total sieving time: 4.07 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000 total time: 4.25 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407685) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 5, 2007

By JMB
3·10¹⁶⁴+7 = 3(0)₁₆₃7_<165> = 93463 · 102367 · 5561993 · 2697746404826036755483_<22> · 4075016412566873951820653_<25> · C102
C102 = P38 · P64
P38 = 85121969595848139659769186241637634013_<38>
P64 = 6024471790877011640388025283913980838326383051453673075231227837_<64>

Sep 4, 2007 (4th)

By Yousuke Koide
(10¹²⁰⁵-1)/9 is divisible by 1231304918915627269216328559032281_<34>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 4, 2007 (3rd)

By Jo Yeong Uk / GGNFS
3·10¹³²+7 = 3(0)₁₃₁7_<133> = C133
C133 = P44 · P90
P44 = 20590611374091488546520676374415000816224551_<44>
P90 = 145697470827641601340741249542086188044830839410971692164392935223681417160709307626970657_<90>

Number: 30007_132 N=3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 ( 133 digits) SNFS difficulty: 132 digits. Divisors found: r1=20590611374091488546520676374415000816224551 (pp44) r2=145697470827641601340741249542086188044830839410971692164392935223681417160709307626970657 (pp90) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.88 hours. Scaled time: 6.17 units (timescale=2.143). Factorization parameters were as follows: n: 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 m: 100000000000000000000000000 c5: 300 c0: 7 skew: 0.47 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:78821, largePrimes:1567294 encountered Relations: rels:1589863, finalFF:196603 Max relations in full relation-set: 28 Initial matrix: 157385 x 196603 with sparse part having weight 11951565. Pruned matrix : 143201 x 144051 with weight 6940341. Total sieving time: 2.78 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.88 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: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407685) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130) Total of 4 processors activated (19246.11 BogoMIPS).

Sep 4, 2007 (2nd)

By JMB
3·10¹⁹⁴+7 = 3(0)₁₉₃7_<195> = 1734986326637479007_<19> · 431168604266382453431_<21> · 248787236500857218390561_<24> · 439982137238951968875436976379228563_<36> · C97
C97 = P40 · P58
P40 = 2181760916727482904956744337987008327579_<40>
P58 = 1679220662527382761557265816940310453170712534544646764943_<58>

Sep 4, 2007

By Sinkiti Sibata / Msieve, GGNFS
3·10¹²⁸+7 = 3(0)₁₂₇7_<129> = 2685101 · 33851255863_<11> · 12978558218195034379386149_<26> · C87
C87 = P36 · P51
P36 = 275313088291577407642928246977003907_<36>
P51 = 923703385381580265251720036954725538332661715176123_<51>

