News and updates, July 2009

Jul 31, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Jul 31, 2009
(28·10¹⁷¹+53)/9 = 3(1)₁₇₀7_<172> = 3² · 23 · 70791068989559_<14> · 7208176534331825153_<19> · C137
C137 = P38 · P99
P38 = 57051566739178370843228849594143099081_<38>
P99 = 516266227940538332202888300931167534392439128247533459514322573271390395942085268059433207374745613_<99>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1536419490 Step 1 took 42867ms Step 2 took 14840ms ********** Factor found in step 2: 57051566739178370843228849594143099081 Found probable prime factor of 38 digits: 57051566739178370843228849594143099081 Probable prime cofactor 516266227940538332202888300931167534392439128247533459514322573271390395942085268059433207374745613 has 99 digits

Jul 31, 2009

By Justin Card / ggnfs, msieve / Jul 31, 2009
(8·10¹⁸⁴+7)/3 = 2(6)₁₈₃9_<185> = 23 · 3331 · 9974131 · 44534953 · 560165357 · 10490142307214064479640205122143_<32> · C126
C126 = P52 · P74
P52 = 1840576491455917515487089567659492600807511867287417_<52>
P74 = 72450051758129853557618859992660448536058606321454023390500476783160491073_<74>

Number: 26669_184 N=133349862070778274177903595909790086247733391434306851920325896211332328606192378743990711854039144978397117642580702153728441 ( 126 digits) Divisors found: r1=1840576491455917515487089567659492600807511867287417 (pp52) r2=72450051758129853557618859992660448536058606321454023390500476783160491073 (pp74) Version: Msieve-1.40 Total time: 62.14 hours. Scaled time: 124.59 units (timescale=2.005). Factorization parameters were as follows: # Murphy_E = 1.553772e-10, selected by Jeff Gilchrist n: 133349862070778274177903595909790086247733391434306851920325896211332328606192378743990711854039144978397117642580702153728441 Y0: -1383792360506376182622027 Y1: 36174105794699 c0: -25094862387985409537622023408320 c1: 497422368223576071131877836 c2: -3851721490457031123500 c3: 1380029445101797 c4: 29089581582 c5: 26280 skew: 376543.69 type: gnfs # selected mechanically rlim: 7200000 alim: 7200000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved algebraic special-q in [3600000, 6800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 971988 x 972236 Total sieving time: 57.96 hours. Total relation processing time: 0.24 hours. Matrix solve time: 3.70 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,7200000,7200000,27,27,53,53,2.5,2.5,100000 total time: 62.14 hours. --------- CPU info (if available) ---------- [ 0.138880] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.231790] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init) [ 0.084029] Calibrating delay using timer specific routine.. 4004.53 BogoMIPS (lpj=8009076) [ 0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000316) [ 0.231806] Total of 2 processors activated (8004.69 BogoMIPS).

Jul 30, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Jul 30, 2009
(28·10¹⁷²+71)/9 = 3(1)₁₇₁9_<173> = 3 · 11² · 19 · 199 · 2063 · 1071859429_<10> · 987784778531_<12> · 3787644855281754211_<19> · C124
C124 = P39 · P41 · P46
P39 = 145981945043538922447045171242551767513_<39>
P41 = 12106747692684234696061311650272036055929_<41>
P46 = 1550268564261924241434791929036957421411556307_<46>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1284649349 Step 1 took 34253ms Step 2 took 4413ms ********** Factor found in step 2: 145981945043538922447045171242551767513 Found probable prime factor of 39 digits: 145981945043538922447045171242551767513 Composite cofactor 18768710363418952533350681677121336057034379650028828291507491066449182303657984694203 has 86 digits ----------------- Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3517402920 Step 1 took 20558ms Step 2 took 10567ms ********** Factor found in step 2: 12106747692684234696061311650272036055929 Found probable prime factor of 41 digits: 12106747692684234696061311650272036055929 Probable prime cofactor 1550268564261924241434791929036957421411556307 has 46 digits

Jul 30, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jul 30, 2009
(55·10¹⁸⁴+53)/9 = 6(1)₁₈₃7_<185> = 7 · 3701 · C181
C181 = P63 · P118
P63 = 299186033889093434494711100919736508233251687550293980333909521_<63>
P118 = 7884274535829624751955048946137314807144323255787431031881040268248974228611948641297326772368968198018694299874423311_<118>

Number: n N=2358864828467638518975995333736484776744166098394685263099205276995063539240788632844833871583398738221759026946814031385768754047597603393334276879264720388740923731466827927244031 ( 181 digits) SNFS difficulty: 186 digits. Divisors found: Thu Jul 30 08:47:27 2009 prp63 factor: 299186033889093434494711100919736508233251687550293980333909521 Thu Jul 30 08:47:27 2009 prp118 factor: 7884274535829624751955048946137314807144323255787431031881040268248974228611948641297326772368968198018694299874423311 Thu Jul 30 08:47:27 2009 elapsed time 02:59:55 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 197.17 hours. Scaled time: 513.83 units (timescale=2.606). Factorization parameters were as follows: name: KA_6_1_183_7 n: 2358864828467638518975995333736484776744166098394685263099205276995063539240788632844833871583398738221759026946814031385768754047597603393334276879264720388740923731466827927244031 m: 10000000000000000000000000000000000000 deg: 5 c5: 11 c0: 106 skew: 1.57 type: snfs lss: 1 rlim: 8800000 alim: 8800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8800000/8800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4400000, 7801231) Primes: RFBsize:590006, AFBsize:590541, largePrimes:21231701 encountered Relations: rels:21472492, finalFF:1016701 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2220134 hash collisions in 23704512 relations Msieve: matrix is 1468917 x 1469164 (396.3 MB) Total sieving time: 196.53 hours. Total relation processing time: 0.65 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,56,56,2.5,2.5,100000 total time: 197.17 hours. --------- CPU info (if available) ----------

Jul 30, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jul 30, 2009
(38·10¹⁶⁸+7)/9 = 4(2)₁₆₇3_<169> = 41 · 3109 · 352271 · 78050827122051106417692700691_<29> · C130
C130 = P62 · P68
P62 = 44517847976265306807164707134605905018604880543571240978940213_<62>
P68 = 27061255665644746692439217262915386433661197680520042446537611351019_<68>

Number: 42223_168 N=1204708865770021054615557951951723014686056920324982297118240921405162844773742860832148665618930386587825784814043462037757627047 ( 130 digits) SNFS difficulty: 171 digits. Divisors found: r1=44517847976265306807164707134605905018604880543571240978940213 r2=27061255665644746692439217262915386433661197680520042446537611351019 Version: Total time: 39.74 hours. Scaled time: 95.03 units (timescale=2.391). Factorization parameters were as follows: n: 1204708865770021054615557951951723014686056920324982297118240921405162844773742860832148665618930386587825784814043462037757627047 m: 10000000000000000000000000000000000 deg: 5 c5: 19 c0: 350 skew: 1.79 type: snfs lss: 1 rlim: 5800000 alim: 5800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2900000, 6000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11347850 Max relations in full relation-set: Initial matrix: Pruned matrix : 962055 x 962303 Total sieving time: 35.98 hours. Total relation processing time: 1.72 hours. Matrix solve time: 1.93 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000 total time: 39.74 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 29, 2009 (3rd)

By Justin Card / GGNFS, Msieve / Jul 29, 2009
(25·10¹⁹³-61)/9 = 2(7)₁₉₂1_<194> = 3 · 7 · 73883 · 26925317 · 19159973142181_<14> · 284017799510891_<15> · 80485311297327121853982640517_<29> · C124
C124 = P54 · P71
P54 = 128613570680091058920064785055072809139946797083167593_<54>
P71 = 11803993992833193782465781270323656372348977417985328398765195618890491_<71>

Number: 27771_193 N=1518153815704622240936737904859078621016147552740776785285576396386699185397561525934124104891750356941221401004594467058163 ( 124 digits) Divisors found: r1=128613570680091058920064785055072809139946797083167593 (pp54) r2=11803993992833193782465781270323656372348977417985328398765195618890491 (pp71) Version: Msieve-1.40 Total time: 58.22 hours. Scaled time: 117.89 units (timescale=2.025). Factorization parameters were as follows: # Murphy_E = 1.861264e-10, selected by Jeff Gilchrist n: 1518153815704622240936737904859078621016147552740776785285576396386699185397561525934124104891750356941221401004594467058163 Y0: -609424693195493084629365 Y1: 14285840635807 c0: 449801078557326487786247371904 c1: 56040688801503068267930764 c2: 249106677690281349198 c3: -2249875713199399 c4: -3915672212 c5: 18060 skew: 221678.63 type: gnfs # selected mechanically rlim: 6400000 alim: 6400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 6400000/6400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [3200000, 6300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 884389 x 884637 Total sieving time: 54.32 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.21 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6400000,6400000,27,27,52,52,2.5,2.5,100000 total time: 58.22 hours. --------- CPU info (if available) ---------- [ 0.138880] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.231790] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init) [ 0.084029] Calibrating delay using timer specific routine.. 4004.53 BogoMIPS (lpj=8009076) [ 0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000316) [ 0.231806] Total of 2 processors activated (8004.69 BogoMIPS).

Jul 29, 2009 (2nd)

By matsui / Msieve / Jul 29, 2009
9·10¹⁸⁸-7 = 8(9)₁₈₇3_<189> = 6689591 · C183
C183 = P61 · P122
P61 = 2889983980206166400633343347830421444067318005274107662508507_<61>
P122 = 46552982294567003262611165131940242875979617104663519183548141215584144647077930746442394215984131576858766423362881560989_<122>

N=134537373062119941263972640479814087288744558523832025007208960906578593519394533985710038177221895927568666006636280155244169636080890446067629545662806590118887686855594011651833423 ( 183 digits) SNFS difficulty: 190 digits. Divisors found: r1=2889983980206166400633343347830421444067318005274107662508507 (pp61) r2=46552982294567003262611165131940242875979617104663519183548141215584144647077930746442394215984131576858766423362881560989 (pp122) Version: Msieve v. 1.42 Total time: 288.28 hours. Scaled time: 646.03 units (timescale=2.241). Factorization parameters were as follows: n: 134537373062119941263972640479814087288744558523832025007208960906578593519394533985710038177221895927568666006636280155244169636080890446067629545662806590118887686855594011651833423 m: 50000000000000000000000000000000000000 deg: 5 c5: 72 c0: -175 skew: 1.19 type: snfs lss: 1 rlim: 10400000 alim: 10400000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 10400000/10400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5200000, 9700001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2068834 x 2069058 Total sieving time: 279.68 hours. Total relation processing time: 0.16 hours. Matrix solve time: 7.81 hours. Time per square root: 0.62 hours. Prototype def-par.txt line would be: snfs,190.000,5,0,0,0,0,0,0,0,0,10400000,10400000,28,28,54,54,2.5,2.5,100000 total time: 288.28 hours.

Jul 29, 2009

By Andreas Tete / GMP-ECM / Jul 29, 2009
(31·10¹⁷⁸-13)/9 = 3(4)₁₇₇3_<179> = 3 · 1353967 · C172
C172 = P37 · P135
P37 = 9537440536427082503420258687477304493_<37>
P135 = 889115142825712264336270323676477942025280940056505408267252597985808653661232222615018940714817662000729558352000823164963884428325251_<135>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2445707087 Step 1 took 18922ms Step 2 took 7161ms ********** Factor found in step 2: 9537440536427082503420258687477304493 Found probable prime factor of 37 digits: 9537440536427082503420258687477304493 Probable prime cofactor 889115142825712264336270323676477942025280940056505408267252597985808653661232222615018940714817662000729558352000823164963884428325251

Jul 28, 2009

By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jul 28, 2009
(34·10¹⁶⁸+11)/9 = 3(7)₁₆₇9_<169> = 112010779 · 1237487765219969_<16> · 216088201207134256529_<21> · C126
C126 = P56 · P70
P56 = 21007045637904397929220783078171057473056938111949250991_<56>
P70 = 6003985612856955994763940375687682631208042011489199930435766202839511_<70>

Number: 37779_168 N=126125999778607480690246033713828018537651058546696590725316441020016541300976869122526673281587490530406309722393433830705401 ( 126 digits) SNFS difficulty: 171 digits. Divisors found: r1=21007045637904397929220783078171057473056938111949250991 r2=6003985612856955994763940375687682631208042011489199930435766202839511 Version: Total time: 32.90 hours. Scaled time: 78.31 units (timescale=2.380). Factorization parameters were as follows: n: 126125999778607480690246033713828018537651058546696590725316441020016541300976869122526673281587490530406309722393433830705401 m: 10000000000000000000000000000000000 deg: 5 c5: 17 c0: 550 skew: 2.00 type: snfs lss: 1 rlim: 5800000 alim: 5800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2900000, 5400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 10879636 Max relations in full relation-set: Initial matrix: Pruned matrix : 958587 x 958835 Total sieving time: 29.47 hours. Total relation processing time: 1.34 hours. Matrix solve time: 1.97 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000 total time: 32.90 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 27, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jul 27, 2009
(31·10¹⁸³-13)/9 = 3(4)₁₈₂3_<184> = 11 · 6271 · C179
C179 = P90 · P90
P90 = 100207618408818769953369343053477573985594867867454028216858231374779324945945217331537721_<90>
P90 = 498297786397843298786484049159684239369074605709847311257469554644236411505194367194905543_<90>

Number: n N=49933234433314165414308932089190421194886192494229489923956516206556072606144365034494200496432995237013734860968157093177026202062081507146090147206396608405857329473977536487503 ( 179 digits) SNFS difficulty: 185 digits. Divisors found: Mon Jul 27 21:53:00 2009 prp90 factor: 100207618408818769953369343053477573985594867867454028216858231374779324945945217331537721 Mon Jul 27 21:53:00 2009 prp90 factor: 498297786397843298786484049159684239369074605709847311257469554644236411505194367194905543 Mon Jul 27 21:53:00 2009 elapsed time 03:09:48 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 179.90 hours. Scaled time: 474.76 units (timescale=2.639). Factorization parameters were as follows: name: KA_3_4_182_3 n: 49933234433314165414308932089190421194886192494229489923956516206556072606144365034494200496432995237013734860968157093177026202062081507146090147206396608405857329473977536487503 m: 5000000000000000000000000000000000000 deg: 5 c5: 248 c0: -325 skew: 1.06 type: snfs lss: 1 rlim: 8800000 alim: 8800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8800000/8800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4400000, 7600193) Primes: RFBsize:590006, AFBsize:590071, largePrimes:20924935 encountered Relations: rels:20804592, finalFF:1225824 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1977048 hash collisions in 22136093 relations Msieve: matrix is 1499067 x 1499315 (407.0 MB) Total sieving time: 179.24 hours. Total relation processing time: 0.66 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,56,56,2.5,2.5,100000 total time: 179.90 hours. --------- CPU info (if available) ----------

Two P90s are the second largest nice split so far in our tables. Congratulations!
(2·10²⁰⁹+1)/3 = (6)₂₀₈7_<209> = 409 · C207
C207 = P88 · P119
P88 = 2052187685408499669360164389950216452837367795140694640921654294506879070840299204220861_<88>
P119 = 79427035920269184206421164842740391735969944599658873023811379866142644488461289389623308760621268628589866983939306783_<119>

Number: n N=162999185004074979625101874490627546862265688671556642216788916055419722901385493072534637326813365933170334148329258353708231458842705786471067644661776691116544417277913610431947840260798696006519967400163 ( 207 digits) SNFS difficulty: 210 digits. Divisors found: Mon Jul 27 22:21:24 2009 prp88 factor: 2052187685408499669360164389950216452837367795140694640921654294506879070840299204220861 Mon Jul 27 22:21:24 2009 prp119 factor: 79427035920269184206421164842740391735969944599658873023811379866142644488461289389623308760621268628589866983939306783 Mon Jul 27 22:21:24 2009 elapsed time 20:52:07 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20050930-k8 Total time: 48.98 hours. Scaled time: 98.64 units (timescale=2.014). Factorization parameters were as follows: name: KA_6_208_7 n: 162999185004074979625101874490627546862265688671556642216788916055419722901385493072534637326813365933170334148329258353708231458842705786471067644661776691116544417277913610431947840260798696006519967400163 m: 1000000000000000000000000000000000000000000 deg: 5 c5: 1 c0: 5 skew: 1.38 type: snfs lss: 1 rlim: 22000000 alim: 22000000 rlim: 25000000 alim: 25000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 25000000/25000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [12500000, 23001929) Primes: RFBsize:1565927, AFBsize:1565758, largePrimes:40927685 encountered Relations: rels:42499863, finalFF:3067740 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 6259415 hash collisions in 46321697 relations Msieve: matrix is 3453945 x 3454193 (931.6 MB) Total sieving time: 47.74 hours. Total relation processing time: 1.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,210,5,0,0,0,0,0,0,0,0,25000000,25000000,29,29,58,58,2.6,2.6,100000 total time: 48.98 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352036k/3407296k available (3118k kernel code, 53976k reserved, 1895k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.51 BogoMIPS (lpj=2830757) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455) Total of 4 processors activated (22644.23 BogoMIPS).

Jul 27, 2009 (3rd)

By Justin Card / cado-nfs for sieving, msieve 1.43 for postprocessing / Jul 27, 2009
(10¹⁸⁸+17)/9 = (1)₁₈₇3_<188> = 13 · 31 · 80423813 · 11725919509_<11> · C167
C167 = P69 · P99
P69 = 101101428297969763167582651911552568964064074821357008687845402353373_<69>
P99 = 289176891454586933473472026592329087156730099564830191435580236364586283574771523426365696790224631_<99>

sieve over 6 days, Sat Jul 25 19:12:35 2009 Sat Jul 25 19:12:35 2009 Sat Jul 25 19:12:35 2009 Msieve v. 1.43 Sat Jul 25 19:12:35 2009 random seeds: d9fcc312 d1ea6900 Sat Jul 25 19:12:35 2009 factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits) Sat Jul 25 19:12:39 2009 Sat Jul 25 19:12:39 2009 Sat Jul 25 19:12:39 2009 Msieve v. 1.43 Sat Jul 25 19:12:39 2009 random seeds: ed3f30ae 2d551ca1 Sat Jul 25 19:12:39 2009 factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits) Sat Jul 25 19:12:41 2009 searching for 15-digit factors Sat Jul 25 19:12:41 2009 commencing number field sieve (167-digit input) Sat Jul 25 19:12:41 2009 R0: -20000000000000000000000000000000000000 Sat Jul 25 19:12:41 2009 R1: 1 Sat Jul 25 19:12:41 2009 A0: 68 Sat Jul 25 19:12:41 2009 A1: 0 Sat Jul 25 19:12:41 2009 A2: 0 Sat Jul 25 19:12:41 2009 A3: 0 Sat Jul 25 19:12:41 2009 A4: 0 Sat Jul 25 19:12:41 2009 A5: 125 Sat Jul 25 19:12:41 2009 skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11 Sat Jul 25 19:12:41 2009 Sat Jul 25 19:12:41 2009 commencing relation filtering Sat Jul 25 19:12:41 2009 estimated available RAM is 972.2 MB Sat Jul 25 19:12:41 2009 commencing duplicate removal, pass 1 Sat Jul 25 19:15:39 2009 found 151952 hash collisions in 18139084 relations Sat Jul 25 19:17:00 2009 added 675602 free relations Sat Jul 25 19:17:00 2009 commencing duplicate removal, pass 2 Sat Jul 25 19:17:23 2009 found 0 duplicates and 18814686 unique relations Sat Jul 25 19:17:23 2009 memory use: 132.2 MB Sat Jul 25 19:17:23 2009 reading ideals above 10551296 Sat Jul 25 19:17:30 2009 commencing singleton removal, initial pass Sat Jul 25 19:21:37 2009 memory use: 298.4 MB Sat Jul 25 19:21:37 2009 reading all ideals from disk Sat Jul 25 19:21:41 2009 memory use: 369.4 MB Sat Jul 25 19:21:44 2009 commencing in-memory singleton removal Sat Jul 25 19:21:47 2009 begin with 18814686 relations and 19739995 unique ideals Sat Jul 25 19:22:13 2009 reduce to 7464939 relations and 5902802 ideals in 19 passes Sat Jul 25 19:22:13 2009 max relations containing the same ideal: 30 Sat Jul 25 19:22:14 2009 reading ideals above 100000 Sat Jul 25 19:22:14 2009 commencing singleton removal, initial pass Sat Jul 25 19:24:22 2009 memory use: 149.2 MB Sat Jul 25 19:24:22 2009 reading all ideals from disk Sat Jul 25 19:24:27 2009 memory use: 287.9 MB Sat Jul 25 19:24:29 2009 keeping 7293870 ideals with weight <= 200, target excess is 40024 Sat Jul 25 19:24:31 2009 commencing in-memory singleton removal Sat Jul 25 19:24:34 2009 begin with 7470460 relations and 7293870 unique ideals Sat Jul 25 19:24:51 2009 reduce to 7462644 relations and 7259412 ideals in 8 passes Sat Jul 25 19:24:51 2009 max relations containing the same ideal: 200 Sat Jul 25 19:25:02 2009 removing 783390 relations and 704988 ideals in 78402 cliques Sat Jul 25 19:25:02 2009 commencing in-memory singleton removal Sat Jul 25 19:25:04 2009 begin with 6679254 relations and 7259412 unique ideals Sat Jul 25 19:25:26 2009 reduce to 6620572 relations and 6494876 ideals in 11 passes Sat Jul 25 19:25:26 2009 max relations containing the same ideal: 190 Sat Jul 25 19:25:35 2009 removing 562841 relations and 484439 ideals in 78402 cliques Sat Jul 25 19:25:36 2009 commencing in-memory singleton removal Sat Jul 25 19:25:38 2009 begin with 6057731 relations and 6494876 unique ideals Sat Jul 25 19:25:52 2009 reduce to 6024322 relations and 5976634 ideals in 8 passes Sat Jul 25 19:25:52 2009 max relations containing the same ideal: 180 Sat Jul 25 19:26:03 2009 relations with 0 large ideals: 704 Sat Jul 25 19:26:03 2009 relations with 1 large ideals: 76 Sat Jul 25 19:26:03 2009 relations with 2 large ideals: 1129 Sat Jul 25 19:26:03 2009 relations with 3 large ideals: 14195 Sat Jul 25 19:26:03 2009 relations with 4 large ideals: 101657 Sat Jul 25 19:26:03 2009 relations with 5 large ideals: 427840 Sat Jul 25 19:26:03 2009 relations with 6 large ideals: 1150165 Sat Jul 25 19:26:03 2009 relations with 7+ large ideals: 4328556 Sat Jul 25 19:26:03 2009 commencing 2-way merge Sat Jul 25 19:26:15 2009 reduce to 3653878 relation sets and 3606190 unique ideals Sat Jul 25 19:26:15 2009 commencing full merge Sat Jul 25 19:28:47 2009 memory use: 449.3 MB Sat Jul 25 19:28:48 2009 found 1907384 cycles, need 1902390 Sat Jul 25 19:28:51 2009 weight of 1902390 cycles is about 133337095 (70.09/cycle) Sat Jul 25 19:28:51 2009 distribution of cycle lengths: Sat Jul 25 19:28:51 2009 1 relations: 218410 Sat Jul 25 19:28:51 2009 2 relations: 247296 Sat Jul 25 19:28:51 2009 3 relations: 242476 Sat Jul 25 19:28:51 2009 4 relations: 209739 Sat Jul 25 19:28:51 2009 5 relations: 179661 Sat Jul 25 19:28:51 2009 6 relations: 147072 Sat Jul 25 19:28:51 2009 7 relations: 124095 Sat Jul 25 19:28:51 2009 8 relations: 103425 Sat Jul 25 19:28:51 2009 9 relations: 85413 Sat Jul 25 19:28:51 2009 10+ relations: 344803 Sat Jul 25 19:28:51 2009 heaviest cycle: 27 relations Sat Jul 25 19:28:51 2009 commencing cycle optimization Sat Jul 25 19:28:57 2009 start with 11102912 relations Sat Jul 25 19:29:48 2009 pruned 252249 relations Sat Jul 25 19:29:48 2009 memory use: 362.4 MB Sat Jul 25 19:29:48 2009 distribution of cycle lengths: Sat Jul 25 19:29:48 2009 1 relations: 218410 Sat Jul 25 19:29:48 2009 2 relations: 252454 Sat Jul 25 19:29:48 2009 3 relations: 250838 Sat Jul 25 19:29:48 2009 4 relations: 213542 Sat Jul 25 19:29:48 2009 5 relations: 182810 Sat Jul 25 19:29:48 2009 6 relations: 147901 Sat Jul 25 19:29:48 2009 7 relations: 123902 Sat Jul 25 19:29:48 2009 8 relations: 102741 Sat Jul 25 19:29:48 2009 9 relations: 84252 Sat Jul 25 19:29:48 2009 10+ relations: 325540 Sat Jul 25 19:29:48 2009 heaviest cycle: 27 relations Sat Jul 25 19:29:54 2009 RelProcTime: 1033 Sat Jul 25 19:29:54 2009 elapsed time 00:17:15 Sat Jul 25 19:30:08 2009 Sat Jul 25 19:30:08 2009 Sat Jul 25 19:30:08 2009 Msieve v. 1.43 Sat Jul 25 19:30:08 2009 random seeds: f59dc650 7a49ec57 Sat Jul 25 19:30:08 2009 factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits) Sat Jul 25 19:30:10 2009 searching for 15-digit factors Sat Jul 25 19:30:10 2009 commencing number field sieve (167-digit input) Sat Jul 25 19:30:10 2009 R0: -20000000000000000000000000000000000000 Sat Jul 25 19:30:10 2009 R1: 1 Sat Jul 25 19:30:10 2009 A0: 68 Sat Jul 25 19:30:10 2009 A1: 0 Sat Jul 25 19:30:10 2009 A2: 0 Sat Jul 25 19:30:10 2009 A3: 0 Sat Jul 25 19:30:10 2009 A4: 0 Sat Jul 25 19:30:10 2009 A5: 125 Sat Jul 25 19:30:10 2009 skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11 Sat Jul 25 19:30:10 2009 Sat Jul 25 19:30:10 2009 commencing linear algebra Sat Jul 25 19:30:11 2009 read 1902390 cycles Sat Jul 25 19:30:16 2009 cycles contain 5965208 unique relations Sat Jul 25 19:32:01 2009 read 5965208 relations Sat Jul 25 19:33:00 2009 using 20 quadratic characters above 268434500 Sat Jul 25 19:33:58 2009 building initial matrix Sat Jul 25 19:36:15 2009 memory use: 732.8 MB Sat Jul 25 19:36:20 2009 read 1902390 cycles Sat Jul 25 19:36:28 2009 matrix is 1902213 x 1902390 (570.9 MB) with weight 169455496 (89.08/col) Sat Jul 25 19:36:28 2009 sparse part has weight 128720555 (67.66/col) Sat Jul 25 19:37:31 2009 filtering completed in 2 passes Sat Jul 25 19:37:32 2009 matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col) Sat Jul 25 19:37:32 2009 sparse part has weight 128715828 (67.68/col) Sat Jul 25 19:38:00 2009 read 1901778 cycles Sat Jul 25 19:38:09 2009 matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col) Sat Jul 25 19:38:09 2009 sparse part has weight 128715828 (67.68/col) Sat Jul 25 19:38:09 2009 saving the first 48 matrix rows for later Sat Jul 25 19:38:11 2009 matrix is 1901554 x 1901778 (541.8 MB) with weight 134697483 (70.83/col) Sat Jul 25 19:38:11 2009 sparse part has weight 123006791 (64.68/col) Sat Jul 25 19:38:11 2009 matrix includes 64 packed rows Sat Jul 25 19:38:11 2009 using block size 10922 for processor cache size 256 kB Sat Jul 25 19:38:23 2009 commencing Lanczos iteration Sat Jul 25 19:38:23 2009 memory use: 538.2 MB Sat Jul 25 19:39:31 2009 lanczos halted after 23 iterations (dim = 1460) Sat Jul 25 19:39:31 2009 BLanczosTime: 561 Sat Jul 25 19:39:31 2009 elapsed time 00:09:23 Sat Jul 25 19:40:06 2009 Sat Jul 25 19:40:06 2009 Sat Jul 25 19:40:06 2009 Msieve v. 1.43 Sat Jul 25 19:40:06 2009 random seeds: eb58ec47 f7b10534 Sat Jul 25 19:40:06 2009 factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits) Sat Jul 25 19:40:08 2009 searching for 15-digit factors Sat Jul 25 19:40:08 2009 commencing number field sieve (167-digit input) Sat Jul 25 19:40:08 2009 R0: -20000000000000000000000000000000000000 Sat Jul 25 19:40:08 2009 R1: 1 Sat Jul 25 19:40:08 2009 A0: 68 Sat Jul 25 19:40:08 2009 A1: 0 Sat Jul 25 19:40:08 2009 A2: 0 Sat Jul 25 19:40:08 2009 A3: 0 Sat Jul 25 19:40:08 2009 A4: 0 Sat Jul 25 19:40:08 2009 A5: 125 Sat Jul 25 19:40:08 2009 skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11 Sat Jul 25 19:40:08 2009 Sat Jul 25 19:40:08 2009 commencing linear algebra Sat Jul 25 19:40:09 2009 read 1901778 cycles Sat Jul 25 19:40:14 2009 cycles contain 5965168 unique relations Sat Jul 25 19:41:38 2009 read 5965168 relations Sat Jul 25 19:42:42 2009 using 20 quadratic characters above 268434500 Sat Jul 25 19:43:41 2009 building initial matrix Sat Jul 25 19:46:58 2009 memory use: 732.8 MB Sat Jul 25 19:47:03 2009 read 1901778 cycles Sat Jul 25 19:47:11 2009 matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col) Sat Jul 25 19:47:11 2009 sparse part has weight 128715828 (67.68/col) Sat Jul 25 19:47:41 2009 filtering completed in 1 passes Sat Jul 25 19:47:42 2009 matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col) Sat Jul 25 19:47:42 2009 sparse part has weight 128715828 (67.68/col) Sat Jul 25 19:48:09 2009 read 1901778 cycles Sat Jul 25 19:48:17 2009 matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col) Sat Jul 25 19:48:17 2009 sparse part has weight 128715828 (67.68/col) Sat Jul 25 19:48:18 2009 saving the first 48 matrix rows for later Sat Jul 25 19:48:19 2009 matrix is 1901554 x 1901778 (541.8 MB) with weight 134697483 (70.83/col) Sat Jul 25 19:48:19 2009 sparse part has weight 123006791 (64.68/col) Sat Jul 25 19:48:19 2009 matrix includes 64 packed rows Sat Jul 25 19:48:19 2009 using block size 10922 for processor cache size 256 kB Sat Jul 25 19:48:31 2009 commencing Lanczos iteration (2 threads) Sat Jul 25 19:48:31 2009 memory use: 552.7 MB Sun Jul 26 15:44:14 2009 Sun Jul 26 15:44:14 2009 Sun Jul 26 15:44:14 2009 Msieve v. 1.43 Sun Jul 26 15:44:14 2009 random seeds: eccd68a9 d80b29f0 Sun Jul 26 15:44:14 2009 factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits) Sun Jul 26 15:44:17 2009 searching for 15-digit factors Sun Jul 26 15:44:18 2009 commencing number field sieve (167-digit input) Sun Jul 26 15:44:19 2009 R0: -20000000000000000000000000000000000000 Sun Jul 26 15:44:19 2009 R1: 1 Sun Jul 26 15:44:19 2009 A0: 68 Sun Jul 26 15:44:19 2009 A1: 0 Sun Jul 26 15:44:19 2009 A2: 0 Sun Jul 26 15:44:19 2009 A3: 0 Sun Jul 26 15:44:19 2009 A4: 0 Sun Jul 26 15:44:19 2009 A5: 125 Sun Jul 26 15:44:19 2009 skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11 Sun Jul 26 15:44:19 2009 Sun Jul 26 15:44:19 2009 commencing linear algebra Sun Jul 26 15:44:20 2009 read 1901778 cycles Sun Jul 26 15:45:51 2009 matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col) Sun Jul 26 15:45:51 2009 sparse part has weight 128715828 (67.68/col) Sun Jul 26 15:45:56 2009 saving the first 48 matrix rows for later Sun Jul 26 15:47:30 2009 matrix is 1901554 x 1901778 (541.8 MB) with weight 134697483 (70.83/col) Sun Jul 26 15:47:30 2009 sparse part has weight 123006791 (64.68/col) Sun Jul 26 15:47:30 2009 matrix includes 64 packed rows Sun Jul 26 15:47:30 2009 using block size 10922 for processor cache size 256 kB Sun Jul 26 15:51:08 2009 commencing Lanczos iteration Sun Jul 26 15:51:08 2009 memory use: 538.2 MB Sun Jul 26 15:51:15 2009 restarting at iteration 23725 (dim = 1500119) Sun Jul 26 16:14:59 2009 lanczos halted after 23730 iterations (dim = 1500436) Sun Jul 26 16:17:00 2009 BLanczosTime: 1961 Sun Jul 26 16:17:00 2009 elapsed time 00:32:46 Sun Jul 26 17:40:20 2009 lanczos halted after 30075 iterations (dim = 1901553) Sun Jul 26 17:40:29 2009 recovered 38 nontrivial dependencies Sun Jul 26 17:40:29 2009 BLanczosTime: 79221 Sun Jul 26 17:40:29 2009 elapsed time 22:00:23 Sun Jul 26 17:40:40 2009 Sun Jul 26 17:40:40 2009 Sun Jul 26 17:40:40 2009 Msieve v. 1.43 Sun Jul 26 17:40:40 2009 random seeds: 40f05cc9 dbd37a0e Sun Jul 26 17:40:40 2009 factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits) Sun Jul 26 17:40:42 2009 searching for 15-digit factors Sun Jul 26 17:40:43 2009 commencing number field sieve (167-digit input) Sun Jul 26 17:40:43 2009 R0: -20000000000000000000000000000000000000 Sun Jul 26 17:40:43 2009 R1: 1 Sun Jul 26 17:40:43 2009 A0: 68 Sun Jul 26 17:40:43 2009 A1: 0 Sun Jul 26 17:40:43 2009 A2: 0 Sun Jul 26 17:40:43 2009 A3: 0 Sun Jul 26 17:40:43 2009 A4: 0 Sun Jul 26 17:40:43 2009 A5: 125 Sun Jul 26 17:40:43 2009 skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11 Sun Jul 26 17:40:43 2009 Sun Jul 26 17:40:43 2009 commencing square root phase Sun Jul 26 17:40:43 2009 reading relations for dependency 1 Sun Jul 26 17:40:44 2009 read 952156 cycles Sun Jul 26 17:40:47 2009 cycles contain 3664144 unique relations Sun Jul 26 17:41:31 2009 read 3664144 relations Sun Jul 26 17:42:00 2009 multiplying 2983448 relations Sun Jul 26 17:50:53 2009 multiply complete, coefficients have about 87.65 million bits Sun Jul 26 17:50:55 2009 initial square root is modulo 1956611 Sun Jul 26 18:03:12 2009 sqrtTime: 1349 Sun Jul 26 18:03:12 2009 prp69 factor: 101101428297969763167582651911552568964064074821357008687845402353373 Sun Jul 26 18:03:12 2009 prp99 factor: 289176891454586933473472026592329087156730099564830191435580236364586283574771523426365696790224631 Sun Jul 26 18:03:12 2009 elapsed time 00:22:32