Mon Sep 03 18:48:38 2007 Mon Sep 03 18:48:38 2007 Msieve v. 1.26 Mon Sep 03 18:48:38 2007 random seeds: 07d98b2f 62ae921d Mon Sep 03 18:48:38 2007 factoring 254307631694787959686868018280051591889464233755615179663625686766286102906651364112561 (87 digits) Mon Sep 03 18:48:39 2007 commencing quadratic sieve (87-digit input) Mon Sep 03 18:48:39 2007 using multiplier of 1 Mon Sep 03 18:48:39 2007 using 64kb Pentium 2 sieve core Mon Sep 03 18:48:39 2007 sieve interval: 10 blocks of size 65536 Mon Sep 03 18:48:39 2007 processing polynomials in batches of 11 Mon Sep 03 18:48:39 2007 using a sieve bound of 1489667 (56613 primes) Mon Sep 03 18:48:39 2007 using large prime bound of 119173360 (26 bits) Mon Sep 03 18:48:40 2007 using double large prime bound of 344447000754720 (42-49 bits) Mon Sep 03 18:48:40 2007 using trial factoring cutoff of 49 bits Mon Sep 03 18:48:40 2007 polynomial 'A' values have 11 factors Tue Sep 04 00:36:23 2007 56728 relations (16053 full + 40675 combined from 592602 partial), need 56709 Tue Sep 04 00:36:31 2007 begin with 608655 relations Tue Sep 04 00:36:33 2007 reduce to 134614 relations in 8 passes Tue Sep 04 00:36:33 2007 attempting to read 134614 relations Tue Sep 04 00:36:45 2007 recovered 134614 relations Tue Sep 04 00:36:45 2007 recovered 109845 polynomials Tue Sep 04 00:36:57 2007 attempting to build 56728 cycles Tue Sep 04 00:36:57 2007 found 56728 cycles in 5 passes Tue Sep 04 00:37:01 2007 distribution of cycle lengths: Tue Sep 04 00:37:01 2007 length 1 : 16053 Tue Sep 04 00:37:01 2007 length 2 : 11398 Tue Sep 04 00:37:01 2007 length 3 : 9968 Tue Sep 04 00:37:01 2007 length 4 : 7465 Tue Sep 04 00:37:01 2007 length 5 : 4987 Tue Sep 04 00:37:01 2007 length 6 : 3064 Tue Sep 04 00:37:01 2007 length 7 : 1814 Tue Sep 04 00:37:01 2007 length 9+: 1979 Tue Sep 04 00:37:01 2007 largest cycle: 20 relations Tue Sep 04 00:37:03 2007 matrix is 56613 x 56728 with weight 3003083 (avg 52.94/col) Tue Sep 04 00:37:07 2007 filtering completed in 3 passes Tue Sep 04 00:37:07 2007 matrix is 52023 x 52087 with weight 2793711 (avg 53.64/col) Tue Sep 04 00:37:10 2007 saving the first 48 matrix rows for later Tue Sep 04 00:37:10 2007 matrix is 51975 x 52087 with weight 2063890 (avg 39.62/col) Tue Sep 04 00:37:10 2007 matrix includes 64 packed rows Tue Sep 04 00:37:10 2007 using block size 10922 for processor cache size 256 kB Tue Sep 04 00:37:11 2007 commencing Lanczos iteration Tue Sep 04 00:40:42 2007 lanczos halted after 824 iterations Tue Sep 04 00:40:43 2007 recovered 15 nontrivial dependencies Tue Sep 04 00:40:47 2007 prp36 factor: 275313088291577407642928246977003907 Tue Sep 04 00:40:47 2007 prp51 factor: 923703385381580265251720036954725538332661715176123 Tue Sep 04 00:40:47 2007 elapsed time 05:52:09

3·10¹³¹+7 = 3(0)₁₃₀7_<132> = 61 · 3889 · 16673127629_<11> · 654750113451724387_<18> · C99
C99 = P45 · P54
P45 = 367843730195277468720927798645873350770134361_<45>
P54 = 314917983297778113935616240983926140815612293301748461_<54>

Number: 30007_131 N=115840605681828788775531586500134003303645081903753785388762305681265629442829309689100981194968421 ( 99 digits) SNFS difficulty: 131 digits. Divisors found: r1=367843730195277468720927798645873350770134361 (pp45) r2=314917983297778113935616240983926140815612293301748461 (pp54) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 6.51 hours. Scaled time: 4.44 units (timescale=0.682). Factorization parameters were as follows: name: 30007_131 n: 115840605681828788775531586500134003303645081903753785388762305681265629442829309689100981194968421 m: 100000000000000000000000000 c5: 30 c0: 7 skew: 0.75 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, 1100001) Primes: RFBsize:63951, AFBsize:63528, largePrimes:1493297 encountered Relations: rels:1473265, finalFF:143512 Max relations in full relation-set: 0 Initial matrix: 127546 x 143512 with sparse part having weight 10871550. Pruned matrix : 123368 x 124069 with weight 8318483. Total sieving time: 6.09 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.28 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.51 hours. --------- CPU info (if available) ----------