Jul 27, 2009 (2nd)

By Jo Yeong Uk / Msieve / Jul 27, 2009
(13·10¹⁶⁸-1)/3 = 4(3)_168<169> = 20947 · 771585846463_<12> · 39603215950776900109_<20> · C133
C133 = P46 · P88
P46 = 1938224840403052580372387224495153919668245331_<46>
P88 = 3492861805147986371594013038659339678087070803636098353203209518029135382931515883660607_<88>

Number: 43333_168 N=6769951514832874024854036768853409897637506303253507175204255793012536446458911961588877677283372873422176238901148203977372816375917 ( 133 digits) SNFS difficulty: 171 digits. Divisors found: r1=1938224840403052580372387224495153919668245331 r2=3492861805147986371594013038659339678087070803636098353203209518029135382931515883660607 Version: Total time: 34.46 hours. Scaled time: 82.46 units (timescale=2.393). Factorization parameters were as follows: n: 6769951514832874024854036768853409897637506303253507175204255793012536446458911961588877677283372873422176238901148203977372816375917 m: 10000000000000000000000000000000000 deg: 5 c5: 13 c0: -100 skew: 1.50 type: snfs lss: 1 rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2700000, 5400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11025872 Max relations in full relation-set: Initial matrix: Pruned matrix : 947012 x 947259 Total sieving time: 30.92 hours. Total relation processing time: 1.46 hours. Matrix solve time: 1.87 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000 total time: 34.46 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 27, 2009

By Andreas Tete / Sys`s Databaseworkers / Jul 27, 2009
(58·10²⁰²+23)/9 = 6(4)₂₀₁7_<203> = 122203 · 287922001189726263337_<21> · C178
C178 = P39 · C139
P39 = 900888654245586171146217023177567172781_<39>
C139 = [2033094880569783215278126749021287699566111873184365711870097919375967568012016979486944089877439038338587424781953667086152516217685482617_<139>]

Syd`s Databaseworkers hit this p39 factor p39 = 900888654245586171146217023177567172781

Jul 26, 2009 (2nd)

By Wataru Sakai / GMP-ECM / Jul 26, 2009
(17·10¹⁷¹+7)/3 = 5(6)₁₇₀9_<172> = 283 · 2808665746949_<13> · C157
C157 = P30 · P128
P30 = 310692117837628822353435398753_<30>
P128 = 22946208622966530086181294683282074760948833484150202522041144943775782218378532782991915144433011255535400598496135511752228619_<128>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1603423327 Step 1 took 52394ms Step 2 took 17646ms ********** Factor found in step 2: 310692117837628822353435398753 Found probable prime factor of 30 digits: 310692117837628822353435398753 Probable prime cofactor 22946208622966530086181294683282074760948833484150202522041144943775782218378532782991915144433011255535400598496135511752228619 has 128 digits

Jul 26, 2009

By Andreas Tete / Syd`s Databaseworkers with ECM / Jul 26, 2009
(47·10¹⁶⁹+43)/9 = 5(2)₁₆₈7_<170> = 3 · 8572033 · 2460206087289861850132545179847589_<34> · C129
C129 = P34 · P96
P34 = 5947600359084872453635233580884281_<34>
P96 = 138783230265768766152371928057610712541819675642385676028172380581542216339866361236637806555397_<96>

Syd`s Database workers hit this p34 with B1=1e6 p34 = 5947600359084872453635233580884281

Jul 25, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jul 25, 2009
(47·10¹⁸²+43)/9 = 5(2)₁₈₁7_<183> = 31 · 401 · C179
C179 = P39 · P140
P39 = 724670646436597737957829265930693298467_<39>
P140 = 57970708996105002215788203509108410471504630076942583716286001043883185692786443798047081444061638563025160902815892854666009628608598216351_<140>

Number: n N=42009671162595303855057696261139266529017956899865032758605278917401835912012084484130176351236603830924480912414304739942259047721198795126878145138944752813307233707845082633917 ( 179 digits) SNFS difficulty: 184 digits. Divisors found: Sat Jul 25 18:54:33 2009 prp39 factor: 724670646436597737957829265930693298467 Sat Jul 25 18:54:33 2009 prp140 factor: 57970708996105002215788203509108410471504630076942583716286001043883185692786443798047081444061638563025160902815892854666009628608598216351 Sat Jul 25 18:54:33 2009 elapsed time 03:09:32 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 216.75 hours. Scaled time: 576.57 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_2_181_7 n: 42009671162595303855057696261139266529017956899865032758605278917401835912012084484130176351236603830924480912414304739942259047721198795126878145138944752813307233707845082633917 m: 2000000000000000000000000000000000000 deg: 5 c5: 1175 c0: 344 skew: 0.78 type: snfs lss: 1 rlim: 8400000 alim: 8400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4200000, 7800409) Primes: RFBsize:564877, AFBsize:565056, largePrimes:21409291 encountered Relations: rels:21835602, finalFF:971958 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2386706 hash collisions in 23549779 relations Msieve: matrix is 1431432 x 1431680 (384.4 MB) Total sieving time: 216.03 hours. Total relation processing time: 0.72 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,56,56,2.5,2.5,100000 total time: 216.75 hours. --------- CPU info (if available) ----------

Jul 25, 2009

By Jo Yeong Uk / GMP-ECM 6.2.3, YAFU 1.10, Msieve / Jul 25, 2009
(34·10¹⁷⁰-61)/9 = 3(7)₁₆₉1_<171> = 7 · 1549 · 1104921407_<10> · 10187536427529899_<17> · 391353153935485813_<18> · C124
C124 = P40 · P41 · P44
P40 = 6725886983982318771880439066030047436221_<40>
P41 = 13026818417600827639174618332243277437991_<41>
P44 = 90267127858585686761229484150679606606868203_<44>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 7908926676514675413083853032827063880118980193445471625562601469958414706043143581401715516956542424923236530406833110566233 (124 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7372562557 Step 1 took 4180ms ********** Factor found in step 1: 90267127858585686761229484150679606606868203 Found probable prime factor of 44 digits: 90267127858585686761229484150679606606868203 Composite cofactor 87616908437642552977838315920860564586991837524724010046764766223080042854872011 has 80 digits 07/25/09 02:40:39 v1.10 @ 조영욱-PC, starting SIQS on c80: 87616908437642552977838315920860564586991837524724010046764766223080042854872011 07/25/09 02:40:39 v1.10 @ 조영욱-PC, random seeds: 4212545165, 4213289736 07/25/09 02:40:39 v1.10 @ 조영욱-PC, ==== sieve params ==== 07/25/09 02:40:39 v1.10 @ 조영욱-PC, n = 80 digits, 266 bits 07/25/09 02:40:39 v1.10 @ 조영욱-PC, factor base: 43638 primes (max prime = 1122259) 07/25/09 02:40:39 v1.10 @ 조영욱-PC, single large prime cutoff: 106614605 (95 * pmax) 07/25/09 02:40:39 v1.10 @ 조영욱-PC, using 13 large prime slices of factor base 07/25/09 02:40:39 v1.10 @ 조영욱-PC, buckets hold 1024 elements 07/25/09 02:40:39 v1.10 @ 조영욱-PC, sieve interval: 7 blocks of size 65536 07/25/09 02:40:39 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors 07/25/09 02:40:39 v1.10 @ 조영욱-PC, using multiplier of 1 07/25/09 02:40:39 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits 07/25/09 02:40:39 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning 07/25/09 02:40:39 v1.10 @ 조영욱-PC, trial factoring cutoff at 95 bits 07/25/09 02:40:39 v1.10 @ 조영욱-PC, ==== sieving started ==== 07/25/09 02:48:32 v1.10 @ 조영욱-PC, sieve time = 244.3230, relation time = 65.8900, poly_time = 162.9600 07/25/09 02:48:32 v1.10 @ 조영욱-PC, 43837 relations found: 21442 full + 22395 from 239791 partial, using 121730 polys (238 A polys) 07/25/09 02:48:32 v1.10 @ 조영욱-PC, on average, sieving found 2.15 rels/poly and 551.53 rels/sec 07/25/09 02:48:32 v1.10 @ 조영욱-PC, trial division touched 3557500 sieve locations out of 111687761920 07/25/09 02:48:32 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 07/25/09 02:48:33 v1.10 @ 조영욱-PC, begin with 261233 relations 07/25/09 02:48:33 v1.10 @ 조영욱-PC, reduce to 63321 relations in 2 passes 07/25/09 02:48:33 v1.10 @ 조영욱-PC, recovered 63321 relations 07/25/09 02:48:33 v1.10 @ 조영욱-PC, recovered 49420 polynomials 07/25/09 02:48:33 v1.10 @ 조영욱-PC, attempting to build 43837 cycles 07/25/09 02:48:33 v1.10 @ 조영욱-PC, found 43837 cycles in 1 passes 07/25/09 02:48:33 v1.10 @ 조영욱-PC, distribution of cycle lengths: 07/25/09 02:48:33 v1.10 @ 조영욱-PC, length 1 : 21442 07/25/09 02:48:33 v1.10 @ 조영욱-PC, length 2 : 22395 07/25/09 02:48:33 v1.10 @ 조영욱-PC, largest cycle: 2 relations 07/25/09 02:48:33 v1.10 @ 조영욱-PC, matrix is 43638 x 43837 (6.5 MB) with weight 1357350 (30.96/col) 07/25/09 02:48:33 v1.10 @ 조영욱-PC, sparse part has weight 1357350 (30.96/col) 07/25/09 02:48:33 v1.10 @ 조영욱-PC, filtering completed in 3 passes 07/25/09 02:48:33 v1.10 @ 조영욱-PC, matrix is 32275 x 32339 (5.2 MB) with weight 1109999 (34.32/col) 07/25/09 02:48:33 v1.10 @ 조영욱-PC, sparse part has weight 1109999 (34.32/col) 07/25/09 02:48:33 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 07/25/09 02:48:33 v1.10 @ 조영욱-PC, matrix is 32227 x 32339 (3.8 MB) with weight 864751 (26.74/col) 07/25/09 02:48:33 v1.10 @ 조영욱-PC, sparse part has weight 669894 (20.71/col) 07/25/09 02:48:33 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 07/25/09 02:48:33 v1.10 @ 조영욱-PC, using block size 12935 for processor cache size 4096 kB 07/25/09 02:48:33 v1.10 @ 조영욱-PC, commencing Lanczos iteration 07/25/09 02:48:33 v1.10 @ 조영욱-PC, memory use: 3.7 MB 07/25/09 02:48:37 v1.10 @ 조영욱-PC, lanczos halted after 511 iterations (dim = 32221) 07/25/09 02:48:37 v1.10 @ 조영욱-PC, recovered 14 nontrivial dependencies 07/25/09 02:48:37 v1.10 @ 조영욱-PC, prp41 = 13026818417600827639174618332243277437991 07/25/09 02:48:38 v1.10 @ 조영욱-PC, prp40 = 6725886983982318771880439066030047436221 07/25/09 02:48:38 v1.10 @ 조영욱-PC, Lanczos elapsed time = 4.1810 seconds. 07/25/09 02:48:38 v1.10 @ 조영욱-PC, Sqrt elapsed time = 1.0450 seconds. 07/25/09 02:48:38 v1.10 @ 조영욱-PC, SIQS elapsed time = 478.8780 seconds. 07/25/09 02:48:38 v1.10 @ 조영욱-PC, 07/25/09 02:48:38 v1.10 @ 조영욱-PC,

(37·10¹⁶⁹+53)/9 = 4(1)₁₆₈7_<170> = 19 · 291511918341504324969778930777933_<33> · C136
C136 = P40 · P97
P40 = 6256622275585770775151492306219379972061_<40>
P97 = 1186340513227261878040769445245614823177468731961871849452046522629392283910274236941531315901911_<97>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 7422484481487542405434963871001284300917097043855519001904556196162796366335291956314614258679614931018465138599301201369883800196508571 (136 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3546435855 Step 1 took 4851ms Step 2 took 4259ms ********** Factor found in step 2: 6256622275585770775151492306219379972061 Found probable prime factor of 40 digits: 6256622275585770775151492306219379972061 Probable prime cofactor 1186340513227261878040769445245614823177468731961871849452046522629392283910274236941531315901911 has 97 digits

Jul 24, 2009 (3rd)

By Wataru Sakai / Msieve / Jul 24, 2009
(22·10¹⁹¹-1)/3 = 7(3)_191<192> = 1297 · C189
C189 = P80 · P110
P80 = 31599751978617979691934192792502734631798298443748846506515340551417632686335601_<80>
P110 = 17892778104022385586692910064435301213675071970966671817147805915015452599464091933241233683195001902978482389_<110>

Number: 73333_191 N=565407350295553842199948599331791313287072731945515291698792084297095862246209200719609354921613980981752762785916216910819840657928553071189925469031097404266255461320997172963248522230789 ( 189 digits) SNFS difficulty: 193 digits. Divisors found: r1=31599751978617979691934192792502734631798298443748846506515340551417632686335601 r2=17892778104022385586692910064435301213675071970966671817147805915015452599464091933241233683195001902978482389 Version: Total time: 483.64 hours. Scaled time: 971.64 units (timescale=2.009). Factorization parameters were as follows: n: 565407350295553842199948599331791313287072731945515291698792084297095862246209200719609354921613980981752762785916216910819840657928553071189925469031097404266255461320997172963248522230789 m: 200000000000000000000000000000000000000 deg: 5 c5: 55 c0: -8 skew: 0.68 type: snfs lss: 1 rlim: 11600000 alim: 11600000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 11600000/11600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [5800000, 10800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1830862 x 1831110 Total sieving time: 483.64 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,193,5,0,0,0,0,0,0,0,0,11600000,11600000,28,28,55,55,2.5,2.5,100000 total time: 483.64 hours. --------- CPU info (if available) ----------

(67·10²⁰⁰+23)/9 = 7(4)₁₉₉7_<201> = 3⁴ · 1153 · C196
C196 = P69 · P128
P69 = 196592506741212520044538167570720429219402274779774438764525711972609_<69>
P128 = 40546279211618582655414497439811038556876425327404273148537996988167822927209105501508855259371162388034501678989737104551746031_<128>

Number: 74447_200 N=7971094669241211273269350427167394177769687711546309085739235750478563109060041378309342717810161837016098042085000422349045907556716718002895767824616881826736955065630662302789764162672196464879 ( 196 digits) SNFS difficulty: 201 digits. Divisors found: r1=196592506741212520044538167570720429219402274779774438764525711972609 r2=40546279211618582655414497439811038556876425327404273148537996988167822927209105501508855259371162388034501678989737104551746031 Version: Total time: 699.71 hours. Scaled time: 1405.71 units (timescale=2.009). Factorization parameters were as follows: n: 7971094669241211273269350427167394177769687711546309085739235750478563109060041378309342717810161837016098042085000422349045907556716718002895767824616881826736955065630662302789764162672196464879 m: 10000000000000000000000000000000000000000 deg: 5 c5: 67 c0: 23 skew: 0.81 type: snfs lss: 1 rlim: 16200000 alim: 16200000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 16200000/16200000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [8100000, 15200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2869202 x 2869450 Total sieving time: 699.71 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,16200000,16200000,29,29,56,56,2.6,2.6,100000 total time: 699.71 hours. --------- CPU info (if available) ----------

Jul 24, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jul 24, 2009
2·10²¹²-1 = 1(9)_212<213> = 23 · C211
C211 = P46 · P61 · P106
P46 = 2659264777745734405392508581327747941839503713_<46>
P61 = 2624192453344997234656310661787467697906712795425020425430953_<61>
P106 = 1246077046444953259325719448796658447093073224853980853958734916369485280891634235590281319558742952446417_<106>

Number: n N=8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913 ( 211 digits) SNFS difficulty: 213 digits. Divisors found: Fri Jul 24 20:24:31 2009 prp46 factor: 2659264777745734405392508581327747941839503713 Fri Jul 24 20:24:31 2009 prp61 factor: 2624192453344997234656310661787467697906712795425020425430953 Fri Jul 24 20:24:31 2009 prp106 factor: 1246077046444953259325719448796658447093073224853980853958734916369485280891634235590281319558742952446417 Fri Jul 24 20:24:31 2009 elapsed time 39:56:00 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 95.16 hours. Scaled time: 191.65 units (timescale=2.014). Factorization parameters were as follows: name: KA_1_9_212 n: 8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913 m: 200000000000000000000000000000000000 deg: 6 c6: 25 c0: -8 skew: 0.83 type: snfs lss: 1 rlim: 25000000 alim: 25000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 25000000/25000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [12500000, 30599990) Primes: RFBsize:1565927, AFBsize:1563644, largePrimes:38836401 encountered Relations: rels:36263602, finalFF:1107921 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 8322646 hash collisions in 48064285 relations Msieve: matrix is 4525782 x 4526029 (1218.8 MB) Total sieving time: 94.03 hours. Total relation processing time: 1.13 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,213,6,0,0,0,0,0,0,0,0,25000000,25000000,29,29,58,58,2.6,2.6,100000 total time: 95.16 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352056k/3407296k available (3119k kernel code, 53956k reserved, 1894k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.68 BogoMIPS (lpj=2830844) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22644.41 BogoMIPS).

Jul 24, 2009

By Andreas Tete / Syd`s Databaseworkers / Jul 24, 2009
(58·10¹⁹⁴+23)/9 = 6(4)₁₉₃7_<195> = 257 · 403464209177_<12> · 3543970882437511879731257595620290877_<37> · C145
C145 = P36 · P109
P36 = 277910928745730887156179766492458017_<36>
P109 = 6310322790083620064791690811822998614035354857083272254295215385444318070690134698155017866341817570459038947_<109>

Syd`s Databaseworkers hit this p36 factor p36 = 277910928745730887156179766492458017

Jul 23, 2009 (3rd)

By Andreas Tete / GGNFS, Msieve v 1.42, Syd`s Database workers / Jul 23, 2009
5·10¹⁹³-3 = 4(9)₁₉₂7_<194> = 139 · 124367 · 416128249 · 5670353807_<10> · 630601422409414751_<18> · 1628951248743679743054506189_<28> · C124
C124 = P44 · P80
P44 = 14620629278240550652432989762103729163476871_<44>
P80 = 81617556881746859330571187100259479960634045948609207766222314981106404568681507_<80>

Thu Jul 23 13:49:00 2009 Msieve v. 1.42 Thu Jul 23 13:49:00 2009 random seeds: 7f123710 3ac4bbe3 Thu Jul 23 13:49:00 2009 factoring 1193300041763731671870987439029906012365042862204137739005604691718275603021397760465734919821660412096935234987760359924597 (124 digits) Thu Jul 23 13:49:02 2009 searching for 15-digit factors Thu Jul 23 13:49:03 2009 commencing number field sieve (124-digit input) Thu Jul 23 13:49:03 2009 R0: -543336852106466897936255 Thu Jul 23 13:49:03 2009 R1: 18897792025541 Thu Jul 23 13:49:03 2009 A0: -56096130083591137671762443568 Thu Jul 23 13:49:03 2009 A1: 18511784021721927080713518 Thu Jul 23 13:49:03 2009 A2: -165566443634317392579 Thu Jul 23 13:49:03 2009 A3: -3652011178397938 Thu Jul 23 13:49:03 2009 A4: 5511588632 Thu Jul 23 13:49:03 2009 A5: 25200 Thu Jul 23 13:49:03 2009 skew 149034.11, size 7.586280e-012, alpha -6.213274, combined = 1.859200e-010 Thu Jul 23 13:49:03 2009 Thu Jul 23 13:49:03 2009 commencing relation filtering Thu Jul 23 13:49:03 2009 estimated available RAM is 3069.5 MB Thu Jul 23 13:49:03 2009 commencing duplicate removal, pass 1 Thu Jul 23 13:49:03 2009 error -15 reading relation 27880 Thu Jul 23 13:50:52 2009 found 1488308 hash collisions in 9178490 relations Thu Jul 23 13:51:22 2009 added 59182 free relations Thu Jul 23 13:51:22 2009 commencing duplicate removal, pass 2 Thu Jul 23 13:51:47 2009 found 1228693 duplicates and 8008978 unique relations Thu Jul 23 13:51:47 2009 memory use: 41.3 MB Thu Jul 23 13:51:47 2009 reading ideals above 100000 Thu Jul 23 13:51:47 2009 commencing singleton removal, initial pass Thu Jul 23 13:53:56 2009 memory use: 149.2 MB Thu Jul 23 13:53:56 2009 reading all ideals from disk Thu Jul 23 13:54:03 2009 memory use: 287.9 MB Thu Jul 23 13:54:05 2009 keeping 8633531 ideals with weight <= 200, target excess is 43827 Thu Jul 23 13:54:07 2009 commencing in-memory singleton removal Thu Jul 23 13:54:09 2009 begin with 8008978 relations and 8633531 unique ideals Thu Jul 23 13:54:21 2009 reduce to 3184608 relations and 3001298 ideals in 15 passes Thu Jul 23 13:54:21 2009 max relations containing the same ideal: 106 Thu Jul 23 13:54:24 2009 removing 456604 relations and 390369 ideals in 66235 cliques Thu Jul 23 13:54:24 2009 commencing in-memory singleton removal Thu Jul 23 13:54:25 2009 begin with 2728004 relations and 3001298 unique ideals Thu Jul 23 13:54:30 2009 reduce to 2687707 relations and 2569635 ideals in 9 passes Thu Jul 23 13:54:30 2009 max relations containing the same ideal: 98 Thu Jul 23 13:54:33 2009 removing 347400 relations and 281165 ideals in 66235 cliques Thu Jul 23 13:54:33 2009 commencing in-memory singleton removal Thu Jul 23 13:54:33 2009 begin with 2340307 relations and 2569635 unique ideals Thu Jul 23 13:54:37 2009 reduce to 2310136 relations and 2257591 ideals in 8 passes Thu Jul 23 13:54:37 2009 max relations containing the same ideal: 85 Thu Jul 23 13:54:40 2009 relations with 0 large ideals: 159 Thu Jul 23 13:54:40 2009 relations with 1 large ideals: 448 Thu Jul 23 13:54:40 2009 relations with 2 large ideals: 5181 Thu Jul 23 13:54:40 2009 relations with 3 large ideals: 37785 Thu Jul 23 13:54:40 2009 relations with 4 large ideals: 157995 Thu Jul 23 13:54:40 2009 relations with 5 large ideals: 402047 Thu Jul 23 13:54:40 2009 relations with 6 large ideals: 632608 Thu Jul 23 13:54:40 2009 relations with 7+ large ideals: 1073913 Thu Jul 23 13:54:40 2009 commencing 2-way merge Thu Jul 23 13:54:43 2009 reduce to 1431580 relation sets and 1379035 unique ideals Thu Jul 23 13:54:43 2009 commencing full merge Thu Jul 23 13:55:20 2009 memory use: 151.7 MB Thu Jul 23 13:55:20 2009 found 735016 cycles, need 727235 Thu Jul 23 13:55:20 2009 weight of 727235 cycles is about 51191425 (70.39/cycle) Thu Jul 23 13:55:20 2009 distribution of cycle lengths: Thu Jul 23 13:55:20 2009 1 relations: 83344 Thu Jul 23 13:55:20 2009 2 relations: 84619 Thu Jul 23 13:55:20 2009 3 relations: 84693 Thu Jul 23 13:55:20 2009 4 relations: 78225 Thu Jul 23 13:55:20 2009 5 relations: 70392 Thu Jul 23 13:55:20 2009 6 relations: 61090 Thu Jul 23 13:55:20 2009 7 relations: 52459 Thu Jul 23 13:55:20 2009 8 relations: 44423 Thu Jul 23 13:55:20 2009 9 relations: 36816 Thu Jul 23 13:55:20 2009 10+ relations: 131174 Thu Jul 23 13:55:20 2009 heaviest cycle: 22 relations Thu Jul 23 13:55:20 2009 commencing cycle optimization Thu Jul 23 13:55:22 2009 start with 4253137 relations Thu Jul 23 13:55:34 2009 pruned 113256 relations Thu Jul 23 13:55:34 2009 memory use: 109.9 MB Thu Jul 23 13:55:34 2009 distribution of cycle lengths: Thu Jul 23 13:55:34 2009 1 relations: 83344 Thu Jul 23 13:55:34 2009 2 relations: 86599 Thu Jul 23 13:55:34 2009 3 relations: 87818 Thu Jul 23 13:55:34 2009 4 relations: 80345 Thu Jul 23 13:55:34 2009 5 relations: 72065 Thu Jul 23 13:55:34 2009 6 relations: 62062 Thu Jul 23 13:55:34 2009 7 relations: 52824 Thu Jul 23 13:55:34 2009 8 relations: 44435 Thu Jul 23 13:55:34 2009 9 relations: 36553 Thu Jul 23 13:55:34 2009 10+ relations: 121190 Thu Jul 23 13:55:34 2009 heaviest cycle: 21 relations Thu Jul 23 13:55:35 2009 RelProcTime: 392 Thu Jul 23 13:55:35 2009 Thu Jul 23 13:55:35 2009 commencing linear algebra Thu Jul 23 13:55:36 2009 read 727235 cycles Thu Jul 23 13:55:38 2009 cycles contain 2259892 unique relations Thu Jul 23 13:56:23 2009 read 2259892 relations Thu Jul 23 13:56:27 2009 using 20 quadratic characters above 134214264 Thu Jul 23 13:56:42 2009 building initial matrix Thu Jul 23 13:57:21 2009 memory use: 265.6 MB Thu Jul 23 13:57:22 2009 read 727235 cycles Thu Jul 23 13:57:23 2009 matrix is 727058 x 727235 (209.7 MB) with weight 69362639 (95.38/col) Thu Jul 23 13:57:23 2009 sparse part has weight 49161753 (67.60/col) Thu Jul 23 13:57:35 2009 filtering completed in 2 passes Thu Jul 23 13:57:35 2009 matrix is 726657 x 726834 (209.7 MB) with weight 69345359 (95.41/col) Thu Jul 23 13:57:35 2009 sparse part has weight 49156190 (67.63/col) Thu Jul 23 13:57:38 2009 read 726834 cycles Thu Jul 23 13:57:40 2009 matrix is 726657 x 726834 (209.7 MB) with weight 69345359 (95.41/col) Thu Jul 23 13:57:40 2009 sparse part has weight 49156190 (67.63/col) Thu Jul 23 13:57:40 2009 saving the first 48 matrix rows for later Thu Jul 23 13:57:40 2009 matrix is 726609 x 726834 (200.2 MB) with weight 54862726 (75.48/col) Thu Jul 23 13:57:40 2009 sparse part has weight 48114957 (66.20/col) Thu Jul 23 13:57:40 2009 matrix includes 64 packed rows Thu Jul 23 13:57:40 2009 using block size 65536 for processor cache size 3072 kB Thu Jul 23 13:57:47 2009 commencing Lanczos iteration Thu Jul 23 13:57:47 2009 memory use: 202.6 MB Thu Jul 23 15:23:28 2009 lanczos halted after 11492 iterations (dim = 726608) Thu Jul 23 15:23:31 2009 recovered 31 nontrivial dependencies Thu Jul 23 15:23:31 2009 BLanczosTime: 5276 Thu Jul 23 15:23:31 2009 Thu Jul 23 15:23:31 2009 commencing square root phase Thu Jul 23 15:23:31 2009 reading relations for dependency 1 Thu Jul 23 15:23:32 2009 read 363673 cycles Thu Jul 23 15:23:32 2009 cycles contain 1398991 unique relations Thu Jul 23 15:23:58 2009 read 1398991 relations Thu Jul 23 15:24:07 2009 multiplying 1130618 relations Thu Jul 23 15:27:48 2009 multiply complete, coefficients have about 51.58 million bits Thu Jul 23 15:27:51 2009 initial square root is modulo 25424593 Thu Jul 23 15:33:23 2009 sqrtTime: 592 Thu Jul 23 15:33:23 2009 prp44 factor: 14620629278240550652432989762103729163476871 Thu Jul 23 15:33:23 2009 prp80 factor: 81617556881746859330571187100259479960634045948609207766222314981106404568681507 Thu Jul 23 15:33:23 2009 elapsed time 01:44:23 Thu Jul 23 15:33:23 2009 total time ~ 125 hours

(58·10¹⁹⁴+23)/9 = 6(4)₁₉₃7_<195> = 257 · 403464209177_<12> · C181
C181 = P37 · C145
P37 = 3543970882437511879731257595620290877_<37>
C145 = [1753707667277490662296596455138203925886352047609268924626142234554596780596769030414778657310009459856568838766914928341099729251362501565388099_<145>]

Syd`s Database workers hit this p37 factor p37 = 3543970882437511879731257595620290877