Sep 3, 2007 (4th)

By Sinkiti Sibata / GGNFS
3·10¹¹⁶+7 = 3(0)₁₁₅7_<117> = 941 · 7229 · 1005413 · 1768241 · C98
C98 = P45 · P53
P45 = 793456171721645674090119834605962552118405123_<45>
P53 = 31263997790510739426533319802087948467956549868101057_<53>

Number: 30007_116 N=24806611999572640200041003401784198951563928958349169644810919349055407530420374739405603430515011 ( 98 digits) SNFS difficulty: 116 digits. Divisors found: r1=793456171721645674090119834605962552118405123 (pp45) r2=31263997790510739426533319802087948467956549868101057 (pp53) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 2.15 hours. Scaled time: 1.47 units (timescale=0.683). Factorization parameters were as follows: name: 30007_116 n: 24806611999572640200041003401784198951563928958349169644810919349055407530420374739405603430515011 m: 100000000000000000000000 c5: 30 c0: 7 skew: 0.75 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:63528, largePrimes:2164983 encountered Relations: rels:2305072, finalFF:137525 Max relations in full relation-set: 0 Initial matrix: 112693 x 137525 with sparse part having weight 6350152. Pruned matrix : 99939 x 100566 with weight 4135837. Total sieving time: 1.92 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.15 hours. --------- CPU info (if available) ----------

Sep 3, 2007 (3rd)

By Yousuke Koide
(10¹¹⁶⁵-1)/9 is divisible by 8789828644372924439634809703641_<31>
(10¹⁵⁰³-1)/9 is divisible by 3641337799926827172864056731857529_<34>
10⁶³⁶+1 is divisible by 706882718657645277228087439919935993_<36>, cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 3, 2007 (2nd)

By Kurt Beschorner
10⁶³⁵+1 is divisible by 202367638102311029520083171135894724910091_<42>, cofactor is prime.
Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Sep 3, 2007

The factor table of 300...007 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.

Sep 2, 2007 (3rd)

By R.D. Silverman
(10³⁴⁵-1)/9 is divisible by 35645906496364306434849378023333297827811383782580351_<53>, cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 2, 2007 (2nd)

By Yousuke Koide
(10¹⁴⁰¹-1)/9 is divisible by 619629939179595688144939635183289_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 2, 2007

By Sinkiti Sibata / GGNFS
3·10¹⁵¹-7 = 2(9)₁₅₀3_<152> = 19 · 156901 · C146
C146 = P64 · P82
P64 = 2776542823659779412773229802771285257042021400690501832194379669_<64>
P82 = 3624412053738393293775064001860434687254067055643958807515278373333482272091019563_<82>

Number: 29993_151 N=10063335277793338675846217477396910354803011889159741694310089600582868379289790176105012916290829047750190448620132238934440389665759736528464647 ( 146 digits) SNFS difficulty: 151 digits. Divisors found: r1=2776542823659779412773229802771285257042021400690501832194379669 (pp64) r2=3624412053738393293775064001860434687254067055643958807515278373333482272091019563 (pp82) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 37.52 hours. Scaled time: 25.63 units (timescale=0.683). Factorization parameters were as follows: name: 29993_151 n: 10063335277793338675846217477396910354803011889159741694310089600582868379289790176105012916290829047750190448620132238934440389665759736528464647 m: 1000000000000000000000000000000 c5: 30 c0: -7 skew: 0.75 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2200001) Primes: RFBsize:176302, AFBsize:175908, largePrimes:5608103 encountered Relations: rels:5543957, finalFF:398769 Max relations in full relation-set: 0 Initial matrix: 352277 x 398769 with sparse part having weight 27944746. Pruned matrix : 328978 x 330803 with weight 21639137. Total sieving time: 33.50 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.62 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 37.52 hours. --------- CPU info (if available) ----------