Jul 23, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve 1.42 / Jul 23, 2009
(56·10²⁰³+43)/9 = 6(2)₂₀₂7_<204> = 3 · C204
C204 = P60 · P144
P60 = 591752848190830505194723691088958573025065122850764427487837_<60>
P144 = 350496677863934757609414005722989412369536157605989693540146711579200859237238102599130471318852834601704462309602498012951936078401332556541157_<144>

Sieving time ~ 40 cpu-days Thu Jul 16 01:25:58 2009 Msieve v. 1.42 Thu Jul 16 01:25:58 2009 random seeds: c56a6980 fe74d888 Thu Jul 16 01:25:58 2009 factoring 207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407409 (204 digits) Thu Jul 16 01:26:05 2009 Thu Jul 16 01:26:05 2009 Thu Jul 16 01:26:05 2009 Msieve v. 1.42 Thu Jul 16 01:26:05 2009 random seeds: f71ce5d8 4f84c420 Thu Jul 16 01:26:05 2009 factoring 207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407409 (204 digits) Thu Jul 16 01:26:07 2009 searching for 15-digit factors Thu Jul 16 01:26:10 2009 commencing number field sieve (204-digit input) Thu Jul 16 01:26:10 2009 R0: -100000000000000000000000000000000000000000 Thu Jul 16 01:26:10 2009 R1: 1 Thu Jul 16 01:26:10 2009 A0: 1075 Thu Jul 16 01:26:10 2009 A1: 0 Thu Jul 16 01:26:10 2009 A2: 0 Thu Jul 16 01:26:10 2009 A3: 0 Thu Jul 16 01:26:10 2009 A4: 0 Thu Jul 16 01:26:10 2009 A5: 14 Thu Jul 16 01:26:10 2009 skew 2.38, size 3.186562e-014, alpha -0.612885, combined = 9.720684e-012 Thu Jul 16 01:26:10 2009 Thu Jul 16 01:26:10 2009 commencing relation filtering Thu Jul 16 01:26:10 2009 commencing duplicate removal, pass 1 Thu Jul 16 01:29:27 2009 error -11 reading relation 24287251 Thu Jul 16 01:31:01 2009 error -11 reading relation 34401760 Thu Jul 16 01:31:07 2009 error -9 reading relation 35087611 Thu Jul 16 01:31:12 2009 error -15 reading relation 35782753 Thu Jul 16 01:31:18 2009 error -9 reading relation 36477916 Thu Jul 16 01:31:24 2009 error -15 reading relation 37169656 Thu Jul 16 01:31:29 2009 error -9 reading relation 37870362 Thu Jul 16 01:31:35 2009 error -9 reading relation 38571298 Thu Jul 16 01:31:41 2009 found 5319528 hash collisions in 39277598 relations Thu Jul 16 01:32:30 2009 added 840 free relations Thu Jul 16 01:32:30 2009 commencing duplicate removal, pass 2 Thu Jul 16 01:33:43 2009 found 3699116 duplicates and 35579322 unique relations Thu Jul 16 01:33:43 2009 memory use: 165.2 MB Thu Jul 16 01:33:43 2009 reading rational ideals above 21168128 Thu Jul 16 01:33:43 2009 reading algebraic ideals above 21168128 Thu Jul 16 01:33:43 2009 commencing singleton removal, pass 1 Thu Jul 16 01:39:13 2009 relations with 0 large ideals: 581552 Thu Jul 16 01:39:13 2009 relations with 1 large ideals: 3668835 Thu Jul 16 01:39:13 2009 relations with 2 large ideals: 10320596 Thu Jul 16 01:39:13 2009 relations with 3 large ideals: 13424743 Thu Jul 16 01:39:13 2009 relations with 4 large ideals: 6899607 Thu Jul 16 01:39:13 2009 relations with 5 large ideals: 20129 Thu Jul 16 01:39:13 2009 relations with 6 large ideals: 663860 Thu Jul 16 01:39:13 2009 relations with 7+ large ideals: 0 Thu Jul 16 01:39:13 2009 35579322 relations and about 31817912 large ideals Thu Jul 16 01:39:13 2009 commencing singleton removal, pass 2 Thu Jul 16 01:44:30 2009 found 11545324 singletons Thu Jul 16 01:44:30 2009 current dataset: 24033998 relations and about 18608908 large ideals Thu Jul 16 01:44:30 2009 commencing singleton removal, pass 3 Thu Jul 16 01:48:14 2009 found 2658569 singletons Thu Jul 16 01:48:14 2009 current dataset: 21375429 relations and about 15826556 large ideals Thu Jul 16 01:48:14 2009 commencing singleton removal, pass 4 Thu Jul 16 01:51:35 2009 found 701176 singletons Thu Jul 16 01:51:35 2009 current dataset: 20674253 relations and about 15115803 large ideals Thu Jul 16 01:51:35 2009 commencing singleton removal, pass 5 Thu Jul 16 01:54:54 2009 found 185715 singletons Thu Jul 16 01:54:54 2009 current dataset: 20488538 relations and about 14929365 large ideals Thu Jul 16 01:54:54 2009 commencing singleton removal, final pass Thu Jul 16 01:58:25 2009 memory use: 351.4 MB Thu Jul 16 01:58:25 2009 commencing in-memory singleton removal Thu Jul 16 01:58:27 2009 begin with 20488538 relations and 18081880 unique ideals Thu Jul 16 01:59:05 2009 reduce to 13835158 relations and 11057496 ideals in 23 passes Thu Jul 16 01:59:05 2009 max relations containing the same ideal: 40 Thu Jul 16 01:59:10 2009 reading rational ideals above 720000 Thu Jul 16 01:59:10 2009 reading algebraic ideals above 720000 Thu Jul 16 01:59:10 2009 commencing singleton removal, final pass Thu Jul 16 02:02:23 2009 keeping 12338074 ideals with weight <= 20, new excess is 1437415 Thu Jul 16 02:02:42 2009 memory use: 360.9 MB Thu Jul 16 02:02:42 2009 commencing in-memory singleton removal Thu Jul 16 02:02:44 2009 begin with 13866106 relations and 12338074 unique ideals Thu Jul 16 02:03:09 2009 reduce to 13835805 relations and 12287758 ideals in 12 passes Thu Jul 16 02:03:09 2009 max relations containing the same ideal: 20 Thu Jul 16 02:03:11 2009 filtering wants 358062 more relations Thu Jul 16 02:03:11 2009 elapsed time 00:37:06 Thu Jul 16 20:16:09 2009 Thu Jul 16 20:16:09 2009 Thu Jul 16 20:16:09 2009 Msieve v. 1.42 Thu Jul 16 20:16:09 2009 random seeds: 641e9e94 e8e91ac0 Thu Jul 16 20:16:09 2009 factoring 207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407409 (204 digits) Thu Jul 16 20:16:11 2009 searching for 15-digit factors Thu Jul 16 20:16:14 2009 commencing number field sieve (204-digit input) Thu Jul 16 20:16:14 2009 R0: -100000000000000000000000000000000000000000 Thu Jul 16 20:16:14 2009 R1: 1 Thu Jul 16 20:16:14 2009 A0: 1075 Thu Jul 16 20:16:14 2009 A1: 0 Thu Jul 16 20:16:14 2009 A2: 0 Thu Jul 16 20:16:14 2009 A3: 0 Thu Jul 16 20:16:14 2009 A4: 0 Thu Jul 16 20:16:14 2009 A5: 14 Thu Jul 16 20:16:14 2009 skew 2.38, size 3.186562e-014, alpha -0.612885, combined = 9.720684e-012 Thu Jul 16 20:16:14 2009 Thu Jul 16 20:16:14 2009 commencing relation filtering Thu Jul 16 20:16:14 2009 commencing duplicate removal, pass 1 Thu Jul 16 20:19:38 2009 error -11 reading relation 24287251 Thu Jul 16 20:22:02 2009 error -11 reading relation 34401760 Thu Jul 16 20:22:08 2009 error -9 reading relation 35087611 Thu Jul 16 20:22:14 2009 error -15 reading relation 35782753 Thu Jul 16 20:22:26 2009 error -9 reading relation 36477916 Thu Jul 16 20:22:37 2009 error -15 reading relation 37169656 Thu Jul 16 20:22:43 2009 error -9 reading relation 37870362 Thu Jul 16 20:22:54 2009 error -9 reading relation 38571298 Thu Jul 16 20:23:04 2009 error -11 reading relation 39277606 Thu Jul 16 20:23:47 2009 found 6511908 hash collisions in 44449153 relations Thu Jul 16 20:24:38 2009 added 390 free relations Thu Jul 16 20:24:38 2009 commencing duplicate removal, pass 2 Thu Jul 16 20:26:09 2009 found 4542027 duplicates and 39907516 unique relations Thu Jul 16 20:26:09 2009 memory use: 165.2 MB Thu Jul 16 20:26:09 2009 reading rational ideals above 22740992 Thu Jul 16 20:26:09 2009 reading algebraic ideals above 22740992 Thu Jul 16 20:26:09 2009 commencing singleton removal, pass 1 Thu Jul 16 20:33:34 2009 relations with 0 large ideals: 716732 Thu Jul 16 20:33:34 2009 relations with 1 large ideals: 4434970 Thu Jul 16 20:33:34 2009 relations with 2 large ideals: 11968351 Thu Jul 16 20:33:34 2009 relations with 3 large ideals: 14857882 Thu Jul 16 20:33:34 2009 relations with 4 large ideals: 7237102 Thu Jul 16 20:33:34 2009 relations with 5 large ideals: 32882 Thu Jul 16 20:33:34 2009 relations with 6 large ideals: 659597 Thu Jul 16 20:33:34 2009 relations with 7+ large ideals: 0 Thu Jul 16 20:33:34 2009 39907516 relations and about 32967969 large ideals Thu Jul 16 20:33:34 2009 commencing singleton removal, pass 2 Thu Jul 16 20:39:52 2009 found 11282742 singletons Thu Jul 16 20:39:52 2009 current dataset: 28624774 relations and about 20371358 large ideals Thu Jul 16 20:39:52 2009 commencing singleton removal, pass 3 Thu Jul 16 20:44:48 2009 found 2206322 singletons Thu Jul 16 20:44:48 2009 current dataset: 26418452 relations and about 18093846 large ideals Thu Jul 16 20:44:48 2009 commencing singleton removal, pass 4 Thu Jul 16 20:49:32 2009 found 472986 singletons Thu Jul 16 20:49:32 2009 current dataset: 25945466 relations and about 17617214 large ideals Thu Jul 16 20:49:32 2009 commencing singleton removal, final pass Thu Jul 16 20:55:53 2009 memory use: 532.8 MB Thu Jul 16 20:55:53 2009 commencing in-memory singleton removal Thu Jul 16 20:55:56 2009 begin with 25945466 relations and 21393353 unique ideals Thu Jul 16 20:56:37 2009 reduce to 19717751 relations and 14872914 ideals in 14 passes Thu Jul 16 20:56:37 2009 max relations containing the same ideal: 48 Thu Jul 16 20:56:43 2009 reading rational ideals above 720000 Thu Jul 16 20:56:43 2009 reading algebraic ideals above 720000 Thu Jul 16 20:56:43 2009 commencing singleton removal, final pass Thu Jul 16 21:03:01 2009 keeping 15815981 ideals with weight <= 20, new excess is 1924615 Thu Jul 16 21:03:40 2009 memory use: 499.5 MB Thu Jul 16 21:03:40 2009 commencing in-memory singleton removal Thu Jul 16 21:03:43 2009 begin with 19718141 relations and 15815981 unique ideals Thu Jul 16 21:04:11 2009 reduce to 19714577 relations and 15810571 ideals in 9 passes Thu Jul 16 21:04:11 2009 max relations containing the same ideal: 20 Thu Jul 16 21:04:26 2009 removing 2731961 relations and 2331961 ideals in 400000 cliques Thu Jul 16 21:04:27 2009 commencing in-memory singleton removal Thu Jul 16 21:04:29 2009 begin with 16982616 relations and 15810571 unique ideals Thu Jul 16 21:04:52 2009 reduce to 16727703 relations and 13217278 ideals in 9 passes Thu Jul 16 21:04:52 2009 max relations containing the same ideal: 20 Thu Jul 16 21:05:05 2009 removing 2046788 relations and 1646788 ideals in 400000 cliques Thu Jul 16 21:05:06 2009 commencing in-memory singleton removal Thu Jul 16 21:05:08 2009 begin with 14680915 relations and 13217278 unique ideals Thu Jul 16 21:05:28 2009 reduce to 14507203 relations and 11392654 ideals in 9 passes Thu Jul 16 21:05:28 2009 max relations containing the same ideal: 20 Thu Jul 16 21:05:40 2009 removing 1838879 relations and 1438879 ideals in 400000 cliques Thu Jul 16 21:05:41 2009 commencing in-memory singleton removal Thu Jul 16 21:05:42 2009 begin with 12668324 relations and 11392654 unique ideals Thu Jul 16 21:05:58 2009 reduce to 12506345 relations and 9787669 ideals in 8 passes Thu Jul 16 21:05:58 2009 max relations containing the same ideal: 20 Thu Jul 16 21:06:08 2009 removing 1726132 relations and 1326132 ideals in 400000 cliques Thu Jul 16 21:06:09 2009 commencing in-memory singleton removal Thu Jul 16 21:06:10 2009 begin with 10780213 relations and 9787669 unique ideals Thu Jul 16 21:06:25 2009 reduce to 10606310 relations and 8282583 ideals in 9 passes Thu Jul 16 21:06:25 2009 max relations containing the same ideal: 20 Thu Jul 16 21:06:34 2009 removing 526329 relations and 435156 ideals in 91173 cliques Thu Jul 16 21:06:34 2009 commencing in-memory singleton removal Thu Jul 16 21:06:36 2009 begin with 10079981 relations and 8282583 unique ideals Thu Jul 16 21:06:45 2009 reduce to 10062987 relations and 7830297 ideals in 6 passes Thu Jul 16 21:06:45 2009 max relations containing the same ideal: 19 Thu Jul 16 21:06:56 2009 relations with 0 large ideals: 271062 Thu Jul 16 21:06:56 2009 relations with 1 large ideals: 1391142 Thu Jul 16 21:06:56 2009 relations with 2 large ideals: 3031669 Thu Jul 16 21:06:56 2009 relations with 3 large ideals: 3193544 Thu Jul 16 21:06:56 2009 relations with 4 large ideals: 1672318 Thu Jul 16 21:06:56 2009 relations with 5 large ideals: 419717 Thu Jul 16 21:06:56 2009 relations with 6 large ideals: 81329 Thu Jul 16 21:06:56 2009 relations with 7+ large ideals: 2206 Thu Jul 16 21:06:56 2009 commencing 2-way merge Thu Jul 16 21:07:06 2009 reduce to 6429038 relation sets and 4196348 unique ideals Thu Jul 16 21:07:06 2009 commencing full merge Thu Jul 16 21:08:12 2009 memory use: 301.3 MB Thu Jul 16 21:08:13 2009 found 3209621 cycles, need 2904548 Thu Jul 16 21:08:14 2009 weight of 2904548 cycles is about 203674766 (70.12/cycle) Thu Jul 16 21:08:14 2009 distribution of cycle lengths: Thu Jul 16 21:08:14 2009 1 relations: 405554 Thu Jul 16 21:08:14 2009 2 relations: 321261 Thu Jul 16 21:08:14 2009 3 relations: 317273 Thu Jul 16 21:08:14 2009 4 relations: 298681 Thu Jul 16 21:08:14 2009 5 relations: 283233 Thu Jul 16 21:08:14 2009 6 relations: 258043 Thu Jul 16 21:08:14 2009 7 relations: 231041 Thu Jul 16 21:08:14 2009 8 relations: 201003 Thu Jul 16 21:08:14 2009 9 relations: 173146 Thu Jul 16 21:08:14 2009 10+ relations: 415313 Thu Jul 16 21:08:14 2009 heaviest cycle: 16 relations Thu Jul 16 21:08:15 2009 commencing cycle optimization Thu Jul 16 21:08:21 2009 start with 15578527 relations Thu Jul 16 21:08:55 2009 pruned 464052 relations Thu Jul 16 21:08:55 2009 memory use: 415.4 MB Thu Jul 16 21:08:55 2009 distribution of cycle lengths: Thu Jul 16 21:08:55 2009 1 relations: 405554 Thu Jul 16 21:08:55 2009 2 relations: 330438 Thu Jul 16 21:08:55 2009 3 relations: 331927 Thu Jul 16 21:08:55 2009 4 relations: 309381 Thu Jul 16 21:08:55 2009 5 relations: 294647 Thu Jul 16 21:08:55 2009 6 relations: 266318 Thu Jul 16 21:08:55 2009 7 relations: 236587 Thu Jul 16 21:08:55 2009 8 relations: 202715 Thu Jul 16 21:08:55 2009 9 relations: 171618 Thu Jul 16 21:08:55 2009 10+ relations: 355363 Thu Jul 16 21:08:55 2009 heaviest cycle: 16 relations Thu Jul 16 21:09:03 2009 RelProcTime: 2681 Thu Jul 16 21:09:03 2009 Thu Jul 16 21:09:03 2009 commencing linear algebra Thu Jul 16 21:09:08 2009 read 2904548 cycles Thu Jul 16 21:09:15 2009 cycles contain 8808029 unique relations Thu Jul 16 21:12:59 2009 read 8808029 relations Thu Jul 16 21:13:19 2009 using 20 quadratic characters above 536869788 Thu Jul 16 21:14:06 2009 building initial matrix Thu Jul 16 21:18:40 2009 memory use: 1022.6 MB Thu Jul 16 21:18:52 2009 read 2904548 cycles Thu Jul 16 21:20:09 2009 matrix is 2903959 x 2904548 (820.7 MB) with weight 259265005 (89.26/col) Thu Jul 16 21:20:09 2009 sparse part has weight 194797795 (67.07/col) Thu Jul 16 21:21:56 2009 filtering completed in 3 passes Thu Jul 16 21:21:57 2009 matrix is 2888026 x 2888226 (818.2 MB) with weight 258365301 (89.45/col) Thu Jul 16 21:21:57 2009 sparse part has weight 194268239 (67.26/col) Thu Jul 16 21:22:23 2009 read 2888226 cycles Thu Jul 16 21:40:33 2009 matrix is 2888026 x 2888226 (818.2 MB) with weight 258365301 (89.45/col) Thu Jul 16 21:40:33 2009 sparse part has weight 194268239 (67.26/col) Thu Jul 16 21:40:33 2009 saving the first 48 matrix rows for later Thu Jul 16 21:40:35 2009 matrix is 2887978 x 2888226 (778.5 MB) with weight 204903337 (70.94/col) Thu Jul 16 21:40:35 2009 sparse part has weight 186738649 (64.66/col) Thu Jul 16 21:40:35 2009 matrix includes 64 packed rows Thu Jul 16 21:40:35 2009 using block size 65536 for processor cache size 6144 kB Thu Jul 16 21:41:03 2009 commencing Lanczos iteration (4 threads) Thu Jul 16 21:41:03 2009 memory use: 859.7 MB Fri Jul 17 16:38:12 2009 lanczos halted after 45672 iterations (dim = 2887977) Fri Jul 17 16:38:34 2009 recovered 37 nontrivial dependencies Fri Jul 17 16:38:42 2009 BLanczosTime: 70179 Fri Jul 17 16:38:42 2009 Fri Jul 17 16:38:42 2009 commencing square root phase Fri Jul 17 16:38:42 2009 reading relations for dependency 1 Fri Jul 17 16:39:10 2009 read 1444749 cycles Fri Jul 17 16:39:13 2009 cycles contain 5349769 unique relations Fri Jul 17 16:45:39 2009 read 5349769 relations Fri Jul 17 16:46:16 2009 multiplying 4394854 relations Fri Jul 17 16:52:56 2009 multiply complete, coefficients have about 124.55 million bits Fri Jul 17 16:52:57 2009 initial square root is modulo 870936721 Fri Jul 17 17:05:43 2009 reading relations for dependency 2 Fri Jul 17 17:05:44 2009 read 1443452 cycles Fri Jul 17 17:05:48 2009 cycles contain 5351642 unique relations Fri Jul 17 17:11:20 2009 read 5351642 relations Fri Jul 17 17:11:57 2009 multiplying 4399136 relations Fri Jul 17 17:18:46 2009 multiply complete, coefficients have about 124.68 million bits Fri Jul 17 17:18:47 2009 initial square root is modulo 889146281 Fri Jul 17 17:31:55 2009 reading relations for dependency 3 Fri Jul 17 17:31:56 2009 read 1442841 cycles Fri Jul 17 17:32:00 2009 cycles contain 5342987 unique relations Fri Jul 17 17:36:56 2009 read 5342987 relations Fri Jul 17 17:37:31 2009 multiplying 4391770 relations Fri Jul 17 17:44:00 2009 multiply complete, coefficients have about 124.47 million bits Fri Jul 17 17:44:01 2009 initial square root is modulo 858842561 Fri Jul 17 17:57:08 2009 sqrtTime: 4706 Fri Jul 17 17:57:08 2009 prp60 factor: 591752848190830505194723691088958573025065122850764427487837 Fri Jul 17 17:57:08 2009 prp144 factor: 350496677863934757609414005722989412369536157605989693540146711579200859237238102599130471318852834601704462309602498012951936078401332556541157 Fri Jul 17 17:57:08 2009 elapsed time 21:40:59

Jul 23, 2009

By Robert Backstrom / GGNFS, Msieve / Jul 23, 2009
(43·10¹⁸²-61)/9 = 4(7)₁₈₁1_<183> = 3 · 2089 · C179
C179 = P88 · P92
P88 = 2548035129424789240102727461554777927306120058219282754067737790435073236169501864294189_<88>
P92 = 29919948397719090871041566799694898064009331023404415989596038975250131952057312120806299317_<92>

Number: n N=76237079587965179157137031718171019272024537701895289257663599453929755509458716734925447227984327074800985763168625782316543446270588443877098735882843111182029324681311277768913 ( 179 digits) SNFS difficulty: 184 digits. Divisors found: Thu Jul 23 08:02:02 2009 prp88 factor: 2548035129424789240102727461554777927306120058219282754067737790435073236169501864294189 Thu Jul 23 08:02:02 2009 prp92 factor: 29919948397719090871041566799694898064009331023404415989596038975250131952057312120806299317 Thu Jul 23 08:02:02 2009 elapsed time 03:04:57 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 225.40 hours. Scaled time: 571.17 units (timescale=2.534). Factorization parameters were as follows: name: KA_4_7_181_1 n: 76237079587965179157137031718171019272024537701895289257663599453929755509458716734925447227984327074800985763168625782316543446270588443877098735882843111182029324681311277768913 m: 2000000000000000000000000000000000000 deg: 5 c5: 1075 c0: -488 skew: 0.85 type: snfs lss: 1 rlim: 8400000 alim: 8400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4200000, 8000023) Primes: RFBsize:564877, AFBsize:563787, largePrimes:21426695 encountered Relations: rels:21796035, finalFF:1216407 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2437177 hash collisions in 23571532 relations Msieve: matrix is 1477220 x 1477468 (396.0 MB) Total sieving time: 224.66 hours. Total relation processing time: 0.74 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,56,56,2.5,2.5,100000 total time: 225.40 hours. --------- CPU info (if available) ----------

Jul 22, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve 1.42 / Jul 22, 2009
2·10¹⁹³+9 = 2(0)₁₉₂9_<194> = 41 · 200183 · 5328527 · 1518763338461_<13> · 711262813661921_<15> · 8504621858298220990261_<22> · C131
C131 = P56 · P76
P56 = 13056246011809721884007205309537122134790655929126011321_<56>
P76 = 3812573573319637471194915345352510153300362083742249817651638622768023693649_<76>

Wed Jul 22 14:19:03 2009 Msieve v. 1.42 Wed Jul 22 14:19:03 2009 random seeds: a5bf0718 1df83478 Wed Jul 22 14:19:03 2009 factoring 49777898511385657017959200641343160463020017114075893159149402568741104300447500577409539628482154712527537552631680837117009800329 (131 digits) Wed Jul 22 14:19:04 2009 searching for 15-digit factors Wed Jul 22 14:19:06 2009 commencing number field sieve (131-digit input) Wed Jul 22 14:19:06 2009 R0: -17132883862694021714256889 Wed Jul 22 14:19:06 2009 R1: 279017036996591 Wed Jul 22 14:19:06 2009 A0: 2507317928392803584490096701088 Wed Jul 22 14:19:06 2009 A1: 179085986367648223641880884 Wed Jul 22 14:19:06 2009 A2: 1315353739759960626176 Wed Jul 22 14:19:06 2009 A3: -4013501703489901 Wed Jul 22 14:19:06 2009 A4: -16033052242 Wed Jul 22 14:19:06 2009 A5: 33720 Wed Jul 22 14:19:06 2009 skew 253679.99, size 1.756545e-012, alpha -6.062530, combined = 8.425983e-011 Wed Jul 22 14:19:06 2009 Wed Jul 22 14:19:06 2009 commencing relation filtering Wed Jul 22 14:19:06 2009 estimated available RAM is 3232.4 MB Wed Jul 22 14:19:06 2009 commencing duplicate removal, pass 1 Wed Jul 22 14:22:45 2009 found 3646224 hash collisions in 24883919 relations Wed Jul 22 14:23:33 2009 added 120024 free relations Wed Jul 22 14:23:33 2009 commencing duplicate removal, pass 2 Wed Jul 22 14:24:31 2009 found 3092029 duplicates and 21911914 unique relations Wed Jul 22 14:24:31 2009 memory use: 106.6 MB Wed Jul 22 14:24:31 2009 reading ideals above 11993088 Wed Jul 22 14:24:35 2009 commencing singleton removal, initial pass Wed Jul 22 14:28:26 2009 memory use: 298.4 MB Wed Jul 22 14:28:26 2009 reading all ideals from disk Wed Jul 22 14:28:26 2009 memory use: 370.8 MB Wed Jul 22 14:28:26 2009 commencing in-memory singleton removal Wed Jul 22 14:28:29 2009 begin with 21911914 relations and 19550344 unique ideals Wed Jul 22 14:28:57 2009 reduce to 11773877 relations and 8107541 ideals in 16 passes Wed Jul 22 14:28:57 2009 max relations containing the same ideal: 44 Wed Jul 22 14:28:59 2009 reading ideals above 720000 Wed Jul 22 14:28:59 2009 commencing singleton removal, initial pass Wed Jul 22 14:31:26 2009 memory use: 149.2 MB Wed Jul 22 14:31:26 2009 reading all ideals from disk Wed Jul 22 14:31:26 2009 memory use: 354.5 MB Wed Jul 22 14:31:26 2009 commencing in-memory singleton removal Wed Jul 22 14:31:29 2009 begin with 11774472 relations and 9569468 unique ideals Wed Jul 22 14:31:47 2009 reduce to 11771578 relations and 9563831 ideals in 7 passes Wed Jul 22 14:31:47 2009 max relations containing the same ideal: 191 Wed Jul 22 14:31:59 2009 removing 2015830 relations and 1615830 ideals in 400000 cliques Wed Jul 22 14:32:00 2009 commencing in-memory singleton removal Wed Jul 22 14:32:03 2009 begin with 9755748 relations and 9563831 unique ideals Wed Jul 22 14:32:20 2009 reduce to 9572181 relations and 7757315 ideals in 8 passes Wed Jul 22 14:32:20 2009 max relations containing the same ideal: 154 Wed Jul 22 14:32:30 2009 removing 1521692 relations and 1121692 ideals in 400000 cliques Wed Jul 22 14:32:30 2009 commencing in-memory singleton removal Wed Jul 22 14:32:32 2009 begin with 8050489 relations and 7757315 unique ideals Wed Jul 22 14:32:44 2009 reduce to 7907442 relations and 6487093 ideals in 7 passes Wed Jul 22 14:32:44 2009 max relations containing the same ideal: 131 Wed Jul 22 14:32:53 2009 removing 1369689 relations and 969689 ideals in 400000 cliques Wed Jul 22 14:32:53 2009 commencing in-memory singleton removal Wed Jul 22 14:32:55 2009 begin with 6537753 relations and 6487093 unique ideals Wed Jul 22 14:33:04 2009 reduce to 6397323 relations and 5370834 ideals in 7 passes Wed Jul 22 14:33:04 2009 max relations containing the same ideal: 111 Wed Jul 22 14:33:11 2009 removing 1286700 relations and 886700 ideals in 400000 cliques Wed Jul 22 14:33:12 2009 commencing in-memory singleton removal Wed Jul 22 14:33:13 2009 begin with 5110623 relations and 5370834 unique ideals Wed Jul 22 14:33:20 2009 reduce to 4952018 relations and 4316640 ideals in 7 passes Wed Jul 22 14:33:20 2009 max relations containing the same ideal: 89 Wed Jul 22 14:33:25 2009 removing 1214883 relations and 814883 ideals in 400000 cliques Wed Jul 22 14:33:26 2009 commencing in-memory singleton removal Wed Jul 22 14:33:26 2009 begin with 3737135 relations and 4316640 unique ideals Wed Jul 22 14:33:32 2009 reduce to 3544361 relations and 3295202 ideals in 8 passes Wed Jul 22 14:33:32 2009 max relations containing the same ideal: 72 Wed Jul 22 14:33:36 2009 removing 466668 relations and 352093 ideals in 114575 cliques Wed Jul 22 14:33:36 2009 commencing in-memory singleton removal Wed Jul 22 14:33:37 2009 begin with 3077693 relations and 3295202 unique ideals Wed Jul 22 14:33:40 2009 reduce to 3041291 relations and 2905657 ideals in 6 passes Wed Jul 22 14:33:40 2009 max relations containing the same ideal: 68 Wed Jul 22 14:33:44 2009 relations with 0 large ideals: 471 Wed Jul 22 14:33:44 2009 relations with 1 large ideals: 2091 Wed Jul 22 14:33:44 2009 relations with 2 large ideals: 28692 Wed Jul 22 14:33:44 2009 relations with 3 large ideals: 163521 Wed Jul 22 14:33:44 2009 relations with 4 large ideals: 481707 Wed Jul 22 14:33:44 2009 relations with 5 large ideals: 813905 Wed Jul 22 14:33:44 2009 relations with 6 large ideals: 827216 Wed Jul 22 14:33:44 2009 relations with 7+ large ideals: 723688 Wed Jul 22 14:33:44 2009 commencing 2-way merge Wed Jul 22 14:33:48 2009 reduce to 2028230 relation sets and 1892596 unique ideals Wed Jul 22 14:33:48 2009 commencing full merge Wed Jul 22 14:34:37 2009 memory use: 196.2 MB Wed Jul 22 14:34:38 2009 found 1047881 cycles, need 1028796 Wed Jul 22 14:34:38 2009 weight of 1028796 cycles is about 72288141 (70.26/cycle) Wed Jul 22 14:34:38 2009 distribution of cycle lengths: Wed Jul 22 14:34:38 2009 1 relations: 83203 Wed Jul 22 14:34:38 2009 2 relations: 111470 Wed Jul 22 14:34:38 2009 3 relations: 123757 Wed Jul 22 14:34:38 2009 4 relations: 122068 Wed Jul 22 14:34:38 2009 5 relations: 113877 Wed Jul 22 14:34:38 2009 6 relations: 101487 Wed Jul 22 14:34:38 2009 7 relations: 86569 Wed Jul 22 14:34:38 2009 8 relations: 71513 Wed Jul 22 14:34:38 2009 9 relations: 57361 Wed Jul 22 14:34:38 2009 10+ relations: 157491 Wed Jul 22 14:34:38 2009 heaviest cycle: 18 relations Wed Jul 22 14:34:39 2009 commencing cycle optimization Wed Jul 22 14:34:41 2009 start with 5912490 relations Wed Jul 22 14:34:56 2009 pruned 179772 relations Wed Jul 22 14:34:56 2009 memory use: 149.2 MB Wed Jul 22 14:34:56 2009 distribution of cycle lengths: Wed Jul 22 14:34:56 2009 1 relations: 83203 Wed Jul 22 14:34:56 2009 2 relations: 114003 Wed Jul 22 14:34:56 2009 3 relations: 128763 Wed Jul 22 14:34:56 2009 4 relations: 125973 Wed Jul 22 14:34:56 2009 5 relations: 117959 Wed Jul 22 14:34:56 2009 6 relations: 104371 Wed Jul 22 14:34:56 2009 7 relations: 88089 Wed Jul 22 14:34:56 2009 8 relations: 71735 Wed Jul 22 14:34:56 2009 9 relations: 56564 Wed Jul 22 14:34:56 2009 10+ relations: 138136 Wed Jul 22 14:34:56 2009 heaviest cycle: 18 relations Wed Jul 22 14:35:00 2009 RelProcTime: 954 Wed Jul 22 14:35:00 2009 Wed Jul 22 14:35:00 2009 commencing linear algebra Wed Jul 22 14:35:00 2009 read 1028796 cycles Wed Jul 22 14:35:02 2009 cycles contain 2962793 unique relations Wed Jul 22 14:36:51 2009 read 2962793 relations Wed Jul 22 14:36:57 2009 using 20 quadratic characters above 268433820 Wed Jul 22 14:37:12 2009 building initial matrix Wed Jul 22 14:37:56 2009 memory use: 347.5 MB Wed Jul 22 14:37:58 2009 read 1028796 cycles Wed Jul 22 14:38:49 2009 matrix is 1028619 x 1028796 (291.5 MB) with weight 97512281 (94.78/col) Wed Jul 22 14:38:49 2009 sparse part has weight 69225192 (67.29/col) Wed Jul 22 14:39:04 2009 filtering completed in 2 passes Wed Jul 22 14:39:04 2009 matrix is 1028282 x 1028459 (291.5 MB) with weight 97497904 (94.80/col) Wed Jul 22 14:39:04 2009 sparse part has weight 69220272 (67.30/col) Wed Jul 22 14:39:09 2009 read 1028459 cycles Wed Jul 22 14:42:03 2009 matrix is 1028282 x 1028459 (291.5 MB) with weight 97497904 (94.80/col) Wed Jul 22 14:42:03 2009 sparse part has weight 69220272 (67.30/col) Wed Jul 22 14:42:04 2009 saving the first 48 matrix rows for later Wed Jul 22 14:42:04 2009 matrix is 1028234 x 1028459 (282.0 MB) with weight 77197089 (75.06/col) Wed Jul 22 14:42:04 2009 sparse part has weight 67760950 (65.89/col) Wed Jul 22 14:42:04 2009 matrix includes 64 packed rows Wed Jul 22 14:42:04 2009 using block size 65536 for processor cache size 6144 kB Wed Jul 22 14:42:12 2009 commencing Lanczos iteration (4 threads) Wed Jul 22 14:42:12 2009 memory use: 312.2 MB Wed Jul 22 16:23:16 2009 lanczos halted after 16260 iterations (dim = 1028232) Wed Jul 22 16:23:19 2009 recovered 28 nontrivial dependencies Wed Jul 22 16:23:20 2009 BLanczosTime: 6500 Wed Jul 22 16:23:20 2009 Wed Jul 22 16:23:20 2009 commencing square root phase Wed Jul 22 16:23:20 2009 reading relations for dependency 1 Wed Jul 22 16:23:20 2009 read 514616 cycles Wed Jul 22 16:23:22 2009 cycles contain 1855521 unique relations Wed Jul 22 16:25:56 2009 read 1855521 relations Wed Jul 22 16:26:07 2009 multiplying 1482034 relations Wed Jul 22 16:29:41 2009 multiply complete, coefficients have about 68.61 million bits Wed Jul 22 16:29:44 2009 initial square root is modulo 84317 Wed Jul 22 16:37:05 2009 reading relations for dependency 2 Wed Jul 22 16:37:06 2009 read 513871 cycles Wed Jul 22 16:37:07 2009 cycles contain 1853804 unique relations Wed Jul 22 16:40:23 2009 read 1853804 relations Wed Jul 22 16:40:36 2009 multiplying 1480638 relations Wed Jul 22 16:44:27 2009 multiply complete, coefficients have about 68.54 million bits Wed Jul 22 16:44:29 2009 initial square root is modulo 83207 Wed Jul 22 16:52:48 2009 sqrtTime: 1768 Wed Jul 22 16:52:48 2009 prp56 factor: 13056246011809721884007205309537122134790655929126011321 Wed Jul 22 16:52:48 2009 prp76 factor: 3812573573319637471194915345352510153300362083742249817651638622768023693649 Wed Jul 22 16:52:48 2009 elapsed time 02:33:45

Jul 22, 2009

By Sinkiti Sibata / Msieve / Jul 22, 2009
(4·10¹⁷⁰-13)/9 = (4)₁₆₉3_<170> = 43 · 49843993 · 2475812821_<10> · 125520143958780691_<18> · C134
C134 = P66 · P69
P66 = 134952326025103652801521248618834398257383508096149729562130206993_<66>
P69 = 494452513887969866030765721406804005551992171945654486556735975996359_<69>

Number: 44443_170 N=66727516858141401074243180482446319845168157241778593460594338756127146244380514569050496334811780938019385938969552861994164084338487 ( 134 digits) SNFS difficulty: 170 digits. Divisors found: r1=134952326025103652801521248618834398257383508096149729562130206993 (pp66) r2=494452513887969866030765721406804005551992171945654486556735975996359 (pp69) Version: Msieve-1.40 Total time: 62.21 hours. Scaled time: 159.50 units (timescale=2.564). Factorization parameters were as follows: name: 44443_170 n: 66727516858141401074243180482446319845168157241778593460594338756127146244380514569050496334811780938019385938969552861994164084338487 m: 10000000000000000000000000000000000 deg: 5 c5: 4 c0: -13 skew: 1.27 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2450000, 4950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 959702 x 959950 Total sieving time: 59.84 hours. Total relation processing time: 0.15 hours. Matrix solve time: 2.12 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 62.21 hours. --------- CPU info (if available) ----------

Jul 21, 2009

By Jo Yeong Uk / GMP-ECM / Jul 21, 2009
(43·10¹⁶⁸-61)/9 = 4(7)₁₆₇1_<169> = 22697 · 847871 · 280048951928996363825795273_<27> · C132
C132 = P38 · P95
P38 = 16901046374539237625557269338688649493_<38>
P95 = 52454187242637751875089575327021264362767456784230240263930131709150203218780655157553340044497_<95>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 886530651126585105903250758298570538352456873152422573299364523119106894143736122032708526032962960174606258358367676475085456490021 (132 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2321597130 Step 1 took 9853ms Step 2 took 5141ms ********** Factor found in step 2: 16901046374539237625557269338688649493 Found probable prime factor of 38 digits: 16901046374539237625557269338688649493 Probable prime cofactor 52454187242637751875089575327021264362767456784230240263930131709150203218780655157553340044497 has 95 digits

(14·10¹⁷⁰-11)/3 = 4(6)₁₆₉3_<171> = 17 · 11317 · 526732469 · 441078895079741_<15> · C143
C143 = P35 · P108
P35 = 35579941592008772423172650690055857_<35>
P108 = 293437047888738978141986455944132593215288834033455785264598594536814464364859742626924248414572744526052939_<108>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 10440473024812813910784256169406112481945315164487396088488010879249685174451988965209380312566607654421939858109611857042610749685869649013723 (143 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=7299964278 Step 1 took 12030ms Step 2 took 5520ms ********** Factor found in step 2: 35579941592008772423172650690055857 Found probable prime factor of 35 digits: 35579941592008772423172650690055857 Probable prime cofactor 293437047888738978141986455944132593215288834033455785264598594536814464364859742626924248414572744526052939 has 108 digits

Jul 20, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jul 20, 2009
(43·10¹⁸²+11)/9 = 4(7)₁₈₁9_<183> = 97 · 353 · C179
C179 = P50 · P129
P50 = 14420577088818323505616863399192301373953570591687_<50>
P129 = 967602241982232345120213379837347731892522485447083941533704978769489168236118988664746004583450464381451226448194873652427696437_<129>

Number: n N=13953382721818223117834694599391892111146805811097157728389292887993276416511719218999964305300013953382721818223117834694599391892111146805811097157728389292887993276416511719219 ( 179 digits) SNFS difficulty: 184 digits. Divisors found: Mon Jul 20 15:34:20 2009 prp50 factor: 14420577088818323505616863399192301373953570591687 Mon Jul 20 15:34:20 2009 prp129 factor: 967602241982232345120213379837347731892522485447083941533704978769489168236118988664746004583450464381451226448194873652427696437 Mon Jul 20 15:34:20 2009 elapsed time 02:54:11 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 193.09 hours. Scaled time: 501.06 units (timescale=2.595). Factorization parameters were as follows: name: KA_4_7_181_9 n: 13953382721818223117834694599391892111146805811097157728389292887993276416511719218999964305300013953382721818223117834694599391892111146805811097157728389292887993276416511719219 m: 2000000000000000000000000000000000000 deg: 5 c5: 1075 c0: 88 skew: 0.61 type: snfs lss: 1 rlim: 8400000 alim: 8400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4200000, 7800571) Primes: RFBsize:564877, AFBsize:565987, largePrimes:20079391 encountered Relations: rels:20295618, finalFF:975193 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2163898 hash collisions in 21874822 relations Msieve: matrix is 1411695 x 1411943 (380.5 MB) Total sieving time: 192.43 hours. Total relation processing time: 0.66 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,56,56,2.4,2.4,100000 total time: 193.09 hours. --------- CPU info (if available) ----------

Jul 20, 2009 (2nd)

By JPascoa / ggnfs, Msieve / Jul 20, 2009
(58·10¹⁶³+23)/9 = 6(4)₁₆₂7_<164> = 89 · 1361722388871787_<16> · 4310597647035065104719854951_<28> · C120
C120 = P52 · P68
P52 = 1394721122046343598898954744537561461564601370683041_<52>
P68 = 88446781495499968050670791016168541995795404733544043226877321557619_<68>

Number: 64447_163 N=123358594328791495556126661691507931865080054364763831788218995633927970659697113723897937644655278724450733932067639379 ( 120 digits) SNFS difficulty: 166 digits. Divisors found: r1=1394721122046343598898954744537561461564601370683041 (pp52) r2=88446781495499968050670791016168541995795404733544043226877321557619 (pp68) Version: Msieve-1.40 Total time: 122.50 hours. Scaled time: 109.52 units (timescale=0.894). Factorization parameters were as follows: n: 123358594328791495556126661691507931865080054364763831788218995633927970659697113723897937644655278724450733932067639379 m: 500000000000000000000000000000000 deg: 5 c5: 464 c0: 575 skew: 1.04 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 4550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 783565 x 783813 Total sieving time: 116.92 hours. Total relation processing time: 0.23 hours. Matrix solve time: 4.71 hours. Time per square root: 0.65 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 122.50 hours. --------- CPU info (if available) ----------

Jul 20, 2009

Msieve version 1.42 now available

Jul 19, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Jul 19, 2009
(52·10¹⁶⁹+11)/9 = 5(7)₁₆₈9_<170> = 4898850088247_<13> · 439584041643524138030023_<24> · C134
C134 = P37 · P97
P37 = 8664505744431290401102450208330703623_<37>
P97 = 3096570505500625044991977990181851031592172948921210009806769010994433962313317765726822407471733_<97>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 26830252932946670433282633304656708361984848210275832396303656863160017951525807757982726879368734099148688994835598198398948373188659 (134 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3033120199 Step 1 took 4243ms Step 2 took 4227ms ********** Factor found in step 2: 8664505744431290401102450208330703623 Found probable prime factor of 37 digits: 8664505744431290401102450208330703623 Probable prime cofactor 3096570505500625044991977990181851031592172948921210009806769010994433962313317765726822407471733 has 97 digits

(58·10¹⁶⁷+23)/9 = 6(4)₁₆₆7_<168> = 383 · 81817 · 116411 · 2539015319297239760208862106037195769_<37> · C119
C119 = P45 · P75
P45 = 374955885683995304806408659651797737916881109_<45>
P75 = 185568237447150266710225357815093455211539272721334490104275510776087852567_<75>

Number: 64447_167 N=69579902826814172117370151834844693730354578571165992862664790776297462544881688493563687017875009631281121822059456803 ( 119 digits) Divisors found: r1=374955885683995304806408659651797737916881109 r2=185568237447150266710225357815093455211539272721334490104275510776087852567 Version: Total time: 26.73 hours. Scaled time: 63.92 units (timescale=2.391). Factorization parameters were as follows: name: 64447_167 n: 69579902826814172117370151834844693730354578571165992862664790776297462544881688493563687017875009631281121822059456803 skew: 47349.17 # norm 2.24e+16 c5: 97680 c4: -13680015272 c3: -938576535914888 c2: 23575289591187172209 c1: 621356567553877682728762 c0: -9041730036885776114944853304 # alpha -5.82 Y1: 8824749378397 Y0: -58957282053378243449603 # Murphy_E 3.17e-10 # M 47344066638380041334839352664793755654023650330881408512311320265554362175946657539853017303858866715609793853414241683 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2000000, 4000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9815119 Max relations in full relation-set: Initial matrix: Pruned matrix : 649556 x 649804 Polynomial selection time: 2.28 hours. Total sieving time: 22.39 hours. Total relation processing time: 0.92 hours. Matrix solve time: 0.86 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000 total time: 26.73 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794) Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 19, 2009

By Andreas Tete / Msieve v.1.42, GGNFS / Jul 19, 2009
(58·10¹⁷⁶+23)/9 = 6(4)₁₇₅7_<177> = 8929 · 495108312917_<12> · 11709965533731842879_<20> · 584523038568799821949_<21> · C122
C122 = P59 · P63
P59 = 45945311893089576120617083406295313405032488551893964974131_<59>
P63 = 463536555085071903813929644352373972274237777973789300237822779_<63>

Sat Jul 18 19:00:08 2009 Msieve v. 1.42 Sat Jul 18 19:00:08 2009 random seeds: 9b67fae0 8958af49 Sat Jul 18 19:00:08 2009 factoring 21297331597231925575431021475147344519208861186265435531663300064057696819420851677903908845421164785867653061776497530049 (122 digits) Sat Jul 18 19:00:09 2009 searching for 15-digit factors Sat Jul 18 19:00:11 2009 commencing number field sieve (122-digit input) Sat Jul 18 19:00:11 2009 R0: -267740348395822115091009 Sat Jul 18 19:00:11 2009 R1: 9996088625369 Sat Jul 18 19:00:11 2009 A0: -12649253990942022464562560360 Sat Jul 18 19:00:11 2009 A1: -29032392364374356043724 Sat Jul 18 19:00:11 2009 A2: 71278176830714457495 Sat Jul 18 19:00:11 2009 A3: 1599979649307247 Sat Jul 18 19:00:11 2009 A4: -14210029177 Sat Jul 18 19:00:11 2009 A5: 15480 Sat Jul 18 19:00:11 2009 skew 70537.14, size 1.157191e-011, alpha -5.675436, combined = 2.303915e-010 Sat Jul 18 19:00:12 2009 Sat Jul 18 19:00:12 2009 commencing relation filtering Sat Jul 18 19:00:12 2009 estimated available RAM is 3069.5 MB Sat Jul 18 19:00:13 2009 commencing duplicate removal, pass 1 Sat Jul 18 19:01:46 2009 found 1157953 hash collisions in 8680732 relations Sat Jul 18 19:02:09 2009 added 58990 free relations Sat Jul 18 19:02:09 2009 commencing duplicate removal, pass 2 Sat Jul 18 19:02:23 2009 found 1051971 duplicates and 7687750 unique relations Sat Jul 18 19:02:23 2009 memory use: 49.3 MB Sat Jul 18 19:02:24 2009 reading ideals above 100000 Sat Jul 18 19:02:24 2009 commencing singleton removal, initial pass Sat Jul 18 19:04:18 2009 memory use: 149.2 MB Sat Jul 18 19:04:18 2009 reading all ideals from disk Sat Jul 18 19:04:24 2009 memory use: 274.8 MB Sat Jul 18 19:04:26 2009 keeping 8454285 ideals with weight <= 200, target excess is 42010 Sat Jul 18 19:04:28 2009 commencing in-memory singleton removal Sat Jul 18 19:04:30 2009 begin with 7687750 relations and 8454285 unique ideals Sat Jul 18 19:04:42 2009 reduce to 2823891 relations and 2738944 ideals in 17 passes Sat Jul 18 19:04:42 2009 max relations containing the same ideal: 99 Sat Jul 18 19:04:44 2009 removing 194198 relations and 176090 ideals in 18108 cliques Sat Jul 18 19:04:44 2009 commencing in-memory singleton removal Sat Jul 18 19:04:45 2009 begin with 2629693 relations and 2738944 unique ideals Sat Jul 18 19:04:50 2009 reduce to 2620563 relations and 2553639 ideals in 9 passes Sat Jul 18 19:04:50 2009 max relations containing the same ideal: 92 Sat Jul 18 19:04:52 2009 removing 143450 relations and 125342 ideals in 18108 cliques Sat Jul 18 19:04:52 2009 commencing in-memory singleton removal Sat Jul 18 19:04:53 2009 begin with 2477113 relations and 2553639 unique ideals Sat Jul 18 19:04:56 2009 reduce to 2471536 relations and 2422684 ideals in 7 passes Sat Jul 18 19:04:56 2009 max relations containing the same ideal: 90 Sat Jul 18 19:04:59 2009 relations with 0 large ideals: 128 Sat Jul 18 19:04:59 2009 relations with 1 large ideals: 447 Sat Jul 18 19:04:59 2009 relations with 2 large ideals: 5310 Sat Jul 18 19:04:59 2009 relations with 3 large ideals: 38239 Sat Jul 18 19:04:59 2009 relations with 4 large ideals: 163031 Sat Jul 18 19:04:59 2009 relations with 5 large ideals: 422649 Sat Jul 18 19:04:59 2009 relations with 6 large ideals: 675623 Sat Jul 18 19:04:59 2009 relations with 7+ large ideals: 1166109 Sat Jul 18 19:04:59 2009 commencing 2-way merge Sat Jul 18 19:05:02 2009 reduce to 1466516 relation sets and 1417664 unique ideals Sat Jul 18 19:05:02 2009 commencing full merge Sat Jul 18 19:05:39 2009 memory use: 153.5 MB Sat Jul 18 19:05:40 2009 found 749622 cycles, need 743864 Sat Jul 18 19:05:40 2009 weight of 743864 cycles is about 52090418 (70.03/cycle) Sat Jul 18 19:05:40 2009 distribution of cycle lengths: Sat Jul 18 19:05:40 2009 1 relations: 94279 Sat Jul 18 19:05:40 2009 2 relations: 90634 Sat Jul 18 19:05:40 2009 3 relations: 87859 Sat Jul 18 19:05:40 2009 4 relations: 78025 Sat Jul 18 19:05:40 2009 5 relations: 69180 Sat Jul 18 19:05:40 2009 6 relations: 57697 Sat Jul 18 19:05:40 2009 7 relations: 49517 Sat Jul 18 19:05:40 2009 8 relations: 41441 Sat Jul 18 19:05:40 2009 9 relations: 34605 Sat Jul 18 19:05:40 2009 10+ relations: 140627 Sat Jul 18 19:05:40 2009 heaviest cycle: 24 relations Sat Jul 18 19:05:40 2009 commencing cycle optimization Sat Jul 18 19:05:42 2009 start with 4383951 relations Sat Jul 18 19:05:54 2009 pruned 102411 relations Sat Jul 18 19:05:54 2009 memory use: 115.6 MB Sat Jul 18 19:05:54 2009 distribution of cycle lengths: Sat Jul 18 19:05:54 2009 1 relations: 94279 Sat Jul 18 19:05:54 2009 2 relations: 92647 Sat Jul 18 19:05:54 2009 3 relations: 90891 Sat Jul 18 19:05:54 2009 4 relations: 79701 Sat Jul 18 19:05:54 2009 5 relations: 70495 Sat Jul 18 19:05:54 2009 6 relations: 58154 Sat Jul 18 19:05:54 2009 7 relations: 49857 Sat Jul 18 19:05:54 2009 8 relations: 41116 Sat Jul 18 19:05:54 2009 9 relations: 34380 Sat Jul 18 19:05:54 2009 10+ relations: 132344 Sat Jul 18 19:05:54 2009 heaviest cycle: 24 relations Sat Jul 18 19:05:55 2009 RelProcTime: 343 Sat Jul 18 19:05:55 2009 Sat Jul 18 19:05:55 2009 commencing linear algebra Sat Jul 18 19:05:55 2009 read 743864 cycles Sat Jul 18 19:05:57 2009 cycles contain 2425496 unique relations Sat Jul 18 19:06:36 2009 read 2425496 relations Sat Jul 18 19:06:41 2009 using 20 quadratic characters above 134216420 Sat Jul 18 19:06:56 2009 building initial matrix Sat Jul 18 19:07:34 2009 memory use: 284.7 MB Sat Jul 18 19:07:35 2009 read 743864 cycles Sat Jul 18 19:07:36 2009 matrix is 743687 x 743864 (213.6 MB) with weight 71084008 (95.56/col) Sat Jul 18 19:07:36 2009 sparse part has weight 50032887 (67.26/col) Sat Jul 18 19:07:46 2009 filtering completed in 2 passes Sat Jul 18 19:07:46 2009 matrix is 743088 x 743265 (213.5 MB) with weight 71058320 (95.60/col) Sat Jul 18 19:07:46 2009 sparse part has weight 50025604 (67.31/col) Sat Jul 18 19:07:49 2009 read 743265 cycles Sat Jul 18 19:07:51 2009 matrix is 743088 x 743265 (213.5 MB) with weight 71058320 (95.60/col) Sat Jul 18 19:07:51 2009 sparse part has weight 50025604 (67.31/col) Sat Jul 18 19:07:51 2009 saving the first 48 matrix rows for later Sat Jul 18 19:07:51 2009 matrix is 743040 x 743265 (203.9 MB) with weight 56099385 (75.48/col) Sat Jul 18 19:07:51 2009 sparse part has weight 48981570 (65.90/col) Sat Jul 18 19:07:51 2009 matrix includes 64 packed rows Sat Jul 18 19:07:51 2009 using block size 65536 for processor cache size 3072 kB Sat Jul 18 19:07:57 2009 commencing Lanczos iteration Sat Jul 18 19:07:57 2009 memory use: 207.0 MB Sat Jul 18 20:29:59 2009 lanczos halted after 11749 iterations (dim = 743039) Sat Jul 18 20:30:01 2009 recovered 33 nontrivial dependencies Sat Jul 18 20:30:02 2009 BLanczosTime: 5047 Sat Jul 18 20:30:02 2009 Sat Jul 18 20:30:02 2009 commencing square root phase Sat Jul 18 20:30:02 2009 reading relations for dependency 1 Sat Jul 18 20:30:02 2009 read 371133 cycles Sat Jul 18 20:30:03 2009 cycles contain 1485520 unique relations Sat Jul 18 20:30:39 2009 read 1485520 relations Sat Jul 18 20:30:48 2009 multiplying 1210228 relations Sat Jul 18 20:34:22 2009 multiply complete, coefficients have about 55.54 million bits Sat Jul 18 20:34:24 2009 initial square root is modulo 94007273 Sat Jul 18 20:40:15 2009 reading relations for dependency 2 Sat Jul 18 20:40:15 2009 read 371938 cycles Sat Jul 18 20:40:16 2009 cycles contain 1488775 unique relations Sat Jul 18 20:40:51 2009 read 1488775 relations Sat Jul 18 20:40:59 2009 multiplying 1213308 relations Sat Jul 18 20:44:33 2009 multiply complete, coefficients have about 55.67 million bits Sat Jul 18 20:44:36 2009 initial square root is modulo 98413577 Sat Jul 18 20:50:27 2009 reading relations for dependency 3 Sat Jul 18 20:50:28 2009 read 371787 cycles Sat Jul 18 20:50:28 2009 cycles contain 1488232 unique relations Sat Jul 18 20:51:02 2009 read 1488232 relations Sat Jul 18 20:51:10 2009 multiplying 1212158 relations Sat Jul 18 20:54:44 2009 multiply complete, coefficients have about 55.62 million bits Sat Jul 18 20:54:47 2009 initial square root is modulo 96742643 Sat Jul 18 21:00:38 2009 reading relations for dependency 4 Sat Jul 18 21:00:38 2009 read 372619 cycles Sat Jul 18 21:00:39 2009 cycles contain 1490002 unique relations Sat Jul 18 21:01:12 2009 read 1490002 relations Sat Jul 18 21:01:22 2009 multiplying 1214630 relations Sat Jul 18 21:04:56 2009 multiply complete, coefficients have about 55.74 million bits Sat Jul 18 21:04:58 2009 initial square root is modulo 100489853 Sat Jul 18 21:10:49 2009 reading relations for dependency 5 Sat Jul 18 21:10:49 2009 read 371616 cycles Sat Jul 18 21:10:50 2009 cycles contain 1487843 unique relations Sat Jul 18 21:11:23 2009 read 1487843 relations Sat Jul 18 21:11:32 2009 multiplying 1212846 relations Sat Jul 18 21:15:06 2009 multiply complete, coefficients have about 55.66 million bits Sat Jul 18 21:15:09 2009 initial square root is modulo 97915031 Sat Jul 18 21:21:01 2009 reading relations for dependency 6 Sat Jul 18 21:21:01 2009 read 371752 cycles Sat Jul 18 21:21:02 2009 cycles contain 1489453 unique relations Sat Jul 18 21:21:37 2009 read 1489453 relations Sat Jul 18 21:21:46 2009 multiplying 1214234 relations Sat Jul 18 21:25:21 2009 multiply complete, coefficients have about 55.72 million bits Sat Jul 18 21:25:23 2009 initial square root is modulo 99859171 Sat Jul 18 21:31:15 2009 sqrtTime: 3673 Sat Jul 18 21:31:15 2009 prp59 factor: 45945311893089576120617083406295313405032488551893964974131 Sat Jul 18 21:31:15 2009 prp63 factor: 463536555085071903813929644352373972274237777973789300237822779 Sat Jul 18 21:31:15 2009 elapsed time 02:31:07

Jul 18, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jul 18, 2009
(58·10¹⁶¹+23)/9 = 6(4)₁₆₀7_<162> = 41119327973436033475483754806134272837_<38> · C125
C125 = P50 · P75
P50 = 26871790039300526486196912904597959855554874021199_<50>
P75 = 583234060233196823479456446336892759281171709697223343472935319966425238269_<75>

Number: 64447_161 N=15672543210355221701053940350577676484197328922241828151784149179051334607839580596202241048609582134533477776622521732064531 ( 125 digits) SNFS difficulty: 162 digits. Divisors found: r1=26871790039300526486196912904597959855554874021199 r2=583234060233196823479456446336892759281171709697223343472935319966425238269 Version: Total time: 20.09 hours. Scaled time: 47.97 units (timescale=2.388). Factorization parameters were as follows: n: 15672543210355221701053940350577676484197328922241828151784149179051334607839580596202241048609582134533477776622521732064531 m: 100000000000000000000000000000000 deg: 5 c5: 580 c0: 23 skew: 0.52 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2000000, 3700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9704756 Max relations in full relation-set: Initial matrix: Pruned matrix : 695279 x 695527 Total sieving time: 18.21 hours. Total relation processing time: 0.80 hours. Matrix solve time: 1.01 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000 total time: 20.09 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794) Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹⁶²+23)/9 = 6(4)₁₆₁7_<163> = 3² · 24247 · 1079831 · 2020506749_<10> · C143
C143 = P42 · P101
P42 = 149341881640836290021255337570732276202949_<42>
P101 = 90633185966835800545817749240634207154524406954605664798680122666388901649995696515931063037625341319_<101>

Number: 64447_162 N=13535330531391096719446805778580505859562186778278308618604894946818978050168809172701900039808903911493436257192219298250447501692737439349731 ( 143 digits) SNFS difficulty: 164 digits. Divisors found: r1=149341881640836290021255337570732276202949 r2=90633185966835800545817749240634207154524406954605664798680122666388901649995696515931063037625341319 Version: Total time: 26.23 hours. Scaled time: 62.57 units (timescale=2.385). Factorization parameters were as follows: n: 13535330531391096719446805778580505859562186778278308618604894946818978050168809172701900039808903911493436257192219298250447501692737439349731 m: 200000000000000000000000000000000 deg: 5 c5: 725 c0: 92 skew: 0.66 type: snfs lss: 1 rlim: 4400000 alim: 4400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2200000, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9867056 Max relations in full relation-set: Initial matrix: Pruned matrix : 798231 x 798479 Total sieving time: 23.63 hours. Total relation processing time: 1.06 hours. Matrix solve time: 1.34 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 26.23 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794) Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 18, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jul 18, 2009
(58·10¹⁶⁴+23)/9 = 6(4)₁₆₃7_<165> = 17 · 71 · 109 · 1811 · C157
C157 = P50 · P108
P50 = 11500057744747399273355108662919213155050608195831_<50>
P108 = 235197794368519156880312362442167554274367596081043998198046134333506670922483690675068444570466640194016809_<108>

Number: n N=2704788216675194980499542551060655021724236388702534810044917685756135276824583595510670303940880582146643295076682884124461339036642305529913813504377723279 ( 157 digits) SNFS difficulty: 166 digits. Divisors found: Sat Jul 18 06:33:52 2009 prp50 factor: 11500057744747399273355108662919213155050608195831 Sat Jul 18 06:33:52 2009 prp108 factor: 235197794368519156880312362442167554274367596081043998198046134333506670922483690675068444570466640194016809 Sat Jul 18 06:33:52 2009 elapsed time 00:48:58 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 33.45 hours. Scaled time: 88.29 units (timescale=2.639). Factorization parameters were as follows: name: KA_6_4_163_7 n: 2704788216675194980499542551060655021724236388702534810044917685756135276824583595510670303940880582146643295076682884124461339036642305529913813504377723279 m: 1000000000000000000000000000000000 deg: 5 c5: 29 c0: 115 skew: 1.32 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 20000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2100000, 3879990) Primes: RFBsize:296314, AFBsize:296441, largePrimes:15128491 encountered Relations: rels:14197589, finalFF:565554 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1497712 hash collisions in 16067174 relations Msieve: matrix is 728489 x 728737 (194.4 MB) Total sieving time: 33.16 hours. Total relation processing time: 0.30 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000 total time: 33.45 hours. --------- CPU info (if available) ----------

2·10²²⁰-1 = 1(9)_220<221> = 7 · 8524543 · C213
C213 = P49 · P165
P49 = 1083123216870509849562557573497140850225905243919_<49>
P165 = 309444654420209152261395329908853882478560572701303797798488365664928863916804072609327933421236573012248026757692102667702446776183075707594247676208587347163650521_<165>

Number: n N=335166689539000171957270067984038222677408379210810144644368954106144709793491904157543359551021428027620617651543649570757886124469412277333476159031968885939943391351636931487956932957327699896304453756976431799 ( 213 digits) SNFS difficulty: 221 digits. Divisors found: Sat Jul 18 23:40:02 2009 prp49 factor: 1083123216870509849562557573497140850225905243919 Sat Jul 18 23:40:02 2009 prp165 factor: 309444654420209152261395329908853882478560572701303797798488365664928863916804072609327933421236573012248026757692102667702446776183075707594247676208587347163650521 Sat Jul 18 23:40:02 2009 elapsed time 66:40:35 (Msieve 1.39 - dependency 5) Version: GGNFS-0.77.1-20050930-k8 Total time: 235.94 hours. Scaled time: 475.41 units (timescale=2.015). Factorization parameters were as follows: name: KA_1_9_220 n: 335166689539000171957270067984038222677408379210810144644368954106144709793491904157543359551021428027620617651543649570757886124469412277333476159031968885939943391351636931487956932957327699896304453756976431799 m: 5000000000000000000000000000000000000 deg: 6 c6: 32 c0: -25 skew: 0.96 type: snfs lss: 1 rlim: 35000000 alim: 35000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 35000000/35000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [17500000, 57299990) Primes: RFBsize:2146775, AFBsize:2145196, largePrimes:38632996 encountered Relations: rels:36859864, finalFF:1918519 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 8934321 hash collisions in 51196493 relations Msieve: matrix is 5501339 x 5501587 (1489.6 MB) Total sieving time: 233.50 hours. Total relation processing time: 2.44 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,221,6,0,0,0,0,0,0,0,0,35000000,35000000,29,29,58,58,2.6,2.6,100000 total time: 235.94 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352056k/3407296k available (3119k kernel code, 53956k reserved, 1894k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.68 BogoMIPS (lpj=2830844) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22644.41 BogoMIPS).

Jul 18, 2009 (2nd)

By JPascoa / ggnfs, Msieve / Jul 18, 2009
(56·10¹⁷⁵+61)/9 = 6(2)₁₇₄9_<176> = 3 · 31 · 2711 · C171
C171 = P48 · P53 · P70
P48 = 388515540492427348907583886855452752043478553029_<48>
P53 = 70798724686624585386544472933176159270934345581903249_<53>
P70 = 8972205695485573426892548531463913519652897767969898815437666920730963_<70>

Number: 62229_175 N=246793121699417436022188464448789766194366330014406548479203492827795251612198102601596134514590982267473503893822547812862064239368174352289248589863765789801891228575823 ( 171 digits) SNFS difficulty: 176 digits. Divisors found: r1=388515540492427348907583886855452752043478553029 (pp48) r2=70798724686624585386544472933176159270934345581903249 (pp53) r3=8972205695485573426892548531463913519652897767969898815437666920730963 (pp70) Version: Msieve-1.40 Total time: 190.37 hours. Scaled time: 170.00 units (timescale=0.893). Factorization parameters were as follows: n: 246793121699417436022188464448789766194366330014406548479203492827795251612198102601596134514590982267473503893822547812862064239368174352289248589863765789801891228575823 m: 100000000000000000000000000000000000 deg: 5 c5: 56 c0: 61 skew: 1.02 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3100000, 6400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1186087 x 1186335 Total sieving time: 175.31 hours. Total relation processing time: 0.43 hours. Matrix solve time: 12.30 hours. Time per square root: 2.33 hours. Prototype def-par.txt line would be: snfs,176.000,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000 total time: 190.37 hours. --------- CPU info (if available) ----------

Jul 18, 2009

By Andreas Tete / Syd`s Database workers / Jul 18, 2009
(58·10¹⁶⁹+23)/9 = 6(4)₁₆₈7_<170> = 19 · 595027205653663_<15> · C154
C154 = P44 · P111
P44 = 25375530110051932248409455637683310452044129_<44>
P111 = 224636299692188654900752577911302035085906908095641797207881999549460700135118306963468485330593067442061655419_<111>

Syd`s Database Workers found this p44 factor 25375530110051932248409455637683310452044129

Jul 17, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Jul 17, 2009
(58·10¹⁵⁸+23)/9 = 6(4)₁₅₇7_<159> = 507258946185199073_<18> · C142
C142 = P52 · P90
P52 = 1278645878079139367561302863672131908561906870215169_<52>
P90 = 993586051553808199193408457585820294273094326234517367149202785954627596743988796894988031_<90>

Number: 64447_158 N=1270444709336204120838955092427862236338311988888771908849602795998904887144640225487688999309661201835162015891793735455328916625770649642239 ( 142 digits) SNFS difficulty: 161 digits. Divisors found: r1=1278645878079139367561302863672131908561906870215169 r2=993586051553808199193408457585820294273094326234517367149202785954627596743988796894988031 Version: Total time: 19.20 hours. Scaled time: 45.85 units (timescale=2.388). Factorization parameters were as follows: n: 1270444709336204120838955092427862236338311988888771908849602795998904887144640225487688999309661201835162015891793735455328916625770649642239 m: 100000000000000000000000000000000 deg: 5 c5: 29 c0: 1150 skew: 2.09 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9559208 Max relations in full relation-set: Initial matrix: Pruned matrix : 662774 x 663022 Total sieving time: 17.47 hours. Total relation processing time: 0.77 hours. Matrix solve time: 0.88 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 19.20 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794) Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹⁶⁷+23)/9 = 6(4)₁₆₆7_<168> = 383 · 81817 · 116411 · C156
C156 = P37 · C119
P37 = 2539015319297239760208862106037195769_<37>
C119 = [69579902826814172117370151834844693730354578571165992862664790776297462544881688493563687017875009631281121822059456803_<119>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 176664439192494500603903652629064270381455362741433055190135752367595572210582780887956047748456308226710844007728629140020317113769890466444789777509866507 (156 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4052174073 Step 1 took 5585ms Step 2 took 4930ms ********** Factor found in step 2: 2539015319297239760208862106037195769 Found probable prime factor of 37 digits: 2539015319297239760208862106037195769 Composite cofactor 69579902826814172117370151834844693730354578571165992862664790776297462544881688493563687017875009631281121822059456803 has 119 digits

Jul 17, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jul 17, 2009
(25·10¹⁸²-7)/9 = 2(7)_182<183> = 17117 · C179
C179 = P56 · P124
P56 = 11668612365029158264973585406781904053320654630592190117_<56>
P124 = 1390755018908550004808948472357508980894052680062194565556521981244963879863839918251881991075491489862525029001916349179393_<124>

Number: n N=16228181210362667393689184890914165903942149779621299163274976793700869181385627024465605992742757362725815141542196516783185007757070618553355014183430377856971302084347594658981 ( 179 digits) SNFS difficulty: 184 digits. Divisors found: Fri Jul 17 20:32:46 2009 prp56 factor: 11668612365029158264973585406781904053320654630592190117 Fri Jul 17 20:32:46 2009 prp124 factor: 1390755018908550004808948472357508980894052680062194565556521981244963879863839918251881991075491489862525029001916349179393 Fri Jul 17 20:32:46 2009 elapsed time 02:17:34 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 144.30 hours. Scaled time: 368.54 units (timescale=2.554). Factorization parameters were as follows: name: KA_2_7_182 n: 16228181210362667393689184890914165903942149779621299163274976793700869181385627024465605992742757362725815141542196516783185007757070618553355014183430377856971302084347594658981 m: 5000000000000000000000000000000000000 deg: 5 c5: 4 c0: -35 skew: 1.54 type: snfs lss: 1 rlim: 8200000 alim: 8200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8200000/8200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4100000, 6500519) Primes: RFBsize:552319, AFBsize:551943, largePrimes:21016285 encountered Relations: rels:21228277, finalFF:1081466 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1872658 hash collisions in 22409992 relations Msieve: matrix is 1283524 x 1283772 (345.3 MB) Total sieving time: 143.77 hours. Total relation processing time: 0.52 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,8200000,8200000,28,28,56,56,2.5,2.5,100000 total time: 144.30 hours. --------- CPU info (if available) ----------

Jul 17, 2009 (2nd)

By Andreas Tete / Syd`s Databaseworkers / Jul 17, 2009
(58·10²⁰⁵+23)/9 = 6(4)₂₀₄7_<206> = 19 · 4673817737_<10> · 5386475191_<10> · C186
C186 = P44 · C142
P44 = 37279635067379744491429662807584297718778261_<44>
C142 = [3613963770556477654016730027656282688127304025375501313679954016553439847689009024896441883490154237053247753961776552755718531951417094099999_<142>]

Syd`s Databaseworkers found this factor with ecm and a B1 with 3000000 p44 = 37279635067379744491429662807584297718778261

(58·10²⁰¹+23)/9 = 6(4)₂₀₀7_<202> = 3 · 7 · 59 · 1077279209_<10> · 1781627747_<10> · C181
C181 = P32 · P149
P32 = 30297092310814121029529794339259_<32>
P149 = 89447453611115384235878445655526795835222280743403456616133385462314670368342358184437926433531052514215730265019173286277064719302589369837790759489_<149>

Syd`s Databaseworkers found this p32 factor 30297092310814121029529794339259

Jul 17, 2009

By Jo Yeong Uk / GMP-ECM / Jul 17, 2009
(58·10¹⁶⁶+23)/9 = 6(4)₁₆₅7_<167> = 67 · 269 · 24659821 · 359583120536779_<15> · 37955506286865983_<17> · C125
C125 = P38 · P87
P38 = 34290262392024774518344843759406959751_<38>
P87 = 309830085865730714982413828543955085580794667849260732917353228988602413576841495364287_<87>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 10624154941279472588706800909070323594739495600215523842393261989133431103918712360142396758107111721514498237754750891812537 (125 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5400989727 Step 1 took 4399ms Step 2 took 4274ms ********** Factor found in step 2: 34290262392024774518344843759406959751 Found probable prime factor of 38 digits: 34290262392024774518344843759406959751 Probable prime cofactor 309830085865730714982413828543955085580794667849260732917353228988602413576841495364287 has 87 digits

Jul 16, 2009 (2nd)

By Jo Yeong Uk / GGNFS/Msieve v1.39 / Jul 16, 2009
(58·10¹⁵³+23)/9 = 6(4)₁₅₂7_<154> = 3³ · 7² · 13386589 · 92319833 · 394377397 · C127
C127 = P45 · P83
P45 = 814705712881851172222015572110575961300237593_<45>
P83 = 12267269943728648564005575671767203078380537568076048469810797003362184815778995757_<83>

Number: 64447_153 N=9994214904619554942976947840573200293185186344913231726692244414931835344290389939721451670688386247341373699755831583038892901 ( 127 digits) SNFS difficulty: 156 digits. Divisors found: r1=814705712881851172222015572110575961300237593 r2=12267269943728648564005575671767203078380537568076048469810797003362184815778995757 Version: Total time: 12.80 hours. Scaled time: 30.18 units (timescale=2.358). Factorization parameters were as follows: n: 9994214904619554942976947840573200293185186344913231726692244414931835344290389939721451670688386247341373699755831583038892901 m: 10000000000000000000000000000000 deg: 5 c5: 29 c0: 1150 skew: 2.09 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1300000, 2500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8451961 Max relations in full relation-set: Initial matrix: Pruned matrix : 479129 x 479377 Total sieving time: 11.73 hours. Total relation processing time: 0.49 hours. Matrix solve time: 0.46 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 12.80 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794) Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 16, 2009

By Robert Backstrom / GGNFS, Msieve / Jul 16, 2009
(14·10¹⁸³+1)/3 = 4(6)₁₈₂7_<184> = 13 · 223 · 647 · C178
C178 = P76 · P103
P76 = 2382309436848608429515710782337046103074905774875135063353620428270919969829_<76>
P103 = 1044374150200446498197582320576516819989106942296904804562163907478690398558019374206562021089536289091_<103>

Number: n N=2488022393623269691497663302682674602747238783861762632356126995060742401002033247443245987752887483274713748580716511351868744734056174925034996700704590170285584096134341835439 ( 178 digits) SNFS difficulty: 185 digits. Divisors found: Thu Jul 16 02:37:54 2009 prp76 factor: 2382309436848608429515710782337046103074905774875135063353620428270919969829 Thu Jul 16 02:37:54 2009 prp103 factor: 1044374150200446498197582320576516819989106942296904804562163907478690398558019374206562021089536289091 Thu Jul 16 02:37:54 2009 elapsed time 02:45:14 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 193.61 hours. Scaled time: 494.47 units (timescale=2.554). Factorization parameters were as follows: name: KA_4_6_182_7 n: 2488022393623269691497663302682674602747238783861762632356126995060742401002033247443245987752887483274713748580716511351868744734056174925034996700704590170285584096134341835439 m: 10000000000000000000000000000000000000 deg: 5 c5: 7 c0: 50 skew: 1.48 type: snfs lss: 1 rlim: 8800000 alim: 8800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8800000/8800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4400000, 7649990) Primes: RFBsize:590006, AFBsize:591015, largePrimes:20956756 encountered Relations: rels:20817925, finalFF:1183054 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2257684 hash collisions in 23732928 relations Msieve: matrix is 1367636 x 1367884 (364.2 MB) Total sieving time: 193.00 hours. Total relation processing time: 0.61 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,56,56,2.5,2.5,100000 total time: 193.61 hours. --------- CPU info (if available) ----------

Jul 15, 2009 (2nd)

By JPascoa / ggnfs, Msieve / Jul 15, 2009
(58·10¹⁵⁶+23)/9 = 6(4)₁₅₅7_<157> = 3 · 307 · 763897 · C148
C148 = P42 · P107
P42 = 120066543180694111133541404474922697213321_<42>
P107 = 76290250756513641445476454090142648409983943145226476005174220199825080683439408569647411791219214819389111_<107>

Number: 64447_156 N=9159906686722926709303097964633626498847435078929596419140294453156929171877364472475281345479703778592573903540222016425335256213162613039271547631 ( 148 digits) SNFS difficulty: 158 digits. Divisors found: r1=120066543180694111133541404474922697213321 (pp42) r2=76290250756513641445476454090142648409983943145226476005174220199825080683439408569647411791219214819389111 (pp107) Version: Msieve-1.40 Total time: 59.23 hours. Scaled time: 52.66 units (timescale=0.889). Factorization parameters were as follows: n: 9159906686722926709303097964633626498847435078929596419140294453156929171877364472475281345479703778592573903540222016425335256213162613039271547631 m: 20000000000000000000000000000000 deg: 5 c5: 145 c0: 184 skew: 1.05 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor base limits: 3100000/3100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1550000, 2750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 604903 x 605151 Total sieving time: 56.56 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.34 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,158.000,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 59.23 hours. --------- CPU info (if available) ----------

Jul 15, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jul 15, 2009
(58·10¹⁴⁵+23)/9 = 6(4)₁₄₄7_<146> = 318103 · 23255597 · 24166991 · 24837440522145492041_<20> · C107
C107 = P42 · P65
P42 = 155862830136335532804447504661369172098147_<42>
P65 = 93114699926353630931013362844178771981034759538690356442350389481_<65>

Number: 64447_145 N=14513120657817110724068948596869268773609716183566522071117683501229380132163791152524290662673843408391707 ( 107 digits) Divisors found: r1=155862830136335532804447504661369172098147 r2=93114699926353630931013362844178771981034759538690356442350389481 Version: Total time: 6.15 hours. Scaled time: 14.67 units (timescale=2.385). Factorization parameters were as follows: name: 64447_145 n: 14513120657817110724068948596869268773609716183566522071117683501229380132163791152524290662673843408391707 skew: 39366.66 # norm 1.35e+15 c5: 10260 c4: -1732448568 c3: -40955835229705 c2: 2591026688417304464 c1: 35043786271468244640188 c0: -384519196336207960118558544 # alpha -6.76 Y1: 94483556057 Y0: -269232718404910182205 # Murphy_E 1.52e-09 # M 1883062411933760718032814856662790779215812496228563671416845431180490880688470056173105140057998316018953 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7242468 Max relations in full relation-set: Initial matrix: Pruned matrix : 327166 x 327414 Polynomial selection time: 0.43 hours. Total sieving time: 4.66 hours. Total relation processing time: 0.66 hours. Matrix solve time: 0.22 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 6.15 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁴⁷+23)/9 = 6(4)₁₄₆7_<148> = 3 · 7 · 19448841488893_<14> · 805559364860507_<15> · C119
C119 = P51 · P69
P51 = 117743176838317603744085092073414896474908231317839_<51>
P69 = 166356261680136035603069369279866858793166950948301687007455754691363_<69>

Number: 64447_147 N=19587314737165695603470071257269254262295902571320784295305733164689395113045338701101302069147682911255882924201124557 ( 119 digits) SNFS difficulty: 149 digits. Divisors found: r1=117743176838317603744085092073414896474908231317839 r2=166356261680136035603069369279866858793166950948301687007455754691363 Version: Total time: 8.55 hours. Scaled time: 20.40 units (timescale=2.387). Factorization parameters were as follows: n: 19587314737165695603470071257269254262295902571320784295305733164689395113045338701101302069147682911255882924201124557 m: 200000000000000000000000000000 deg: 5 c5: 725 c0: 92 skew: 0.66 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1500000, 3225001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6995787 Max relations in full relation-set: Initial matrix: Pruned matrix : 442563 x 442811 Total sieving time: 7.39 hours. Total relation processing time: 0.72 hours. Matrix solve time: 0.38 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,49,49,2.3,2.3,75000 total time: 8.55 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Jul 14, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM, YAFU 1.10 / Jul 14, 2009
(58·10¹²⁸+23)/9 = 6(4)₁₂₇7_<129> = 131 · 41813 · 21245655914760583_<17> · C106
C106 = P36 · P70
P36 = 760985107913167809574082276999951959_<36>
P70 = 7277070100650168876742315488211887360553220961176794222662356452710017_<70>

Number: 64447_128 N=5537741975834955696163581925148970165169810424088982787295926273785929205033292036428911457802364358073303 ( 106 digits) SNFS difficulty: 131 digits. Divisors found: r1=760985107913167809574082276999951959 r2=7277070100650168876742315488211887360553220961176794222662356452710017 Version: Total time: 1.72 hours. Scaled time: 4.09 units (timescale=2.378). Factorization parameters were as follows: n: 5537741975834955696163581925148970165169810424088982787295926273785929205033292036428911457802364358073303 m: 100000000000000000000000000 deg: 5 c5: 29 c0: 1150 skew: 2.09 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 1000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2901625 Max relations in full relation-set: Initial matrix: Pruned matrix : 158539 x 158787 Total sieving time: 1.53 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 1.72 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁷¹+23)/9 = 6(4)₁₇₀7_<172> = 3² · 7 · 163 · 229 · 43607 · 355636003 · 1269791928287_<13> · 111929378928377_<15> · 29987432328229516862586197167_<29> · C98
C98 = P31 · P32 · P36
P31 = 5256085350367721968365243508879_<31>
P32 = 14889514327152662463708208717849_<32>
P36 = 529786685826043275442599790114501549_<36>

Number: 64447_171 N=41461401722079143647924150625301340578093020537184821796736112311143710226687952818709906878188779 ( 98 digits) Divisors found: r1=5256085350367721968365243508879 r2=14889514327152662463708208717849 r3=529786685826043275442599790114501549 Version: Total time: 2.08 hours. Scaled time: 4.95 units (timescale=2.384). Factorization parameters were as follows: name: 64447_171 n: 41461401722079143647924150625301340578093020537184821796736112311143710226687952818709906878188779 skew: 7857.64 # norm 2.45e+13 c5: 11880 c4: 788898 c3: -613633019573 c2: -6822373166044091 c1: -68762375014291434697 c0: 108707619335330199856823 # alpha -5.99 Y1: 2407654091 Y0: -5111701737676163862 # Murphy_E 4.55e-09 # M 6269349845825020629740171875377268828302419233862240622567814041128462207806673633291997154454334 type: gnfs rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [500000, 900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4333827 Max relations in full relation-set: Initial matrix: Pruned matrix : 144083 x 144331 Polynomial selection time: 0.13 hours. Total sieving time: 1.71 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000 total time: 2.08 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹²⁹+23)/9 = 6(4)₁₂₈7_<130> = 3 · 7 · 71 · 421 · 1390317957013_<13> · C112
C112 = P53 · P59
P53 = 75763157022055757160940379455506947440975308080533513_<53>
P59 = 97466091234717045166053084915874283627086578275412208937333_<59>

Number: 64447_129 N=7384338774541879783190749762116627536820641207265619697558830813010085523088627253291340919120199082377423340829 ( 112 digits) SNFS difficulty: 131 digits. Divisors found: r1=75763157022055757160940379455506947440975308080533513 r2=97466091234717045166053084915874283627086578275412208937333 Version: Total time: 1.47 hours. Scaled time: 3.50 units (timescale=2.386). Factorization parameters were as follows: n: 7384338774541879783190749762116627536820641207265619697558830813010085523088627253291340919120199082377423340829 m: 100000000000000000000000000 deg: 5 c5: 29 c0: 115 skew: 1.32 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2805388 Max relations in full relation-set: Initial matrix: Pruned matrix : 147296 x 147539 Total sieving time: 1.27 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.05 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 1.47 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹³⁶+23)/9 = 6(4)₁₃₅7_<137> = 317 · 463 · 4231 · C129
C129 = P40 · P89
P40 = 6119790257462840180408171750175750836047_<40>
P89 = 16957650012616993070182468852439375057528923539892416047822926309148813178064338505119101_<89>

Number: 64447_136 N=103777261336678083054677475123544185985045862327150201617863921750804117975272515639465440328049771189487645987027446190059033747 ( 129 digits) SNFS difficulty: 137 digits. Divisors found: r1=6119790257462840180408171750175750836047 r2=16957650012616993070182468852439375057528923539892416047822926309148813178064338505119101 Version: Total time: 2.64 hours. Scaled time: 6.30 units (timescale=2.389). Factorization parameters were as follows: n: 103777261336678083054677475123544185985045862327150201617863921750804117975272515639465440328049771189487645987027446190059033747 m: 1000000000000000000000000000 deg: 5 c5: 580 c0: 23 skew: 0.52 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1450001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3620190 Max relations in full relation-set: Initial matrix: Pruned matrix : 246289 x 246537 Total sieving time: 2.28 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,50000 total time: 2.64 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁴¹+23)/9 = 6(4)₁₄₀7_<142> = 3 · 7 · 436439 · 103617691367_<12> · 2579254893476128243_<19> · C106
C106 = P50 · P56
P50 = 76186258682820596721818032631403693765457390966091_<50>
P56 = 34533278839482980957953122866654334570356354654042530003_<56>

Number: 64447_141 N=2630961314830825037808404552418118055910889450264586094583925505760367689427304261765390068171674023128273 ( 106 digits) SNFS difficulty: 142 digits. Divisors found: r1=76186258682820596721818032631403693765457390966091 r2=34533278839482980957953122866654334570356354654042530003 Version: Total time: 4.22 hours. Scaled time: 10.08 units (timescale=2.387). Factorization parameters were as follows: n: 2630961314830825037808404552418118055910889450264586094583925505760367689427304261765390068171674023128273 m: 10000000000000000000000000000 deg: 5 c5: 580 c0: 23 skew: 0.52 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [1100000, 2050001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4380215 Max relations in full relation-set: Initial matrix: Pruned matrix : 298553 x 298801 Total sieving time: 3.66 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.17 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,48,48,2.3,2.3,50000 total time: 4.22 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁴⁸+23)/9 = 6(4)₁₄₇7_<149> = 17 · 15737 · 1600057148951_<13> · 281957788581047651_<18> · C114
C114 = P30 · P84
P30 = 957229269729820319274362209397_<30>
P84 = 557800703761628951235813012289882908409521924268072584602236892834526943369023125519_<84>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 533943160316523918951469911012731137258971520498099742586223078317083887622231588054788137903703903967979292302043 (114 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6037326045 Step 1 took 3463ms Step 2 took 3806ms ********** Factor found in step 2: 957229269729820319274362209397 Found probable prime factor of 30 digits: 957229269729820319274362209397 Probable prime cofactor 557800703761628951235813012289882908409521924268072584602236892834526943369023125519 has 84 digits

(58·10¹⁴⁹+23)/9 = 6(4)₁₄₈7_<150> = 51307 · 814665077 · 125452973878408950737_<21> · C117
C117 = P36 · P38 · P44
P36 = 239805938435749179530628678236164969_<36>
P38 = 41430417338281880250147847818250316533_<38>
P44 = 12369996045565239429686508194506888049892077_<44>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 122899128267307932285652056221776691270027659426723777828073895284388924281020552605381106797530820720034481264684729 (117 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5739799736 Step 1 took 4602ms Step 2 took 3994ms ********** Factor found in step 2: 239805938435749179530628678236164969 Found probable prime factor of 36 digits: 239805938435749179530628678236164969 Composite cofactor 512494098640664391257456959015229005123844681619807604130051122581206101738809041 has 81 digits 07/14/09 22:52:48 v1.10 @ 조영욱-PC, starting SIQS on c81: 512494098640664391257456959015229005123844681619807604130051122581206101738809041 07/14/09 22:52:48 v1.10 @ 조영욱-PC, random seeds: 703900670, 2446589440 07/14/09 22:52:48 v1.10 @ 조영욱-PC, ==== sieve params ==== 07/14/09 22:52:48 v1.10 @ 조영욱-PC, n = 81 digits, 274 bits 07/14/09 22:52:48 v1.10 @ 조영욱-PC, factor base: 45938 primes (max prime = 1188269) 07/14/09 22:52:48 v1.10 @ 조영욱-PC, single large prime cutoff: 112885555 (95 * pmax) 07/14/09 22:52:48 v1.10 @ 조영욱-PC, using 14 large prime slices of factor base 07/14/09 22:52:48 v1.10 @ 조영욱-PC, buckets hold 1024 elements 07/14/09 22:52:48 v1.10 @ 조영욱-PC, sieve interval: 7 blocks of size 65536 07/14/09 22:52:48 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors 07/14/09 22:52:48 v1.10 @ 조영욱-PC, using multiplier of 41 07/14/09 22:52:48 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits 07/14/09 22:52:48 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning 07/14/09 22:52:48 v1.10 @ 조영욱-PC, trial factoring cutoff at 95 bits 07/14/09 22:52:48 v1.10 @ 조영욱-PC, ==== sieving started ==== 07/14/09 23:01:04 v1.10 @ 조영욱-PC, sieve time = 249.9540, relation time = 70.0050, poly_time = 175.6000 07/14/09 23:01:04 v1.10 @ 조영욱-PC, 46066 relations found: 23464 full + 22602 from 247296 partial, using 129790 polys (164 A polys) 07/14/09 23:01:04 v1.10 @ 조영욱-PC, on average, sieving found 2.09 rels/poly and 545.80 rels/sec 07/14/09 23:01:04 v1.10 @ 조영욱-PC, trial division touched 3687831 sieve locations out of 119082844160 07/14/09 23:01:04 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 07/14/09 23:01:04 v1.10 @ 조영욱-PC, begin with 270760 relations 07/14/09 23:01:04 v1.10 @ 조영욱-PC, reduce to 65824 relations in 2 passes 07/14/09 23:01:05 v1.10 @ 조영욱-PC, recovered 65824 relations 07/14/09 23:01:05 v1.10 @ 조영욱-PC, recovered 51617 polynomials 07/14/09 23:01:05 v1.10 @ 조영욱-PC, attempting to build 46066 cycles 07/14/09 23:01:05 v1.10 @ 조영욱-PC, found 46066 cycles in 1 passes 07/14/09 23:01:05 v1.10 @ 조영욱-PC, distribution of cycle lengths: 07/14/09 23:01:05 v1.10 @ 조영욱-PC, length 1 : 23464 07/14/09 23:01:05 v1.10 @ 조영욱-PC, length 2 : 22602 07/14/09 23:01:05 v1.10 @ 조영욱-PC, largest cycle: 2 relations 07/14/09 23:01:05 v1.10 @ 조영욱-PC, matrix is 45938 x 46066 (7.0 MB) with weight 1467122 (31.85/col) 07/14/09 23:01:05 v1.10 @ 조영욱-PC, sparse part has weight 1467122 (31.85/col) 07/14/09 23:01:05 v1.10 @ 조영욱-PC, filtering completed in 3 passes 07/14/09 23:01:05 v1.10 @ 조영욱-PC, matrix is 33395 x 33459 (5.5 MB) with weight 1182778 (35.35/col) 07/14/09 23:01:05 v1.10 @ 조영욱-PC, sparse part has weight 1182778 (35.35/col) 07/14/09 23:01:05 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 07/14/09 23:01:05 v1.10 @ 조영욱-PC, matrix is 33347 x 33459 (3.8 MB) with weight 882310 (26.37/col) 07/14/09 23:01:05 v1.10 @ 조영욱-PC, sparse part has weight 673096 (20.12/col) 07/14/09 23:01:05 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 07/14/09 23:01:05 v1.10 @ 조영욱-PC, using block size 13383 for processor cache size 4096 kB 07/14/09 23:01:05 v1.10 @ 조영욱-PC, commencing Lanczos iteration 07/14/09 23:01:05 v1.10 @ 조영욱-PC, memory use: 3.7 MB 07/14/09 23:01:08 v1.10 @ 조영욱-PC, lanczos halted after 529 iterations (dim = 33343) 07/14/09 23:01:08 v1.10 @ 조영욱-PC, recovered 16 nontrivial dependencies 07/14/09 23:01:08 v1.10 @ 조영욱-PC, prp44 = 12369996045565239429686508194506888049892077 07/14/09 23:01:10 v1.10 @ 조영욱-PC, prp38 = 41430417338281880250147847818250316533 07/14/09 23:01:10 v1.10 @ 조영욱-PC, Lanczos elapsed time = 4.2900 seconds. 07/14/09 23:01:10 v1.10 @ 조영욱-PC, Sqrt elapsed time = 1.2940 seconds. 07/14/09 23:01:10 v1.10 @ 조영욱-PC, SIQS elapsed time = 501.6600 seconds. 07/14/09 23:01:10 v1.10 @ 조영욱-PC, 07/14/09 23:01:10 v1.10 @ 조영욱-PC,

(58·10¹⁵⁰+23)/9 = 6(4)₁₄₉7_<151> = 3 · 2003 · 92551 · 107201 · 3391945245606732612163_<22> · C116
C116 = P46 · P71
P46 = 2399679341298100809951191715143165897321865029_<46>
P71 = 13280098068807257841052877871669566506875479890479596261399064850887679_<71>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 31867976986129581142577553204069184977118961756426749952446804034640512899999263466243557329301492399086906477077691 (116 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4284733017 Step 1 took 3806ms Step 2 took 3307ms ********** Factor found in step 2: 2399679341298100809951191715143165897321865029 Found probable prime factor of 46 digits: 2399679341298100809951191715143165897321865029 Probable prime cofactor 13280098068807257841052877871669566506875479890479596261399064850887679 has 71 digits

Jul 14, 2009 (4th)

By JPascoa / Chris Monico ggnfs-0.77.1, Msieve / Jul 14, 2009
(58·10¹²³+23)/9 = 6(4)₁₂₂7_<124> = 3 · 7 · 24391 · 13990433 · C111
C111 = P50 · P62
P50 = 50773799828332712760339199634604292107704204758339_<50>
P62 = 17711924842507332373590758448378995774984298667244766404457271_<62>

Number: 64447_123 N=899301726527940702964232341357666906090579560911871755134417338433041568548838314131597612984873335457006432869 ( 111 digits) SNFS difficulty: 126 digits. Divisors found: r1=50773799828332712760339199634604292107704204758339 (pp50) r2=17711924842507332373590758448378995774984298667244766404457271 (pp62) Version: Msieve-1.40 Total time: 1.92 hours. Scaled time: 2.28 units (timescale=1.188). Factorization parameters were as follows: n: 899301726527940702964232341357666906090579560911871755134417338433041568548838314131597612984873335457006432869 m: 5000000000000000000000000 deg: 5 c5: 464 c0: 575 skew: 1.04 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 795001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 121689 x 121919 Total sieving time: 1.84 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 1.92 hours. --------- CPU info (if available) ----------

(58·10¹⁴²+23)/9 = 6(4)₁₄₁7_<143> = 1249 · 2347 · 24919 · 466183 · 15523710638280211453_<20> · C108
C108 = P37 · P71
P37 = 5264538448831778063739858965185820207_<37>
P71 = 23156188327031872626489300434370560937362355885611469744116956097040047_<71>

Number: 64447_142 N=121906643776048900653845760483176682051303097738362726296929265059517001216762243933421499551133248620829729 ( 108 digits) Divisors found: r1=5264538448831778063739858965185820207 (pp37) r2=23156188327031872626489300434370560937362355885611469744116956097040047 (pp71) Version: Msieve-1.40 Total time: 10.92 hours. Scaled time: 13.02 units (timescale=1.192). Factorization parameters were as follows: name: 64447_142 n: 121906643776048900653845760483176682051303097738362726296929265059517001216762243933421499551133248620829729 skew: 10330.88 # norm 2.86e+014 c5: 64620 c4: 1239404382 c3: -30319770518560 c2: -91176158701992677 c1: 1056015459864830190240 c0: 2423349024698880698893011 # alpha -5.08 Y1: 331395755999 Y0: -285187278252824020054 # Murphy_E 1.38e-009 # M 121691403354176194190776471266168161078137481667477963639797578008571176758933027729971584524949945150524271 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, 2450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 324103 x 324347 Polynomial selection time: 1.12 hours. Total sieving time: 9.47 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.20 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 10.92 hours. --------- CPU info (if available) ----------

(58·10¹⁴⁶+23)/9 = 6(4)₁₄₅7_<147> = 225240727286207539_<18> · C130
C130 = P40 · P90
P40 = 7984979862480793926125756973956199182887_<40>
P90 = 358314792650653686950640911375423315769676174740273424441797231618837823936703464982949779_<90>

Number: 64447_146 N=2861136403744450867384364181988944676233621211196267931286517974372854120293817015912673374579164624145954637643177163066757231973 ( 130 digits) SNFS difficulty: 148 digits. Divisors found: r1=7984979862480793926125756973956199182887 (pp40) r2=358314792650653686950640911375423315769676174740273424441797231618837823936703464982949779 (pp90) Version: Msieve-1.40 Total time: 22.89 hours. Scaled time: 20.49 units (timescale=0.895). Factorization parameters were as follows: n: 2861136403744450867384364181988944676233621211196267931286517974372854120293817015912673374579164624145954637643177163066757231973 m: 200000000000000000000000000000 deg: 5 c5: 145 c0: 184 skew: 1.05 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 344816 x 345049 Total sieving time: 21.95 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.69 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 22.89 hours. --------- CPU info (if available) ----------

Jul 14, 2009 (3rd)

By Robert Backstrom / GGNFS / Jul 14, 2009
(58·10¹²⁰+23)/9 = 6(4)₁₁₉7_<121> = 3 · 16481 · 670037 · C111
C111 = P52 · P59
P52 = 3592422000876207144080797101689943790151669878642591_<52>
P59 = 54149510756258711112608068985210572030309207474345155051487_<59>

Number: n N=194527893777466619665691553316121652261080764904403871430472308721459150022852335874986627652427044538276082817 ( 111 digits) SNFS difficulty: 121 digits. Divisors found: r1=3592422000876207144080797101689943790151669878642591 (pp52) r2=54149510756258711112608068985210572030309207474345155051487 (pp59) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.72 hours. Scaled time: 3.13 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_4_119_7 n: 194527893777466619665691553316121652261080764904403871430472308721459150022852335874986627652427044538276082817 m: 1000000000000000000000000 deg: 5 c5: 58 c0: 23 skew: 0.83 type: snfs lss: 1 rlim: 560000 alim: 560000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 10000 Factor base limits: 560000/560000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [280000, 540001) Primes: RFBsize:46072, AFBsize:45556, largePrimes:3217734 encountered Relations: rels:2682895, finalFF:110424 Max relations in full relation-set: 48 Initial matrix: 91694 x 110424 with sparse part having weight 10891784. Pruned matrix : 88456 x 88978 with weight 6502223. Total sieving time: 1.60 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.04 hours. Total square root time: 0.03 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,560000,560000,28,28,56,56,2.3,2.3,50000 total time: 1.72 hours. --------- CPU info (if available) ----------

Jul 14, 2009 (2nd)

By Sinkiti Sibata / Msieve / Jul 14, 2009
(58·10¹³⁹+23)/9 = 6(4)₁₃₈7_<140> = C140
C140 = P67 · P74
P67 = 1938058158904057175420875818268265892536340598520596225753765591909_<67>
P74 = 33252069422357691954035197580335551879441443411363876229822358630860524083_<74>

Number: 64447_139 N=64444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 ( 140 digits) SNFS difficulty: 141 digits. Divisors found: r1=1938058158904057175420875818268265892536340598520596225753765591909 (pp67) r2=33252069422357691954035197580335551879441443411363876229822358630860524083 (pp74) Version: Msieve-1.40 Total time: 6.74 hours. Scaled time: 17.36 units (timescale=2.575). Factorization parameters were as follows: name: 64447_139 n: 64444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 m: 10000000000000000000000000000 deg: 5 c5: 29 c0: 115 skew: 1.32 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 240937 x 241174 Total sieving time: 6.55 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 6.74 hours. --------- CPU info (if available) ----------

Jul 14, 2009

By Dmitry Domanov / ECMNET / Jul 14, 2009
(58·10¹⁷⁹+23)/9 = 6(4)₁₇₈7_<180> = C180
C180 = P39 · P141
P39 = 672685683356861337041796175253604246571_<39>
P141 = 958017184531880621373920860801042598243408868260257248390356768611005235992717460853265486439899270704857151033067923579387134911377797556957_<141>

C180=P39*P141 C180=672685683356861337041796175253604246571<39>*958017184531880621373920860801042598243408868260257248390356768611005235992717460853265486439899270704857151033067923579387134911377797556957<141>

(58·10¹⁸⁴+23)/9 = 6(4)₁₈₃7_<185> = C185
C185 = P36 · C150
P36 = 176588117670435309434329024092440363_<36>
C150 = [364942133675814393150109614547698249357635271656814604537174727470973783441581875210983228248347867250016918641191589005044762359987857325025874363869_<150>]

C185=P36*C150 C185=176588117670435309434329024092440363<36>*364942133675814393150109614547698249357635271656814604537174727470973783441581875210983228248347867250016918641191589005044762359987857325025874363869<150>

Jul 13, 2009 (6th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Jul 13, 2009
(58·10¹⁶¹+23)/9 = 6(4)₁₆₀7_<162> = C162
C162 = P38 · C125
P38 = 41119327973436033475483754806134272837_<38>
C125 = [15672543210355221701053940350577676484197328922241828151784149179051334607839580596202241048609582134533477776622521732064531_<125>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 644444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 (162 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1512772174 Step 1 took 4876ms Step 2 took 2675ms ********** Factor found in step 2: 41119327973436033475483754806134272837 Found probable prime factor of 38 digits: 41119327973436033475483754806134272837 Composite cofactor 15672543210355221701053940350577676484197328922241828151784149179051334607839580596202241048609582134533477776622521732064531 has 125 digits

(58·10¹⁰⁶+23)/9 = 6(4)₁₀₅7_<107> = 492161744461753_<15> · C93
C93 = P35 · P58
P35 = 78129326361730982026375097231768957_<35>
P58 = 1675959621960563483941991874954435017512192924461523251107_<58>

Number: 64447_106 N=130941596273240143468946640593072846211856885990677267608981904319231734474929512919318485399 ( 93 digits) SNFS difficulty: 107 digits. Divisors found: r1=78129326361730982026375097231768957 (pp35) r2=1675959621960563483941991874954435017512192924461523251107 (pp58) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.43 hours. Scaled time: 1.01 units (timescale=2.378). Factorization parameters were as follows: n: 130941596273240143468946640593072846211856885990677267608981904319231734474929512919318485399 m: 1000000000000000000000 deg: 5 c5: 580 c0: 23 skew: 0.52 type: snfs lss: 1 rlim: 280000 alim: 280000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 280000/280000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [140000, 260001) Primes: RFBsize:24432, AFBsize:24500, largePrimes:879266 encountered Relations: rels:775786, finalFF:56964 Max relations in full relation-set: 28 Initial matrix: 48999 x 56964 with sparse part having weight 2637228. Pruned matrix : 46847 x 47155 with weight 1733764. Total sieving time: 0.41 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,107,5,0,0,0,0,0,0,0,0,280000,280000,25,25,44,44,2.2,2.2,20000 total time: 0.43 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁷⁵+23)/9 = 6(4)₁₇₄7_<176> = 1613 · 35656160338682906683_<20> · 1247169141570102577601527931_<28> · 1096361019585145532582908854881_<31> · C96
C96 = P47 · P50
P47 = 14983018931158829173921366367260641067839096419_<47>
P50 = 54693821851703361473715645811927745590131721657777_<50>

Number: 64447_175 N=819478568221499914100326001606299190096919170281909322951110135326279607201011575509404424200563 ( 96 digits) Divisors found: r1=14983018931158829173921366367260641067839096419 r2=54693821851703361473715645811927745590131721657777 Version: Total time: 1.73 hours. Scaled time: 4.14 units (timescale=2.389). Factorization parameters were as follows: name: 64447_175 n: 819478568221499914100326001606299190096919170281909322951110135326279607201011575509404424200563 skew: 1272.92 # norm 1.92e+13 c5: 558540 c4: 521847935 c3: -5408470572471 c2: 351181997744970 c1: 2401135397826069759 c0: 347351341918533091555 # alpha -5.04 Y1: 1132506419 Y0: -1079683784185786326 # Murphy_E 5.04e-09 # M 584362212936005472064082310212869558798949791281506276000328577915598457378327795135603722194649 type: gnfs rlim: 800000 alim: 800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 40000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [400000, 760001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3757091 Max relations in full relation-set: Initial matrix: Pruned matrix : 133248 x 133496 Polynomial selection time: 0.10 hours. Total sieving time: 1.42 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: gnfs,95,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,800000,800000,26,26,48,48,2.5,2.5,40000 total time: 1.73 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356) Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Jul 13, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve 1.41, ECMNET / Jul 13, 2009
(58·10¹³⁵+23)/9 = 6(4)₁₃₄7_<136> = 3² · 7 · C135
C135 = P35 · P48 · P53
P35 = 23082255542566823599333086556290313_<35>
P48 = 186979259626794060686307795753842713194685315639_<48>
P53 = 23701359305376003078608706474526261487024092056393967_<53>

N=102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292769 ( 135 digits) SNFS difficulty: 136 digits. Divisors found: r1=23082255542566823599333086556290313 (pp35) r2=186979259626794060686307795753842713194685315639 (pp48) r3=23701359305376003078608706474526261487024092056393967 (pp53) Version: Msieve v. 1.41 Total time: 3.57 hours. Scaled time: 7.10 units (timescale=1.988). Factorization parameters were as follows: n: 102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292769 m: 1000000000000000000000000000 deg: 5 c5: 58 c0: 23 skew: 0.83 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1340001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 221572 x 221820 Total sieving time: 3.39 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.07 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 3.57 hours. --------- CPU info (if available) ----------

(58·10¹⁸⁷+23)/9 = 6(4)₁₈₆7_<188> = 19 · C187
C187 = P39 · P149
P39 = 191379776483330109719074784422593962641_<39>
P149 = 17722942976644742493298788382265098427947056575301551556533727688497872316694355856538018670950859864388326426079285337993714319660444511908472818293_<149>

C187=P39*P149 C187=191379776483330109719074784422593962641<39>*17722942976644742493298788382265098427947056575301551556533727688497872316694355856538018670950859864388326426079285337993714319660444511908472818293<149>

(58·10¹⁵⁴+23)/9 = 6(4)₁₅₃7_<155> = 2221 · 64282310843_<11> · C141
C141 = P48 · P93
P48 = 826950947036232072542160696882965155619752449697_<48>
P93 = 545840424644446244851714823114328414970104900490414450438285896386706980952189028867721389217_<93>

N=451383256090383890332880823304054936956210199597621515127139018576080529748946023299415520701134993942877093671512974234181514772719750717249 ( 141 digits) SNFS difficulty: 156 digits. Divisors found: r1=826950947036232072542160696882965155619752449697 (pp48) r2=545840424644446244851714823114328414970104900490414450438285896386706980952189028867721389217 (pp93) Version: Msieve v. 1.41 Total time: 19.28 hours. Scaled time: 38.21 units (timescale=1.982). Factorization parameters were as follows: n: 451383256090383890332880823304054936956210199597621515127139018576080529748946023299415520701134993942877093671512974234181514772719750717249 m: 10000000000000000000000000000000 deg: 5 c5: 29 c0: 115 skew: 1.32 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 531694 x 531942 Total sieving time: 18.65 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.41 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 19.28 hours. --------- CPU info (if available) ----------

Jul 13, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jul 13, 2009
(14·10¹⁸²+1)/3 = 4(6)₁₈₁7_<183> = 71 · 359 · C179
C179 = P80 · P99
P80 = 99337268011377573858694433257182813159834985248138871718472604050896795517134809_<80>
P99 = 184306975295123807994275531879649282427027278526009180015853910534954578635427995339599927648804467_<99>

Number: n N=18308551401258059032000732342056050322361280029293682242012894451201171747289680515778048046869891587220631121921874795663488825244876874991826539553009795074999673061582120391803 ( 179 digits) SNFS difficulty: 185 digits. Divisors found: Mon Jul 13 22:15:46 2009 prp80 factor: 99337268011377573858694433257182813159834985248138871718472604050896795517134809 Mon Jul 13 22:15:46 2009 prp99 factor: 184306975295123807994275531879649282427027278526009180015853910534954578635427995339599927648804467 Mon Jul 13 22:15:46 2009 elapsed time 02:40:38 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 150.06 hours. Scaled time: 397.50 units (timescale=2.649). Factorization parameters were as follows: name: KA_4_6_181_7 n: 18308551401258059032000732342056050322361280029293682242012894451201171747289680515778048046869891587220631121921874795663488825244876874991826539553009795074999673061582120391803 m: 5000000000000000000000000000000000000 deg: 5 c5: 56 c0: 125 skew: 1.17 type: snfs lss: 1 rlim: 8600000 alim: 8600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8600000/8600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4300000, 6900977) Primes: RFBsize:577439, AFBsize:576914, largePrimes:20806339 encountered Relations: rels:20705108, finalFF:1024227 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1805413 hash collisions in 21853565 relations Msieve: matrix is 1379817 x 1380065 (373.7 MB) Total sieving time: 149.50 hours. Total relation processing time: 0.56 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,8600000,8600000,28,28,56,56,2.5,2.5,100000 total time: 150.06 hours. --------- CPU info (if available) ----------

(58·10¹¹¹+23)/9 = 6(4)₁₁₀7_<112> = 3 · 7² · 32789 · 48039247 · 577672633 · C89
C89 = P38 · P51
P38 = 50196008649124066760669118985278755117_<38>
P51 = 959826657005513846552635296036664574714149430138227_<51>

Number: n N=48179467176708612066383883797455042200586297273188553625101637577681136825893259793557559 ( 89 digits) SNFS difficulty: 112 digits. Divisors found: r1=50196008649124066760669118985278755117 (pp38) r2=959826657005513846552635296036664574714149430138227 (pp51) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.65 hours. Scaled time: 1.18 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_4_110_7 n: 48179467176708612066383883797455042200586297273188553625101637577681136825893259793557559 m: 10000000000000000000000 deg: 5 c5: 580 c0: 23 skew: 0.52 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 10000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [250000, 360001) Primes: RFBsize:41538, AFBsize:41462, largePrimes:2818335 encountered Relations: rels:2338662, finalFF:106501 Max relations in full relation-set: 48 Initial matrix: 83067 x 106501 with sparse part having weight 7902956. Pruned matrix : 75721 x 76200 with weight 3818881. Total sieving time: 0.57 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Total square root time: 0.02 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.3,2.3,50000 total time: 0.65 hours. --------- CPU info (if available) ----------

Jul 13, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jul 13, 2009
3·10¹⁶⁹-1 = 2(9)_169<170> = 29 · 257 · 1187 · 893281 · 162352619114966156197_<21> · C137
C137 = P55 · P83
P55 = 2228251805235709353313536175233325312147783871786905403_<55>
P83 = 10493678433883386533453073734793889071910451026636427224419520005990497132630462879_<83>

Number: 29999_169 N=23382557913863687360210358549889939699253493723541318867971867107182684122332981322256389039762608813026488643802138025103343450876035237 ( 137 digits) SNFS difficulty: 170 digits. Divisors found: r1=2228251805235709353313536175233325312147783871786905403 (pp55) r2=10493678433883386533453073734793889071910451026636427224419520005990497132630462879 (pp83) Version: Msieve-1.40 Total time: 59.94 hours. Scaled time: 154.35 units (timescale=2.575). Factorization parameters were as follows: name: 29999_169 n: 23382557913863687360210358549889939699253493723541318867971867107182684122332981322256389039762608813026488643802138025103343450876035237 m: 10000000000000000000000000000000000 deg: 5 c5: 3 c0: -10 skew: 1.27 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2450000, 4850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 871097 x 871345 Total sieving time: 57.67 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.72 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 59.94 hours. --------- CPU info (if available) ----------

(58·10¹¹⁴+23)/9 = 6(4)₁₁₃7_<115> = 3 · C115
C115 = P37 · P78
P37 = 4335063118793507391728654777432128393_<37>
P78 = 495528689959651579368664634248240159079415334936580114911985607106035232953293_<78>

Number: 64447_114 N=2148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149 ( 115 digits) SNFS difficulty: 116 digits. Divisors found: r1=4335063118793507391728654777432128393 (pp37) r2=495528689959651579368664634248240159079415334936580114911985607106035232953293 (pp78) Version: Msieve-1.40 Total time: 1.16 hours. Scaled time: 2.98 units (timescale=2.564). Factorization parameters were as follows: name: 64447_114 n: 2148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149 m: 100000000000000000000000 deg: 5 c5: 29 c0: 115 skew: 1.32 type: snfs lss: 1 rlim: 610000 alim: 610000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 610000/610000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [305000, 505001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 63265 x 63492 Total sieving time: 1.13 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116.000,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000 total time: 1.16 hours. --------- CPU info (if available) ----------

(58·10¹²⁵+23)/9 = 6(4)₁₂₄7_<126> = C126
C126 = P45 · P81
P45 = 974736791340018918589686620786549510151975781_<45>
P81 = 661147142664528713748930535458851545304856790693588371526999971594298072964481587_<81>

Number: 64447_125 N=644444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 ( 126 digits) SNFS difficulty: 126 digits. Divisors found: r1=974736791340018918589686620786549510151975781 (pp45) r2=661147142664528713748930535458851545304856790693588371526999971594298072964481587 (pp81) Version: Msieve-1.40 Total time: 2.33 hours. Scaled time: 5.98 units (timescale=2.564). Factorization parameters were as follows: name: 64447_125 n: 644444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 m: 10000000000000000000000000 deg: 5 c5: 58 c0: 23 skew: 0.83 type: snfs lss: 1 rlim: 910000 alim: 910000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 910000/910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [455000, 805001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 131857 x 132089 Total sieving time: 2.24 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000 total time: 2.33 hours. --------- CPU info (if available) ----------

(58·10¹³²+23)/9 = 6(4)₁₃₁7_<133> = 3 · 17 · 83 · 107 · 113 · 9377839 · 54324469205731_<14> · 131229719259439253_<18> · C88
C88 = P40 · P48
P40 = 4760339406616587863684474719485370271377_<40>
P48 = 395645847713421982074206853379199386478310056581_<48>

Mon Jul 13 17:31:00 2009 Msieve v. 1.41 Mon Jul 13 17:31:00 2009 random seeds: 9c99e448 049c84d4 Mon Jul 13 17:31:00 2009 factoring 1883408519934428084391724377309822647511270420467472934806096807678123332226068194782037 (88 digits) Mon Jul 13 17:31:01 2009 searching for 15-digit factors Mon Jul 13 17:31:02 2009 commencing quadratic sieve (88-digit input) Mon Jul 13 17:31:02 2009 using multiplier of 1 Mon Jul 13 17:31:02 2009 using 32kb Intel Core sieve core Mon Jul 13 17:31:02 2009 sieve interval: 24 blocks of size 32768 Mon Jul 13 17:31:02 2009 processing polynomials in batches of 9 Mon Jul 13 17:31:02 2009 using a sieve bound of 1507487 (57333 primes) Mon Jul 13 17:31:02 2009 using large prime bound of 120598960 (26 bits) Mon Jul 13 17:31:02 2009 using double large prime bound of 351899202753840 (42-49 bits) Mon Jul 13 17:31:02 2009 using trial factoring cutoff of 49 bits Mon Jul 13 17:31:02 2009 polynomial 'A' values have 11 factors Mon Jul 13 18:26:51 2009 57588 relations (15601 full + 41987 combined from 609488 partial), need 57429 Mon Jul 13 18:26:52 2009 begin with 625089 relations Mon Jul 13 18:26:53 2009 reduce to 139946 relations in 10 passes Mon Jul 13 18:26:53 2009 attempting to read 139946 relations Mon Jul 13 18:26:54 2009 recovered 139946 relations Mon Jul 13 18:26:54 2009 recovered 119557 polynomials Mon Jul 13 18:26:55 2009 attempting to build 57588 cycles Mon Jul 13 18:26:55 2009 found 57588 cycles in 6 passes Mon Jul 13 18:26:55 2009 distribution of cycle lengths: Mon Jul 13 18:26:55 2009 length 1 : 15601 Mon Jul 13 18:26:55 2009 length 2 : 10874 Mon Jul 13 18:26:55 2009 length 3 : 10150 Mon Jul 13 18:26:55 2009 length 4 : 7660 Mon Jul 13 18:26:55 2009 length 5 : 5469 Mon Jul 13 18:26:55 2009 length 6 : 3342 Mon Jul 13 18:26:55 2009 length 7 : 2101 Mon Jul 13 18:26:55 2009 length 9+: 2391 Mon Jul 13 18:26:55 2009 largest cycle: 17 relations Mon Jul 13 18:26:55 2009 matrix is 57333 x 57588 (13.4 MB) with weight 3275321 (56.88/col) Mon Jul 13 18:26:55 2009 sparse part has weight 3275321 (56.88/col) Mon Jul 13 18:26:56 2009 filtering completed in 4 passes Mon Jul 13 18:26:56 2009 matrix is 53263 x 53327 (12.5 MB) with weight 3057108 (57.33/col) Mon Jul 13 18:26:56 2009 sparse part has weight 3057108 (57.33/col) Mon Jul 13 18:26:56 2009 saving the first 48 matrix rows for later Mon Jul 13 18:26:56 2009 matrix is 53215 x 53327 (8.0 MB) with weight 2418609 (45.35/col) Mon Jul 13 18:26:56 2009 sparse part has weight 1776241 (33.31/col) Mon Jul 13 18:26:56 2009 matrix includes 64 packed rows Mon Jul 13 18:26:56 2009 using block size 21330 for processor cache size 1024 kB Mon Jul 13 18:26:56 2009 commencing Lanczos iteration Mon Jul 13 18:26:56 2009 memory use: 7.9 MB Mon Jul 13 18:27:14 2009 lanczos halted after 843 iterations (dim = 53212) Mon Jul 13 18:27:14 2009 recovered 14 nontrivial dependencies Mon Jul 13 18:27:15 2009 prp40 factor: 4760339406616587863684474719485370271377 Mon Jul 13 18:27:15 2009 prp48 factor: 395645847713421982074206853379199386478310056581 Mon Jul 13 18:27:15 2009 elapsed time 00:56:15

Jul 13, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3 / Jul 13, 2009
(58·10¹⁷¹+23)/9 = 6(4)₁₇₀7_<172> = 3² · 7 · 163 · 229 · 43607 · 355636003 · 1269791928287_<13> · 111929378928377_<15> · C127
C127 = P29 · C98
P29 = 29987432328229516862586197167_<29>
C98 = [41461401722079143647924150625301340578093020537184821796736112311143710226687952818709906878188779_<98>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3348063929 Step 1 took 2525ms Step 2 took 2580ms ********** Factor found in step 2: 29987432328229516862586197167 Found probable prime factor of 29 digits: 29987432328229516862586197167 Composite cofactor has 98 digits

(58·10¹⁷⁰+23)/9 = 6(4)₁₆₉7_<171> = 1153 · 2213 · 123493 · 466866407317_<12> · C148
C148 = P32 · P117
P32 = 19446241608838036363980356232313_<32>
P117 = 225270393946095807438626231453873038111507697639127097761464724268163034474733434977524246262956615989308890849723891_<117>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3684692784 Step 1 took 3013ms Step 2 took 2936ms ********** Factor found in step 2: 19446241608838036363980356232313 Found probable prime factor of 32 digits: 19446241608838036363980356232313 Probable prime cofactor has 117 digits

Jul 13, 2009

Factorizations of 644...447 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jul 12, 2009 (3rd)

By Dmitry Domanov / ECMNET / Jul 12, 2009
2·10¹⁹⁵+9 = 2(0)₁₉₄9_<196> = 7 · 263 · 5309 · 376787 · 398925029 · C175
C175 = P45 · C130
P45 = 208929543907045046083316767984164355764039923_<45>
C130 = [6515930300278598936340223067286726695961677601878157142390817149184366337340674057734940096025365308355623172051113615953328308609_<130>]

C175=P45*C130 C175=208929543907045046083316767984164355764039923<45>6515930300278598936340223067286726695961677601878157142390817149184366337340674057734940096025365308355623172051113615953328308609<130> B1: 3000000 sigma: 4163169800 (found in step 2)

Jul 12, 2009 (2nd)

By Wataru Sakai / Msieve / Jul 12, 2009
(49·10¹⁸⁴-13)/9 = 5(4)₁₈₃3_<185> = 107 · C183
C183 = P60 · P124
P60 = 108429772521892036019932427297734099076545943820349377756029_<60>
P124 = 4692683307900570769148796885419169826114104309020076727251929872520649206197793144002184678282254116463836283410737873023781_<124>

Number: 54443_184 N=508826583592938733125649013499480789200415368639667705088265835929387331256490134994807892004153686396677050882658359293873312564901349948078920041536863966770508826583592938733125649 ( 183 digits) SNFS difficulty: 186 digits. Divisors found: r1=108429772521892036019932427297734099076545943820349377756029 r2=4692683307900570769148796885419169826114104309020076727251929872520649206197793144002184678282254116463836283410737873023781 Version: Total time: 345.65 hours. Scaled time: 693.38 units (timescale=2.006). Factorization parameters were as follows: n: 508826583592938733125649013499480789200415368639667705088265835929387331256490134994807892004153686396677050882658359293873312564901349948078920041536863966770508826583592938733125649 m: 10000000000000000000000000000000000000 deg: 5 c5: 49 c0: -130 skew: 1.22 type: snfs lss: 1 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 7800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1552391 x 1552639 Total sieving time: 345.65 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000 total time: 345.65 hours. --------- CPU info (if available) ----------

(53·10¹⁸¹-71)/9 = 5(8)₁₈₀1_<182> = 3 · 2879 · C178
C178 = P53 · P126
P53 = 24081340990091404175861057053153272486112035432620191_<53>
P126 = 283132532303703333726830050085836989037702953632307132314359052811450789821802506909621984361284526068569973287653670838199643_<126>

Number: 58881_181 N=6818211055793549715050236064477120399315605984588270104074202719565692820295112757773403831062740406262462532000566040163122483372570208277050930750131861628909214876564650791813 ( 178 digits) SNFS difficulty: 182 digits. Divisors found: r1=24081340990091404175861057053153272486112035432620191 r2=283132532303703333726830050085836989037702953632307132314359052811450789821802506909621984361284526068569973287653670838199643 Version: Total time: 303.42 hours. Scaled time: 610.18 units (timescale=2.011). Factorization parameters were as follows: n: 6818211055793549715050236064477120399315605984588270104074202719565692820295112757773403831062740406262462532000566040163122483372570208277050930750131861628909214876564650791813 m: 1000000000000000000000000000000000000 deg: 5 c5: 530 c0: -71 skew: 0.67 type: snfs lss: 1 rlim: 7800000 alim: 7800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5Factor base limits: 7800000/7800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3900000, 7500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1382118 x 1382366 Total sieving time: 303.42 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,53,53,2.5,2.5,100000 total time: 303.42 hours. --------- CPU info (if available) ----------

7·10¹⁹⁴+3 = 7(0)₁₉₃3_<195> = 37 · 89 · C192
C192 = P48 · P144
P48 = 711549423651204178804703845878926067199337895119_<48>
P144 = 298745407724036587596846553046331517575087722040410770709987309288456174674024401314163963624147750872498764458224098031975479126729720370314609_<144>

Number: 70003_194 N=212572122684482235044032796841785605830549650774369875493470999088976617066504706954145156392347403583358639538414819313695718190100212572122684482235044032796841785605830549650774369875493471 ( 192 digits) SNFS difficulty: 195 digits. Divisors found: r1=711549423651204178804703845878926067199337895119 r2=298745407724036587596846553046331517575087722040410770709987309288456174674024401314163963624147750872498764458224098031975479126729720370314609 Version: Total time: 644.03 hours. Scaled time: 1297.07 units (timescale=2.014). Factorization parameters were as follows: n: 212572122684482235044032796841785605830549650774369875493470999088976617066504706954145156392347403583358639538414819313695718190100212572122684482235044032796841785605830549650774369875493471 m: 1000000000000000000000000000000000000000 deg: 5 c5: 7 c0: 30 skew: 1.34 type: snfs lss: 1 rlim: 12900000 alim: 12900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 12900000/12900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6450000, 13550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2257343 x 2257591 Total sieving time: 644.03 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,12900000,12900000,28,28,55,55,2.5,2.5,100000 total time: 644.03 hours. --------- CPU info (if available) ----------

Jul 12, 2009

By Robert Backstrom / GGNFS, Msieve / Jul 12, 2009
(47·10¹⁸¹+43)/9 = 5(2)₁₈₀7_<182> = 3 · 19 · 53 · 67 · C177
C177 = P67 · P110
P67 = 3094835724684298386572815120341122852673816403442738454046575319003_<67>
P110 = 83366624838085431210186778249034161471498200759267403583313199233944387222928835815581162767824210168479063087_<110>

Number: n N=258006008795260155143953629183883078264201446700075700060878439096583725969073313779771560381914766891571053482449827437896032361638788293992906481604994996330276236603586942261 ( 177 digits) SNFS difficulty: 182 digits. Divisors found: Sun Jul 12 05:10:16 2009 prp67 factor: 3094835724684298386572815120341122852673816403442738454046575319003 Sun Jul 12 05:10:16 2009 prp110 factor: 83366624838085431210186778249034161471498200759267403583313199233944387222928835815581162767824210168479063087 Sun Jul 12 05:10:16 2009 elapsed time 02:20:56 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 173.15 hours. Scaled time: 449.34 units (timescale=2.595). Factorization parameters were as follows: name: KA_5_2_180_7 n: 258006008795260155143953629183883078264201446700075700060878439096583725969073313779771560381914766891571053482449827437896032361638788293992906481604994996330276236603586942261 m: 1000000000000000000000000000000000000 deg: 5 c5: 470 c0: 43 skew: 0.62 type: snfs lss: 1 rlim: 7800000 alim: 7800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 7800000/7800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [3900000, 6919261) Primes: RFBsize:527154, AFBsize:526275, largePrimes:21057951 encountered Relations: rels:21147738, finalFF:896232 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2222770 hash collisions in 23551262 relations Msieve: matrix is 1239049 x 1239297 (334.1 MB) Total sieving time: 172.51 hours. Total relation processing time: 0.64 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,56,56,2.5,2.5,100000 total time: 173.15 hours. --------- CPU info (if available) ----------

Jul 11, 2009

By Dmitry Domanov / ECMNET / Jul 11, 2009
(16·10²⁰³-7)/9 = 1(7)_203<204> = 3² · 31 · 181 · 433 · 1262321 · 131918527086451153_<18> · 16900507086168024103951_<23> · C151
C151 = P43 · P109
P43 = 1984302645679619731376987460864431244810793_<43>
P109 = 1455873198199023485232568455687174282481878946320103856260317493093157285145974619345505379447385520317097309_<109>

C151=P43*P109 C151=1984302645679619731376987460864431244810793<43>*1455873198199023485232568455687174282481878946320103856260317493093157285145974619345505379447385520317097309<109>

(16·10²²⁹-7)/9 = 1(7)_229<230> = 37517 · 90221661740474669_<17> · 332893959945287358687593_<24> · C185
C185 = P40 · P145
P40 = 7535122564049591986328629082758999170461_<40>
P145 = 2093834309762269347842472452170929506605387419506516970926981601603119887876945670672882976345795440384666710964898063989946892665696919631391413_<145>

C185=P40*P145 C185=7535122564049591986328629082758999170461<40>*2093834309762269347842472452170929506605387419506516970926981601603119887876945670672882976345795440384666710964898063989946892665696919631391413<145>

2·10¹⁸⁹+9 = 2(0)₁₈₈9_<190> = 7 · 601769500435849_<15> · 262389630418130593543987483_<27> · C148
C148 = P30 · P118
P30 = 231192776199581655479023863569_<30>
P118 = 7826739065615167308219291506990415678354983695078282263339825293001255086110103549843948541000279804194903492659561669_<118>

�R148=P30*P118 C148=231192776199581655479023863569<30>*7826739065615167308219291506990415678354983695078282263339825293001255086110103549843948541000279804194903492659561669<118>

2·10¹⁷⁹+9 = 2(0)₁₇₈9_<180> = 71174055487_<11> · C169
C169 = P34 · P136
P34 = 1456349062809436989167539279826921_<34>
P136 = 1929491201087555608892709636519787278782502149025926069860554864817462889929790905160468424725930351070637487831883300700726830778091167_<136>

C169=P34*P136 C169=1456349062809436989167539279826921<34>*1929491201087555608892709636519787278782502149025926069860554864817462889929790905160468424725930351070637487831883300700726830778091167<136>

2·10¹⁷⁸+9 = 2(0)₁₇₇9_<179> = 11 · 41 · 2011 · 2559497 · C166
C166 = P40 · P127
P40 = 3607936990392616468032632672857678386811_<40>
P127 = 2387964213017067719981893822914230918809066561665386940290151207986766746538763247553089857459596549258060136674347450493027907_<127>

C166=P40*P127 C166=3607936990392616468032632672857678386811<40>*2387964213017067719981893822914230918809066561665386940290151207986766746538763247553089857459596549258060136674347450493027907<127>

Jul 10, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jul 10, 2009
(2·10¹⁹⁸+61)/9 = (2)₁₉₇9_<198> = 7 · 29 · 2083 · C192
C192 = P37 · P155
P37 = 5689948804110787089471594196039551347_<37>
P155 = 92362104428415880975825131451967519518894020450568859764644147577928065166772145782496981113824330367418104744872686986693051596921000832713247614731925143_<155>

C192=P37*P155 C192=5689948804110787089471594196039551347<37>*92362104428415880975825131451967519518894020450568859764644147577928065166772145782496981113824330367418104744872686986693051596921000832713247614731925143<155>

(2·10¹⁹⁷+43)/9 = (2)₁₉₆7_<197> = 3 · 157 · C194
C194 = P40 · C154
P40 = 4830297726724849664432111078077719825109_<40>
C154 = [9767708238695844640979066239202354443960649371290018537019416802234300736463213550385464206052611393709860351340957430875026878358838457653530043363189393_<154>]

C194=P40*C154 C194=4830297726724849664432111078077719825109<40>*9767708238695844640979066239202354443960649371290018537019416802234300736463213550385464206052611393709860351340957430875026878358838457653530043363189393<154>

Jul 10, 2009

By Robert Backstrom / GGNFS, Msieve / Jul 10, 2009
(89·10¹⁸¹+1)/9 = 9(8)₁₈₀9_<182> = 3⁵ · 11 · C179
C179 = P44 · P55 · P81
P44 = 40086795901480525822645927616850833828200151_<44>
P55 = 4401347710531047444920804384243769376286461546304783503_<55>
P81 = 209682175547011199524064175561135108760786096939706109059852576036837707179292081_<81>

Number: n N=36995469094234526333291765390530822629588061686827118925884357983123415222180654279419711518476950575716007814773246872012304111069543168308600407365839464604896703662135760901193 ( 179 digits) SNFS difficulty: 184 digits. Divisors found: Fri Jul 10 06:11:59 2009 prp44 factor: 40086795901480525822645927616850833828200151 Fri Jul 10 06:11:59 2009 prp55 factor: 4401347710531047444920804384243769376286461546304783503 Fri Jul 10 06:11:59 2009 prp81 factor: 209682175547011199524064175561135108760786096939706109059852576036837707179292081 Fri Jul 10 06:11:59 2009 elapsed time 02:39:51 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 141.03 hours. Scaled time: 375.14 units (timescale=2.660). Factorization parameters were as follows: name: KA_9_8_180_9 n: 36995469094234526333291765390530822629588061686827118925884357983123415222180654279419711518476950575716007814773246872012304111069543168308600407365839464604896703662135760901193 m: 2000000000000000000000000000000000000 deg: 5 c5: 445 c0: 16 skew: 0.51 type: snfs lss: 1 rlim: 8200000 alim: 8200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8200000/8200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4100000, 6500029) Primes: RFBsize:552319, AFBsize:551788, largePrimes:20639948 encountered Relations: rels:20319258, finalFF:1160014 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1760100 hash collisions in 21647752 relations Msieve: matrix is 1348819 x 1349067 (365.5 MB) Total sieving time: 140.52 hours. Total relation processing time: 0.51 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,8200000,8200000,28,28,56,56,2.5,2.5,100000 total time: 141.03 hours. --------- CPU info (if available) ----------

Jul 9, 2009

By Dmitry Domanov / GGNFS/msieve 1.42beta, ECMNET / Jul 9, 2009
(10²²²+17)/9 = (1)₂₂₁3_<222> = C222
C222 = P51 · P51 · P120
P51 = 551004498127928469834445340613015226657914601778213_<51>
P51 = 676677276408056094567102599764052489094573413056051_<51>
P120 = 298003080664845879339921984943623072483939555335465806206783935206506443967104530715870831039336178009293998396643169751_<120>

Sieving took about 150 cpu-days on various cpu's. Using siever 14e for sieving on rational side in 5M-43M for 57.7M relations. Postprocessing took 6 days on Xeon E5430 x 1 thread. Factors found in 6th dependency: C222=P51 �E P51 �E P120. I'm very surprised that this split is similar to Serge Batalov's �R222=P55 �E P55 �E P114 Postprocessing log below. ================================= Wed Jul 01 14:11:35 2009 Msieve v. 1.42 Wed Jul 01 14:11:35 2009 random seeds: f8ebc210 61bba000 Wed Jul 01 14:11:35 2009 factoring 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 (222 digits) Wed Jul 01 14:11:37 2009 searching for 15-digit factors Wed Jul 01 14:11:41 2009 commencing number field sieve (222-digit input) Wed Jul 01 14:11:41 2009 R0: -10000000000000000000000000000000000000 Wed Jul 01 14:11:41 2009 R1: 1 Wed Jul 01 14:11:41 2009 A0: 17 Wed Jul 01 14:11:41 2009 A1: 0 Wed Jul 01 14:11:41 2009 A2: 0 Wed Jul 01 14:11:41 2009 A3: 0 Wed Jul 01 14:11:41 2009 A4: 0 Wed Jul 01 14:11:41 2009 A5: 0 Wed Jul 01 14:11:41 2009 A6: 1 Wed Jul 01 14:11:41 2009 skew 1.60, size 6.533884e-011, alpha 1.099275, combined = 2.482264e-012 Wed Jul 01 14:11:41 2009 Wed Jul 01 14:11:41 2009 commencing relation filtering Wed Jul 01 14:11:41 2009 commencing duplicate removal, pass 1 ... <errors skipped> ... Wed Jul 01 14:20:30 2009 found 12936357 hash collisions in 57701157 relations Wed Jul 01 14:20:56 2009 added 9 free relations Wed Jul 01 14:20:56 2009 commencing duplicate removal, pass 2 Wed Jul 01 14:23:12 2009 found 11910252 duplicates and 45790914 unique relations Wed Jul 01 14:23:12 2009 memory use: 298.4 MB Wed Jul 01 14:23:12 2009 reading rational ideals above 42926080 Wed Jul 01 14:23:12 2009 reading algebraic ideals above 42926080 Wed Jul 01 14:23:12 2009 commencing singleton removal, pass 1 Wed Jul 01 14:30:55 2009 relations with 0 large ideals: 1510351 Wed Jul 01 14:30:55 2009 relations with 1 large ideals: 6811639 Wed Jul 01 14:30:55 2009 relations with 2 large ideals: 14796919 Wed Jul 01 14:30:55 2009 relations with 3 large ideals: 15230713 Wed Jul 01 14:30:55 2009 relations with 4 large ideals: 6426946 Wed Jul 01 14:30:55 2009 relations with 5 large ideals: 11119 Wed Jul 01 14:30:55 2009 relations with 6 large ideals: 0 Wed Jul 01 14:30:55 2009 relations with 7+ large ideals: 1003227 Wed Jul 01 14:30:55 2009 45790914 relations and about 35545167 large ideals Wed Jul 01 14:30:55 2009 commencing singleton removal, pass 2 Wed Jul 01 14:38:32 2009 found 10279629 singletons Wed Jul 01 14:38:32 2009 current dataset: 35511285 relations and about 24146004 large ideals Wed Jul 01 14:38:32 2009 commencing singleton removal, pass 3 Wed Jul 01 14:44:37 2009 found 2264708 singletons Wed Jul 01 14:44:37 2009 current dataset: 33246577 relations and about 21818327 large ideals Wed Jul 01 14:44:37 2009 commencing singleton removal, pass 4 Wed Jul 01 14:50:24 2009 found 493843 singletons Wed Jul 01 14:50:24 2009 current dataset: 32752734 relations and about 21321359 large ideals Wed Jul 01 14:50:24 2009 commencing singleton removal, final pass Wed Jul 01 14:56:34 2009 memory use: 542.2 MB Wed Jul 01 14:56:34 2009 commencing in-memory singleton removal Wed Jul 01 14:56:38 2009 begin with 32752734 relations and 26008754 unique ideals Wed Jul 01 14:57:39 2009 reduce to 25669667 relations and 18602735 ideals in 15 passes Wed Jul 01 14:57:39 2009 max relations containing the same ideal: 29 Wed Jul 01 14:57:47 2009 reading rational ideals above 720000 Wed Jul 01 14:57:47 2009 reading algebraic ideals above 720000 Wed Jul 01 14:57:47 2009 commencing singleton removal, final pass Wed Jul 01 15:04:42 2009 keeping 21666592 ideals with weight <= 20, new excess is 2133916 Wed Jul 01 15:05:28 2009 memory use: 695.6 MB Wed Jul 01 15:05:28 2009 commencing in-memory singleton removal Wed Jul 01 15:05:34 2009 begin with 25669677 relations and 21666592 unique ideals Wed Jul 01 15:06:28 2009 reduce to 25657866 relations and 21654721 ideals in 10 passes Wed Jul 01 15:06:28 2009 max relations containing the same ideal: 20 Wed Jul 01 15:06:56 2009 removing 3005017 relations and 2605017 ideals in 400000 cliques Wed Jul 01 15:06:58 2009 commencing in-memory singleton removal Wed Jul 01 15:07:03 2009 begin with 22652849 relations and 21654721 unique ideals Wed Jul 01 15:07:46 2009 reduce to 22377318 relations and 18768304 ideals in 9 passes Wed Jul 01 15:07:46 2009 max relations containing the same ideal: 20 Wed Jul 01 15:08:10 2009 removing 2232892 relations and 1832892 ideals in 400000 cliques Wed Jul 01 15:08:12 2009 commencing in-memory singleton removal Wed Jul 01 15:08:16 2009 begin with 20144426 relations and 18768304 unique ideals Wed Jul 01 15:08:54 2009 reduce to 19976966 relations and 16764856 ideals in 9 passes Wed Jul 01 15:08:54 2009 max relations containing the same ideal: 20 Wed Jul 01 15:09:16 2009 removing 1985426 relations and 1585426 ideals in 400000 cliques Wed Jul 01 15:09:17 2009 commencing in-memory singleton removal Wed Jul 01 15:09:21 2009 begin with 17991540 relations and 16764856 unique ideals Wed Jul 01 15:09:51 2009 reduce to 17842569 relations and 15027706 ideals in 8 passes Wed Jul 01 15:09:51 2009 max relations containing the same ideal: 20 Wed Jul 01 15:10:10 2009 removing 1626832 relations and 1287312 ideals in 339520 cliques Wed Jul 01 15:10:11 2009 commencing in-memory singleton removal Wed Jul 01 15:10:15 2009 begin with 16215737 relations and 15027706 unique ideals Wed Jul 01 15:10:41 2009 reduce to 16105168 relations and 13627906 ideals in 8 passes Wed Jul 01 15:10:41 2009 max relations containing the same ideal: 20 Wed Jul 01 15:11:00 2009 relations with 0 large ideals: 188734 Wed Jul 01 15:11:00 2009 relations with 1 large ideals: 934969 Wed Jul 01 15:11:00 2009 relations with 2 large ideals: 2781036 Wed Jul 01 15:11:00 2009 relations with 3 large ideals: 4487783 Wed Jul 01 15:11:00 2009 relations with 4 large ideals: 4224982 Wed Jul 01 15:11:00 2009 relations with 5 large ideals: 2362319 Wed Jul 01 15:11:00 2009 relations with 6 large ideals: 790965 Wed Jul 01 15:11:00 2009 relations with 7+ large ideals: 334380 Wed Jul 01 15:11:00 2009 commencing 2-way merge Wed Jul 01 15:11:25 2009 reduce to 10513011 relation sets and 8035749 unique ideals Wed Jul 01 15:11:25 2009 commencing full merge Wed Jul 01 15:14:22 2009 memory use: 668.7 MB Wed Jul 01 15:14:24 2009 found 5321363 cycles, need 4983949 Wed Jul 01 15:14:25 2009 weight of 4983949 cycles is about 348959609 (70.02/cycle) Wed Jul 01 15:14:25 2009 distribution of cycle lengths: Wed Jul 01 15:14:25 2009 1 relations: 646624 Wed Jul 01 15:14:25 2009 2 relations: 592897 Wed Jul 01 15:14:25 2009 3 relations: 585016 Wed Jul 01 15:14:25 2009 4 relations: 540378 Wed Jul 01 15:14:25 2009 5 relations: 485992 Wed Jul 01 15:14:25 2009 6 relations: 431904 Wed Jul 01 15:14:25 2009 7 relations: 374722 Wed Jul 01 15:14:25 2009 8 relations: 322521 Wed Jul 01 15:14:25 2009 9 relations: 271731 Wed Jul 01 15:14:25 2009 10+ relations: 732164 Wed Jul 01 15:14:25 2009 heaviest cycle: 17 relations Wed Jul 01 15:14:27 2009 commencing cycle optimization Wed Jul 01 15:14:40 2009 start with 26812971 relations Wed Jul 01 15:15:54 2009 pruned 764649 relations Wed Jul 01 15:15:54 2009 memory use: 702.9 MB Wed Jul 01 15:15:54 2009 distribution of cycle lengths: Wed Jul 01 15:15:54 2009 1 relations: 646624 Wed Jul 01 15:15:54 2009 2 relations: 608083 Wed Jul 01 15:15:54 2009 3 relations: 609511 Wed Jul 01 15:15:54 2009 4 relations: 558036 Wed Jul 01 15:15:54 2009 5 relations: 502517 Wed Jul 01 15:15:54 2009 6 relations: 441832 Wed Jul 01 15:15:54 2009 7 relations: 381306 Wed Jul 01 15:15:54 2009 8 relations: 323543 Wed Jul 01 15:15:54 2009 9 relations: 269057 Wed Jul 01 15:15:54 2009 10+ relations: 643440 Wed Jul 01 15:15:54 2009 heaviest cycle: 17 relations Wed Jul 01 15:16:18 2009 RelProcTime: 3714 Wed Jul 01 15:16:18 2009 Wed Jul 01 15:16:18 2009 commencing linear algebra Wed Jul 01 15:16:34 2009 read 4983949 cycles Wed Jul 01 15:16:48 2009 cycles contain 14619558 unique relations Wed Jul 01 15:24:04 2009 read 14619558 relations Wed Jul 01 15:24:44 2009 using 20 quadratic characters above 536870730 Wed Jul 01 15:26:02 2009 building initial matrix Wed Jul 01 15:30:16 2009 memory use: 1620.3 MB Wed Jul 01 15:30:38 2009 read 4983949 cycles Wed Jul 01 15:34:16 2009 matrix is 4983422 x 4983949 (1411.7 MB) with weight 433789956 (87.04/col) Wed Jul 01 15:34:16 2009 sparse part has weight 335172179 (67.25/col) Wed Jul 01 15:37:37 2009 filtering completed in 3 passes Wed Jul 01 15:37:39 2009 matrix is 4960805 x 4961005 (1408.5 MB) with weight 432669651 (87.21/col) Wed Jul 01 15:37:39 2009 sparse part has weight 334512750 (67.43/col) Wed Jul 01 15:38:37 2009 read 4961005 cycles Wed Jul 01 16:11:38 2009 matrix is 4960805 x 4961005 (1408.5 MB) with weight 432669651 (87.21/col) Wed Jul 01 16:11:38 2009 sparse part has weight 334512750 (67.43/col) Wed Jul 01 16:11:39 2009 saving the first 48 matrix rows for later Wed Jul 01 16:11:42 2009 matrix is 4960757 x 4961005 (1336.0 MB) with weight 344782488 (69.50/col) Wed Jul 01 16:11:42 2009 sparse part has weight 320465925 (64.60/col) Wed Jul 01 16:11:42 2009 matrix includes 64 packed rows Wed Jul 01 16:11:42 2009 using block size 65536 for processor cache size 6144 kB Wed Jul 01 16:12:22 2009 commencing Lanczos iteration Wed Jul 01 16:12:22 2009 memory use: 1379.2 MB Tue Jul 07 06:20:38 2009 lanczos halted after 78450 iterations (dim = 4960755) Tue Jul 07 06:21:31 2009 recovered 34 nontrivial dependencies Tue Jul 07 06:21:51 2009 BLanczosTime: 486333 Tue Jul 07 06:21:51 2009 Tue Jul 07 06:21:51 2009 commencing square root phase Tue Jul 07 06:21:51 2009 reading relations for dependency 1 Tue Jul 07 06:22:29 2009 read 2480662 cycles Tue Jul 07 06:22:37 2009 cycles contain 8947738 unique relations Tue Jul 07 06:37:31 2009 read 8947738 relations Tue Jul 07 06:38:47 2009 multiplying 7302868 relations Tue Jul 07 07:01:05 2009 multiply complete, coefficients have about 177.09 million bits Tue Jul 07 07:01:07 2009 initial square root is modulo 2265643 Tue Jul 07 07:30:25 2009 reading relations for dependency 2 Tue Jul 07 07:30:27 2009 read 2481818 cycles Tue Jul 07 07:30:35 2009 cycles contain 8947960 unique relations Tue Jul 07 07:44:37 2009 read 8947960 relations Tue Jul 07 07:45:54 2009 multiplying 7304400 relations Tue Jul 07 08:07:55 2009 multiply complete, coefficients have about 177.13 million bits Tue Jul 07 08:07:57 2009 initial square root is modulo 2273239 Tue Jul 07 08:37:11 2009 reading relations for dependency 3 Tue Jul 07 08:37:13 2009 read 2482950 cycles Tue Jul 07 08:37:21 2009 cycles contain 8953002 unique relations Tue Jul 07 08:51:19 2009 read 8953002 relations Tue Jul 07 08:52:29 2009 multiplying 7306608 relations Tue Jul 07 09:15:24 2009 multiply complete, coefficients have about 177.18 million bits Tue Jul 07 09:15:26 2009 initial square root is modulo 2282737 Tue Jul 07 09:40:26 2009 reading relations for dependency 4 Tue Jul 07 09:40:29 2009 read 2481076 cycles Tue Jul 07 09:40:36 2009 cycles contain 8944839 unique relations Tue Jul 07 09:52:26 2009 read 8944839 relations Tue Jul 07 09:53:35 2009 multiplying 7300174 relations Tue Jul 07 10:13:57 2009 multiply complete, coefficients have about 177.03 million bits Tue Jul 07 10:13:59 2009 initial square root is modulo 2254477 Tue Jul 07 10:39:07 2009 reading relations for dependency 5 Tue Jul 07 10:39:09 2009 read 2482085 cycles Tue Jul 07 10:39:16 2009 cycles contain 8950605 unique relations Tue Jul 07 10:51:17 2009 read 8950605 relations Tue Jul 07 10:52:27 2009 multiplying 7305078 relations Tue Jul 07 11:14:34 2009 multiply complete, coefficients have about 177.14 million bits Tue Jul 07 11:14:36 2009 initial square root is modulo 2276503 Tue Jul 07 11:43:26 2009 reading relations for dependency 6 Tue Jul 07 11:43:28 2009 read 2478711 cycles Tue Jul 07 11:43:35 2009 cycles contain 8941063 unique relations Tue Jul 07 11:57:15 2009 read 8941063 relations Tue Jul 07 11:58:30 2009 multiplying 7295494 relations Tue Jul 07 12:20:25 2009 multiply complete, coefficients have about 176.91 million bits Tue Jul 07 12:20:27 2009 initial square root is modulo 2233243 Tue Jul 07 12:48:44 2009 sqrtTime: 23213 Tue Jul 07 12:48:44 2009 prp51 factor: 551004498127928469834445340613015226657914601778213 Tue Jul 07 12:48:44 2009 prp51 factor: 676677276408056094567102599764052489094573413056051 Tue Jul 07 12:48:44 2009 prp120 factor: 298003080664845879339921984943623072483939555335465806206783935206506443967104530715870831039336178009293998396643169751 Tue Jul 07 12:48:44 2009 elapsed time 142:37:09

c222 is the second largest number factored by SNFS in our tables so far. Congratulations!
8·10¹⁹⁸+3 = 8(0)₁₉₇3_<199> = 11 · 53 · C197
C197 = P43 · P155
P43 = 1350678383321052486001773788083398163612589_<43>
P155 = 10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969_<155>

C197=P43*P155 C197=1350678383321052486001773788083398163612589<43>*10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969<155>

Jul 8, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jul 8, 2009
(56·10¹⁸⁰+61)/9 = 6(2)₁₇₉9_<181> = 13 · 7789 · C176
C176 = P41 · P136
P41 = 26838646500920498855907522727441822854563_<41>
P136 = 2289601238125406496463685953870925367871067431406768811372523359546903375516654651574265382783432990689047815439704473437274675097675119_<136>

Number: n N=61449798258117682947571251589739200472285592326675906082761905075424140772709266739309106750370070436831253367394078653547134738558541357360204452257347365833692704921360717997 ( 176 digits) SNFS difficulty: 181 digits. Divisors found: Wed Jul 08 12:08:03 2009 prp41 factor: 26838646500920498855907522727441822854563 Wed Jul 08 12:08:03 2009 prp136 factor: 2289601238125406496463685953870925367871067431406768811372523359546903375516654651574265382783432990689047815439704473437274675097675119 Wed Jul 08 12:08:03 2009 elapsed time 02:00:02 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 131.47 hours. Scaled time: 349.70 units (timescale=2.660). Factorization parameters were as follows: name: KA_6_2_179_9 n: 61449798258117682947571251589739200472285592326675906082761905075424140772709266739309106750370070436831253367394078653547134738558541357360204452257347365833692704921360717997 m: 1000000000000000000000000000000000000 deg: 5 c5: 56 c0: 61 skew: 1.02 type: snfs lss: 1 rlim: 7600000 alim: 7600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 7600000/7600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [3800000, 6049990) Primes: RFBsize:514565, AFBsize:514353, largePrimes:20842136 encountered Relations: rels:20918964, finalFF:999667 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1886231 hash collisions in 22789853 relations Msieve: matrix is 1141759 x 1142007 (307.6 MB) Total sieving time: 130.96 hours. Total relation processing time: 0.51 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7600000,7600000,28,28,56,56,2.5,2.5,100000 total time: 131.47 hours. --------- CPU info (if available) ----------

Jul 8, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Jul 8, 2009
(16·10²¹³-7)/9 = 1(7)_213<214> = C214
C214 = P37 · C177
P37 = 8468548142759467301501936286449486551_<37>
C177 = [209927102947128172255527477476720550184027075544562096491537855794730425872278030664899902187563513228333907561760924717146946260073314975849230630876994684540632973031211495927_<177>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 1777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777 (214 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=623747480 Step 1 took 23282ms Step 2 took 8537ms ********** Factor found in step 2: 8468548142759467301501936286449486551 Found probable prime factor of 37 digits: 8468548142759467301501936286449486551 Composite cofactor 209927102947128172255527477476720550184027075544562096491537855794730425872278030664899902187563513228333907561760924717146946260073314975849230630876994684540632973031211495927 has 177 digits

Jul 8, 2009 (2nd)

By Dmitry Domanov / ECMNET, GMP-ECM 6.2.3 / Jul 8, 2009
(16·10²²²-7)/9 = 1(7)_222<223> = 199 · 12149 · 98448869 · 54361144210102643223435316458471837889181_<41> · C168
C168 = P37 · P131
P37 = 2235567584419681037453681562092795977_<37>
P131 = 61460592182154974496730933652470829014663740816329411758327108206469005324682537072299516656101839833858534462709909285629495029859_<131>

C168=P37*P131 C168=2235567584419681037453681562092795977<37>*61460592182154974496730933652470829014663740816329411758327108206469005324682537072299516656101839833858534462709909285629495029859<131>

(4·10²³⁹-1)/3 = 1(3)_239<240> = 4667580867677873203_<19> · 24503401321619517515329_<23> · C199
C199 = P46 · C153
P46 = 7376676687266393712046503536607829252598737391_<46>
C153 = [158037358971372761393703399726706499974585107747002750603566153342837853221986516569540101910758293615058417151095031685002002369382801730594252944626649_<153>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=4266053392 Step 1 took 358031ms Step 2 took 112531ms ********** Factor found in step 2: 7376676687266393712046503536607829252598737391 Found probable prime factor of 46 digits: 7376676687266393712046503536607829252598737391 Composite cofactor 158037358971372761393703399726706499974585107747002750603566153342837853221986516569540101910758293615058417151095031685002002369382801730594252944626649 has 153 digits

Jul 8, 2009

By Dmitry Domanov / GGNFS/msieve 1.41 / Jul 8, 2009
(44·10¹⁷¹-71)/9 = 4(8)₁₇₀1_<172> = 3 · 41 · 5153 · C166
C166 = P70 · P97
P70 = 5271981044836967768271841973392602581073085695664717820937384152442373_<70>
P97 = 1463090104635461951610590987260210884486775026240659609393710273204440955431228652088681530430663_<97>

N=7713383298526691198731639299056810996339473712351458206347378177190789308759896577554300027119554460956343828267831808274742298493558711381149648225895545713979683299 ( 166 digits) SNFS difficulty: 173 digits. Divisors found: r1=5271981044836967768271841973392602581073085695664717820937384152442373 (pp70) r2=1463090104635461951610590987260210884486775026240659609393710273204440955431228652088681530430663 (pp97) Version: Msieve v. 1.41 Total time: 78.11 hours. Scaled time: 154.35 units (timescale=1.976). Factorization parameters were as follows: n: 7713383298526691198731639299056810996339473712351458206347378177190789308759896577554300027119554460956343828267831808274742298493558711381149648225895545713979683299 m: 20000000000000000000000000000000000 deg: 5 c5: 55 c0: -284 skew: 1.39 type: snfs lss: 1 rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2700000, 6700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 865106 x 865354 Total sieving time: 76.66 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.19 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,173.000,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000 total time: 78.11 hours. --------- CPU info (if available) ----------

(58·10¹⁷⁷-13)/9 = 6(4)₁₇₆3_<178> = 43 · 1549 · C173
C173 = P42 · P132
P42 = 320496404483144759257844472217374390250391_<42>
P132 = 301885635787849997076654250208736448301418211103547828735709980133081356860492761093044763198026788449829497936680286375958621773939_<132>

N=96753260835114093780600303938691795823929083196127200511124122756533764385791950462330452421583984332644383389800538148309403582873338304449148654712634474521363286808360149 ( 173 digits) SNFS difficulty: 179 digits. Divisors found: r1=320496404483144759257844472217374390250391 (pp42) r2=301885635787849997076654250208736448301418211103547828735709980133081356860492761093044763198026788449829497936680286375958621773939 (pp132) Version: Msieve v. 1.41 Total time: 124.28 hours. Scaled time: 246.33 units (timescale=1.982). Factorization parameters were as follows: n: 96753260835114093780600303938691795823929083196127200511124122756533764385791950462330452421583984332644383389800538148309403582873338304449148654712634474521363286808360149 m: 200000000000000000000000000000000000 deg: 5 c5: 725 c0: -52 skew: 0.59 type: snfs lss: 1 rlim: 6800000 alim: 6800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5Factor base limits: 6800000/6800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3400000, 9100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1433017 x 1433265 Total sieving time: 119.07 hours. Total relation processing time: 0.31 hours. Matrix solve time: 4.49 hours. Time per square root: 0.41 hours. Prototype def-par.txt line would be: snfs,179.000,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000 total time: 124.28 hours. --------- CPU info (if available) ----------

Jul 7, 2009 (4th)

By Dmitry Domanov / ECMNET / Jul 7, 2009
(16·10²¹⁰-7)/9 = 1(7)_210<211> = 2306753 · 707999891526611_<15> · C190
C190 = P38 · C152
P38 = 34982088008588268790615606126668383363_<38>
C152 = [31116981374511626666850275119962721699651581221812870177327853705301792800990178959233683888734687635721087961901222646746337176618805370691748725153913_<152>]

C190=P38*C152 C190=34982088008588268790615606126668383363<38>*31116981374511626666850275119962721699651581221812870177327853705301792800990178959233683888734687635721087961901222646746337176618805370691748725153913<152>

(16·10²²²-7)/9 = 1(7)_222<223> = 199 · 12149 · 98448869 · C208
C208 = P41 · C168
P41 = 54361144210102643223435316458471837889181_<41>
C168 = [137399307601663329338762819303363451250324761459293058906011655115908353350470871508735481361435253702571547696510840260773732323164290945411600641942028811070410077243_<168>]

C208=P41*C168 C208=54361144210102643223435316458471837889181<41>*137399307601663329338762819303363451250324761459293058906011655115908353350470871508735481361435253702571547696510840260773732323164290945411600641942028811070410077243<168>

Jul 7, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Jul 7, 2009
(44·10¹⁶⁹-71)/9 = 4(8)₁₆₈1_<170> = 19 · 1171 · 22455238546372133233_<20> · 74729759475524672408129_<23> · C124
C124 = P40 · P84
P40 = 3267030704112780993938561807475804129877_<40>
P84 = 400806907449015252453908806551676977356384665542185400498682627662013210514398914421_<84>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 1309448473056422545730772508368357667208736293707271039656288264706133216883595462837863086408288211165694921802757292256217 (124 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1407767135 Step 1 took 9999ms Step 2 took 4851ms ********** Factor found in step 2: 3267030704112780993938561807475804129877 Found probable prime factor of 40 digits: 3267030704112780993938561807475804129877 Probable prime cofactor 400806907449015252453908806551676977356384665542185400498682627662013210514398914421 has 84 digits

Jul 7, 2009 (2nd)

By Tyler Cadigan / GGNFS and Msieve / Jul 7, 2009
6·10¹⁷⁷+1 = 6(0)₁₇₆1_<178> = 1711983023_<10> · C169
C169 = P72 · P98
P72 = 130909460131276140628552263669024355006100394847355624263188932213877563_<72>
P98 = 26771996829082488321535109586807695003489696065663320871538381541557110996579284791617298469559549_<98>

Number: 60001_177 N=3504707651531425262270255585355766696758884857236110570939931569636832783008269352446726920609188774648263553487352543682321317037966912128660752496258837024694023499087 ( 169 digits) SNFS difficulty: 178 digits. Divisors found: r1=130909460131276140628552263669024355006100394847355624263188932213877563 (pp72) r2=26771996829082488321535109586807695003489696065663320871538381541557110996579284791617298469559549 (pp98) Version: Msieve v. 1.41 Total time: 97.06 hours. Scaled time: 242.85 units (timescale=2.502). Factorization parameters were as follows: n: 3504707651531425262270255585355766696758884857236110570939931569636832783008269352446726920609188774648263553487352543682321317037966912128660752496258837024694023499087 m: 200000000000000000000000000000000000 deg: 5 c5: 75 c0: 4 skew: 0.56 type: snfs lss: 1 rlim: 6600000 alim: 6600000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 6600000/6600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3300000, 7300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1080232 x 1080480 Total sieving time: 93.75 hours. Total relation processing time: 0.28 hours. Matrix solve time: 2.27 hours. Time per square root: 0.77 hours. Prototype def-par.txt line would be: snfs,178.000,5,0,0,0,0,0,0,0,0,6600000,6600000,28,28,53,53,2.5,2.5,100000 total time: 97.06 hours. --------- CPU info (if available) ----------

Jul 7, 2009

By Serge Batalov / GMP-ECM 6.2.3 / Jul 7, 2009
(16·10²⁰⁴-7)/9 = 1(7)_204<205> = 709 · 2971 · 7477 · 120847 · 374635434906319_<15> · C175
C175 = P38 · P137
P38 = 92895077195030726821601908997157473833_<38>
P137 = 26838842347296090104640832675754230252174815008475997450915157004722749871051392000924279403189951850376102607159797256027317218632935411_<137>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3235440799 Step 1 took 13861ms Step 2 took 12025ms ********** Factor found in step 2: 92895077195030726821601908997157473833 Found probable prime factor of 38 digits: 92895077195030726821601908997157473833 Probable prime cofactor has 137 digits

Jul 6, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Jul 6, 2009
(8·10¹⁸⁰+7)/3 = 2(6)₁₇₉9_<181> = 31053624792761_<14> · C167
C167 = P71 · P97
P71 = 18555315928842020306493901187909913884372345209699756189928787759669539_<71>
P97 = 4627943814599199983007985544839411028986120597910669643331539446594085228777254658333014535246311_<97>

Number: n N=85872959580818437049970776116010943591051241377859585751193600043739729134078369036913847819945516023470865699406926030247953668830042774115289314260254925621328820629 ( 167 digits) SNFS difficulty: 180 digits. Divisors found: Mon Jul 06 14:14:43 2009 prp71 factor: 18555315928842020306493901187909913884372345209699756189928787759669539 Mon Jul 06 14:14:43 2009 prp97 factor: 4627943814599199983007985544839411028986120597910669643331539446594085228777254658333014535246311 Mon Jul 06 14:14:43 2009 elapsed time 01:38:07 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 131.74 hours. Scaled time: 344.63 units (timescale=2.616). Factorization parameters were as follows: name: KA_2_6_179_9 n: 85872959580818437049970776116010943591051241377859585751193600043739729134078369036913847819945516023470865699406926030247953668830042774115289314260254925621328820629 m: 1000000000000000000000000000000000000 deg: 5 c5: 8 c0: 7 skew: 0.97 type: snfs lss: 1 rlim: 7200000 alim: 7200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [3600000, 5849990) Primes: RFBsize:489319, AFBsize:488218, largePrimes:20564182 encountered Relations: rels:20278778, finalFF:1064369 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2117894 hash collisions in 24343356 relations Msieve: matrix is 1015493 x 1015741 (270.0 MB) Total sieving time: 131.24 hours. Total relation processing time: 0.50 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,56,56,2.5,2.5,100000 total time: 131.74 hours. --------- CPU info (if available) ----------

(53·10¹⁸⁰+1)/9 = 5(8)₁₇₉9_<181> = 3 · 67 · 7753 · C175
C175 = P36 · P40 · P99
P36 = 467712874948997340147347573908507417_<36>
P40 = 9277642778843380347719533680822774228073_<40>
P99 = 870864419203635722315194328196734611935239863623475289867757749407372405846045984600645870268689193_<99>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 3778918440744098987128647289085906010312739725138584703779495973562401387162529214426313478967146011775822864837998122947040169261321978325122028762988160505924452860737515113 (175 digits) Using B1=746000, B2=696728352, polynomial Dickson(3), sigma=338678068 Step 1 took 11500ms Step 2 took 4765ms ********** Factor found in step 2: 467712874948997340147347573908507417 Found probable prime factor of 36 digits: 467712874948997340147347573908507417 Composite cofactor 8079568990176245407164908138855960352414027399430389385104249725327392997027699414008883250333152166638569639697780145903076291872132315089 has 139 digits GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 8079568990176245407164908138855960352414027399430389385104249725327392997027699414008883250333152166638569639697780145903076291872132315089 (139 digits) Using B1=2958000, B2=4281751120, polynomial Dickson(6), sigma=314658206 Step 1 took 31781ms Step 2 took 12547ms ********** Factor found in step 2: 9277642778843380347719533680822774228073 Found probable prime factor of 40 digits: 9277642778843380347719533680822774228073 Probable prime cofactor 870864419203635722315194328196734611935239863623475289867757749407372405846045984600645870268689193 has 99 digits

Jul 6, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jul 6, 2009
(16·10²³²-7)/9 = 1(7)_232<233> = 19 · 104953 · 1986217 · 34068054807426322294331_<23> · 13848896772790568546388233869_<29> · C169
C169 = P35 · C135
P35 = 56772616833085221976414195028964401_<35>
C135 = [167571783671037912466408452319759362185008616848696629101669918550562953076710717850252795352341060164798120833972449628332765915929797_<135>]

C169=P35*C135 C169=56772616833085221976414195028964401<35>*167571783671037912466408452319759362185008616848696629101669918550562953076710717850252795352341060164798120833972449628332765915929797<135>

(16·10²⁴²-7)/9 = 1(7)_242<243> = 3 · 1377031 · 60563440146936004113491_<23> · C213
C213 = P39 · C175
P39 = 199420903525207265891662998119875755307_<39>
C175 = [3563126863272287848309474508421502859292999903007398926700694144385671714094680930698204166079585664849282637049457051242987232608454018562371651837455217182196840947072062397_<175>]

C213=P39*C175 C213=199420903525207265891662998119875755307<39>*3563126863272287848309474508421502859292999903007398926700694144385671714094680930698204166079585664849282637049457051242987232608454018562371651837455217182196840947072062397<175>

Jul 6, 2009

By Serge Batalov / PFGW / Jul 6, 2009
(2·10⁸⁴²³⁹+1)/3 = (6)₈₄₂₃₈7_<84239> is PRP.
This is the largest unprovable near-repdigit PRP in our tables so far. Congratulations!

Jul 5, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1 / Jul 5, 2009
(2·10¹⁷¹-17)/3 = (6)₁₇₀1_<171> = 19 · 87468884265379_<14> · 13595175907013101_<17> · C140
C140 = P48 · P93
P48 = 138014820965046102634644206118683890867588471483_<48>
P93 = 213791776249621319224967337487968765723499969651474502298025592355774144477612711702325518067_<93>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1868644906 Step 1 took 42626ms Step 2 took 14881ms ********** Factor found in step 2: 138014820965046102634644206118683890867588471483 Found probable prime factor of 48 digits: 138014820965046102634644206118683890867588471483 Probable prime cofactor 213791776249621319224967337487968765723499969651474502298025592355774144477612711702325518067 has 93 digits

Jul 5, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jul 5, 2009
(49·10¹⁸⁹+23)/9 = 5(4)₁₈₈7_<190> = 13 · C189
C189 = P59 · P130
P59 = 53523756078031042692936382182191372168741504118891852257677_<59>
P130 = 7824626847802964571499691889298350464401845544687833939953026301943157931919076380865693694386248286843653044176844425312737763847_<130>

Number: n N=418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803419 ( 189 digits) SNFS difficulty: 191 digits. Divisors found: Sun Jul 05 02:18:18 2009 prp59 factor: 53523756078031042692936382182191372168741504118891852257677 Sun Jul 05 02:18:18 2009 prp130 factor: 7824626847802964571499691889298350464401845544687833939953026301943157931919076380865693694386248286843653044176844425312737763847 Sun Jul 05 02:18:18 2009 elapsed time 06:28:34 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 339.86 hours. Scaled time: 878.55 units (timescale=2.585). Factorization parameters were as follows: name: KA_5_4_188_7 n: 418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803419 m: 100000000000000000000000000000000000000 deg: 5 c5: 49 c0: 230 skew: 1.36 type: snfs lss: 1 rlim: 11000000 alim: 11000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 11000000/11000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [5500000, 11549990) Primes: RFBsize:726517, AFBsize:725473, largePrimes:21473915 encountered Relations: rels:21946074, finalFF:1409691 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2757639 hash collisions in 24407207 relations Msieve: matrix is 1838300 x 1838548 (495.2 MB) Total sieving time: 338.97 hours. Total relation processing time: 0.89 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,56,56,2.5,2.5,100000 total time: 339.86 hours. --------- CPU info (if available) ----------

2·10²¹⁶-1 = 1(9)_216<217> = 71 · 1801 · C212
C212 = P87 · P125
P87 = 361107090626796555790432520736349127614104388447835771607771886723658185918374320268583_<87>
P125 = 43313364268944003504537958096108351815974418622703052728674628970748248006983423154634967569396860724808442556827278605720343_<125>

Number: n N=15640762956417014021943990427853070672787418570277858153920748254099834989950809800502068490900986150104402092734083568596476136105919246740856018956604703177420994596116398557921655418351307176764082551946883969 ( 212 digits) SNFS difficulty: 216 digits. Divisors found: Sun Jul 5 17:47:36 2009 prp87 factor: 361107090626796555790432520736349127614104388447835771607771886723658185918374320268583 Sun Jul 5 17:47:36 2009 prp125 factor: 43313364268944003504537958096108351815974418622703052728674628970748248006983423154634967569396860724808442556827278605720343 Sun Jul 5 17:47:36 2009 elapsed time 48:29:06 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 137.94 hours. Scaled time: 277.95 units (timescale=2.015). Factorization parameters were as follows: name: KA_1_9_216 n: 15640762956417014021943990427853070672787418570277858153920748254099834989950809800502068490900986150104402092734083568596476136105919246740856018956604703177420994596116398557921655418351307176764082551946883969 m: 1000000000000000000000000000000000000 deg: 6 c6: 2 c0: -1 skew: 0.89 type: snfs lss: 1 rlim: 28000000 alim: 28000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 28000000/28000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [14000000, 39599990) Primes: RFBsize:1741430, AFBsize:1740559, largePrimes:38050311 encountered Relations: rels:34729186, finalFF:1144510 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 8345464 hash collisions in 49109482 relations Msieve: matrix is 4939937 x 4940185 (1333.9 MB) Total sieving time: 136.84 hours. Total relation processing time: 1.10 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,216,6,0,0,0,0,0,0,0,0,28000000,28000000,29,29,58,58,2.6,2.6,100000 total time: 137.94 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352056k/3407296k available (3119k kernel code, 53956k reserved, 1894k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.68 BogoMIPS (lpj=2830844) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22644.41 BogoMIPS).

Jul 5, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve 1.41 / Jul 5, 2009
(19·10¹⁶⁹+11)/3 = 6(3)₁₆₈7_<170> = 419 · 17359 · 435144769 · 1092261451_<10> · 46604867967947_<14> · 6863100712193171991021877484483863219321_<40> · C92
C92 = P46 · P47
P46 = 1460642205399019519450717523391965728267997741_<46>
P47 = 39213693243907045538796060396726173069533192289_<47>

N=57277175381621018844894128396734834310011455677358063497176811475656530660931802849970619149 ( 92 digits) Divisors found: r1=1460642205399019519450717523391965728267997741 (pp46) r2=39213693243907045538796060396726173069533192289 (pp47) Version: Msieve v. 1.41 Total time: 3.16 hours. Scaled time: 6.26 units (timescale=1.982). Factorization parameters were as follows: name: 0028 n: 57277175381621018844894128396734834310011455677358063497176811475656530660931802849970619149 m: 1144412806986536595868 deg: 4 c4: 33392640 c3: 219871128503 c2: -93123226998648841 c1: -905220131677318023 c0: 65367225897505650092961 skew: 1635.250 type: gnfs # adj. I(F,S) = 53.225 # E(F1,F2) = 1.050945e-004 # GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1246725776. # maxskew=2000.0 # These parameters should be manually set: rlim: 700000 alim: 700000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.4 alambda: 2.4 qintsize: 40000 type: gnfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [350000, 1030001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 111083 x 111313 Polynomial selection time: 0.17 hours. Total sieving time: 2.91 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000 total time: 3.16 hours. --------- CPU info (if available) ----------

Jul 5, 2009 (2nd)

By Tyler Cadigan / GGNFS, Msieve / Jul 5, 2009
6·10¹⁸⁰+1 = 6(0)₁₇₉1_<181> = 7 · 53 · 5189 · 1530654942827_<13> · C163
C163 = P80 · P83
P80 = 77961257465282390200811842235367085099161175733216672157092688181205275825630537_<80>
P83 = 26117856802019915612096483598867398142659189050194588384216401897862531400938257621_<83>

Number: 60001_180 N=2036180958583651599919324369895283334276379392748411313706838298632139875636431258517052429423184385967502888554627103436454845173306061562588430970166718470572477 ( 163 digits) SNFS difficulty: 180 digits. Divisors found: r1=77961257465282390200811842235367085099161175733216672157092688181205275825630537 (pp80) r2=26117856802019915612096483598867398142659189050194588384216401897862531400938257621 (pp83) Version: Msieve v. 1.41 Total time: 143.05 hours. Scaled time: 363.92 units (timescale=2.544). Factorization parameters were as follows: n: 2036180958583651599919324369895283334276379392748411313706838298632139875636431258517052429423184385967502888554627103436454845173306061562588430970166718470572477 m: 1000000000000000000000000000000000000 deg: 5 c5: 6 c0: 1 skew: 0.70 type: snfs lss: 1 rlim: 7200000 alim: 7200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3600000, 5600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 948967 x 949215 Total sieving time: 141.12 hours. Total relation processing time: 0.30 hours. Matrix solve time: 1.53 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,180.000,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000 total time: 143.05 hours. --------- CPU info (if available) ----------

Jul 5, 2009

By Sinkiti Sibata / Msieve / Jul 5, 2009
(58·10¹⁶⁹-13)/9 = 6(4)₁₆₈3_<170> = 3 · 7 · 179 · 147853 · 236891 · 338197 · 4258508879_<10> · C141
C141 = P66 · P75
P66 = 408116836703356135186758597068735340933347535194023264090041406897_<66>
P75 = 832765330571507511987519992376332246212140238340768446412802228965601239809_<75>

Number: 64443_169 N=339865552429068321970877680355397427709972520150182950223233553657884687447900712560490043251329534766131338706168982613469177225889843562673 ( 141 digits) SNFS difficulty: 171 digits. Divisors found: r1=408116836703356135186758597068735340933347535194023264090041406897 (pp66) r2=832765330571507511987519992376332246212140238340768446412802228965601239809 (pp75) Version: Msieve-1.40 Total time: 83.78 hours. Scaled time: 172.42 units (timescale=2.058). Factorization parameters were as follows: name: 64443_169 n: 339865552429068321970877680355397427709972520150182950223233553657884687447900712560490043251329534766131338706168982613469177225889843562673 m: 10000000000000000000000000000000000 deg: 5 c5: 29 c0: -65 skew: 1.18 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 5600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 976748 x 976996 Total sieving time: 79.62 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.71 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 83.78 hours. --------- CPU info (if available) ----------

Jul 4, 2009 (5th)

By Dmitry Domanov / ECMNET / Jul 4, 2009
(52·10²⁰¹+11)/9 = 5(7)₂₀₀9_<202> = 61 · 9439 · C197
C197 = P36 · P161
P36 = 327574010996440651174881028085255183_<36>
P161 = 30633426295854463882304563603886870527666531320541302771617844658424271598181095302778430382149016907140565796158720390106944926598693879577187939072797793406847_<161>

C197=P36*P161 C197=327574010996440651174881028085255183<36>*30633426295854463882304563603886870527666531320541302771617844658424271598181095302778430382149016907140565796158720390106944926598693879577187939072797793406847<161>

Jul 4, 2009 (4th)

By Sinkiti Sibata / GGNFS / Jul 4, 2009
(58·10¹⁶⁴-13)/9 = 6(4)₁₆₃3_<165> = 634425495437_<12> · 34223943495856159696154680142313760883_<38> · C116
C116 = P40 · P77
P40 = 1039702390453237753079616431433676773883_<40>
P77 = 28547347651007753290977819563148421178571364515389527937841544853464340338951_<77>

Number: 64443_164 N=29680745593852382710885424670845104038289735607516074357223266600260200692718744499668077307158865998260008404416733 ( 116 digits) Divisors found: r1=1039702390453237753079616431433676773883 (pp40) r2=28547347651007753290977819563148421178571364515389527937841544853464340338951 (pp77) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 68.52 hours. Scaled time: 32.48 units (timescale=0.474). Factorization parameters were as follows: name: 64443_164 n: 29680745593852382710885424670845104038289735607516074357223266600260200692718744499668077307158865998260008404416733 skew: 37882.17 # norm 2.16e+15 c5: 28080 c4: -1783304174 c3: -106987684895637 c2: 3254798532959727963 c1: 69333921661141863276279 c0: 311328355938046670337322130 # alpha -5.10 Y1: 1694242071773 Y0: -16025667352605280542669 # Murphy_E 5.09e-10 # M 725564486423152580698825252463775544412007927936381050353624717871811877831131875924797212721560785860023394686973 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, 3630001) Primes: RFBsize:315948, AFBsize:315817, largePrimes:7563902 encountered Relations: rels:7629959, finalFF:773927 Max relations in full relation-set: 28 Initial matrix: 631846 x 773927 with sparse part having weight 60032329. Pruned matrix : 507204 x 510427 with weight 34236305. Total sieving time: 56.96 hours. Total relation processing time: 0.79 hours. Matrix solve time: 10.35 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 68.52 hours. --------- CPU info (if available) ----------

Jul 4, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Jul 4, 2009
(19·10¹⁶⁹+11)/3 = 6(3)₁₆₈7_<170> = 419 · 17359 · 435144769 · 1092261451_<10> · 46604867967947_<14> · C132
C132 = P40 · C92
P40 = 6863100712193171991021877484483863219321_<40>
C92 = [57277175381621018844894128396734834310011455677358063497176811475656530660931802849970619149_<92>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 393099023154016432157135307697657905002456098719696585711733263469545952679141551813013727666722143370112848288521607667698749377829 (132 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4273467981 Step 1 took 4228ms Step 2 took 1341ms ********** Factor found in step 2: 6863100712193171991021877484483863219321 Found probable prime factor of 40 digits: 6863100712193171991021877484483863219321 Composite cofactor 57277175381621018844894128396734834310011455677358063497176811475656530660931802849970619149 has 92 digits

Jul 4, 2009 (2nd)

By Tyler Cadigan / PRIMO 3.0.7 / Jun 30, 2009
(10²⁵⁷⁶+53)/9 = (1)₂₅₇₅7_<2576> is prime.

Jul 4, 2009

By Dmitry Domanov / GGNFS/msieve 1.41 / Jul 4, 2009
(16·10²³⁹-7)/9 = 1(7)_239<240> = 3⁵ · 15217 · 3990316637461614359759_<22> · 13273181924432571534347_<23> · 17417511129931705819879_<23> · 72157436681702848816201_<23> · 155862880557226828959411237263_<30> · C115
C115 = P52 · P64
P52 = 1242805601725594914246288145126368484394847860891111_<52>
P64 = 3728607415830210175214413350865767470697342530579606832265121657_<64>

N=4633934183029379848911059683421025765683695811198960419440580945122087499442227338278163891999244250812708844890927 ( 115 digits) Divisors found: r1=1242805601725594914246288145126368484394847860891111 (pp52) r2=3728607415830210175214413350865767470697342530579606832265121657 (pp64) Version: Msieve v. 1.41 Total time: 33.30 hours. Scaled time: 65.56 units (timescale=1.969). Factorization parameters were as follows: name: 0024 n: 4633934183029379848911059683421025765683695811198960419440580945122087499442227338278163891999244250812708844890927 skew: 52277.85 # norm 1.53e+016 c5: 49140 c4: 2023517382 c3: -770576692952680 c2: -6669643093844814455 c1: 675255332437029036418800 c0: -3360776601203873812598149827 # alpha -6.82 Y1: 530957486939 Y0: -9883317554939838314860 # Murphy_E 5.71e-010 # M 453967889756118697662348222666525420739985869353770678696114680314130139019054861861552037690994500371427353763936 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, 2950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 527177 x 527424 Polynomial selection time: 2.72 hours. Total sieving time: 29.25 hours. Total relation processing time: 0.13 hours. Matrix solve time: 1.00 hours. Time per square root: 0.20 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: 33.30 hours. --------- CPU info (if available) ----------

Jul 3, 2009 (3rd)

By Jo Yeong Uk / Msieve / Jul 2, 2009
(19·10¹⁷⁰+11)/3 = 6(3)₁₆₉7_<171> = 7² · 13 · 2423 · 5407 · 225212486252296836198773323_<27> · 362095319198698267549534353999723137_<36> · C99
C99 = P32 · P68
P32 = 41530639745908770097077908377763_<32>
P68 = 22407795549198754888680238994593224139411080039444874423497865033157_<68>

Number: 63337_170 N=930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791 ( 99 digits) Divisors found: r1=41530639745908770097077908377763 r2=22407795549198754888680238994593224139411080039444874423497865033157 Version: Total time: 2.38 hours. Scaled time: 5.69 units (timescale=2.391). Factorization parameters were as follows: name: 63337_170 n: 930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791 skew: 5805.56 # norm 3.75e+13 c5: 45540 c4: -576098332 c3: -4840732325267 c2: 15563382954064314 c1: 66030856022033971056 c0: -120065763798487403936640 # alpha -5.08 Y1: 10461064597 Y0: -7279080541546534673 # Murphy_E 3.46e-09 # M 887173262205881371076995863496444461793338535162077103711482507558309594394743821872645967092394012 type: gnfs rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [500000, 1000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4147948 Max relations in full relation-set: Initial matrix: Pruned matrix : 183967 x 184215 Polynomial selection time: 0.14 hours. Total sieving time: 1.96 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.07 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000 total time: 2.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)

By Jo Yeong Uk / GMP-ECM / Jul 3, 2009
(16·10²²⁵-7)/9 = 1(7)_225<226> = 17 · 5705120952499567_<16> · 7113174568135224977_<19> · 1430577548090886473232512029_<28> · 23372859706894522584303715363_<29> · C134
C134 = P32 · P103
P32 = 41233351031948151692868641186159_<32>
P103 = 1869081935791828972707833126568044399578183366750010335624802395418611310169927142305210058932642675863_<103>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 77068511565977660174709421461132555031362999146292468101240450879997543709927873527529777203465840908885241587100820037642140078980217 (134 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5175414927 Step 1 took 4227ms Step 2 took 5835ms ********** Factor found in step 2: 41233351031948151692868641186159 Found probable prime factor of 32 digits: 41233351031948151692868641186159 Probable prime cofactor 1869081935791828972707833126568044399578183366750010335624802395418611310169927142305210058932642675863 has 103 digits

Jul 3, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jul 3, 2009
(16·10²²⁶-7)/9 = 1(7)_226<227> = 131 · 6181811 · 132752221159_<12> · C207
C207 = P38 · P170
P38 = 12500755410149652578208142530844687751_<38>
P170 = 13228554790752363275540751728437998199424055178673431699716124390155931820330522849342635457892494755615875231329856621245128124011040693202135088807739033447001924553033_<170>

C207=P38*P170 C207=12500755410149652578208142530844687751<38>*13228554790752363275540751728437998199424055178673431699716124390155931820330522849342635457892494755615875231329856621245128124011040693202135088807739033447001924553033<170>

Jul 3, 2009

By Sinkiti Sibata / Msieve / Jul 3, 2009
(58·10¹⁶³-13)/9 = 6(4)₁₆₂3_<164> = 3² · 7 · 17 · 94951763 · 1450443787417_<13> · C141
C141 = P62 · P80
P62 = 15200010854050980264951294490005750472092205391836031200627031_<62>
P80 = 28744064597297114282228101355955883403740289127783595364008637430740971151148233_<80>

Number: 64443_163 N=436910093868458656181692890758665810048223451661281827184511045317685332128359134867190394080416164666242215892704309860218883494745227686223 ( 141 digits) SNFS difficulty: 166 digits. Divisors found: r1=15200010854050980264951294490005750472092205391836031200627031 (pp62) r2=28744064597297114282228101355955883403740289127783595364008637430740971151148233 (pp80) Version: Msieve-1.40 Total time: 50.73 hours. Scaled time: 130.08 units (timescale=2.564). Factorization parameters were as follows: name: 64443_163 n: 436910093868458656181692890758665810048223451661281827184511045317685332128359134867190394080416164666242215892704309860218883494745227686223 m: 500000000000000000000000000000000 deg: 5 c5: 464 c0: -325 skew: 0.93 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 4250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 751768 x 752016 Total sieving time: 49.14 hours. Total relation processing time: 0.14 hours. Matrix solve time: 1.27 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 50.73 hours. --------- CPU info (if available) ----------

Jul 2, 2009 (4th)

By Dmitry Domanov / ECMNET / Jul 2, 2009
(4·10²²⁷-1)/3 = 1(3)_227<228> = 495976721 · C219
C219 = P34 · P185
P34 = 7182449182846041226834457037788413_<34>
P185 = 37428711930030411787026467533746685794015580944665280706076447106637077636188492634909171909470494931514913929830815389062003443743128089759181928735384732113688639097074216322185271721_<185>

C219=P34*P185 C219=7182449182846041226834457037788413<34>*37428711930030411787026467533746685794015580944665280706076447106637077636188492634909171909470494931514913929830815389062003443743128089759181928735384732113688639097074216322185271721<185>

Jul 2, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM, GGNFS, MSieve v1.39 / Jul 2, 2009
(17·10¹⁶⁹-11)/3 = 5(6)₁₆₈3_<170> = 47 · 131 · 149 · 33340437841741841839489_<23> · C142
C142 = P36 · P106
P36 = 588740553020417727859616696880760387_<36>
P106 = 3146856900197104709044954193359079359458730289636307786252071116222364226809318587050803371596885848515837_<106>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 1852682271698160903203411897901451415112616705715726434096600854560620468380525285725615537888596666176564066317954738261417293548183971748919 (142 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3541219365 Step 1 took 4157ms Step 2 took 2373ms ********** Factor found in step 2: 588740553020417727859616696880760387 Found probable prime factor of 36 digits: 588740553020417727859616696880760387 Probable prime cofactor 3146856900197104709044954193359079359458730289636307786252071116222364226809318587050803371596885848515837 has 106 digits

(19·10¹⁷⁰+11)/3 = 6(3)₁₆₉7_<171> = 7² · 13 · 2423 · 5407 · 225212486252296836198773323_<27> · C135
C135 = P36 · C99
P36 = 362095319198698267549534353999723137_<36>
C99 = [930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791_<99>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 336969555579808682573243870523617049873844489586121451739694245328141713281148910920472473599665329157656373568688539063780045360720367 (135 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6088997955 Step 1 took 3440ms Step 2 took 2148ms ********** Factor found in step 2: 362095319198698267549534353999723137 Found probable prime factor of 36 digits: 362095319198698267549534353999723137 Composite cofactor 930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791 has 99 digits GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 336969555579808682573243870523617049873844489586121451739694245328141713281148910920472473599665329157656373568688539063780045360720367 (135 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6088997955 Step 1 took 3440ms Step 2 took 2148ms ********** Factor found in step 2: 362095319198698267549534353999723137 Found probable prime factor of 36 digits: 362095319198698267549534353999723137 Composite cofactor 930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791 has 99 digits

Jul 2, 2009 (2nd)

By Tyler Cadigan / GGNFS, Msieve / Jul 2, 2009
6·10¹⁸¹+1 = 6(0)₁₈₀1_<182> = 23 · 61 · 22921 · 1872699346433998020537767237_<28> · C147
C147 = P52 · P96
P52 = 3221817407318169274057683443449767963151785037276817_<52>
P96 = 309236703947623304730799733324982576204663378968922310111028745418217199315661984343512735564463_<96>

Number: 60001_181 N=996304195760147997067562108673821534929496595129015951823604834209205894024502191944842412261659576950028689198887149061532283496510397260878954271 ( 147 digits) SNFS difficulty: 182 digits. Divisors found: r1=3221817407318169274057683443449767963151785037276817 (pp52) r2=309236703947623304730799733324982576204663378968922310111028745418217199315661984343512735564463 (pp96) Version: Msieve v. 1.41 Total time: 223.86 hours. Scaled time: 573.97 units (timescale=2.564). Factorization parameters were as follows: n: 996304195760147997067562108673821534929496595129015951823604834209205894024502191944842412261659576950028689198887149061532283496510397260878954271 m: 2000000000000000000000000000000000000 deg: 5 c5: 15 c0: 8 skew: 0.88 type: snfs lss: 1 rlim: 7800000 alim: 7800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 7800000/7800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3900000, 6900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 851034 x 851282 Total sieving time: 221.71 hours. Total relation processing time: 0.83 hours. Matrix solve time: 1.22 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,182.000,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,53,53,2.5,2.5,100000 total time: 223.86 hours. --------- CPU info (if available) ----------

Jul 2, 2009

Factorizations of 177...77 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jul 1, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jul 1, 2009
(53·10²⁰³+1)/9 = 5(8)₂₀₂9_<204> = 7 · 281 · C201
C201 = P40 · C161
P40 = 6991094456219571760445366554492296155281_<40>
C161 = [42823664738654024146753494596611162996197643707455475080552632365269730895208935483894078392027330205442062850153313457655994824376155448514431058020416853642407_<161>]

C201=P40*C161 C201=6991094456219571760445366554492296155281<40>*42823664738654024146753494596611162996197643707455475080552632365269730895208935483894078392027330205442062850153313457655994824376155448514431058020416853642407<161>

(4·10²³¹-1)/3 = 1(3)_231<232> = 2917 · 51824844853_<11> · 23692560197239551081270833387477_<32> · C186
C186 = P37 · C150
P37 = 1862546921637290351531952691671776489_<37>
C150 = [199868835314352006303616101691173511035981142016504847269115886853153738185472417870991193724827260514112019164316369241384478739018564658717340450161_<150>]

C186=P37*C150 C186=1862546921637290351531952691671776489<37>*1998688353143520063036161016911735110359811420165048472691158868531537381854724178709911937248272605 14112019164316369241384478739018564658717340450161<150>

Jul 1, 2009

By Sinkiti Sibata / Msieve / Jul 1, 2009
(58·10¹⁴⁹-13)/9 = 6(4)₁₄₈3_<150> = 17680101259_<11> · 612631184541141230147_<21> · C119
C119 = P52 · P68
P52 = 5449278379117159731544956271485792375419509366641329_<52>
P68 = 10918491534763876929867522805580453713263965653671863520590735670379_<68>

Number: 64443_149 N=59497899852962528961232804765393480978112046870788785804578711096597251999116268207960584747284901586476215186462493691 ( 119 digits) SNFS difficulty: 151 digits. Divisors found: r1=5449278379117159731544956271485792375419509366641329 (pp52) r2=10918491534763876929867522805580453713263965653671863520590735670379 (pp68) Version: Msieve-1.40 Total time: 16.99 hours. Scaled time: 43.57 units (timescale=2.564). Factorization parameters were as follows: name: 64443_149 n: 59497899852962528961232804765393480978112046870788785804578711096597251999116268207960584747284901586476215186462493691 m: 1000000000000000000000000000000 deg: 5 c5: 29 c0: -65 skew: 1.18 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 379906 x 380154 Total sieving time: 16.47 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.32 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 16.99 hours. --------- CPU info (if available) ----------

(58·10¹⁴⁷-13)/9 = 6(4)₁₄₆3_<148> = 17 · 3963777162971_<13> · 334646085665334337_<18> · C117
C117 = P52 · P66
P52 = 1724643839436206727262081314038604977199883913024927_<52>
P66 = 165707498267325136214000770286795308021181237711990781533096525551_<66>

Number: 64443_147 N=285786416035128196683289121621064667771773532733338769241158392752477998247710329546637739266886534072113858155409777 ( 117 digits) SNFS difficulty: 149 digits. Divisors found: r1=1724643839436206727262081314038604977199883913024927 (pp52) r2=165707498267325136214000770286795308021181237711990781533096525551 (pp66) Version: Msieve-1.40 Total time: 14.66 hours. Scaled time: 30.67 units (timescale=2.092). Factorization parameters were as follows: name: 64443_147 n: 285786416035128196683289121621064667771773532733338769241158392752477998247710329546637739266886534072113858155409777 m: 200000000000000000000000000000 deg: 5 c5: 725 c0: -52 skew: 0.59 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 2800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 397682 x 397930 Total sieving time: 13.68 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.54 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000 total time: 14.66 hours. --------- CPU info (if available) ----------

More: June 2009